GENERAL INTRODUCTION

ancer is the leading cause of death worldwide. It is now accepted that cancer is a highly heterogeneous disease and that subpopulations of cells within a single tumor can exhibit distinct genomic and phenotypic profiles. Tumor heterogeneity arises from clonal evolution, microenvironment interaction and phenotypic plasticity [START_REF] Marusyk | Tumor heterogeneity: Causes and consequences[END_REF] . There are still open questions about tumor heterogeneity and original experimental approaches are required to distinguish the relative contributions of the different sources of heterogeneity to disease progression.

In the last decade Next-Generation Sequencing (NGS) has emerged as relevant tool to tackle such challenges both in clinics and life sciences. Some groups developed disruptive technologies such as Drop-Seq 2 and inDrop [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] , based on droplets microfluidics barcoding and NGS to study gene expression at single-cell level at high-throughput. These methods have been initially applied for transcriptomics studies, but other droplet microfluidics-based technologies were also used to analyze genomics [START_REF] Fu | Uniform and accurate single-cell sequencing based on emulsion whole-genome amplification[END_REF] , proteomics [START_REF] Shahi | Ultrahigh-throughput single cell protein profiling with droplet microfluidic barcoding[END_REF] or epigenomics [START_REF] Rotem | Single-cell ChIP-seq reveals cell subpopulations defined by chromatin state[END_REF] . Despite the efficiency and the disruptive character of these microfluidic-based technologies, they are generally limited to one modality.

Since then, great technological advances have enabled multimodal single-cell analysis, thanks to which multiple modalities can be dissected from each cell. 2019 was a very prolific year for singlecell multi-omics regarding the numerous new methods that appeared, to the point that the journal Nature Methods selected it as the method of the year [START_REF]Method of the Year 2019: Single-cell multimodal omics[END_REF] . While droplet microfluidics has been very useful to provide accessible high-throughput methods for single-cell study of one modality, there are a very few high-throughput methods adapted to multi-omics. These methods often require a physical separation step of analytes, which has not been integrated in high-throughput droplet microfluidics so far.

Besides, our group developed an original solid support extraction approach based on magnetic tweezers that allows the transfer of functionalized magnetic microparticles between sub-microliter droplets [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] . The microparticles can be then used as a solid support to selectively extract analytes from the sample and therefore allow "omics" separation.

After its introduction in 2012, this approach has been shown suitable by our group to purify proteins [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] , mRNA [START_REF] Ferraro | Microfluidic platform combining droplets and magnetic tweezers: application to HER2 expression in cancer diagnosis[END_REF] , gDNA 10 and chromatin [START_REF] Teste | Chromatin immunoprecipitation in microfluidic droplets: towards fast and cheap analyses[END_REF] . Despite the efficiency of these systems, they are still limited to quite big droplets -around hundreds of nanoliters -and low throughput compared to stateof-the-art droplet microfluidics, making them not well suited to single-cell analysis.

C

The main objective of this PhD project is to develop a new generation of microfluidic chip, by adapting the above-mentioned magnetic tweezers approach to high-throughput analysis, and to reduce droplet sizes by two order of magnitudes to reach the sub-nanoliter scale, more adapted to single-cell analysis. Ultimately, this device would allow us to physically separate the "-omics" from single-cells encapsulated in the droplets. However, downscaling the system dramatically changes the balance between the involved forces. Basically, at smaller scales, capillary forces become predominant against magnetic forces, resulting in difficulties to perform physical extraction from droplets. We had to find a way to reduce the scale, while keeping a strong magnetic force.

Our approach was to fabricate micro-magnetic-tweezers by means of an electroplating method, allowing the production of structures made of permalloy which is a nickel-iron alloy, known for its very good magnetic properties. Placed from either side of a microfluidic channel, the micromagnetic-tweezers are able to trap and extract magnetic particles from a flowing droplet. The magnetic field gradient decreasing exponentially with the distance from the magnets, the microfabricated soft-magnets were placed as close as possible from the channel, thus keeping a high magnetic field gradient. Figure 1 below shows the capture process of microparticles by the micro-magnetictweezers. In a first stage, the particles are collected between the tweezers (Figure 1b) into a compact cluster, that is extracted in a second stage (Figure 1c,d). In the third stage (Figure 1e,f) another droplet can push the cluster away. Video 1, provided in appendix with the manuscript, shows this capture process. experimental protocols that were developed. Optimization and characterization of the micro-magnetic-tweezers will be then exposed and discussed.

• Chapter 4 will present some computational work, inspired by the ferrohydrodynamics theory 12 , to simulate dense magnetic particles laden flows. This model was applied to simulate the magnetic particle capture in the micro-magnetic-tweezers, as well as another magnetic particles-based device developed in our group: the microfluidic magnetic fluidized bed.

• Chapter 5 will show some developments on the biological aspects. This work, done in collaboration with Mathilde Richerd, aims at showing that the magnetic tweezers can be used to separate the "-omics" from biological samples. In a first part, we will present an attempt to develop a multiplex RT-qPCR assay to quantify simultaneously genomic DNA (gDNA)

and messenger RNA (mRNA). This assay would be used to assess the efficiency and specificity of magnetic particle based bioseparation. In a second part, we will show our first experiments of gDNA/mRNA separation in the magnetic tweezers platform.

• Chapter 6 will describe the different modules that were implemented in the microfluidic chip, other than the micro-magnetic-tweezers themselves. We will first present a dropleton-demand module that was developed at the beginning of the PhD project. Then we will

show how we implemented the other above-mentioned modules, namely the paired reinjection, electro-coalescence and magnetic sorting.

• Chapter 7 will present the results of two successive internships that I supervised, carried out by Elina Gilbert and Grégoire Lemahieu. The aim of this project is to develop magnetic hydrogel beads as a new class of solid support for bioseparation in droplet microfluidics.

These hydrogels aim at being used in place of magnetic microparticles in the micro-magnetic-tweezers device to improve its efficiency and facilitate its applicability.

CHAPTER 1

Introduction

This introductive chapter will first present the basic concepts of droplet microfluidics, from a physical and technological point-of-view. In a second part, the main biological applications will be presented. A quick review of single-cell analysis methods will be given either for single and multiomics study, with particular considerations for advances brought by microfluidics. The last part of this chapter will focus on magnetism in microfluidics, from theoretical aspects to applications.

1 Droplet microfluidics

History and definitions

Microfluidics is currently undergoing a particularly fast development and is now offering new and innovative solutions for modern bioanalysis [START_REF] Sackmann | The present and future role of microfluidics in biomedical research[END_REF] . The power of microfluidics results directly from miniaturization. By handling small volumes of fluid -from femto to microliters -microfluidic devices scale down existing analytical protocols, decreasing sample volume, experimental cost, diffusion and reaction times. Every steps of an experiment can be integrated in the same miniaturized device, leading to advanced automation and massive parallelization. For that reason, such systems are often referred to as Lab-on-a-chip or µTAS (for Micro Total Analysis Systems).

Despite an early and quite unnoticed work on a miniaturized gas chromatography device by Terry et al. in 1979 14 , the concept of Lab-on-a-chip or µTAS -which are de facto used as synonyms -was popularized in 1990 by A. Manz et al. [START_REF] Manz | Miniaturized total chemical analysis systems: A novel concept for chemical sensing[END_REF] who put forward the idea that using smaller channels would, in principle, dramatically increase the performances of analytical chemistry systems such as chromatography or electrophoresis. They add that all the steps of the experiment, including sampling, transport, separation and detection could be carried out in a row in the same device. In parallel, the very active development of the semi-conductor industry, and particularly the MEMS (Micro Electro Mechanical Systems) technology, provided in the 1990s a strong technological knowledge on complex microstructures fabrication, and several silicon-based microfluidic devices were developed in this period [START_REF] Tabeling | Introduction à la microfluidique[END_REF] . A key milestone was the introduction of soft lithography by G. M.

Whitesides group in 1998: this technique has enabled simplified fabrication, and fast prototyping of elastomer-based, transparent and biocompatible microfluidic devices [START_REF] Xia | Soft lithography[END_REF] . Soft lithography became the gold standard method for microfluidic devices fabrication, and paved the way to the development of plenty of biology-oriented microfluidic devices, which is today one of the most active application field of microfluidics.

Droplet microfluidics enables the manipulation of micro-droplets of a volume ranging from femto to microliter in an immiscible phase. The phase constituting the droplets and the one surrounding them are respectively referred to as "dispersed" and "continuous" phases. Although both waterin-oil and oil-in-water droplets can be generated, most applications involve water-based droplets in an immiscible carrier oil, in a way that each droplet can be considered as a small aliquot in which controlled reactions can occur. Offering the possibility to manipulate extremely small volumes of fluid, droplet microfluidics has emerged as a powerful tool for high throughput bioanalytical experiments such as drug screening or single-cell analysis.

Three approaches can be distinguished:

• Continuous droplet microfluidics was the first to be introduced and is today the most common one. Droplets are generated in a continuous manner by shearing or squeezing the dispersed phase under the action of the streaming continuous phase in specific channel geometries such as T-Junction or Flow Focusing. They then follow a predetermined path in a microchannel or a tubing filled by the continuous phase, going through the different operations specific to the experiment, namely merging, splitting, sorting, cell encapsulation etc. [START_REF] Seemann | Droplet based microfluidics[END_REF] A non-exhaustive review of those functionalities is given in section 1d of this chapter.

Compared to the other strategies, continuous droplet microfluidics allows ultra-high throughput experiments (up to kHz) and the handling of very small droplets (tenth of picoliter). However, it does not allow individual control and tracking among droplets, and also needs a specific external pumping equipment.

• Stationary droplet microfluidics aims at producing an array of stationary aqueous microdroplets on a patterned substrate, similarly to a microtiter plate. This approach is more easily adaptable to conventional tools (e.g. liquid handling robots, microplate readers, multi-channel micropipettes) and is for this reason very versatile [START_REF] Popova | Droplet-Array (DA) Sandwich Chip: A Versatile Platform for High-Throughput Cell Screening Based on Superhydrophobic-Superhydrophilic Micropatterning[END_REF][START_REF] Huemmer | Microfluidic Platform for Multimodal Analysis of Enzyme Secretion in Nanoliter Droplet Arrays[END_REF] . Another approach consists in trapping flowing droplets in a closed microfluidic chip with an array of holes or obstacles acting like traps [START_REF] Dangla | Trapping microfluidic drops in wells of surface energy[END_REF] . Static droplet microfluidics has the advantage of enabling long term observation of droplets and has thus been extensively used for cell and spheroid culture in a controlled environment [START_REF] Huebner | Quantitative detection of protein expression in single cells using droplet microfluidics[END_REF][START_REF] Tomasi | Studying 3D cell cultures in a microfluidic droplet array under multiple time-resolved conditions[END_REF] .

• Digital Microfluidics is another well-established approach and is based on a technology called Electrowetting On Dielectric (EWOD). Droplets deposited on a flat dielectric surface can be moved on demand by actuating patterned electrodes placed under the substrate.

This technology relies on electrowetting: the contact angle between a droplet and the solid surface can be modified locally by means of electrostatic effects, this modification of wettability, which is reversible, results to an asymmetry in surface tension that leads to pressure gradients in the droplet and thus to its displacement [START_REF] Nelson | Droplet actuation by electrowetting-on-dielectric (EWOD): A review[END_REF] . Digital microfluidics has the advantage not to require any pumping system, and to allow a high degree of control. However, it doesn't allow high throughput experiments and require complex fabrication and operation [START_REF] Serra | The power of solid supports in multiphase and droplet-based microfluidics: towards clinical applications[END_REF] . In the community, the term "digital microfluidics" refers to this technology only, and shouldn't be confused with digital PCR which is another technique involving droplet microfluidics.

This chapter gives an overview of the droplet microfluidics state-of-the-art, from the knowledge on its physics and technological advances. It will however mainly focus on continuous droplet microfluidics systems with water-based droplets.

Physics of droplets

Physics of confined droplets in a microchannel is far from being straightforward. Although there is yet no general model to fully describe their behavior, this section will discuss the main elements to understand it.

Microscale flows are in their vast majority characterized by a laminar behavior. A flow is called laminar -as opposed to turbulent -when viscosity predominates inertial effects resulting in parallel streamlines, predictable and reversible flow. It comes with a low Reynolds number (!" = $%& ' ⁄ < 1 ), and in the case of incompressible fluids, the Navier-Stokes equation describing the motion of fluids can be simplified into a linear partial derivative equation (PDE): the Stokes equation.

'∇ , u -∇/ = 0

Where ' is the dynamic viscosity (Pa.s), ∇ , u is the Laplacian of the velocity field and ∇/ is the pressure gradient [START_REF] Quéré | perles et ondes[END_REF] .

In single phase microfluidics, fluid flows are generally described by a parabolic velocity profile with a maximum velocity at the center of the channel and no slip at the walls. This particular flow, called a Poiseuille flow, makes the fluid close to the wall to move slower than in the center, and this can be a problem when an accurate control of residence time in the chip is needed. In addition,

To have an efficient displacement of confined droplets in a microfluidic channel without crosscontamination between droplets, wetting of the dispersed phase on the channel walls have to be avoided. For this reason, chip material, continuous phase nature, and surface treatment have to be carefully chosen so that the continuous phase has greater affinity with the walls than the dispersed phase. Basically, highly hydrophobic walls are preferred in water-in-oil systems. As a result, the content of the droplets is never directly in contact with the walls. A thin lubrication film of a tenth of nanometers remains between the walls and the droplets. Its thickness, as well as its consequences on droplets velocity are absolutely not straightforward to determine, and there is yet no general model linking the velocity of the droplets with the velocity of the continuous phase [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF] .

The role of surfactants

A surfactant is an amphiphilic molecule, having a hydrophilic "head" and a hydrophobic "tail".

These molecules have a particular affinity for interfaces: the hydrophilic head will tend to stay in the aqueous phase while the hydrophobic part remains in the oil (Figure 5a). The hydrophilic head can be anionic, cationic of non-ionic. The hydrophobic tail generally consists in a carbonated chain CH 3 -[-CH , -] ?or a fluorinated chain CF 3 -[-CF , -] ? -.

Surfactants spontaneously adsorb at liquid-liquid interfaces as a monolayer, reducing their surface energy and thus the surface tension. In excess of surfactants, the interfaces are fully occupied and surfactant molecules spontaneously form aggregates called micelles. The concentration from which micelles form is called Critical Micelle Concentration (CMC). Surfactants are an essential ingredient to stabilize an emulsion, by adsorbing at the interfaces, they prevent coalescence between the droplets composing the emulsion due to steric effects. With an appropriate surfactant, emulsions can remain stable for months, and have been for this reason studied extensively in cosmetic and food industries. Surfactants can also arrange in a water-oil-water bilayer to form a thin membrane. One of the most remarkable example is the plasma membrane of cells that consists in a double layer of lipids, which are biological surfactants [START_REF] Brochard-Wyart | Physique de la matière molle[END_REF] .

In droplet microfluidics, surfactants are dissolved in the carrier oil at a concentration above the CMC. They aim at reducing surface tension, avoiding erratic droplet behaviors by stabilizing the interfaces, preventing from undesired wetting, coalescence and cross-contamination between droplets. The oil-surfactant combination has to be carefully chosen depending on the application.

In early droplet microfluidics, hydrocarbon oils such as hexadecane or mineral oil were the most used with Span-80 as a surfactant. Fluorinated oils such as FC-40 or HFE-7500 (commercially aviable under the name Novec-7500) were rapidly preferred over hydrocarbon oils due to their interesting properties: they are chemically inert, have a low viscosity, are highly hydrophobic, biocompatible and permeable to gas. Fluorinated oils are notably the only example to date in droplet microfluidics allowing cell survival and proliferation over more than two hours [START_REF] Clausell-Tormos | Droplet-Based Microfluidic Platforms for the Encapsulation and Screening of Mammalian Cells and Multicellular Organisms[END_REF][START_REF] Baret | Surfactants in droplet-based microfluidics[END_REF] .

These remarkable properties are also explained by the use of appropriate surfactants. The gold standard in droplet microfluidics is a PFPE-PEG-PFPE triblock-copolymer [START_REF] Holtze | Biocompatible surfactants for water-in-fluorocarbon emulsions[END_REF] as illustrated on Figure 5b. It is synthetized from: i. Krytox, a fluorinated lubricant containing a PFPE block (perfluoropolyether) which is highly hydrophobic and ii. polyethylene glycol (PEG) which is the constituent of the biocompatible, nonionic, hydrophilic head. This molecule, or similar, is commercialized by different companies with various names such as Picosurf (Sphere Microfluidics), Fluosurf (Emulseo) or EA-Surfactant (Raindance Tech.), RAN Biotech. In addition, similar surfactants based on PFPE were developed replacing the PEG group by glycerol [START_REF] Wagner | Biocompatible fluorinated polyglycerols for droplet microfluidics as an alternative to PEG-based copolymer surfactants[END_REF][START_REF] Chowdhury | Dendronized fluorosurfactant for highly stable water-in-fluorinated oil emulsions with minimal inter-droplet transfer of small molecules[END_REF] , allowing surfactant modification and functionalization. PEG-PFPE surfactants structure was also changed to a 3-arm or a brushlike polymer molecule, giving improved biocompatibility and stability at temperatures up to 90°C. [START_REF] Scanga | Click chemistry approaches to expand the repertoire of PEG-based fluorinated surfactants for droplet microfluidics[END_REF] Figure 5: Surfactants principle a. Surfactants adsorb at the interface (1). The PEG polymer block gives a non-ionic functionalization inside the interface, preventing adsorbtion of biomolecules (2) or cells (3). b. The surfactant sutrcture is PFPE-PEG-PFPE block-copolymer. Adapted from Holtze et al. [START_REF] Holtze | Biocompatible surfactants for water-in-fluorocarbon emulsions[END_REF]

Droplets manipulation

This part gives a non-exhaustive review of the main techniques to manipulate micro-droplets in a chip (see Figure 6). 37

Generation

Continuous production of a monodisperse droplet stream can be performed by shearing or squeezing the dispersed phase with the continuous phase in a dedicated geometry. We review here only passive techniques relying on flow-induced droplet breakup, as opposed to active techniques needing an external actuation to produce droplets on demand. The latter are reviewed in another chapter.

Co-flow systems can be seen as a coaxial version of flow-focusing (Figure 6 top right). Here, the two liquid streams are flowing in the same direction, with the continuous phase surrounding the dispersed phase. This was first obtained before the introduction of flow-focusing and T-junction using a tapered capillary dipped into moving carrier oil [START_REF] Umbanhowar | Monodisperse emulsion generation via drop break off in a coflowing stream[END_REF] , and later with two coaxial glass capillaries [START_REF] Utada | Monodisperse double emulsions generated from a microcapillary device[END_REF] , allowing generation of droplet of 10-50µm at a 100-5,000Hz frequency.

For each geometry, ultra-high throughput generation can be achieved, up to several kHz in jetting regime. Unfortunately, it turns abruptly into a stationary co-flow where no droplets are produced at a too high capillary number, giving limitations to the generation throughput.

Mixing

As previously mentioned, the laminar nature of single-phase microscale flows makes mixing difficult to achieve. This is no longer the case in segmented flows where droplet interfaces are constantly moving, generating recirculation flows within the droplets. These flows have been widely characterized experimentally [START_REF] Sarrazin | Mixing characterization inside microdroplets engineered on a microcoalescer[END_REF][START_REF] Kinoshita | Three-dimensional measurement and visualization of internal flow of a moving droplet using confocal micro-PIV[END_REF] or numerically [START_REF] Stone | Imaging and quantifying mixing in a model droplet micromixer[END_REF][START_REF] Wang | Fluid mixing in droplet-based microfluidics with a serpentine microchannel[END_REF] . It has been shown that using a serpentine channel breaks the flow symmetry and leads to chaotic advection in the droplets, accelerating the mixing considerably [START_REF] Song | A microfluidic system for controlling reaction networks in time[END_REF][START_REF] Song | Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels[END_REF] . This technique, although very simple, is enough in most situations to achieve rapid mixing in droplets.

Merging and pico-injection

Mastering coalescence is essential to trigger reactions in a controlled way by adding reagents in droplets. Since early years of droplet microfluidics, passive merging was simply carried out by putting surfactant-free droplets into close contact, inducing their spontaneous merging. This can be achieved either with two synchronized droplet trains meeting each other at a Y-junction, or by slowing down or trapping a droplet until it is in contact with the following one (Figure 6 middle left) [START_REF] Xu | Droplet Coalescence in Microfluidic Systems[END_REF] .

However, surfactant-stabilized droplets are more difficult to merge due to steric effects. It has been shown that a rapid deconfinement of droplets leads to a local and transient depletion of surfactants facilitating their fusion [START_REF] Bremond | Decompressing emulsion droplets favors coalescence[END_REF] . It has also been observed that two droplets with different interfacial surfactant coverage can merge after a critical contact time [START_REF] Mazutis | Selective droplet coalescence using microfluidic systems[END_REF] . Despite the two above mentioned examples, passive merging is generally not suitable with fluorosurfactant-stabilized droplets in fluorinated oil.

Active merging relies on the destabilization of droplets interfaces in close contact to each other thanks to an external energy supply. The source of energy can be a laser spot, heating, pneumatic valves, but the most common one is electric fields. This approach was first introduced in 2005 by Chabert et al., [START_REF] Chabert | Droplet fusion by alternating current (AC) field electrocoalescence in microchannels[END_REF] . They achieved electrocoalescence by applying a localized alternative current (AC)

field. The conductivity of the droplets being higher than the one of the oil, dielectrophoretic effects provoke instabilities on interfaces leading to droplet fusion. An easy method to fabricate microelectrodes is to use low temperature melting metal that can fill a microfluidic channel. This technique, called microsolidics [START_REF] Siegel | Microsolidics: Fabrication of three-dimensional metallic microstructures in poly(dimethylsiloxane)[END_REF] made electrocoalescence much simpler to integrate into PDMS devices and is for this reason extensively used. [START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF][START_REF] Mazutis | Droplet-Based Microfluidic Systems for High-Throughput Single DNA Molecule Isothermal Amplification and Analysis[END_REF][START_REF] Frenz | Droplet-based microreactors for the synthesis of magnetic iron oxide nanoparticles[END_REF][START_REF] Lee | Synchronized reinjection and coalescence of droplets in microfluidics[END_REF] Thanks to electrocoalescence, pico-injection can be performed to dispense small quantities of reagent in droplets. A secondary channel, connected to the main one, is filled by the reagent to be injected in a way that the meniscus, pinched by a constriction, can be brought into contact with droplets passing in the main channel. Reagent is then directly injected in droplets by applying electric pulses through microfabricated electrodes [START_REF] Abate | High-throughput injection with microfluidics using picoinjectors[END_REF] .

Detection

A crucial requirement, in addition to droplet manipulation, is to be able to detect and quantify species of interest in droplets. The detection can be done either on-chip or off-chip.

Detection on-chip is challenging because droplets produced at high-throughput are generally moving very fast in the system and are not physically accessible. Detection of droplets was done with integrated electrodes to measure capacitance variations induced by droplets passing in a channel at a frequency up to 10kHz. This approach, however, was not suited to measure small quantities of biological compounds [START_REF] Niu | Real-time detection, control, and sorting of microfluidic droplets[END_REF] . Despite a few other examples based on capacitive [START_REF] Yesiloz | Label-free high-throughput detection and content sensing of individual droplets in microfluidic systems[END_REF] or potentiometric sensors [START_REF] Han | Measuring rapid enzymatic kinetics by electrochemical method in droplet-based microfluidic devices with pneumatic valves[END_REF] , optical detection is generally preferred, allowing a fast and highly sensitive sensing [START_REF] Suea-Ngam | Droplet microfluidics: from proofof-concept to real-world utility?[END_REF] .

Most of them are based on lasers to excite fluorophores carried in droplets and to detect them with a fast camera, a photodiode or a photomultiplier tube [START_REF] Baret | Fluorescence-activated droplet sorting (FADS): Efficient microfluidic cell sorting based on enzymatic activity[END_REF][START_REF] Casadevall I Solvas | Fluorescence detection methods for microfluidic droplet platforms[END_REF][START_REF] Mai | Single-step immunoassays and microfluidic droplet operation: towards a versatile approach for detection of amyloid-β peptide-based biomarkers of Alzheimer's disease[END_REF] . (Figure 6 middle bottom) These techniques are also used to measure the generation frequency and size of droplets.

Alternatively, an off-chip readout with an external instrument can be performed, taking advantage of the high precision and wide diversity of information that can be extracted with conventional equipment such as mass spectrometry (MS) [START_REF] Pereira | A Nano LC-MALDI Mass Spectrometry Droplet Interface for the Analysis of Complex Protein Samples[END_REF][START_REF] Mesbah | MALDI: Droplet based microfluidic combined to MALDI-TOF for focused peptide detection[END_REF] , nuclear magnetic resonance (NMR) spectroscopy [START_REF] Hale | High-resolution nuclear magnetic resonance spectroscopy in microfluidic droplets[END_REF] or qPCR thermocycler [START_REF] Ferraro | Microfluidic platform combining droplets and magnetic tweezers: application to HER2 expression in cancer diagnosis[END_REF] . However, these devices were not developed to analyze a large number of small samples, and therefore don't allow an individual analysis of every droplets produced at highthroughput.

Another elegant approach is to associate a unique nucleic acid barcode to a target analyte present in each droplet. After the barcoding step in droplets, the emulsion is broken and analyzed with Next Generation Sequencing (NGS). Barcodes indicate from which droplet the sequenced transcripts come from. This method fully takes advantage of both droplet microfluidics throughput and NGS power, it has been demonstrated simultaneously by Klein et al. [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] and Macosko et al. [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF] in 2015 and is now a common approach for single-cell analysis. This technology is detailed in the third part of this chapter.

Sorting

Sorting is another fundamental operation of many droplet-based experiments. Droplets are sorted depending on a measurable criterion, typically fluorescence. In a recent publication, Xi et al. provided a comprehensive review of existing active droplet sorting methods [START_REF] Xi | Active droplet sorting in microfluidics: a review[END_REF] . These methods rely on an external energy source to apply a momentary force on a droplet, deflecting it to a secondary channel. Approaches relying on electric, thermal, pneumatic, magnetic or acoustic actuation were demonstrated. The most popular one, inspired by Fluorescence Activated Cell Sorting (FACS), is based on dielectrophoretic actuation of droplets with microfabricated electrodes (Figure 6 bottom right) [START_REF] Baret | Fluorescence-activated droplet sorting (FADS): Efficient microfluidic cell sorting based on enzymatic activity[END_REF] . The former approach has been recently improved to perform multiplexed sorting of five droplet populations into separate output channels [START_REF] Caen | High-throughput multiplexed fluorescence-activated droplet sorting[END_REF] .

Splitting

Droplet fission is of interest to carry out parallel experiment or consecutive dilutions. Unlike merging, splitting can always be achieved in a passive manner. The simplest way to perform droplet fission is to use a bifurcating junction, making the droplet to be split in two parts of relative size depending on the fluidic resistance of the downstream channels (Figure 6 center) [START_REF] Seemann | Droplet based microfluidics[END_REF] . It has been observed that a droplet arriving at a T-junction first deforms and then is either split into two parts, or pushed into one of the downstream channel, the splitting occurs only at high enough capillary number and only with long and confined droplets [START_REF] Link | Geometrically Mediated Breakup of Drops in Microfluidic Devices[END_REF] .

Incubation, storage and reinjection

Some reactions have slow kinetics, making an incubation of droplets needed. This can be either performed on-chip or off-chip for short term or long-term incubation respectively.

For on-chip incubation, Frenz et al. [START_REF] Frenz | Reliable microfluidic on-chip incubation of droplets in delay-lines[END_REF] introduced a delay-line in which the droplets remain for a controlled time period. They showed that using close-packed emulsion makes the droplets move all at the same speed and thus have the same residence time in the delay-line (Figure 6 bottom left).

For a non-closed-packed emulsion, consecutive constrictions in the delay-line are necessary to redistribute the droplets, equalizing their total residence time in the chip. [START_REF] Frenz | Reliable microfluidic on-chip incubation of droplets in delay-lines[END_REF] Emulsions can otherwise be collected off-chip in a vial or a syringe and remain stable for days to months, depending on the nature of their content, and of the surfactants. They can be then reinjected in a chip as a close-packed emulsion, after which carrier oil is injected between droplets to retrieve a controlled spacing between them (Figure 6 middle right) [START_REF] Lee | Synchronized reinjection and coalescence of droplets in microfluidics[END_REF][START_REF] Guo | Droplet microfluidics for high-throughput biological assays[END_REF] . If a thermal treatment is needed, a mineral oil layer is added on top of the emulsion to prevent evaporation of droplets and carrier oil [START_REF] Zilionis | Single-cell barcoding and sequencing using droplet microfluidics[END_REF] .

Encapsulation

Single-cell compartmentalization is one of the fundamental steps for single-cell analysis, making encapsulation of single-cells in droplets a major concern in the field. A single-cell emulsion can be produced by simply introducing a solution of cells in a flow-focusing chip. The probability of a cell to be encapsulated follows a Poisson distribution, the initial solution should be thus diluted to avoid encapsulation of two or more cells in one droplet. As a result, the vast majority of droplets are empty (85%-95%). However, the high throughput allowed by droplet microfluidics (100 to 1,000 Hz) easily counterbalance this problem, and still surpass conventional liquid handling tools [START_REF] Kintses | Microfluidic droplets: New integrated workflows for biological experiments[END_REF] .

In single-cell analysis, co-encapsulation of cells with a barcoded bead is often needed (see part 3), reducing dramatically the occurrence of valid droplets because of a double Poisson distribution [START_REF] Mazutis | Single-cell analysis and sorting using droplet-based microfluidics[END_REF] .

To reduce this limitation, hydrogel beads instead of solid beads, allowing their deterministic injection as with a close-packed emulsion [START_REF] Abate | Beating Poisson encapsulation statistics using close-packed ordering[END_REF] . The latter has been extensively used, notably in the inDrop [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] system for single-cell RNA sequencing, that will be described in more details in Part 3 if this chapter. To illustrate, Figure 7 shows the hydrogel beads-based encapsulation of inDrop, the close-packed beads are reinjected at the same frequency than droplet formation, allowing their deterministic encapsulation. Note than in inDrop, cells are co-encapsulated with the gel beads, they cannot however be deterministically reinjected like the beads, and their encapsulation still relies on Poisson statistics. These techniques to decrease the variance of objects per droplet allow a sub-Poisson loading, but they are often mistakenly called "super-Poisson" loading in the microfluidics community.

Biological applications

The number of publications on droplet microfluidics has considerably grown in the past few years.

As an illustration, Shang et al. [START_REF] Shang | Emerging Droplet Microfluidics[END_REF] listed in a recent review more than 400 application papers published between 2001 and 2017 that rely on droplet microfluidics. This section attempts to give a short insight into the biology-oriented applications. However, studies aiming at studying heterogeneity of cell populations -single-cell omics -will be described more in detail in Part 3 of this chapter.

Digital PCR

Although the concept of digitalizing Polymerase Chain Reaction (PCR) was put forward several times in the 1990s, the term "digital PCR" (dPCR) was first introduced by Vogelstein and Kinzler in 1999. It is a method to improve PCR sensitivity, making it suitable for rare mutations quantification. Conventional end point PCR consists in measuring the amount of amplification product after a certain number of PCR cycles. It is very difficult to go back to the initial amount of DNA/RNA because the exponential nature of the amplification will strongly amplify all reaction bias, making difficult the correlation between the initial and final quantity. In dPCR, a highly diluted sample is partitioned in a way to have, on average, zero or one target molecule per PCR reaction. After amplification and detection of the targeted gene with a TaqMan probe, the number of fluorescent over non-fluorescent wells is counted, and a simple linear relation is applied to go back to the initial sample concentration (Figure 8) 85,[START_REF] Morley | Digital PCR: A brief history[END_REF] .

A widely spread approach is to produce size-controlled hydrogel particles by cross-linking droplets of hydrophilic polymer. This has been demonstrated with different polymer such as polyacrylamide [START_REF] Abate | Beating Poisson encapsulation statistics using close-packed ordering[END_REF] , polyNIPAm [START_REF] Kim | Fabrication of monodisperse gel shells and functional microgels in microfluidic devices[END_REF] , PEG [START_REF] Rossow | Controlled synthesis of cell-laden microgels by radical-free gelation in droplet microfluidics[END_REF] , PEGDA [START_REF] Kamperman | Single Cell Microgel Based Modular Bioinks for Uncoupled Cellular Microand Macroenvironments[END_REF] , alginate 100 or agarose 101 . Gelation of liquid droplets is achieved either by means of i. a heat-induced cross-linking, that is often performed off-chip in an oven or ii. a light-induced cross-linking, that has the advantage to be very fast and allows a rapid on-chip polymerization. Such hydrogel beads can be loaded with macromolecules or cells, injected in droplets, and manipulated off-chip in bulk while keeping their integrity and composition. They are often used as a barcode carrier for droplet indexing, allowing to differentiate the droplets between them 102 . This barcoding approach will be discussed more in details in Part 3 this chapter, and a more general review on hydrogel beads applications in microfluidics will be provided in Chapter 7.

Similarly, generation of oil-water-oil double emulsions was used to produce polymeric shells [START_REF] Kim | Fabrication of monodisperse gel shells and functional microgels in microfluidic devices[END_REF]103 .

Degradation of such capsules can be controlled in time, or triggered under certain conditions, making them interesting materials for drug delivery 104,105 . (Figure 9a)

Hydrogel beads can also serve as bricks to assemble bio-inspired structures mimicking natural soft materials. In this way, a single layer of hydrogel droplets was used to produce hexagonal prismatic hydrogel sheet (Figure 9b) 106 . They are also often used as scaffold to reproduce cellular micro-environment (Figure 9c) [START_REF] Kamperman | Single Cell Microgel Based Modular Bioinks for Uncoupled Cellular Microand Macroenvironments[END_REF]107,108 .

Cell-based drug screening

Drug discovery is a major concern in the pharmaceutical industry. In-vitro drug screening on cultured cells is routinely performed to select candidates from a library of hundreds of thousand molecules 109 . This is conventionally done with automated liquid-handling robots and 96-well plates, allowing to test around 10,000 compounds a day in a volume around 1 mL per reaction, which is extremely time and reagent consuming. The drug-containing droplets were merged with single-cell droplets, after which an optical live-dead assay was performed to assess drug efficiency [START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF] . Similarly, a dose-response analysis of an hormone at 8 concentrations on single-cells was accomplished 119 .

Antibody discovery often relies on the production of particular immortalized B cells called hybridoma cells. Each one of them are able to produce a single species of monoclonal antibody and must be screened for the desired one 120 . This technique is time consuming, to illustrate, only » 200 cells are analyzed in 10-12 weeks in a typical 96-well plate [START_REF] Guo | Droplet microfluidics for high-throughput biological assays[END_REF] then placed under a magnetic field so that the particles form aggregates to focus the fluorescent signal, which is read by a camera under microscope.

Directed evolution and synthetic biology

Compartmentalization of single molecules offers news possibilities in biochemistry and synthetic biology. Tawfik et al. proposed in 1998 a protocol to perform directed proteins evolution in droplets 123 . An emulsion is produced in a way for droplets to contain a unique gene that can be transcribed into RNA and then translated into proteins. A substrate molecule is attached to each compartmentalized gene. The gene is transcribed and translated into an enzyme that may, or not, turn the substrate into a detectable product. By recovering droplets containing the product, genes coding for the desired protein can be selected. It is then possible to perform further mutagenesis and selection rounds with another substrate. It was applied to produce a variant of methyltransferase enzyme 124 , and more recently to engineer a 10-fold improved mutant of horseradish peroxidase enzyme 125 . Other enzymes were evolved with this technique such as RNA ligase, phosphotriesterase, polymerase and ribosymes 126 .

Droplet microfluidics is also a tool to produce cell-like phospholipid vesicles, also called liposomes 127,128 . They aim at reproducing the different biochemical functions of a cell with a bottomup approach. Producing such artificial cells represents an opportunity for researchers to have a simplified system offering a better control of biochemical mechanisms More originally, droplet microfluidics was used to study the origin of life 133 . Single RNA molecules were isolated in droplets to mimic abiological environments similar to those existing during life apparition period, and the mechanisms or early molecular replicators were studied.

Medical diagnosis

Microfluidics have given rise to innovative medical diagnosis approaches, allowing for more rapid and sensitive tests with reduced volume requirements. We can distinguish between two categories of diagnosis-oriented microfluidic devices. i. The ones that aim at producing fast and inexpensive tests at an industrial scale. They must be very simple to operate out of laboratory to provide a point-on-care diagnosis 134 . ii. The second category is more oriented toward precision and personalized medicine. More complex microfluidic devices, that often need external equipment and a trained operator, are used to detect rare biomarkers from complex samples. Devices involving droplet microfluidics are generally in the latter category.

Mutated tumoral DNA is a highly specific biomarker of cancer, present in stool, blood or lymph, it can be used for early-stage diagnosis. Unfortunately, it is present in very small quantities compared to non-mutated DNA, and is below the detection limit of conventional assays. By isolating the molecules in small droplets, dPCR removes the background noise and is therefore a method of choice to detect small amounts of DNA. It has been used to detect a mutation in KRAS oncogene in gDNA, in the presence of a 200,000-fold excess of unmutated genes 135 . Similarly, it has been applied to detect 7 common mutations in KRAS on 50 plasma samples from patients suffering from metastatic colorectal cancer 136 . A similar study was carried out to detect miRNA from non-treated plasma of colon cancer patients 137 . Our group developed another technology to perform in-situ qPCR in droplets flowing in a capillary, this was applied to the quantification of HER2 gene, a breast cancer biomarker 118,138 .

While droplet microfluidics has been extensively used for nucleic acid detection, there is much less studies on proteins. Assays such as ELISA often need a washing step which is difficult to perform in droplets, hence microfluidic devices based on other technologies are generally preferred. Our group developed a technology implementing washing step in droplet microfluidics to detect both proteins [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] and peptides [START_REF] Mai | Single-step immunoassays and microfluidic droplet operation: towards a versatile approach for detection of amyloid-β peptide-based biomarkers of Alzheimer's disease[END_REF] through an ELISA assay on magnetic beads. This technology is presented more in details in part 4. Alternatively, a one-step fluorescent immunoassay on a single bead to focus the weak fluorescent signal can be performed in droplets to detect small amounts of proteins without need for an extraction step 139 . Besides, cell surface proteins can be directly detected in droplets thanks to an enzymatic transformation of a substrate into fluorophore 140,141 or by using an antibody conjugated with DNA that is further amplified and detected through rolling circle amplification (RCA) 142 .

Single-cell omics

Cells constituting a tissue, even from the same cell-line of sub-population, can exhibit different phenotypes or genotypes. This is of particular importance in tumor tissues that are inherently heterogeneous systems composed of mutated cells evolving in a healthy tissue 1 . To highlight this cellto-cell variability, investigation at the single-cell resolution need to be reached (see Figure 11). In "single-cell omics". Unlike previous single-cell studies that were focused on specific parameters in selected cells, the omics approach aims at extracting as much information as possible from a large number of cells to provide the most comprehensive description of a biological system 143 . Single-cell sequencing is seen by some researchers as a revolution in life-science 144 and was recognized by the journal Science as the method of the year in 2018.

We propose here a brief technological review of the methods for cell isolation and analysis, with both conventional and microfluidics approaches. Then a short view of the current state-of-the-art in single-cell multi-omics is given. Note that this is a very active field, and the technological landscape has changed a lot since the beginning of my PhD project, many of the mentioned papers in this part were published after 2017. This part is based on several reviews on single-cell omics, notably:

• Hu et al. (2016) 146 for the basics on single-cell isolation and analysis.

• Prakadan et al. (2017) 147 for the advances in single-cell omics enabled by microfluidics.

• Matuła et al. (2020) [START_REF] Matuła | Single-Cell Analysis Using Droplet Microfluidics[END_REF] for a complete review on all single-cell methods in droplet microfluidics, explained with simple schematics.

Conventional cell isolation techniques

Cell isolation is the first fundamental step in single-cell assays. In early single-cell studies, cells were dissociated and manually picked with a micropipette under microscope before being distributed in a microtiter-plate. This technique however requires high skills and is very time consuming.

Laser capture microdissection (LCM) is another technique to isolate cells. Here, a tissue on a glass slide is covered by a thermoplastic film under a microscope equipped with a laser. The laser is used to melt the film over a selected cell, making them stick to each other so that the cell remains on the film when it is pulled out. The advantage of LCM is that the cells of interest can be visually chosen from the starting tissue, it is however difficult to collect many cells and require a highly trained user.

Fluorescence activated cell sorting (FACS) is a common method to sort cells that was introduced in 1972 151 . A cell suspension is focused in a nozzle to form a continuous stream of single-cell systems can be efficient, they are complicated to fabricate and operate, and need advanced external equipment such as pressure controllers.

Ultimately, the Fluidigm C1 machine was released in 2014 and was the first fully integrated platform for single-cell analysis available on the market. Using disposable microfluidic devices, it is able to trap and isolate up to 96 cells automatically to perform several experimental steps in parallel including lysis, staining, amplification and harvesting prior to sequencing. Results provided by this device were reported in more than 200 publications. The last version of the device can process up to 800 cells. However, we could speak with some users of this machine, who reported to us a problem that can be critical: quite often, the machine do not differentiate if one or two cells are present in a trap, and no simple control can be done to fix this problem. This can lead to outliers or inconsistent results.

Droplets

Unlike valve-based devices, droplet microfluidics allows for high scalability: more than 100,000 cells can be encapsulated in a single experiment. Cells cannot however be individually followed upon time and this technology remained for this reason limited to continuous analysis in the same way as flow cytometry. Several techniques to index droplets were proposed, most of them relying on adding different dyes in droplets [START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF] .

A key milestone for single-cell omics resides in the publication in 2015 of two coincident papers by Macosko et al. [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF] and Klein et al. [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] reporting a high-throughput single-cell RNA sequencing (scRNAseq) strategy that relies on the barcoding of single-cells encapsulated in droplets [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF][START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] . A barcode consists in a short DNA sequence that binds specifically to messenger RNA (mRNA) in each droplet.

The droplets are then pooled together and the whole product is sequenced through NGS. After sequencing, the barcode sequences indicate from which cell the transcripts come from.

This method, bringing together the multiplexing potential of NGS with the high throughput enabled by droplet microfluidics, allows for massive parallelization of single-cell studies. For these reasons, droplet microfluidics became rapidly the gold standard approach for scRNA-seq and several platforms are now available including DropSeq, inDrop, 10X Genomics Chromium or BioRad-Illumina ddSEQ. While originally developed for transcriptomics, this droplet barcoding approach applies now to genomics, epigenomics and proteomics.

Wells

Using a nanowell patterned substrate is another common approach to isolate cells. A dilute cell solution is loaded on top of the plate to have at most one cell per well. Though having a low throughput compared to droplet microfluidics, its operational simplicity makes its a method of choice for single-cell studies, without the need of an external pumping or specialized reagents. As an early work, Love et al. reported an ELISA assay using a substrate containing 25,000 wells sealed by an antibody pattered glass slide 156 . This strategy, combined with barcoded beads, was chosen by several companies such as SeqWell, Microwell-seq, BD Rhapsody and Takara ICELL8 to commercialize a single-cell sequencing device 157 . Well-based devices are a good compromise between valves and droplets approaches in terms of throughput and control, but are also a simpler and cheaper alternative.

Transcriptomics

Transcriptomics is the study of gene expression, it is carried out by isolating and sequencing mRNA from cells. Although mRNA is not as rare as DNA in cells, its quantity is still not enough to perform NGS from single-cells, it needs to be reverse transcribed into cDNA and amplified.

Single-cell PCR amplification of cDNA followed by sequencing was reported in the 90s 158 . Unlike DNA, mRNA have a poly(A) tail, allowing for simple PCR transcriptome-wide amplification using poly(T) primers 159 . Due to its ease of isolation and amplification, transcriptome was the first sequenced object from single-cells.

PCR-based methods however suffer from critical biases, and improved methods were developed such as: TPEA (3" End Amplification), SMA (Semi Random Amplification) that uses semi random 2014 and 2016 based on this tool [165][166][167] . This approach, though giving a high molecular efficiency, is limited to a few cells and remains very expensive.

The introduction of barcoded beads leverage the power of microfluidics to enable high-throughput scRNA-seq. Three platforms has emerged almost simultaneously in 2015: the microwell-based Cy-toSeq 168 , and the droplet-based DropSeq by Macosko et al. [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF] and inDrop by Klein et al. [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] . The latter two exploit droplet microfluidics to co-encapsulate cells and beads. The idea is to label the transcripts of each cell with a unique barcode prior to sequencing. Compartmentalization is necessary only for this barcoding step, while reverse transcription (RT), amplification and sequencing can be performed in bulk without the need to follow each cell independently. To illustrate, Figure 13 shows the workflow for DropSeq. inDrop is a very similar protocol but uses hydrogel beads instead of hard particles, allowing super-Poisson loading, another difference is that inDrop performs the RT step in droplets (see Figure 7 in Part 1.4.8 of this chapter). This barcoding strategy became rapidly the gold standard for high-throughput scRNA-seq, and a range of commercial platforms based either on droplets or on wells are now available. Note that in addition to the cell barcode, as shown on Figure 13, each primer have a unique barcode called UMI (for Unique Molecular Identifier) that is useful to get rid of amplification bias after sequencing.

Figure 13: a. DropSeq workflow. Cells are co-encapsulated with barcoded beads and lysed (1-4). mRNA of the lysed cell binds to poly(T) primers on the beads (5). The emulsion is then broken and reverse transcription is performed on beads followed by amplification and sequencing (6-9). b. DropSeq microfluidic device for co-encapsulation of cells with beads. c. After sequencing, the barcodes indicate from which cell the transcript comes from. Besides the cell barcode, there is also a unique molecular identifier (UMI) that is different on each primer, even from the same cell. It allows us to count the molecules that were captured for each cell and thus to remove the PCR bias. Adapted from Macosko et al. [START_REF] Macosko | Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets[END_REF] These technologies were derived for other omics including genomics, proteomics and epigenomics.

They are presented in the following parts of this report.

Genomics

Single-cell genome sequencing can give great insights on tumor evolution, gamete genesis or subpopulation heterogeneity. However, a normal mammalian cell contains only two copies of a single gene, making it almost undetectable and requiring a reliable amplification. Conventional exponential PCR have critical biases on such small starting DNA quantities, a single error in the replication process is exponentially amplified 169 . Many improved PCR-based method were developed to perform an unbiased whole genome amplification (WGA). The most popular ones are DOP-PCR, MDA and MALBAC 170 . Even though these three methods work with different reactions, primers and enzymes, the idea is always to prime the DNA at many different random locations, and to amplify simultaneously everywhere, resulting in many DNA fragments of various sizes that are further amplified. WGA was performed on single-cells isolated with conventional method 170 , valve-based microfluidic chips [171][172][173][174] and microwells 175,176 for downstream exome or whole genome sequencing.

Before the introduction of the barcoding strategy for single-cell sequencing by Macosko et al. and Klein et al. in 2015, droplet microfluidics was restricted to targeted studies. Three platforms for targeted genome analysis were developed, all of them are based on PCR with gene-specific probes and fluorescence to evaluate the presence of a gene in single-cells [177][178][179] . Barcoding strategy, combined with WGA, allowed for whole genome sequencing from single-cells. It was demonstrated in droplets by Lan et al. in 2017. Their platform -called SiC-Seq -labels each cell with a unique DNA barcode by merging single-cells lysis encapsulated in agarose beads with droplets containing barcodes 180 . A similar device was developed and commercialized by the company 10X Genomics.

Here, the cell are embedded in hydrogel beads which are reinjected in droplets among with other hydrogel beads carrying the barcodes. This double hydrogel beads reinjection achieved an efficient super-Poisson co-encapsulation with 80% of droplets that contains one cell and one barcoding bead 181 .

Proteomics

Conventional protein analysis assays such as gel electrophoresis, chromatography or immunoassays require a large number of cells and are thus not compatible with single-cell analysis. In addition, a single mammalian cell contains a thousand of different proteins for a total mass below 1 ng, which is far below the detection limit of these techniques. Unlike DNA or RNA, there is no amplification possible with proteins and peptides, it is therefore necessary to have a detection limit as low as the single-cell level.

In addition of being used for cell sorting, flow cytometry is a powerful tool to measure fluorescence in single-cells, providing quantitative and multiparameter data. By reducing volumes, and thus dilution factor, microfluidics enables higher sensitivity

immunoassays. An approach called spatial barcoding consists in patterning stripes of different antibodies in a micro-chamber containing a single-cell lysis, on which an ELISA assay is performed. It has been demonstrated on valve-based 184,185 and well-based microfluidic devices to detect up to 42 proteins 186 . In addition, immunoassays that are more sensitive than EILSA, such as proximity ligation assay (PLA) 187 and proximity extension assay (PEA) 188 were performed on single-cells in microfluidic devices.

In droplet microfluidics, the first studies were focused on targeted detection of proteins secreted by encapsulated living cells. It has been used for cytokines [189][190][191] and antibodies detection [START_REF] Mazutis | Single-cell analysis and sorting using droplet-based microfluidics[END_REF]122 .

Following the "omics" trend, Shahi et al. developed in 2017 a single-cell sequencing method to detect membrane proteins of cells with no multiplexing limitations: Abseq 5 .

Briefly, cells are immunostained with antibodies tagged with a DNA barcode using traditional flow cytometry staining (Figure 14a). This first barcode, called Ab-barcode, indicates what antibodies could attach to the cell. The stained cells are then encapsulated in droplets with another barcode for cell indexing. Antibody and cell barcodes hybridize together thanks to a specific overlapping sequence (Figure 14b-d). The sequences are then elongated, amplified and sequenced. As with scRNA-seq protocols (inDrop, Drop-seq), each barcode also contains a UMI to remove amplification biases.

Epigenomics

Epigenetics refers to changes in DNA that does not involve a sequence modification. The most studied epigenetic features in single-cell analysis are DNA methylation, histone modification and chromatin accessibility.

DNA methylation

DNA methylation is one of the most studied epigenetic aspect. The whole methylation state of genomic DNA (gDNA) is often referred to as "methylome". Briefly, a methyl-transferase (DNMT) enzyme can give a methyl group to cytosine bases in DNA, repressing gene expression in specific regions. Methylation is involved in several cellular mechanism regulation and plays an important role in cancer development.

The gold standard method for the study of single-cell methylome relies on a sodium bisulfite treatment that turns cytosine into an uracil in DNA, but doesn't affect methylated cytosines. This treatment is followed by amplification and sequencing 192 . In addition to this single-cell bisulfite se-

Histone modifications

Chromatin is wrapped around specific proteins, histones, that can be subject to a range of modifications such as methylation or acetylation. These modifications plays a role in DNA accessibility and transcription. Traditional methods to study histone modifications include MS and immunoblotting, but the gold standard is chromatin immunoprecipitation (ChIP) 200 . This protocol was miniaturized on microarrays (ChIP-on-chip), combined with qPCR (ChIP-qPCR) and with sequencing (ChIP-seq). ChIP is however very challenging to perform on single-cells because of the high background noise caused by non-specific antibody pull-down.

This was overcome with a droplet microfluidics device: Drop-ChIP. Briefly, accessible chromatin is cut and digested in droplets, then barcodes are added to label the non-digested remaining chromatin. Droplets are de-emulsified and the barcoded chromatin is immunoprecipitated and sequenced [START_REF] Rotem | Single-cell ChIP-seq reveals cell subpopulations defined by chromatin state[END_REF] . This was recently adapted in another droplet based device that uses barcoded hydrogel beads 201 .

Chromatin accessibility

Chromatin can arrange into complex and packed structures that change its accessibility to macromolecules, modifying its transcription, differentiation and repair. To identify the active state of chromatin in single-cells, methods such as scDNase-seq and scATAC-seq were demonstrated, though only the latter was transferred to microfluidics 200 .

To identify accessible DNA regions, scATAC-seq (single-cell Assay for Transposase-Accessible Chromatin using sequencing) uses a modified Tn5 transposase, an enzyme that fragments preferentially DNA in opened regions of the chromatin and inserts adapters. This process, called "tagmentation" allows for amplification and further sequencing of the accessible regions. It has been applied to single-cells in the different microfluidic formats such as valves with the Fluidigm C1 202 , nanowells with the Takara ICELL8 203 and more recently in droplet microfluidics using barcoded tagmentation primers [204][205][206] .

In-situ combinatorial indexing

All previously described single-cell sequencing methods require cell isolation to perform individual steps including lysis, barcoding, RT or amplification. In-situ cell barcoding has emerged to circumvent the need for compartmentalization, and thus for specific and expansive equipment.

The principle is to barcode directly the cells following a split-and-pool strategy similar to the one used for beads barcoding. Once the cells contain their own barcode, they are manipulated in bulk, and don't need further compartmentation as they act as their own compartment. The binding between the targeted analyte and the barcode occurs within the cell, after which lysis, amplification and sequencing are performed.

A split-and-pool method refers to as the combinatorial technique to produce the barcodes. Cu- This method was adapted to whole genome sequencing with SCI-seq. Unlike epigenomics, genomic analysis cannot be performed on native chromatin but needs the nucleosome proteins to be 17d). A similar Fluidigm C1 protocol called sc-GEM was developed to perform a targeted transcriptomics RT-qPCR, a targeted DNA genotyping and a DNA methylation analysis in parallel 221 .

This splitting strategy however makes sense only for molecules that are present in high quantity or that can be easily amplified because of a high loss of molecules during splitting.

A common approach is to physically separate the nucleus from the cytosol (Figure 17b). This is achieved with a hyptonic solution to disrupt the cell membrane, keeping the integrity of the nucleus unaffected. They are then separated either by centrifugation [222][223][224] or by magnetically assisted separation 225,226 . It allows for genomic or epigenomic study with the nucleic content, simultaneously with transcriptomic or proteomic analysis with the cytosol. Valve-based microfluidic chips were also used to trap the nucleus and separate it from the cytosol, but these devices are currently limited to the study of only 8 cells in parallel, and might be interesting only with rare cells 227,228 .

Another way to separate the omics is to use functionalized magnetic beads (Figure 17a). In a protocol called G&T-seq and published in 2015, oligo(dT) beads have been used to specifically separate mRNA from single-cell lysates, then IVT + RNA-seq and WGA + DNA-seq were performed in two separate microtiter-plates to sequence both genome and transcriptome 229 . This approach was reproduced to perform simultaneous transcriptome and epigenome analysis 230,231 , as well as a triple omics study combining transcriptome, methylome and chromatin accessibility 232 . Bead-based techniques however require several washing steps to avoid gDNA loss.

Multi-omics analysis are also achievable without any physical separation (Figure 17c). DR-seq is a protocol allowing simultaneous amplification of mRNA and gDNA in one reaction with a specific molecular adaptor that differentiates gDNA from cDNA. analysis. This approach enables the profiling of more than 20,000 transcripts and 100 membrane proteins per cell. CITE-seq was recently expanded to also detect single guide RNA (sgRNA) to investigate on CRISPR modifications 240 .

There is a high technological challenge for omics separation at high-throughput, making genometranscriptome study difficult in droplet microfluidics. Chen et al. however used a special adaptor to allow for gDNA to bind to oligo(dT) beads. This, combined with the DropSeq platform, enabled simultaneous sequencing of gDNA and mRNA from single-cells 241 . High-throughput multi-omics methods were also developed with the combinatorial indexing approach to analyze transcriptome and chromatin accessibility 242,243 .

Multi-omics methods are very promising to decipher new fundamental biological mechanisms.

But they are facing several challenges, most of them are limited to a small number of cells revealing a real need for scalability. Tools such as mass cytometry, combinatorial indexing and droplet microfluidics are interesting candidates to tackle this issue though having respective complications.

Another difficulty resides in the data sparsity, making technical noise and intrinsic cell-to-cell variability difficult to distinguish. Further development to integrate additional information layers such as spatial 244 or temporal data 245 to single-cell analysis will also greatly expand the omics toolbox and provide a better understanding of many complex biological networks 220 .

Magnetism in microfluidics

4.1 Theoretical aspects

Magnetic materials

Even though magnetic phenomena are observed since antiquity, they have been fully understood only after the introduction of modern physical concepts such as spin, showing the quantic origin of magnetic fields. A source of magnetic field, called dipole, is described by its magnetic moment: a vector giving its strength and orientation. A magnetic material contains many dipoles, so we define the magnetization vector field as the volume density of magnetic moments:

M = BC BD
M is the magnetization (A/m), m is the magnetic moment (A•m 2 ) and V the volume (m 3 ).

In magnetostatics, the two expressions of magnetic field B (T) and H (A/m) are linked with the relation:

E = ' F (H + I)
Where µo is the permeability of free space ' K = 4M × 10 OP H/m

This relation shows that in a non-magnetized material (M=0), the distinction between B and H is not relevant 246 .

Any material placed in a magnetic field gets magnetized. This behavior can be depicted with a BH or MH curve called magnetization curve. Both curves are equivalent and we can switch from one to the other with equation 2. We can distinguish three main class of materials 247 .

• Paramagnetic materials get a magnetization that is aligned with the external field. They lose their magnetization in the absence of an external field. The slope of the MH curve, called magnetic susceptibility, measures the ability of the material to get magnetized under an external field (see footnote * ). This parameter is close to zero in paramagnetic materials, meaning that they obtain a weak magnetization.

• Diamagnetic materials have a slightly negative susceptibility, leading to a weak alignment of the magnetic moments opposed to the external field. All materials are diamagnetic, but this effect is covered when there is another type of magnetism.

• Ferromagnetic materials can be highly magnetized. The MH curve shows a high magnetic susceptibility but saturates quickly at a maximum value Msat. When the external field is turned off, a remanent magnetization Mr is kept in the material (Figure 18). This is characterized by a hysteresis loop in the magnetization curve. When warmed up above a certain temperature, called Curie temperature, the remanent magnetization is lost. Two categories of ferromagnetic materials can be distinguished. i: Hard magnetic materials that have a large hysteresis loop and a high remanence. They are used for fabricating permanent magnets. ii: Soft magnetic materials that have a low remanence and a high susceptibility. Their hysteresis loop is narrower. These properties make them particularly easy to magnetize or demagnetize and are thus used in electromagnet cores. Soft magnetic materials, often referred to as soft iron, are mainly alloys composed of iron, nickel and cobalt.

* For BH curves, the slope is called magnetic permeability ' (H/m) so that Q = 'R.

For MH curves, it is called magnetic susceptibility S (dimensionless) so that T = SR.

They are linked by Equation 2 leading to ' = ' K (1 + S) Permeability is often given in its relative form

' U = V V W = 1 + S
Due to the absence of hysteresis loop, the magnetization in the particle depends on the external magnetic field alone. The force applied by a magnetic field B on a superparamagnetic particle of magnetic moment m can then be easily calculated with:

X = (C • ∇)E
Note that for a superparamagnetic particle, the magnetization is uniform and we can simply switch from magnetic moment to magnetization with I = C/D [ and its value is given by the magnetization curve.

• In a weak external magnetic field, the magnetic moment increases linearly with the magnetic field.

C = S [ D [ ' K E

Where S [ is the magnetic susceptibility of the particle, D [ the volume of the particle and ' K the permeability of vacuum. The force can be rewritten as follows 253 :

X = S [ D [ ' K (E • \)E
The latter equation is often expressed with the difference of susceptibility between the particle and the surrounding medium ΔS = S [ -S ^. However, diamagnetic media such as air or water have a susceptibility close to zero, and S ^is often negligible 254 .

• In a strong magnetic field, where saturation is reached (C = _ `ab E c ), the force can be rewritten as:

X = _ `ab \Q
Where _ `ab is the magnetic moment at saturation. Manufacturers generally give the saturation in terms of mass magnetization (Am 2 /kg or emu/g). The force is then calculated as follows:

X = $D [ T `ab \Q
Importantly, the magnetic force does not depend on the absolute value of the magnetic field but on its gradient, particles are attracted from low to high magnetic fields. In addition, it is a conservative force and a magnetic potential energy d ^ (J) can be defined so that X = -\d ^ .

Superparamagnetic particles in single phase microfluidics

Bioseparation with superparamagnetic microspheres is a routine method in life science and medical research to select, isolate or purify specific molecules. Microspheres offer a high surface/volume ratio, maximizing the interaction between their solid surface and the surrounding fluid. Most of superparamagnetic microspheres available in the market are made of iron oxide magnetic nanoparticles embedded in a polymer matrix. They are of various size -typically from 100 nm to 10 µm -and can be functionalized with various biomolecules including antibodies, nucleic acids, aptamers or streptavidin, in order to bind specific target molecules. Superparamagnetic microparticles have been extensively used in microfluidics to create a new generation of biosensors and to miniaturize existing bioassays. A common approach is to immobilize particles to capture specific species in a continuous flow. To illustrate, a sandwich ELISA assay was developed using beads immobilized on microfabricated electromagnets as solid substrate (Figure 20a). After have passed all the buffers and samples in the chip, the beads are recovered by turning off the magnetic field for downstream detection 255 . The same approach was applied with a magnetic field generated by a simple wire placed in the chip and connected to a generator 256 . Thanks to external magnets placed close to a microfluidic channel, it is possible to trap magnetic particles in a localized region as shown on Figure 20c. It results in a porous, reversible, functionalized, magnetic plug, through which liquid can percolate. Biomolecule immobilization in a magnetic particle plug was performed to capture and detect various biomolecules 257 , this was also applied to protein digestion 258 (Figure 20c). However, using an immobile and packed plug does not fully take advantage of the magnetic particles, making some of them not interact optimally with the medium.

By switching on and off the magnetic field, it is possible to rearrange the particles in the plug, maximizing the interactions 259 . Another approach was introduced by our group: the magnetic fluidized bed. Here, the particles are continuously moving in an equilibrium between drag and magnetic forces (Figure 20d). It was used to capture and detect salmonella from raw milk 260 , DNA with further detection 261 , and more recently, it was used to restore the angiogenic balance between two biomarker involved in preeclampsia -sFlt-1 and PlGF -from human plasma, and even from raw blood 262 . Alternatively, specific capture of circulating tumor cells from patient blood was demonstrated by our group on a microfluidic device embedding an array of self-assembled magnetic bead columns 263 . A similar device allowed the detection of attomolar protein concentration in an array of magnetic posts 264 . Other techniques relying on the displacement of magnetic beads were also developed. Peyman et al. presented a device taking advantage of laminar co-flow streams for magnetic beads to pass through the different buffers in a row (Figure 20b), offering a versatile tool for complex, highthroughput bioassays 265 . The magnetic force being higher on big particles, it is also possible to sort them according to their size 267 and to separate particles that were in contact with the target 268 . Bioassays based on immuno-agglutination were also developed. Here, the target makes the particles bind to one another. The formation of clusters indicates the presence of the target 269,270 .

A smart approach to quantify proteins was introduced by Rissin et al. 266 (Figure 20e). They used a large number of beads, higher than the number of target molecules in the sample to enable a digital quantification of targets. This way, most of the beads will statistically bind zero or one molecule.

The beads are then isolated with the diluted sample and ELISA reagents in microwells, after which the concentration of target is estimated by counting the number of fluorescent wells. However, this approach requires either to work with very low concentrations, or to use a large amount of beads 266 .

Magnetic particles for biomolecule extraction in droplet microfluidics

In a recent publication, Serra et al. provided a comprehensive review on the handling of magnetic particles in biphasic systems and their bioanalytical applications [START_REF] Serra | The power of solid supports in multiphase and droplet-based microfluidics: towards clinical applications[END_REF] . They distinguished between three classes of system to extract a magnetic solid phase. i: Stationary droplet microfluidics, ii: digital droplet microfluidics and iii: continuous droplet microfluidics.

Stationary droplet microfluidics is when the aqueous phase reservoirs or droplets are immobile and separated by an immiscible phase. A cluster of magnetic particles can be formed under the effect of an external magnet and is then extracted from its reservoir with magnet translation. A constriction present between the reservoirs leads to a pinning effect that deforms the membrane until it breaks, facilitating the separation of the cluster from the reservoir of origin. A typical example of stationary magnetic separation is shown on Figure 21a 271 . This approach has the advantage of being very simple to operate, with very low carryover (supernatant) compared to pipetting techniques, but it also suffers from high initial volumes, and low parallelization.

Alternatively, digital microfluidics, or EWOD (described in section 1) can be used to perform magnetic separation. Here, the magnet remains at a fixed position while the droplets are moving. An example is shown on Figure 21b 272 . This part focus on continuous droplet microfluidics. According to Serra et al., solid support manipulation was limited to stationary and digital microfluidics before 2010, suffering of low-throughput and discontinuous process. This year, a work showing deflection of ferrofluid droplets under a magnetic field was published, this was the first attempt to manipulate magnetic material in continuous droplet microfluidics 273 . The following year, Lombardi and Dittrich developed the first magnetic separation device in droplet microfluidics (Figure 21c). They generate droplets loaded with magnetic particles in a microfluidic device. An external magnet is used to accumulate all the particles on one side of the droplet that are then symmetrically broken at a T-junction, leaving a daughter droplet that contains almost all the particles, and another one without particles 274 . A magnetic particles recovery rate of 95% was reported for particle concentration of 1 to 3.3 ng/nL on 1.25 nL droplets. This splitting concept was reproduced for protein extraction 275 , and for DNA extraction using sequential separation steps 276 . Further, Lee and coworkers implemented a washing step by synchronizing a second stream of droplets that are locally merged by electro-coalescence and split again. Thanks to an external magnet, the particles are transferred from the first to the second droplet stream upon merging, as shown on Figure 21d 277 . A symmetrical splitting limits the purification rate. To tackle this, Brouzes et al. optimized the concept, using an asymmetric 1:3 splitting junction (Figure 21e), they reported a capture efficiency up to 98.1% at a frequency of 15 droplet per second 278 . A similar device was proposed by Verbruggen et al. Here, the splitting ratio is not controlled by the geometry but by an additional oil flow that changes the hydrodynamic resistance, allowing a fine tuning of the purification rate. Extraction rates of 98% and 84% with a 1:9 and 1:19 splitting ratio, respectively, were reported 279,280 . More recently, similar results were shown with a K-shaped junction that allowed an extraction rate of 96% at around 400 Hz. It is by now the highest throughput achieved with the splitting method 281,282 . Despite its ease of use and efficiency, this splitting approach always needs for compromise between extraction rate (number of particles extracted / total number of particles) and purification rate (size of the daughter droplet / size of the parent droplet). As a result, a high extraction efficiency leads to an important content loss in the original droplet.

An original device was proposed by Doonan et al. to wash microparticles in droplets by replacing their buffer 283 . As shown on Figure 21f, an emulsion of droplets containing particles are reinjected in the device, and are merged with a continuous stream of another buffer. They are deflected by an external magnet though the continuous stream ending to a droplet maker. Though this device is not able to extract particles while keeping the original droplet, it allows a washing of particles, which remains an important challenge. Gu et al. developed in 2011 a method to extract particles from droplets with a minimal content loss 284 . They presented first an automated method -DropLab -to produce trains of sub-nanoliter droplet of different composition in a glass capillary. Then ferromagnetic particles can be transferred from a droplet to the next by using an external permanent magnet. First, they form a compact cluster at the approach of the magnet, the cluster is then immobilized in the maximum magnetic field region, deforming the interface of the moving droplet. This deformation ultimately leads to the droplet breakup and thus the separation of the magnetic cluster (Figure 22a). The difficulty is to deform and break the droplet, and resides in the competition between the magnetic force and the high interfacial force. These ferromagnetic particles are not functionalized and act as a secondary magnet to focus the magnetic field and being able to attract functionalized magnetic particles present in the sample.

Based on a similar concept, our group developed the magnetic tweezers technology (Figure 22b) [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] .

Here, the droplets are generated in a PTFE tubing thanks to a programmable robotic arm combined with an intermittently aspirating syringe pump to produce consecutive droplet trains. The magnetic field is generated by a soft-iron magnetic tip actuated by a coil as shown on Figure 22b,i. In the first proof-of-concept paper, the magnetic tweezers technology was used to do a sandwich ELISA on beads with direct fluorescence monitoring to detect thyroid-stimulating hormone (TSH) in serum. Clinical diagnosis of congenital hypothyroidism was performed with a sensitivity of 14 pM in less than 15min per analysis [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] . More recently, the same concept was reproduced with 4 magnetic tweezers in series to detect simultaneously two amyloid-b peptide-based biomarkers of Alzheimer disease [START_REF] Mai | Single-step immunoassays and microfluidic droplet operation: towards a versatile approach for detection of amyloid-β peptide-based biomarkers of Alzheimer's disease[END_REF] . Similarly, a breast cancer diagnosis was carried out by doing an mRNA Oligo(dT) beads purification in droplets thanks to the magnetic tweezers technology for further qPCR detection of the HER2 gene. This protocol, depicted on Figure 22c, could reduce the sample consumption about 100 fold compared to conventional robotized platforms, and was validated on a cohort of 21 patients suffering from breast cancer [START_REF] Ferraro | Microfluidic platform combining droplets and magnetic tweezers: application to HER2 expression in cancer diagnosis[END_REF] . In a different context, the magnetic tweezers were used to perform chemical modifications of g-Fe2O3 nanoparticles 285 .

The magnetic tweezers technology was modified by Serra et al. in 2020. 10 Instead of using an external electro-magnet, they integrated soft magnetic elements in a PDMS chip. The soft magnetic elements are made of iron oxide loaded PDMS, and can attract magnetic particles when a permanent magnet is placed next to the chip. As shown on Figure 22d, two magnetic elements were designed in a way to attract the particles in between them. Once the particles are in the "pocket", the droplet is broken by the effect of shear stress. Unlike in the previous magnetic tweezers platform where the extraction was due only to the magnetic force, the extraction is here caused by both magnetic and hydrodynamic shear forces. This device has also the advantage to give the possibility to discard the cluster in a secondary channel (the vertical channel in Figure 22d). Its functionalities were exploited to perform DNA size selection for NGS libraries preparation. A droplet is approaching the magnetic tip (ii). The magnetic field is turned on, leading to the accumulation of particles close to the tip (iii) and to the extraction of the magnetic cluster (iv). Adapted from Ferraro et al. 9 c. mRNA extraction with the magnetic tweezers. Oligo(dT) beads are first captured (i-ii) and extracted (iii). A droplet containing total RNA is approaching (iii) and merged with the cluster of Oligo(dT) beads (iv). After binding of mRNA to the beads, the cluster is captured again and passed in a washing buffer droplet (v) before being released into an RT-qPCR mix (vi). Adapted from Ferraro et al. 9 d. Modified magnetic tweezers with integrated soft magnetic elements. The particles are attracted between the two soft magnets (i-ii), deforming the droplet interface (iii). The droplet is then broken by shear force (iv), while keeping the particles in the magnetic region (v). Adapted from Serra et al. [START_REF] Serra | Integrated droplet microfluidic device for magnetic particles handling: Application to DNA size selection in NGS libraries preparation[END_REF]

Chapter conclusion

Droplet microfluidics has come a long way since its introduction two decades ago. From a simple physical curiosity, it became an important technological advance allowing for high-throughput experiment. Great improvements have been done to improve stability and control of droplets. Several functionalities such as droplet generation, electro-coalescence, splitting or sorting are now well established, and specific components such as fluorinated oil and surfactants became standardized, allowing for room to researchers to focus on more sophisticated applications. Among the emerging applications of droplet microfluidics, we can notably mention drug screening, material synthesis and medical diagnosis. But it was a particular breakthrough in the field of single-cell analysis, enabling the compartmentation of single-cells at an unprecedented throughput. Combined with NGS and barcoding strategies, droplet microfluidics now plays a central role in many single-cell sequencing protocols. approach, often referred to as "multi-omics", aim at offering a complete picture of the cell at the levels of transcriptome, genome, proteome, epigenome and metabolome. Many protocols have emerged, but only a few were adapted to droplet microfluidics. This is explained by the difficulty of omics separation from single-cell lysates. Indeed, current highly scalable methods only need a single reaction per cell. The separation of omics into different compartments could allow us to perform several molecular analyses from the same cell in parallel. Today however, there is a lack of high-throughput physical separation method.

Superparamagnetic microparticles are often used to perform bio-separation. They have been successfully applied to separate omics from single-cell lysates in microtiter-plates. Alternatively, such microparticles are used in droplet microfluidics to extract and purify proteins or nucleic acids. Our purpose will be to combine those two features, by proposing a superparamagnetic beads-based single-cell omics separation in droplet microfluidics.

OBJECTIVES AND APPROACH

The main objective of this thesis is to bring together superparamagnetic particles-based bio-separation with high-throughput droplet microfluidics. We developed a tool, based on the previously presented magnetic tweezers concept, to allow physical separation of omics from single-cells at high-throughput.

The magnetic tweezers technologies presented in the previous part, and shown on Figure 22, could operate only at low throughput (<1Hz), and with high droplet volumes (~10 2 nL), which is not well adapted to single-cell omics analysis, where high-throughput (10-100Hz) and small droplets (~1nL) are generally required. In this context, our purpose is to downscale the system dimensions, to work with two orders of magnitude smaller droplets, and to make it compatible with state-ofthe-art high-throughput droplet microfluidics workflows.

The magnetic tweezer technology relies on the physical extraction of a cluster of superparamagnetic particles. A necessary condition is that the magnetic force is strong enough to break the droplets interface. However, at smaller scales, the force balance can dramatically change, and capillary forces can become dominant. As it will be shown in Chapter 3, the capillary force scales linearly with the magnetic particles cluster size e fgh ∝ &, while the magnetic force scales linearly with the magnetic particles cluster volume e jgk ∝ & l . In other words, if we scale the system dimensions down by a factor 10, the balance e jgk /e fgh will be decreased by a factor 100. In these conditions, it will be impossible to extract magnetic particles clusters from sub-nanoliter droplets (Ø<120µm) by employing the previously mentioned approaches. This became obvious to us when applying the above-written simple scaling law:

• In the first magnetic tweezers platform, the one shown on Figure 22b, the magnetic field is generated by a soft-iron tip, magnetized by an electric coil. This way, we can obtain high magnetic fields at the tip (~1T). The magnetic force e jgk is proportional to the magnetic field gradient, but decreases exponentially with the distance from the tip, and the capillary thickness of 150µm does not allow for very high magnetic gradients. Thanks to numerical simulations, Ali-Cherif et al. [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] could estimate the maximum magnetic gradient in the capillary to be around 500 T/m.

• In the second generation of magnetic tweezers, the one shown on Figure 22d, the magnetic elements were very close to the droplets, but they had a low magnetization (~0.25T).

Thanks to numerical simulations, Serra et al. [START_REF] Serra | Integrated droplet microfluidic device for magnetic particles handling: Application to DNA size selection in NGS libraries preparation[END_REF] estimated a maximum gradient value of 430 T/m. Note that this gradient was not high enough to directly break the droplet, and the previously described fingering and shear-induced breakup mechanism (see Figure 22d) had to be used to enable particles extraction.

In this project, we want to scale down the system to go from ~100nL droplets evolving in a Ø300µm capillary, to sub-nanoliter droplets (Ø<120µm) flowing into typical droplet microfluidic channel size (30-100µm side). It means that the system dimensions will be reduced by a factor 3-10, which will consequently reduce the balance e jgk /e fgh by a factor 30-100. As a result, and as mentioned before, these conditions are extremely unfavorable for magnetic particles cluster extraction.

The strategy that we decided to adopt for this work was inspired by Tseng et al. 286 , where microsoft-magnets made of permalloy, an alloy of nickel and iron (80Ni:20Fe) known for its very good magnetic properties, were fabricated by means of an electroplating method, and integrated into a microfluidic chip. Such micro-magnets would allow us to place some highly magnetized tips (~1T) at very short distances from the microfluidic channel. In the first months of this project, we had the intuition that it was a good strategy, but we weren't sure if it would be better than what was done in our past works. So even before going into microfabrication or chip design, we performed a few test numerical simulations. With 35µm thick magnetic tips facing each other with a space of 75µm between them, the simulation gave us magnetic gradients values up to 20,000 T/m, which convinced us to go deeper into this strategy and to start the fabrication with these dimensions.

The theoretical, numerical and experimental aspects briefly introduced in this introductive paragraph, will be exposed in details in Chapter 3. The next chapter will focus on the microfabrication aspects.

CHAPTER 2 Fabrication of the Micro-Magnetic-Tweezers chips 1 Electroplating principles and history

Electroplating, also called electrodeposition is a process to deposit a metal layer on a substrate. As illustrated on Figure 23a, it uses an electric current to reduce metal cations dissolved in an electrolytic bath at the anode where they form a coherent solid coating. The part to be plated is thus used as the anode, and needs to be electrically conductive. The cathode is oxidized and its atoms are dissolved in the electrolyte, it is for this reason generally made of the metal to be plated to continually supply the bath with metal ions. Electroplating origin dates back to the early times of electrochemistry. The exact date of the first electrolytic metal deposition is debatable, but it is generally accepted that it was done by Beccaria in 1772 287 . The electrical source however consisted in a Leyden jar, which is a primitive form of condenser that was not able to deliver continuous currents.

Plating technology truly emerged only after the introduction of the pile by Volta in 1796, allowing

Brugnatelli to successfully plate gold on a silver coin in 1801. Since then, many scientists developed electroplating processes at industrial scale. Notably, Jacobi developed in 1838 a method called electroforming (also known as electrotyping or galvanoplasty) as a technique to fabricate a metal replica of any object 287 . This technique was extensively used in the 19 th century to produce sculptures, in fact, many bronze sculptures of this period are actually electrotypes as the one shown on Figure 23b 288 . Nowadays, electroplating is used in industry to produce metal coatings for different purposes (Figure 23c-d). Chromium, zinc, aluminum and tin are plated to improve wear resistance of mechanical parts. Gold, chromium and silver are used a lot in jewelry for aesthetics. Iron, nickel and cobalt are used to produce soft magnetic structures in computer memories and in the MEMS industry. Copper and gold are often used to improve electrical conductivity and to produce printed circuit boards (PCB) 289 . Electroplating is an empirical science. Though the mechanisms of electrodeposition are well understood, it is very difficult to predict the properties of a coating before testing. Many experimental conditions greatly influence the resulting coating like bath composition and metallic ions concentration, the presence of additives, the presence of dust in the bath, temperature, pH, stirring, current intensity, power source type (direct or pulsed), distance between the electrodes, substrate preparation etc. However, some general guidelines can be followed to successfully achieve electroplating. A plating bath is composed of dissolved metal salts combined with an acid to keep the pH constant. A highly concentrated bath lead to faster deposition. The electrical current is another important parameter to tune, it is expressed in terms of current density (A/m 2 ) to take into account the area to be plated. Deposition rate increases with current density, more precisely, it is theoretically proportional to the quantity of electricity passing through the electrolyte. High deposition rates, however, generally lead to weak mechanical properties, high surface roughness and internal stress and strains causing cracks or ultimately film delamination. This can be improved by adding a stress reducing agent 290 . Such chemical are usually aromatic organic compounds containing sulfur (e.g. saccharin, sulphonamide, benzene sulfonic acid). By introducing sulfur in the deposit, they provide obstacles on the growth, and create smaller and finer grains, they are for the same reason also used as brighteners to produce decorative coatings 291,292 . During electrodeposition, several reactions can occur simultaneously at the cathode. It is characterized by a current efficiency below 100%. The current efficiency can be understood as the quantity of electricity actually involved in deposition over the one supplied by the power source 293 . Notably, the reduction of hydrogen ions is a secondary reaction that leads to the formation of gaseous H2 bubbles that can be incorporated into the film creating undesired voids, and should be evacuated by means of an appropriate stirring 294 . Another way to reduce the effect of dihydrogen formation is to use a pulse reverse current source. Here, the hydrogen is oxidized during the reverse phase, it thus increases the current efficiency and reduces roughness and internal stress 295 .

In the semiconductor industry, electroplating is combined with photolithography to fabricate conductive tracks and metal microstructures 296 . A substrate, generally a silicon or glass wafer, is made conductive by depositing a metal seed layer. The seed layer is chosen to have good conductivity and adhesion with the metal to be plated. Most applications use gold or copper deposited by means of Physical Vapor Deposition (PVD). The seed layer often needs an adhesion promoter to avoid delamination. The best adhesion layer for most metal and substrate is a thin film of titanium or chromium, also deposited through PVD 297 . Then a photoresist mold is produced on the substrate by photolithography, leaving the seed layer accessible where the metal will be deposited. The substrate is then plated as shown on Figure 23c. After plating, photoresist and seed layer can eventually be dissolved to keep the plated structures alone on the substrate.

Permalloy plating and microfluidics

Permalloys are a class of NiFe alloys exhibiting a very high magnetic susceptibility and a low remanence. These soft magnetic materials are used for electromagnet cores and magnetic shielding 298 .

They exist in various proportions but NiFe (80:20) is the most used in MEMS because of its ability to be plated at high thicknesses (> 100µm) with fairly low stress, and because it has a relatively high susceptibility (200-5000) and saturation (0.8-1.1T) 294,299 . Alloy electrodeposition is however not as straightforward as for single metal. Both metals have to be plated simultaneously while controlling the deposition ratio. In practice, iron is the metal with the lowest reduction potential (the less noble) and is deposited preferentially to nickel. To compensate this, the Ni:Fe proportion has to be chosen much higher than the desired stoichiometry in a way that iron ions in the vicinity of the anode is depleted rapidly, and its deposition is then limited by diffusion of iron ions in the bath 294 . Another concern is that Fe 2+ ions can be oxidized into Fe 3+ and forms an iron oxide compound called hematite FeO(OH) which is insoluble to water and can form particles that are incorporated in the film. To avoid this, the exposition of the bath with air has to be limited, and additional filtration is beneficial to remove eventual hematite particles 294 . Deposition of threemetal alloys such as NiFeMo 300 and NiFeCo 301,302 were demonstrated, enabling flux density at saturation up to 2.1T, but were limited to thin films (< 5µm) due to a high increase in internal stress that is often a cause of film delamination. However, P. Tang used pulse-reverse plating to achieve a NiFeCo film with internal stress comparable to standard electroplated permalloy.

In the 2000s, many MEMS labs came into microfluidics. They combined electrical, magnetic and mechanical features with microfluidic channels. Electroplating being a clean-room technique commonly used in the MEMS industry, it is not surprising to find microfluidic devices containing electroplated parts. It was mostly used to fabricate electrically conductive tracks for sensors [303][304][305] , microheaters 306,307 or micro coils to produce magnetic fields 308,309 . Various metals were used including Au 308,309 ,Cu 303,306 , Ag/AgCl 304 , Pd 305 or Ni 307 . Another technique to fabricate conductive parts consists in introducing molten solder in dedicated microfluidic channels [START_REF] Siegel | Microsolidics: Fabrication of three-dimensional metallic microstructures in poly(dimethylsiloxane)[END_REF]310 . This technique, called microsolidics, gives a simpler alternative to electroplating and is now extensively used, leaving electroplating as a marginal technique to produce conductive parts in microfluidics.

Alternatively, nickel electroforming is used to replicate molds produced by standard SU-8 photolithography. It allows the production of metal counter-molds with higher mechanical resistance than SU-8 and are thus compatible with polymer hot embossing to fabricate microfluidic chips in other materials than PDMS [311][312][313] .

Permalloy plating is used in microfluidics to produce soft magnetic parts that can be actuated by an external source of magnetic field. This way, moving parts could be implemented in microfluidic chips. Ryu et al. demonstrated a micro magnetic stirrer embedded in a micro channel and actuated by a rotating field (Figure 24a) 314 . The same approach was used to implement cooling functionality 315 . Yamanishi et al. introduced a magnetically driven microtool able to move around an axis that can serve as a controllable door (Figure 24b) 316 . Despite these few examples, the main application of micro-soft-magnets is the manipulation of magnetic particles. To do so, immobile micro-softmagnets can be magnetized on demand by means of electroplated micro-coils (Figure 24c) 317,318 , or more commonly by external magnets 319 . As shown on Figure 24d, an array of permalloy posts can be placed under a microfluidic chamber to trap magnetic particles. This has been employed by C.

H. Ahn lab for bioassay purposes 320,255,321 . Other groups used the same approach with different geometries to trap or separate magnetic particles [322][323][324]325,326 . More recently, permalloy posts were used to apply forces within cells. Iron-oxide nanoparticles are internalized by cells that are immobilized close to the permalloy posts. Placing a permanent magnet below the substrate attracts the nanoparticles toward the posts, pulling on the cell membrane. This helps to understand the cell response against mechanical stimuli. (Figure 24e) 286,327 The same group adapted the fabrication method to produce a permalloy post array embedded in a flexible and stretchable PDMS membrane 328 . (Figure 24f) negative tone, epoxy-based AZ-125nXT (Microchemicals) that is suited for thicknesses from 20 to 100µm. Prior to photoresist application, TI-Prime (Microchemicals) was spin coated to promote resist adhesion on copper, limiting the risk of film delamination during plating.

The plating bath was prepared as in Tseng et al. 286 with a composition shown in Table 1, resulting in a dark green solution. Saccharin, used at concentration of 1-3g/L, is a common additive for reducing internal stress, and sodium dodecyl sulphate is added as a wetting agent to allow for the solution to enter small photoresist patterns. The bath was filtered with Millipore Express Plus (0.22µm) before each use to avoid dust from being incorporated in the film.

250g/L NiSO4 • 7H2O 5g/L FeSO4 • 7H2O 50g/L boric acid 2g/L saccharin 0.1g/L sodium dodecyl sulphate

Table 1: Plating bath composition

To ensure wetting and thus a good contact between the solution and the copper, the substrate was placed under UV-Ozone (Jelight Company Inc.) for 15 minutes prior to plating. The substrate and the pure nickel anode (Goodfellow) were then placed in a 1L beaker and held by 3D printed jigs.

Good electrical contact is ensured by alligator clips and copper tape, that are connected to a DC power supply (ELC ALR3002M). We performed electroplating at a current density of 7mA/cm 2 in the beaker placed on a hotplate at 40°C with magnetic stirring, resulting in a deposition rate around 3µm/h (measured afterwards with Veeco profilometer). Although Tseng et al. recommend a current density of 5mA/cm 2 , increasing it to 7mA/cm 2 allows a faster deposition, without depreciating magnetic properties. Electroplating was stopped after 9-12h to reach a thickness of 31-35µm.

Photoresist and Cu were then dissolved in TechniStrip 1316 (Technic) heated at 65°C under agitation for around 30min, until no resist residues are observed, ultrasonic bath can accelerate the process (Figure 25d). Unlike copper, the titanium layer cannot be removed easily and needs hydrofluoric acid (HF) etching. Considering the hazardousness of HF, and that our Ti layer is thin and transparent, we decided to keep it. Figure 26a shows a soft magnetic structure deposited with our protocol. The detailed protocol for micromagnet fabrication is given Appendix A.

The magnetization curve of the deposited alloy was measured by David Hrabovsky on electroplated disks of 800µm diameter and 35µm thickness by vibrating sample magnetometry (VSM) at MPBT platform at Sorbonne Université. The magnetization curve is given on Figure 26b, it shows a very low hysteresis, and a flux density at saturation of 0.93T, which is in the expected range for permalloy (see Figure B1 in Appendix B1 for a more detailed view of the curve). Permeability is more complicated to evaluate: the measured value depends on the orientation of the measurement because of demagnetizing fields. For disks, there is an analytical formula for demagnetization field correction 294 . After correction, we obtained a susceptibility of 74.4. Details on the magnetization characterization are given in Appendix B1.

To characterize the composition of our structures, we used a XXX which combines Scanning Electron Microscopy (SEM) with Energy-Dispersive X-ray (EDX). SEM allowed us to produce pictures as the one shown on Figure 26c, and EDX was used to extract the percentage of each element present in the sample. This measurement was done by Bertrand Cinquin (IPGG). He obtained 74.65% for the nickel and 19.76% for the iron, which is very close to the 80:20 ratio that we expected. The other detected materials were mainly oxygen at 5.02%, probably present because of iron oxidation, and silicon at 0.51%, present in glass. Other SEM pictures as well as the EDX spectrum are given in Appendix B2 and B3.

Protocol optimization and troubleshooting

Throughout the PhD project, we did more than a hundred of electrodeposition with both successes and failures. Each step of the process had to be optimized until we found a reliable protocol. In table 2 are listed the main causes of failure and how they were solved.

A few points have to be noted to supplement Table 2: • The process of optimization was empirical, some effects such as magnet detachment or photoresist cracking are not completely explained and could sometimes happen, sometimes not, even without any change in our experimental protocol.

• It was difficult to investigate on the effect of each experimental parameter since they are numerous, and that the deposition took 12 hours, limiting the number of experiments.

• Magnet detachment during plating was by far the most complicated problem to solve. We observed it after a few hours of deposition, suggesting that thin films adhere better. This effect was probably due to internal stress in the film. We finally solved this problem by i: using titanium instead of chromium for the seed layer which gave much better results, and ii. making pauses during deposition which was the ultimate tip and allowed an almost 100% success rate. This tip was given to us by Olivier Lefebvre (C2N) who works on a very similar fabrication protocol 331 . While he couldn't explain why, he reported that plating in several steps avoided structures detachment. Following his advices, we performed the deposition with pause steps out of the bath with the following protocol:

Plating 10min → Pause 10min → Plating 30min → Pause 30min → (Plating 3h → Pause 30min) × 3

Microfluidic chip fabrication

We aimed at integrating the micromagnets in a microfluidic chip. Among all the available microfluidic chip fabrication methods, we chose SU-8 soft lithography because i: it is the gold standard method, and ii: it is well adapted to our required chip dimensions (channels <30µm 27a,i) 332 . Luckily, this is the machine we have in the IPGG clean room, and we could easily reproduce their protocol. In the meantime, I realized that one of our colleagues, Céline Braïni, developed a very similar protocol, also using the MJB4, that she presented in a recent publication 333 . For both, the idea is to perform an oxygen plasma on the two parts to bond, and to put them into contact precisely with the mask aligner. In Cottet et al. 332 , the PDMS part is placed as shown in Figure 27a,ii on the quartz mask holder and sticks on it reversibly thanks to Van der Waals interaction. The patterned substrate is placed on the MJB4 chuck and held in place with magnets (Figure 27a,iii). After X and Y positioning of the substrate, the chuck is moved up until contact with the PDMS. Note that PDMS shrinkage during curing had to be taken into account in the design to recover the right distances between patterned magnets and the channels. A shrinkage of 1.5% was reported and gave satisfying results.

Covalent irreversible bonding normally occurs between glass and PDMS after an O2 plasma treatment of both parts. It was however not our case because of the titanium layer that remains on glass and caused bad adhesion. We solved this problem by performing an SiO2 deposition on the substrate through PVD to obtain a surface equivalent to glass. Unfortunately, after a breakdown of magnetron 3 in the sputtering machine present in our lab, we weren't able to use the SiO2 target for a few weeks. Another way had to be found. Silanes were reported as an interesting alternative to bond different materials. For example, aminopropyltriethoxy-silane (APTES) can be used to bond PDMS to metals such as Au, Pt, Cu, Fe, Al and polymers like polypropylene and teflon 334 .

We tried to treat our substrate with tetraethyl orthosilicate (TEOS) which is a silane similar to APTES but with another ethyl group instead of the amine group. TEOS was chosen to provide silanol groups that promote PDMS-glass bonding after plasma treatment. We applied it by vapor deposition after O2 plasma treatment for 20min under vacuum. The reaction that we believe is occurring is shown on Figure 27b. This treatment, though not characterized, provided immediately good bonding performances, better than what we obtained with SiO2 PVD.

Just after bonding, the microfluidic channels are treated with a perfluorinated silane to make them hydrophobic 335 . A standard protocol was applied: a solution of trichloro(1H,1H,2H,2H-perfluorooctyl)silane at 1% in Novec-7500 fluorinated oil is passed through the channels for a few minutes after which they are flushed with nitrogen and heated at 80°C until they dry completel. 336 . Finally, Figure 27c shows a finished PDMS chip embedding micro-magnets. b. TEOS treatment on the titanium layer. Ti has a native protective oxide layer (TiO2) on its surface. We create OH groups with plasma treatment, after which TEOS is applied by vapor deposition. After silanization, another plasma treatment can provide silanol groups SiOH that are needed for PDMS bonding.

c. Micrograph of the micro-magnetic-tweezers embedded in the PDMS microfluidic chip. The central channel is 30µm wide and 35µm thick. The magnets are 35µm thick.

CHAPTER 3

Dynamics of magnetic particles capture in the micro-magnetic-tweezers

As mentioned in the introduction, the micro-magnetic-tweezers aim at extracting superparamagnetic beads from droplets in a continuous droplet stream, and to redisperse them into other droplets. The tweezers, made of Permalloy, are designed to focus a magnetic field generated by an external permanent magnet. It leads to high magnetic field gradients in the region of capture, thus resulting in a magnetic force attracting the particles between the tips. This extraction process involves complex physics, where a biphasic flow, magnetophoresis and capillary effects coexist. To illustrate, Figure 28 (and Video 1) shows the complete process of capture on a device of last generation. This chapter will explain this process in more details, from a theoretical and experimental point-of-view. Three stages are observed:

• The cluster formation stage: the particles present in the droplet migrate and are collected between the tweezers to form a compact cluster. (Figure 28a-b)

• The droplet breakup stage: after droplet breakup, the previously formed cluster remains trapped in the tweezers while the droplet continues on its way (Figure 28c-d). Note that after extraction, the particles are still in a small droplet, and thus are not directly in contact with the carrier oil.

• The cluster release stage: the next droplet is able to push the cluster and release it (Figure 28e-f). Once released, the cluster can be merged with the following droplet in a subsequent electrocoalescence step, described in Chapter 6. While the previous generation of tweezers needed us to switch on and off the magnetic field, this approach allows us to keep the external magnet steady, thus avoiding any synchronization.

The first part of this chapter aims at giving insights on the physics involved during magnetic particles extraction. It will provide simple theoretical criterions to guarantee the proper execution of each of the three above-mentioned stages.

The second part, based on the theoretical criterions, physical properties measurements, and finite elements analysis (FEA), attempts to evaluate the involved forces to i. ensure that particle extraction is a priori possible and ii. optimize the shape and dimensions of the tweezers before having to fabricate them.

The third part describes our experimental setup, image analysis, and results for the characterisation of the micro-magnetic-tweezers capture efficiency. Different conditions were examined including particle size, magnetization, particles loading in droplets, as well as the influence of micro-magnetic-tweezers size and shape on capture efficiency. 1 Theoretical criterions

Cluster formation criterion (Magnetic vs. viscosity)

Before being extracted out from the droplet, the particles must be collected between the tweezers and form an aggregate referred to as "cluster" (Figure 29a-b). The cluster is formed only if the magnetic force is strong enough to stop the particles moving in the flow direction, we discuss here on the conditions to enable trapping, first for single particles, and then for particle aggregates.

A particle is subject to two opposed forces: a magnetic force that attracts and keeps it between the tweezers, and a viscous drag force that pushes it in the direction of droplet displacement (Figure 29a-b). They are given by the following equations:

Magnetic force

e mag = $ [ D [ T [ ∇Q Eq. 1
Viscous drag force (Stokes law) e pqgk = -6Mst [ % slip Eq. 2

The above equation applies only for a particle which is ideally centered in the channel and that progresses in a single direction, but the particle is actually also experiencing a transverse deflection toward one magnet or the other. Such magnetic particle transport in the transverse direction to a flow has been extensively studied both theoretically 338 and experimentally 254,267,339,340 , and has been widely used in microfluidic devices 341 . The magnetophoretic velocity in the transverse direction can be derived as well from the balance between drag and magnetic forces, and lead to the same formula as Eq. 4 but with the magnetic gradient expressed in the transverse direction:

% jâk = 2$ [ t [ , T [ 9s áQ áä Eq. 5
These simple criterions are however not directly exploitable because the highly non-uniform gradients present around the tweezers makes difficult the choice of the reference value for ∇Q to enter in the formulas. It is thus not obvious to find a universal dimensionless number that would describe the whole system.

Several particles: cooperative magnetophoresis

When considering several particles, the problem is even more complex. Due to dipole-dipole interactions amongst particles, they tend to form aggregates and columns that are aligned in the direction of the field. 269 These aggregates, or columns, are transported as a whole and act as bigger and non-spherical particles. The Stokes law has therefore to be modified to take into account the shape of such objects. As a general rule, particle aggregation always leads to an increased magnetophoretic velocity. This phenomenon, sometimes referred to as "cooperative magnetophoresis", was studied both theoretically [342][343][344] and experimentally 344,345 . However, most studies were focused on nanoparticles, which are subjected to Brownian motion, and that were placed in a uniform magnetic field. For such nanoparticles, the aggregates spontaneously form when the attractive dipoledipole interaction overtake Brownian motion as well as the repulsive double-layer electrostatic interaction. A uniform field allows them to estimate the degree of aggregation according to distance from the magnet.

In our case however, the particles already enter in the system as preformed columnar aggregates (Fig. 1a), and we can therefore consider each column as a single object. The magnetic force on a column made of N beads is:

e mag,N = åe mag = å$ [ D [ T [ ∇Q Eq. 6
However, the Stokes drag force needs to be modified to take into account the shape and orientation of such column of beads. Eq. 15

Cluster release criterion (Magnetic vs. pressure)

Once the cluster is extracted, it can be pushed out of its position by the following droplet (Figure 28e-f). This allows us to release the cluster without needing to turn of the magnetic field, of to remove the external magnet. This is one of the best advantage of this technology compared to our previous magnetic tweezers, it avoids us from having to synchronize the field switching with the droplets, allowing us to work at higher throughputs. As it will be shown here, this pushing mechanism arises from pressure forces and droplet deformation. Importantly, we used a fluorinated surfactant (Picosurf, 2% in Novec-7500) that prevents the droplets from merging together instead of pushing each other.

The magnetic force can sometimes however strongly hold the cluster between the tweezers, so the droplet may not be able to push it. When the empty droplet enters into contact with the droplet containing the cluster, both of them deform their interface after which they move together toward the outlet. Before the contact, all the droplets in the system, except the trapped cluster, move at constant speed from inlet to outlet. This is only possible because the cluster droplet don't actually occupy the whole channel cross section but has gutters allowing oil to flow around it (Figure 32a).

Such gutters are typical for droplets flowing in rectangular channels and play a significant role in their dynamics [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF] .

Figure 32: a. Before contact, the gutters (top right) allows for the oil stream to flow. b. After contact, the system can be obstructed because of droplet deformation. The gutters shrink and not allow the oil stream to pass any longer. At this stage, the pressure difference across the droplet + cluster plug is ò inò out .

We observed from our experiments that with an insufficient pressure at the inlet, the droplet in contact with the cluster is not able to push it but stops and remains stuck on it. We also noted that in these conditions, all the droplets upstream and downstream stops as well, indicating that the oil does no longer stream. Our interpretation is that when the droplets are in contact, the deformation of their interface can compress the gutters, and ultimately obstructs the oil stream (Figure 32b). In the worse situation, the hydrodynamic resistance of the plug becomes very high, resulting in a total immobilization of all the droplets present in the system. Because of the absence of flow, the upstream pressure becomes equal to the chip inlet pressure ò in while the downstream pressure becomes equal to the outlet pressure ò out . At this stage, the force applied by the droplet on the cluster simply arises from the pressure difference:

e pressure = & , (ò in -ò out )
Eq. 16

The cluster is released from the tweezers if e pressure > e mag,C . We can write down the ratio of both forces for a cluster of diameter L (D ñ = M& l /6) by combining Eq. 13 and Eq. 16:

e pressure e mag,C = 6(ò in -ò out ) $ [ ïM&T [ ∇Q Eq. 17

Evaluation of the forces

As mentioned in Chapter II, the fabrication process was long and delicate. We weren't able to fabricate any functional electroplated magnet during the first year of the project. Although the physics of particle extraction from droplets was already well described for our previous magnetic-tweezer platform [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF] , the droplets we aim at working with in this project are two order of magnitude smaller (~nL instead of ~100nL), and thus the balance between the forces involved is expected to change dramatically. We had a particular apprehension on the predominance of capillary effects at small scales (see Eq. 14), that could ultimately hinder particle extraction. For this reason, at the beginning of the project, we couldn't tell a priori if the extraction was even possible, and we wanted to have a numerical estimation to ensure that we were in the right conditions. When looking at our three theoretical criterions (Eq. 10, 15, 17), most parameters are hardly tuneable because they are either intrinsic properties of the beads, of the fluid, or because they are constrained by our specifications.

We listed in Table 4 the involved parameters and how they can be estimated.

Parameter

Simulation of the magnetic field

A key parameter that we can eventually tune by changing the tweezers design is the term ∇Q, which is involved in our three theoretical criterions. The magnetic field gradient is however difficult to evaluate analytically and cannot be measured. For this reason, we performed Finite Element Analysis (FEA) with the software COMSOL Multiphysics to compute the magnetic field around the micro-magnetic-tweezers.

FEA allows us to find solutions of partial derivative equations (PDE) on arbitrary geometries. The governing equations to solve for magnetostatics with no electric currents are:

Gauss's law ∇ • E = 0 Eq. 18
Ampère's law ∇ × H = 0 Eq. 19

Magnetic flux density E and magnetic field H are linked by the magnetization field M following:

E = ' K (H + I) Eq. 20
In practice, COMSOL finds a solution for a quantity D ^ called magnetic scalar potential, from which all the above-mentioned vector fields can be derived. It is defined by:

H = -∇D ^ Eq. 21
We set the simulation to be as close as possible to the experimental setup. In the example shown on Figure 33a, a neodymium cubic external magnet of 5mm side is placed at a distance of 3mm from the tweezers. The tweezers were modelled as two triangular prisms facing each other for which size and shape can be easily modified, in the example shown on Figure 33, we used triangles of base 600µm, height 600µm and thickness 35µm, which are spaced from 75µm apart. The microchannel passing through the tweezers is 30µm wide (y direction) and 35µm thick (z direction).

The magnetic field generated by the permanent magnet is modelled by entering in COMSOL its remanent flux density, which is according to the supplier between 1.40 and 1.45T for our magnets (Supermagnete neodymium N50). We took a remanence value Q U = 1.43T for this particular magnet. The magnetic response of the tweezers is computed by applying in the material properties the magnetization curve measured by David Hrabovsky (see Chap. 2 Figure 26b). The remaining domains, comprising the microchannel and the surrounding air, are considered as non-magnetizable, and thus does not interact with the magnetic field. It is simply done by considering the linear relationship E = ' K H, normally only valid in vacuum, but that is a good approximation for diamagnetic materials like air and water. More details on the simulation implementation and meshing are given in Appendix D.

We see on Figure 33b that as expected, the external magnetic field is focused by the tweezers, increasing the magnetic field strength between the tips. Figure 33c shows the magnetic flux density strength B in the microfluidic channel, note a sharp increase reaching around 1T between the tweezers.

Nevertheless, the magnetic force is proportional to the gradient of the magnetic field, and thus a high field strength does not always mean a high magnetic force. Figure 33d shows the magnetic field gradient in the flow direction áQ áà ⁄ and the in transverse direction áQ áä ⁄ . In the flow direction, we see positive values before the tweezers and negative values after the tweezers, indicating an attractive force pointing from low to high magnetic fields. In the transverse direction, there is an attraction force toward the sides of the channel, in the direction of the tweezers. Based on the simulations, we can estimate the term T [ ∇Q present in the formula for the force applied on superparamagnetic particles. The magnetic field gradient ∇Q is directly computed from the simulations, while the particle magnetization per mass unit T [ (R) is given by the magnetization curve provided by the particle's supplier in function of the field Q or R (Appendix D). We can then estimate the magnetic force applied on a particle with Eq. 1, the force applied on a column of particles with Eq. 6, or the force applied on a cluster of particles with Eq. 13, 14.

Measurement of interfacial tension

At the beginning of the project, we used Krytox 157FSH (DuPont) as a surfactant. This surfactant is composed of a hydrophobic perfluoropolyether (PFPE) combined with a carboxylic acid hydrophilic head. While this surfactant was efficient to generate stable nanoliter droplets, we noticed some disadvantages: it didn't prevent droplets from merging, and we observed important differences in droplet size when generating droplets (see footnote † ) of pure water or of a salt-containing buffer. This can be explained by the acido-basic properties of the carboxylic acid group, its charge can be modified as function of the droplet content and in case of negative charge, some electrostatic interaction with the droplet content could also take place and be critical for applications with biomolecules in droplets.

We decided to switch to a non-ionic fluorinated surfactant. There are many fluorinated surfactants dedicated to droplet microfluidics available in the market, most of them consist in a PFPE polymer combined with a hydrophilic polyethylene glycol (PEG) head (see Chap. I 1.3), they are biocompatible, prevent merging and non-specific adsorption at the droplet interface.

We performed pendant drop interfacial tension measurements for fluorinated oil with water and phosphate buffered saline (PBS) at different concentrations of several surfactants including the ionic Krytox 157FSH (DuPont) and non-ionic dSurf (Fluigent) and PicoSurf (Sphere Microfluidics).

Measurements were performed on a pendant drop tensiometer at the MMN laboratory (ESPCI, IPGG). Figure 34 shows the results of our measurements. For each case, the interfacial tension decreases with surfactant concentration until it reaches a plateau. This happens when the surfactants are in excess, when the interfaces cannot carry more surfactant molecules. The concentration from which it occurs corresponds to the critical micelle concentration (CMC, see Chap. I 1.3). With Krytox 157FSH at different concentrations in Novec-7500 (HFE-7500), we measured a much higher interfacial tension with PBS compared to pure water. In contrast, with the non-ionic fluorosurfactant dSurf (Fluigent), the presence of salts does not seem to influence the interfacial tension, which is in accordance with our above-mentioned observations. The microfluidics experiments presented afterwards in this chapter were performed with the Picosurf from Sphere Fluidics diluted in Novec-7500. We chose this one because we evidently needed a non-ionic surfactant to avoid merging and to do experiments involving biology, and because it was cheaper than dSurf.

Note that in the experiments shown on Chapter 7, we switched to the FluoSurf (Emulseo), which has similar properties. An interfacial tension of 3.2 to 2.3 mN/m was measured for concentrations ranging from 0.1% to 1% w/v (green curve in Figure 34). These values are consistent with literature [START_REF] Holtze | Biocompatible surfactants for water-in-fluorocarbon emulsions[END_REF][START_REF] Wagner | Biocompatible fluorinated polyglycerols for droplet microfluidics as an alternative to PEG-based copolymer surfactants[END_REF][START_REF] Scanga | Click chemistry approaches to expand the repertoire of PEG-based fluorinated surfactants for droplet microfluidics[END_REF] . where the spheres arrange themselves in a non-organized way. The RCP is determined experimentally: balls are poured into a large container which is vibrated to allow the balls to rearrange in a more packed way. The packing density values obtained this way, or with numerical simulations reproducing the experiment, range from 0.6 to 0. 68. 347 In colloidal systems, the particles can repel one another because of the electrical double layer interaction. This phenomenon, preventing particles to enter into contact or to form aggregates, is at the origin of the colloid stability, it can also increase space between particles. In our experiments, we work with carboxylic acid-functionalized microsphere of diameters ranging from 0.2 to 1µm (Ademtech and Thermofisher). For that reason, because of electrostatic repulsion due to the carboxylic acid groups, we expect the packing density of our microparticles clusters to be lower than RCP.

Measurement of particle packing density

We performed a series of experiment to assess the packing density of our magnetic particles during cluster formation. To do that, we used our first generation of macro magnetic tweezer device described in Chapter 1, 4.3 (see Figure 22b). Briefly, a transparent PTFE capillary is connected to a programmable syringe pump (Nemesys, Cetoni) at one end and to a robotic arm (Rotaxys, Cetoni) at the other end (Figure 35a). The capillary, which was filled by oil (FC-40 + 2% w/v Perfloro-decanol) beforehand, can be sequentially immersed into different wells to aspirate droplets of desired size and composition. This technique allows us to generate droplets of size ranging from 100nL to 1µL. The droplets are then transported close to a magnetic tweezer, made of a permalloy tip placed in an electric coil. The tip is magnetized when putting current in the coil (1A DC) and is able to extract magnetic particles from droplets (See Chap. 1, 4.3, Figure 22b). A camera (Basler) placed above the capillary allows us to take pictures of the extracted clusters. We can see on Figure 35b,i-iii a cluster of Ademtech Masterbeads (AE0.5µm, T `= 40emu/g, $ = 1600kg/m l , COOHfunctionalized) being extracted out of a droplet.

We generated PBS droplets of 50-500nL containing known quantities of particles. Two types of particles were tried out, the MyOne from Thermofisher (AE1µm, T `= 23emu/g, $ = 1800kg/m l , COOH-functionalized) and the Masterbeads from Ademtech (AE0.5µm, T `= 40 emu/g, $ = 1600kg/m l , COOH-functionalized). We performed the particles extraction with the tweezer, and then, by measuring the size of resulting cluster, we can estimate the cluster compacity with:

ï = ó $ [ D ñ ⁄ Eq. 22
Where ó is the mass of beads in the cluster, $ [ is the density of particles and D ñ is the measured cluster volume.

We measured the cluster surface on a picture, and by considering it to be spherical, we could roughly estimate its volume with D ñ = û l√ü † l , ⁄ . However, we observed that the images taken by the camera (Figure 35b,iv) were deformed because of refraction. This arises because of the cylindrical shape of the tubing, and that the refractive indexes of PTFE and FC-40 are not equal to 1 (1.31 and 1.29, respectively). We sorted out this problem by writing a MATLAB code that deforms back the image in accordance with Snell-Descartes law (Figure 35b,v). The program is detailed in Appendix E.

To have a good estimation for ó, we had to consider that all the particles present in the droplet were collected. To ensure this, we performed the extraction as slow as possible to let all the particles to migrate until no single particle could be seen.

Theoretical criterion Formula

Cluster formation (not corrected) Inlet pressure (ò in -ò out ) Between 0 and 325 mbar Table 5: Values that were used to calculate the theoretical criterions. Two types of beads were considered: Masterbeads and MyOne. Three parameters were not fixed on purpose because we want them to be maximized (droplet velocity and pressure) or minimized (channel dimensions).

e
The second is the droplet breakup criterion. At small dimensions, the capillary force is expected to overpass the magnetic force, preventing droplet breakup. We plotted this criterion e mag e cap ⁄ against the channel size on Figure 37b. The curves scales with & , , droplet breakup is not supposed to occur when the curves are below 1. With the values of Table 5, the curves suggest that droplet breakup does not occur at dimensions below 20µm for both type of beads.

The last criterion e pres e mag ⁄ is to ensure that the cluster could be released when it is pushed by the following droplet. This criterion is plotted against pressure on Figure 37c. The curves suggest that below 25mbar, it would be difficult to release a Masterbeads cluster. In our experiments, this pressure corresponds to a velocity around 5mm/s, but can vary depending on the chip and the quantity of droplets and oil in the reservoirs. MyOne beads have a lower magnetization, and are therefore easier to release. They can be released from a minimal pressure of around 13mbar, which is below the range we usually work in. Finally, we can expect a proper operation of the device for droplet velocities in the order of 0-30mm/s, channels dimension above 20µm, and pressures above 20mbar.

Figure 37:

The three theoretical criterions were calculated with the values shown in Table 5. We considered two types of beads for each: MyOne (red lines) and Masterbeads (blue lines). The grey dotted line indicates the theoretical value below which the system does not operate properly. a. Cluster formation criterion e mag e drag ⁄ in function of the droplet velocity. Dashed lines represent it without correction for cooperative magnetophoresis. This criterion was calculated for a 35µm channel. We can predict from these curves a better capture efficiency at low velocities. b. Droplet breakup criterion e mag e cap ⁄ in function of the channel size. It suggests that the cluster could not be extracted in a too small channel. c. Cluster release criterion e pres e mag ⁄ in function of the inlet pressure, according to which the cluster cannot be released below a certain pressure..

Characterization of the capture efficiency

After having described the system from a theoretical point-of-view, chosen the operating conditions and dimensions, we had to characterize it experimentally. This part describes how we operated the device and how we measured the capture efficiency of the micro-magnetic-tweezers. Figure 38: a. Droplets containing magnetic particles (i) or not (ii) are generated and stored in reservoirs (iii,iv). b. They are synchronously reinjected in the chip (i) and are imaged before (ii) and after (iii) passing through the micro-magnetic-tweezers (iv). The images are then analysed to assess the capture efficiency of the tweezers. In addition, movies are taken in (iii) to measure droplets velocity.

Material and methods

The microfluidic chips were placed on an inverted microscope (Zeiss Axiovert) equipped with a camera (Basler). Droplets of 450pL of PBS were generated through a flow-focusing chip using Novec-7500 + 2% w/v Picosurf as continuous phase. For the dispersed phase, we used either PBS, or PBS + magnetic particles. The magnetic particles were rinsed 4 times in PBS and diluted at different concentrations ranging from 25mg/mL to 50mg/mL in PBS prior to being injected in the flow-focusing chip. Droplets were collected in reservoirs made of a pipette cone to enable easy subsequent reinjection (Figure 39). All the liquids were flown in the chip using a pressure controller dedicated to microfluidics (MFCS, Fluigent) working in the range of 0 to 325mbar. During droplet generation, a homemade LabView program grabbed the microscope images, detected the droplets and measured their size continuously, allowing us to precisely adjust the inlet pressures to keep the right droplet sizes. The program is briefly explained in Appendix F. After generation, the droplets could be kept in the reservoirs for days to weeks before being reinjected in a micro-magnetictweezers chip.

The droplets were reinjected in the micro-magnetic-tweezers chip in a way to have an alternation between PBS and particles carrying droplets in the microchannel. Different methods exist for such paired reinjection, however, this chapter focuses on the micro-magnetic-tweezers part, and this aspect will be described in Chapter 5.

In these experiments, several parameters were tried out to see their influence on the capture efficiency, including the nature of beads, the beads concentration, the strength and distance of the external magnet, and the size and shape of the micro-magnetic-tweezers. For each condition, we took pictures of the droplets in the microchannel before and after passing through the tweezers, allowing us to estimate the capture efficiency of the system through subsequent image analysis, described in the next part.

As suggested in part 1.1 of this chapter, the capture efficiency was expected to decrease with droplet velocity. For this reason, the pictures were acquired at different inlet pressures ranging from Figure 39: Experimental setup that was used for the micro-magnetic-tweezers characterization. The chip (i) is placed under the microscope. The magnet (ii) is placed at 3mm from the magnetic tweezers in a 3D printed holder. Droplets are reinjected from reservoirs made of pipette cones (iii) which are pressurized by a Fluigent MFCS pressure controller. 40mbar to 150mbar. However, plotting the capture efficiency against inlet pressure is not very appropriate because the droplet velocity depends on the hydraulic resistance within the chip, which can vary from chip to chip, but also vary with the quantity of droplets/oil remaining in the reservoirs. So, to correlate capture efficiency with droplet velocity, we took videos of the droplets flowing in the main channel for each pressure right after having taken the pictures. These videos allowed us to measure the droplet velocity in each condition afterwards through a LabView program detailed in the next part.

Image acquisition and analysis

Capture percentage

We developed a LabView program to take the pictures during the experiment. It is able to detect when a droplet is in the center of the field of view and saves the picture. Details on the program Then, an image taken at the same place without droplets is subtracted to remove the background (2). The program is able to detect droplets outline of and to measure the intensity within the selected region. This is done for droplets before (B) and after (A) extraction, as well as for empty droplets (E). The efficiency of capture is then calculated based on 15 measurements for B, A and E with the formula (3). Finally, the standard deviation of the capture efficiency is calculated by considering uncertainties propagation.

are given in Appendix G. Examples of pictures taken this way are shown on Figure 40. They were taken before and after the passing through the magnetic tweezers.

To evaluate the capture efficiency, we compared the pixel intensity on droplets pictures taken before and after extraction. A MATLAB program was developed for this purpose (Figure 40). After subtracting the background, the pixel intensity of a droplet that contains particles before extraction provides us an upper reference value that corresponds to 100% of particles present in the droplet.

Similarly, the lower reference value corresponding to 0% of particles, is measured on empty droplets. Then, we measured the pixel intensity in droplets that were depleted of particles after passing through the tweezers. We write the measured values as follows: B for droplets before extraction (100% of particles), E for empty droplets (0% of particles) and A for droplets after extraction (unknown particle quantity). Assuming a linear relationship between the pixel intensity and the quantity of particles in the droplets, we can estimate the percentage of extracted particles for each image by:

%1 = 1 - © -d Q -d Eq. 23
This linear relationship of pixel intensity with the particle quantity is a strong assumption. The particles form irregular clusters (visible on Figure 40) that lead to a non-homogeneous distribution of particles within the droplets, causing a high variability in intensity amongst droplets. We decided to average all of our measurements on 15 droplets. The dispersion of data for A, B and E was characterized by their standard deviation ™ ´, ™ ¨ and ™ ≠ , respectively. The standard deviation of the capture percentage was calculated by considering the propagation of uncertainties as follows ‡ :

™ %AE = %1 × 5 ™ ´+ ™ ≠ © ̅ + d ∞ + ™ ¨+ ™ ≠ Q ∞ + d ∞ 8
Eq. 24

The MATLAB program is given in Appendix H1.

Droplet velocity

The velocity of droplets passing through the channel was measured on videos taken during the experiments. All the videos were taken at 100fps. Then, a MATLAB program was used to detect droplet centers and calculate their displacement between each frame. The velocity is then averaged over the whole video, and the standard deviation is computed for each velocity. The program is detailed in Appendix H2. ‡ For additions and subtractions, absolute errors are added: ™ a±≤ = ™ aO≤ = ™ a + ™ ≤ For multiplication and division, relative errors are added:

≥ ¥×µ a×≤ = ≥ ¥/µ a/≤ = ≥ ¥ a + ≥ µ ≤
The channel is narrower between the tweezers compared to where we take the movies. As a result, the measured velocities are smaller than the actual droplet velocity in the capture region. The framerate of our camera was too low to measure accurately velocities in the tweezers region. To convert our measured velocity into actual velocity, we had to consider that the flow rate is conserved, so that we can simply multiply the measured values with the cross-sections ratio. In all the experiments presented in this part, the cross sections are 30µm × 35µm in the capture region and 120µm

× 35µm in the region where we take the movies, so we can calculate the velocity in the center with:

% tweezers = 120µm × 35µm 30µm × 35µm % movie = 4% movie
Eq. 25

Results

We measured the capture percentage for different conditions. For each one of them, the capture efficiencies are reported on Figure 41 and Figure 43 as a function of droplet velocity.

Triangle shaped tweezers

We first evaluate the beads capture efficiency for triangle shaped tweezers of different sizes:

100µm, 200µm and 400µm as illustrated on Figure 41a. For these experiments, the magnets were 35µm thick, the channel was 35µm thick, 30µm wide, and the external magnet was placed at 5mm from the micro-magnets. We used Masterbeads at a concentration of 50ng/nL, corresponding to 22.5ng of beads per 450pL droplet. As expected, the efficiency decreased with velocity, but could be improved with bigger magnets. We observed a drop in capture efficiency going from 80% to 5%

with the smaller triangles when increasing the droplet velocity from 4mm/s to 24mm/s. The slope was modified with bigger magnets and a drop going from 80% to 40% was obtained. However, increasing the magnet size from 200µm to 400µm didn't show any important progress compared to what we could expect from simulations.

Interestingly, unlike what we could expect from the first theoretical criterion (Figure 37a), we can note that the slope seems to be linear. We don't explain for now this observation, but it clearly reveals the complexity of the physical involved mechanisms.

We then investigated how the distance of the external magnet affects the beads capture efficiency (Figure 41b). We showed that we were able to improve significantly the efficiency with the magnet at 3mm from the tweezers compared to 5 and 7mm, which is consistent with our simulations, where we clearly see higher gradients when approaching the magnet. To give an example, and as shown on Figure 41b, the capture efficiency was increased from 10% to 70% at 24mm/s. To assess the influence of bead quantity on the capture, we tried three different concentrations: 50, 40 and 25ng/nL, that correspond to respectively, 22.5, 18 and 11.25ng of beads per droplet. A slight improvement in capture efficiency was observed at lower concentrations. An explanation of this might be that when increasing bead quantity, the cluster is bigger, so the particles located at the cluster borders are further from the high gradient region than if the cluster would have been smaller, and are then more subjected to drag force.

We could observe this phenomenon, as shown on Figure 42. We can see a loss of particles during cluster formation, even at low droplet velocities. With triangular tweezers, gradient is strong close to the tip but decreases fast with the distance so only particles close to the tip can be trapped.

During the cluster formation, the particles progressively occupy this space where trapping is possible, until it reaches a certain quantity, and all the particles are no longer trapped.

According to our first theoretical criterion, we should be able to improve magnetophoresis, and thus the capture efficiency, by using MyOne instead of Masterbeads (See Figure 37). However, the above described experiments could be performed only with Masterbeads because of the low magnetization of MyOne, that was insufficient to fulfill the droplet breakup criterion. We performed the experiment with both types of beads in the same droplets at different ratios.

Surprisingly, we see on Figure 41d that adding MyOne did not help to collect more beads in the tweezers. Ultimately, with only MyOne, the droplet didn't even break: the particles were not extracted. This is explained by the low magnetization of MyOne compared to Masterbeads (23emu/g against 40emu/g) that was not sufficient with respect to the droplet breakup criterion. To avoid/limit the particle loss shown in Figure 42, we had to find another geometry that increases the region of capture, which is presented in the following part.

Figure 42: Particle loss during cluster formation at low velocity. At the beginning of cluster formation, all the particles seem to be trapped (i), but after a certain particle quantity in the cluster, all the particles are no longer trapped (ii), resulting in an observable particle loss (iii). Droplet velocity is 4.6mm/s. The droplet volume is 450pL and it contains a total of 18ng of Masterbeads and MyOne at a ratio of 1:1. (Red line in Figure 41d)

Flat tweezers

The idea behind the flat tweezers was to adapt the triangle shaped tweezers but with a larger region of capture to limit the effect mentioned above and shown in Figure 42. We fabricated two chips embedding trapezoidal tweezers as shown on Figure 43a, that have a flat side of 40µm and 80µm. On Figure 43, Type A refers to the triangle shaped magnets presented in the previous paragraph. Type B and C refer to trapezoids with flat sides of 40µm and 80µm respectively. All the magnetic tweezers used in this experiment were 400µm wide and high, and 35µm thick.

Simulations on these new geometries didn't show much higher values in terms of magnetic field and field gradient, but they act on a longer distance, providing more time and space for magnetophoresis to occur. Experimentally, we clearly obtained better efficiencies by widening the flat side of the trapezoid, as shown on Figure 43a. For example, with 18ng of Masterbeads, and at a droplet velocity of 24mm/s, the triangle-shaped tweezers provided a capture efficiency of 50%, while it could be increased to 80% with flat tweezers of 80µm side.

Considering the simulations, we thought that MyOne beads wouldn't be extracted like on triangle tweezers because the force is not higher. But surprisingly, we remarked that they could increase noticeably the efficiency, keeping an efficiency of around 100% at velocities below 12mm/s (Figure 43a). This can be explained by the increased range of action of the magnetic force that helps to maintain all the particles in the cluster, preventing the earlier described beads loss of Figure 42, increasing the total number of beads, and thus the total magnetic force acting on the cluster. In also increases the magnetophoretic time for the cluster formation, resulting in a more efficient particles collection. The process of capture for 18ng of MyOne beads on the trapezoidal tweezers of type B and C is shown on Figure 43b. We then tried to use a bigger external magnet. The magnet is a neodymium cube of 10mm side having a remanent flux density of 1.31T (Supermagnete N42). We though that it wouldn't change much the results because in the simulations, our micromagnets were already close to saturation.

However, as shown on Figure 43c, we could observe a slight improvement in terms of capture percentage, and it is consistent with simulations. Also, a higher external field can help to form aggregates before entering into the magnetic tweezers.

Chapter conclusion

In brief, we designed the micro-magnetic-tweezers to trap and extract magnetic particles from droplets. Starting from simple theoretical scaling laws, we investigated on the balance between each force involved in the process of capture. The main limiting parameters are: i. the capillary force that can inhibit droplet breakup at our small scale, and ii. the droplet velocity that, if too high, prevents the particles of being trapped, which is critical for the operating throughput.

To assess if the conditions we planned to work with were in a range allowing a good extraction, we performed some measurements and FEA simulations. Ultimately, we could predict a proper operation at a droplet speed in the order of 10 -2 m/s and with a channel width higher than 20µm (Figure 37).

Based on simulations and experiments, we were able to optimize the micro-magnetic tweezers shape to obtain better efficiencies in a wider range of speeds. Trapezoidal tweezers with MyOne beads gave the better results, ensuring up to 100% at velocities below 12mm/s.

Even though the droplets are flowing at fairly high speeds, we could not reach a throughput that is comparable to what is done in single-cell-oriented droplet microfluidics. To illustrate, a capture efficiency of around 100% with MyOne and trapezoidal tweezers is reached at a speed of 12mm/s (Figure 43c), above which the capture efficiency rapidly drops. This maximum speed corresponds in our device to a throughput of only 7 droplets per second, which makes the applicability of our system in the high-throughput single-cell analysis field questionable, or at least limited.

CHAPTER 4

Ferrohydrodynamics modelling of dense magnetic-particle-laden microfluidics flows

The work presented in this chapter was initiated during the Covid-19 confinement, preventing us from doing experiments, but not simulations. The goal of this work was to develop simulations for the whole process of magnetic particles cluster formation in the micro-magnetic-tweezers, and more generally for any dense magnetic particle-laden flows in microfluidics. For this chapter, I would like to thank my father, whose knowledge in electromagnetism was of great help to find the correct magnetic force expression. All the equations presented in this chapter are taken from the literature, and we didn't established any new model. This work however is an attempt at combining two well established modelling approaches: ferrohydrodynamics and continuous biphasic dense particle-laden flows to describe our experimental results.

Modelling particle-laden flows is an old, but complex problem in Computational Fluid Dynamics (CFD). These particular flows are defined as two-phase flows, with one phase being the continuous, or carrier phase, and the other one being made of small, immiscible, solid or liquid particles, referred to as the dispersed phase. Examples of particle-laden flows in nature include rain formation in clouds, dust sedimentation, volcano eruptions, sand flows, blood flow 348 , but they are also commonly encountered in engineering for example in sprays, liquid-fueled combustion, fluidization, pollution dispersion in atmosphere, magnetophoresis, or ferrofluids 339,349 .

Their complexity resides in the fact that both phases exchange momentum and thus cannot be treated separately. The nature of this coupling depends on the type of flow and particles. In practice, additional complexity is added by the interaction with various other phenomena such as heat exchange, evaporation, particle-particle interaction, deposition, clogging, chemical reactions. For this reason, plenty of semi-empirical models were derived for various application which are meant to be used in their range of applicability only 349 .

Three main approaches exist to model solid-fluid systems 350,351 :

• The Euler-Lagrange model treats the carrier phase as a continuum by solving the Navier-Stokes equations, while the dispersed phase is treated as discrete particles, for which trajectories are solved individually. The fluid action on the particles is characterized by a drag force. At the same time, the displacement of the particles modifies the flow. This approach has the advantage to be simple to setup, inter-particles forces can be easily added. However, it can become prohibitively expensive in terms of computational resources for a high number of particles (>10 3 ). This method is the most widely encountered in microfluidics papers. It has been used to study magnetophoresis, dielectrophoresis, cell or particle sorting without any interaction between the particles 340,[352][353][354] . In contrast, it was used to simulate particle-particle interactions like superparamagnetic beads column formation and aggregation, but has remained limited to a small amount of particles 355 .

• The Mixture model treats both phases as interpenetrating continua. The presence of particles is determined by a solid volume fraction scalar field which is defined everywhere in the geometry. It solves a single Navier-Stokes equation for the whole mixture, where the mixture velocity and viscosity are corrected to take into account the presence and momentum of particles. The Mixture model is however limited to relatively low particle density, and is not able to handle packed beds. More precisely, when the packed state is reached, particles volume fraction cannot increase, and there is a discontinuity for density and viscosity, the Mixture model does not take into account this discontinuity, and only assumes that density and viscosity vary continuously with volume fraction. It has been used in microfluidics to simulate magnetic separation of beads in microchannels 356,357 .

• The Euler-Euler model is the most versatile and accurate multiphase approach for particleladen flows, but also the most expensive with respect to computational cost. As in the mixture model, both phases are treated as interpenetrating continua, but both having their own Navier-Stokes momentum and continuity equations. There are coupled by the volume fraction of each phase (ï ñ + ï ∏ = 1) and a momentum exchange coefficient present for both phases. This term can be calculated following various semi-empirical models to take into account the viscous friction between the phases. Unlike the Mixture model, Euler-Euler model is valid from dispersed to packed suspensions, we will show in this chapter how its models the dilute to packed transition.

Considering the large number of particles present in our microfluidic systems (100k to 200k), as well as the large variety of packing states involved, we decided to use the Euler-Euler model. This model is provided in the CFD module of the Finite-Element-Analysis (FEA) software COMSOL Multiphysics 5.5. The first part of this chapter describes the governing equations and hypothesis for the Euler-Euler model.

This model was originally developed for fluidized beds, which are a type of industrial chemical reactors where particles are subjected to a flow (liquid or gas) in the reactor. Since they are also subjected to gravity, they will be in an equilibrium state between the two forces, resulting in a "fluidized" state, where the particles are well dispersed and very mobile. This is used in the chemical industry to maximize the interaction between the solid and fluid phases. For this reason, the Euler-Euler model does not natively implement the magnetic force, but only gravity, which does not apply in microfluidics.

While the force acting on a single superparamagnetic particle is well-known, the one applied on an arbitrarily dense suspension of particles is far from being trivial because of interparticle dipoledipole interactions and magnetic field modification due to the presence of magnetized particles 12 .

The study of hydrodynamics of magnetic suspensions is often referred to as Ferrohydrodynamics 12 , and will be presented and discussed in the second part of this chapter.

The third part will show preliminary results on the simulation of the cluster formation in the micromagnetic-tweezers as described in the previous chapter.

The last part will present preliminary simulations for another magnetic-particle-based microfluidic device developed in our team: the microfluidic magnetic fluidized bed.

Continuous multiphase model for dense particleladen flows

All the equations presented in this part can be found in the COMSOL documentation 350 , in other software's documentation such as Fluent Inc. 351 , or in various research publications showing simulations of fluidized beds, or dense particle-laden flows 358 .

Equations of motion

The Euler-Euler approach assumes both phases as interpenetrating continua. The presence of each phase is determined by their volume fraction, denoted ï ñ and ï ∏ , for the continuous and dispersed phase respectively. They are linked by ï ñ + ï ∏ = 1. Two coupled sets of equations of motion are solved 350 .

The mass balance (continuity equation) is written as follows:

á áπ ($ ñ ï ñ ) + ∇ • ($ ñ ï ñ ∫ ñ ) = 0 Eq. 26 á áπ ($ ∏ ï ∏ ) + ∇ • ($ ∏ ï ∏ ∫ ∏ ) = 0 Eq. 27
Where $ ñ , $ ∏ is the density (kg/m 3 ) and ∫ ñ , ∫ ∏ the velocity (m/s) of the continuous and dispersed phase

The momentum balance (Navier-Stokes) for two incompressible phases is:

$ ñ ï ñ ª á∫ ñ áπ + (∫ ñ • ∇)∫ ñ º = -ï ñ ∇/ + ï ñ ' ñ ∇ , ∫ ñ + X ñ + X ^,ñ
Eq. 28

$ ∏ ï ∏ ª á∫ ∏ áπ + (∫ ∏ • ∇)∫ ∏ º = -ï ∏ ∇/ + ï ∏ ' ∏ ∇ , ∫ ∏ + X ∏ + X ^,∏ Eq. 29
Where ' ñ , ' ∏ are the viscosities (Pa•s) for both phase. the pressure gradient ∇/ is shared between both phases. X ñ and X ∏ are the sum of external forces acting of the phases (e.g. gravity, magnetic force). X ^,ñ and X ^,∏ are the interphase momentum transfer terms. They describe the drag interaction between both phases, their modelling is described in the following section.

Drag models

The interphase moment transfer terms X ^,ñ and X ^,∏ need to be modelled to take into account the friction between phases. The way to model them can differ depending on the nature of the phases to be modelled. The momentum has to be conserved, so we can write:

X ^,ñ = -X ^,∏ = Ωu slip Eq. 30

Where u slip = u du c is the slip velocity and Ω is the drag force coefficient.

The Euler-Euler approach is very versatile and can be adapted to many different types of flow (e.g. bubbly, droplets, powder), for which Ω is determined differently. We describe here only the one formulated by Gidaspow, which is appropriate for dilute to packed solid particles, and was originally developed for fluidized beds.

The Gidaspow model combines two exisiting models: the Wen and Yu expression for fluidized state as follows:

For ï ñ > 0. Where 2 is the particle diameter and 1 ae is the drag coefficient for a single particle, and ø the particles sphericity coefficient. Note that the drag coefficient appears only in the Wen-Yu model (Eq. 31), implying that it matters only in dilute suspensions where the particles move freely. The Ergun formula (Eq. 32) however treats the flow as a porous system where the particles are restricted in their movement 359 .

The most important parameter is the drag coefficient 1 ae . A wide diversity of formulations for 1 ae which have been compared in the case of fluidized bed 359 . The simplest one is the Stokes drag for spheres at low Reynolds number:

1 ae = 24 !" ` for !" `< 1
Eq. 33

The one recommended in the COMSOL manual for the Gidaspow model is the Schiller-Naumann formula:

1 ae = ƒ 24 !" `(1 + 0.15!" K.¡≈P ) for !" `< 1000 0.44 for !" `> 1000

Eq. 34

For Eq. 33 and 34, the Renolds number !" ` is referred to as the "particle Reynolds number", and is defined as follows:

!" `= 2$ ñ ¿u slip ¿ ' ñ Eq. 35

This drag model was initially developed for gas fluidized beds where turbulence can occur, we used it here because it was provided and recommended with Gidaspow formulation. But we will probably in the future consider other drag formulations.

In addition, for non-spherical particles, a sphericity parameter ø can be added in Eq. 31, 32, It is equal to one for spherical particles and decreases to zero with aspect-ratio. There is no universally accepted formula to calculate this parameter, and previous studies suggest that it must experimentally chosen 359 . We can note that in the Gidaspow model, the sphericity is added in the drag force coefficient Ω but not in the drag coefficient 1 ae , but other existing formulations put the sphericity coefficient directly in 1 ae . 360

Particle-particle interactions

For solid-liquid systems, a dense state can exist where the interparticle interaction hinders the particles free movement. It can ultimately reach a packed state where a maximum ï ∏ is reached, decreasing dramatically the particles mobility. This is often modelled by semi-empirical models according to which the viscosities present in Eq. 28 and 29 are set equal to a "mixture viscosity" which is artificially increased with particle volume fraction, thus hindering the mixture movement.

An alternative to the "mixture viscosity" approach is to use a solid pressure. The viscous term for the particle phase in replaced by an artificial, localized pressure field that mimics the particles collisions and friction. The viscous term in Eq. 29 is replaced by the solid pressure gradient ∇/ `:

$ ∏ ï ∏ ª á∫ ∏ áπ + (∫ ∏ • ∇)∫ ∏ º = -ï ∏ ∇/ + ∇/ `+ X ∏ + X ^,∏ Eq. 36
The solid pressure is defined by: ∇/ `= -∆(ï ñ )∇ï ñ Eq. 37

With ∆(ï ñ ) being similar to a modulus of elasticity (unit Pa). Figure 44 shows different empirical formulations to model ∆(ï ñ ).

smart materials, whose properties can be remotely and reversibly modified. However, this field does not study fluid flows but remains in the field of rheology and material science.

• Magnetophoresis (MP) studies the dynamics of magnetic particles immersed in a liquid under magnetic field. It is the approach of choice to predict the trajectory of big particles (>1µm) driven by the magnetic gradient force (Kelvin force). However, it does not allow to treat the fluid as a whole, and thus require an Euler-Lagrange formulation of the problem (see previous section).

Among the four fields presented above, FHD evidently was the one closer to our situation for several reasons: as mentioned above, the high number of particles (~10 5 ) does not allow a discrete MP approach. MHD and MR approaches are used in different contexts, respectively when the fluid is electrically conductive, and when the rheology is specifically studied. In this project, we decided to combine the Euler-Euler model presented in the previous part with the equations of FHD. All the equations presented in the next paragraph were taken from the book of Rosensweig 12 , which is the reference in the field of FHD. In the last chapter of this book, Rosensweig showed the applicability of FHD equations on two phases flows with the Euler-Euler approach. This, plus the availability of the Euler-Euler model in COMSOL, motived us to go in this direction.

Magnetization in magnetic fluids

FHD mainly focuses on ferrofluids, namely colloidal suspensions of superparamagnetic particles which are stabilized by ions or surfactants. Superparamagnetic materials are characterized by a non-linear magnetization curve T(R) that has the shape of the Langevin function:

&( ) = coth - 1 Eq. 38
In superparamagnetic materials, the magnetization field I align with the external magnetic field.

A ferrofluid containing superparamagnetic particles as dispersed phase at volume fraction ï ∏ creates a magnetization field written:

I = T(R) H R with T(R) = ï ∏ $ ∏ T `5coth(3R) - 1 3R 8
Eq. 39

Where H is the magnetic field (A/m). R and T are the magnetic field and volumetric magnetization norms (A/m) respectively. $ ∏ is the density of the particles (kg/m 3 ). T ` is the magnetization at saturation per mass unit of particles (A•m 2 /kg or emu/g). 3 is a constant to fit with the experimental T(R) curve. It is shown to be equal to 3 = _R/à ¨Õ, where _ is the magnetic moment of the particles, Õ the temperature and à ¨ the Boltzmann constant [362][363][364] .

There is no magnetization in the ferrofluid without an external magnetic field, so we can define T(R = 0) = 0 to avoid the division by zero with no magnetic field, and allow the continuity of the Langevin-like function.

The magnetic flux density B can then be written:

E = OE ' K (H + I) in the fluid ' K H
out of the fluid Eq. 40

Body force density

Many authors proposed various formulations for the force acting of a magnetic fluid. Finding the right formulation for it is still subject of debate [365][366][367][368] . In addition, many authors provide an equation without any proper derivation. As an example, and despite the high quality of his review 339 , N. Nguyen proposed a formula based on some questionable assumptions § . So one must be very careful in the choice of the formula. The first article of the field, simply titled Ferrohydrodynamics 369 by Neuringer and Rosensweig in 1964, proposed the following equation for the body force density acting in the bulk of a material of magnetization M under a magnetic field H:

X jgk = ' K (I • ∇)H Eq. 41
This force density (N/m 3 ) is often called Kelvin force density, even though Kelvin never formulated it, and acts in the bulk of the material, like gravity would do.

The magnetization is defined as in Eq. 39, and is thus by assumption colinear to the magnetic field.

By the use of some vector identities and the current-free Ampère law ∇ × H = 0, one can simplify the expression force and write it in function of the field norms alone 12,362,369 :

X jgk = ' K T∇R Eq. 42
In a later-published paper 370 , Cowley and Rosensweig proposed a more complete formulation for the force, derived from thermodynamics. They show that the stress tensor applied on a volume of ferrofluid can be written: § He claims that no currents leads to ∇ × Q = 0. It should be in fact ∇ • Q = 0 and ∇ × R = 0. This is a fundamental difference between Q and R, and the above assumption can be true only in vacuum or in non-magnetizable medium. The Kelvin force he proposed (I • ∇)E is only true with the assumption that B and H are proportional, in addition, the article he cited to support this did not even formulate it this way.

oejgk = --" ' K ª áT" á" º

',' BR + 1 2 ' K R , ' K ÷ ◊ ̅ + EH Eq. 43
Where " = 1/$ (m 3 /kg) is the specific volume, so that the product T" is the magnetization per mass unit of the fluid. ◊ ̅ is the identity matrix. Note that in vacuum, where T = 0 and E = ' K H, this tensor is equivalent to the general form of the Maxwell stress tensor.

The force is then calculated as the divergence of the stress tensor as follows:

X jgk = ∇ • oe -jgk = -∇ ÿ" ' K ª áT" á" º ',' BR + 1 2 ' K R , ' K Ÿ + Q∇R Eq. 44
Or with Q = ' K (R + T):

X jgk = ∇ • oe -jgk = -∇ ÿ" ' K ª áT" á" º ',' BR ' K Ÿ + ' K T∇R Eq. 45
We recognize the Kelvin force on the last term. The integral term is more difficult to interpret.

Rosensweig suggests in his book that it can be omitted in dilute colloids, but represent the influence of dipole-dipole interaction in dense suspensions 12 . Alternatively, this term can be split into two pressure-like terms as follows:

" ' K ª áT" á" º ',' BR ' K = ' K " " ª áT á" º ',' BR ' K ⁄¤¤¤¤¤‹¤¤¤¤¤› [ fi + ' K " TBR ' K ⁄¤¤‹¤¤› [ fl

Eq. 46

Where the first one / ` is the magnetostrictive pressure, which is zero for incompressible media, and / ^ is the magnetic-fluid pressure.

These additional terms are however largely omitted in the literature, and in most of the case not even mentioned. We decided in this work to take only the Kelvin force into account because i: The magnetostrictive pressure is zero for incompressible fluids, and ii: the magnetic-fluid pressure seems to be opposed to the Kelvin force, and is not well described in the literature. A dedicated study would have to be done in the future to assess the relevance of this term in a microfluidics framework.

Biphasic ferrohydrodynamics

In the last chapter of his book, Rosensweig describes a magnetically stabilized fluidized bed. Fluidization is a state where particles in suspension are in an equilibrium between the drag force and the gravity, resulting in a fluid-like state where the particles move smoothly and are homogeneously dispersed in the continuous phase (Figure 45a). Fluidization is used in the chemical industry to maximize the interaction between the percolating fluid and the solid particles. The fluidized regime is however not always reached, and many nonoptimal states are encountered including channeling or chaotic bubbling (Figure 45b). It has been

shown that with magnetizable particles in the presence of a magnetic field, the particles can orient parallel to the flow, avoiding bubbles, and allowing a proper expansion of the bed (Figure 45c) 371 .

Such stabilized fluidized beds are well described in the literature, and motivated the development of biphasic ferrohydrodynamic models 12,372 .

The fluid motion is governed by the equations following the Euler-Euler approach shown in the previous part (Eq. 26-29) with the Kelvin force plugged in the dispersed phase momentum equation:

$ ∏ ï ∏ ª á∫ ∏ áπ + (∫ ∏ • ∇)∫ ∏ º = -ï ∏ ∇/ + X ^,∏ + ' K T∇R Eq. 47
Where the magnetization of the fluid T is calculated with the magnetic field R and the local particle volume fraction ï ∏ as in Eq. 39.

It now remains the question of how to calculate the magnetic field in Eq. 47. A magnetizable material placed in a magnetic field H K get a magnetization I K . Because it is magnetized, it produces its own magnetic field, opposed to the external field H K . This "demagnetization field" will reduce the total magnetic field following H = H K -3I K where 3 is a demagnetizing factor, that has an analytical description in some simple problems, but can be calculated numerically by solving Maxwell equations. 373 Should we take into account there "demagnetization fields" for the calculated of the field R in Eq.

47?

The literature is not very clear on that point. In his book, Rosensweig split the magnetic field into two parts following R = ï ∏ R ∏ + ï ñ R ñ , without defining precisely how R ∏ and R ñ should be calculated. Under a strong magnetic field, as generated by neodymium magnets, the modification of the field by the presence of particles might not be very significant. Also, taking the modified field implies a two-way coupling between magnetism and fluid, where the magnetic field needs to be recomputed between each iteration to take into account the new particles distribution, which is more computationally expensive.

Probably for these reasons, added with the lack of consensus for a correct formulation of the force, many authors took the external field and could achieve physically coherent results, however with relatively low density suspensions 356,357,374 .

To start with, we will take in this study the simplest form possible, that is the Kelvin force only ' K T∇R, considering that the particles does not modify the field R, and with the magnetization T calculated as in Eq. 39. This way the problem can be solved in two steps: we first compute the magnetic field without particles in the system, and then introduce them to simulate the biphasic problem with the Kelvin force expressed thanks to the previously calculated field.

Simulations of superparamagnetic-particle-laden flows applied to microfluidics

This part will show some preliminary results of simulations based on the above-described equations. Simulations were performed in COMSOL Multiphysics 5.5 with the Euler-Euler module. The main advantage of using COMSOL (or other expensive proprietary FEA software) is that a very few efforts have to be provided by the user in the computational and numerical aspects, the algorithms being already optimized for each implemented models. In COMSOL, we were able to simply plug the Kelvin force (Eq. 42) in the Navier-Stokes equation for the dispersed phase. The mathematical principles behind finite-element-method, as well as the computational aspects are not of our interest, and will not be discussed here, they can be found easily in the literature. However, some general good practices have to be known to perform satisfactory simulations, especially with such complex problems, thus, a general understanding of basic FEA principles is still needed.

Briefly, the central notion in FEA is discretization. The geometry is split into small elements to form a mesh (or grid). The elements can be triangles or rectangles in 2D, tetrahedra or parallelepipeds in 3D. The solution is then estimated in each element of the mesh, by assuming it to be linear in each element (first order discretization), quadratic (second order), or cubic (third order) etc. The solution is estimated in each element of the mesh by an iterative solver that progressively converges to a single value. Between each iterations, a quantity called residual is calculated to indicate how different the new solution is from the previous iteration. After several iterations, when the residual goes below a specified threshold, the simulation is considered as successfully converged and is stopped, for this reason, residual is often called convergence factor. For time-dependent simulations, a discretization in time has also to be done, a new solution is calculated by the same iterative procedure for each time step.

Some general good practices include:

• Mesh size have to be small enough to capture the behaviour at all scales. A too coarse mesh leads either to non-convergence, or to inaccurate results. Refining the mesh improves the accuracy but also generally increases the computational time. The mesh can be coarse in regions where the solved quantity has low gradients, while it must be fine in high gradients regions.

• Discretization order can be increased to provide smoother results. It however increases considerably the computational cost and it is generally preferred to refine the mesh.

• Time step size has to be small enough to capture fast events, but large enough to ensure fast computation. In COMSOL, the time step size is automatically adjusted thorough computation to remain below threshold residual, called tolerance factor. Decreasing the tolerance factor results in smaller time steps, and thus, a better accuracy but also a longer computation because more time steps have to be calculated.

In any case, a balance has to be found between accuracy and computational cost. One must perform a test simulation with different mesh refinements and time step sizes to ensure that the results are not too much dependent on the discretization. This practice, called "grid convergence study", can be seen as a control experiment that is absolutely necessary to validate any FEA work. It is unfortunately often omitted in publications.

We show in the next parts some preliminary simulations for two microfluidic systems developed in our group based on magnetic particles handling. The first part will be focused on my main PhD project, in particular on the particle cluster formation in micro-magnetic-tweezers as described in Chapter 3. The second part will show simulation of the microfluidic magnetic fluidized bed, a technology that has been widely used in our group 260,375-377 .

Simulation of particles capture in the micro-magnetictweezers

In this part, we will describe the simulation of the magnetic cluster formation in the micro-magnetic-tweezers. Note that we do not simulate interfacial effects, and we simplify the system from a triphasic (particles in water in oil) to a biphasic (particles in water) one. Only the first stage of the captured is modelled, as shown in the introduction of this manuscript on Figure 1a-b.

Simulation setup

We modelled the cluster formation process in the micro-magnetic-tweezers. This simplified model did not take into account interfacial effects, droplet breakup or recirculation flows in the droplet.

To approximate our system, we considered a simple plug of magnetic particles advancing in a rectangle microchannel at the speed of a droplet, and attracted by the tweezers. The simulation setup is explained below, and illustrated on Figure 46a-c.

Geometry

The three geometries of tweezers described in Chapter 3, part 3.3.2 were tried out, namely: triangles and trapezoids with a 40 or 80 µm flat tip. In any case, to be as close as possible to experiments, the tweezers were 35 µm thick, the channel was 30 µm wide and 35 µm high, and the gap between the tweezers tip and the channel side was of 14 µm. (Figure 46a)

Boundary and initial conditions for fluid simulations

To mimic a segmented flow, we modelled a plug flow instead of a Poiseuille flow. In a plug flow, the velocity profile is flat (while it's parabolic in a Poiseuille flow), meaning that there is no friction at the walls. This is done in COMSOL by adding a slip condition at the walls for both phases, thus the velocity is not zero at the walls. A zero-pressure boundary condition was set at the outlet, and a constant velocity between 5 and 50 mm/s at the inlet, which is in the experimental velocity range (Figure 46a).

For the initial conditions, we introduced particles in a 2 mm long channel portion, corresponding to the initial position of the magnetic particle plug, in which the particle density was set to ï ∏ = 0.111 (Figure 46b), in a way that the total amount of particles ∭ $ ∏ ï ∏ BD is 18 ng, as in the experiments shown in Chapter 3. The initial particle density is zero elsewhere.

The Gidaspow model (described in part 1.2 and 1.3 of this chapter) was applied to model the interaction between water and the particles. The viscosity of water was set as ' ñ = 1 mPa•s, and its density $ ñ = 1000 kg m 3 ⁄ . To start with, we did not consider aggregates nor sphericity, so for My-One beads, the particle diameter was set at 2 = 1 µm, the sphericity at ø = 1 and the particle density at $ ∏ = 1800 kg m 3 ⁄ .

Magnetic field simulation

For simplicity, the external magnet was not included in the model, only the magnetic tweezers were considered. They were modelled by imposing an average magnetization value of 6.5´10 [START_REF] Shahi | Ultrahigh-throughput single cell protein profiling with droplet microfluidic barcoding[END_REF] A/m in the tweezers (Figure 46a,c). This value was taken from previous simulations, presented in Chapter 3, part 2.1. The field was calculated in a separate steady simulation, and the results were used in the fluid simulation to compute the Kelvin force.

The magnetization was calculated as in Eq. 39 during the fluid simulation. We took T `= 23 emu/g and 3 = 9.4723 × 10 ¬ (S.I.) to fit the magnetization curve of the beads provided by ThermoFisher.

Model simplifications and optimization

Such 3D multiphase simulations are known to be very computationally expensive, so we had to find some ways to reduce the model size. The presence of two planes of symmetry allowed us to solve the problem on a quarter of the geometry only (Figure 46a).

A mesh refinement study, as well as tolerance factor study was carried out to optimize the computational time (see Appendix I). After simplification and mesh optimization, a single simulation took

Results

The results presented here are preliminary, not quantitative and need some further optimization and validation. They however reflect quite well the main observed mechanisms, are in agreement with the experiments, and can eventually provide us new insights on the cluster formation process.

Figure 47a shows some simulation results. We can observe the cluster formation over time, the first striking observation is that the particles arrange in the same sandglass-like shape than what we have in experiments. They form a compact cluster, in which ï ∏ > 0.5, that remains stable. 3D pictures were plotted (Figure 47b-d) to understand how the flow circulates around the cluster. The same sandglass-like shape is observed in the xz-plan (Figure 47d), leaving holes where the continuous phase can penetrate. For an inlet velocity of 5mm/s, the flow within the holes can go up to 45mm/s. We also measured a continuous phase velocity inside the cluster (percolating velocity) of 0.5mm/s. With a higher inlet velocity of 25mm/s, the velocity in the holes could reach speeds above 100mm/s and 2mm/s for the percolating velocity.

So once the cluster formed, most of the water goes around it and only a small percentage percolates through it. However, one must be careful with these results because the maximum packing density was ruled by Gidaspow solid pressure model (Eq. 37), which is semi-empirical and wasn't developed for such situation. But the simulations are in good agreement with our previous compacities measurements on bead clusters (Chapter 3, part 2.3) where we obtained a maximum value around 0.5 for MyOne beads.

Surprisingly, we did not have to artificially increase the hydrodynamic diameter (diameter that enters in the drag coefficient in Eq. 33-35) of the particles to obtain qualitatively good capture. As we know that particle aggregation plays an important role in magnetophoresis, and thus in capture efficiency (see Chapter 3), we expected that it would have been necessary to increase the diameter to take into account particle aggregates and columns. While the physics of the microfluidic magnetic fluidized bed has been well described in the past 375 , no numerical study have been yet carried out to model the fluidization process. We attempt here to apply the above described ferrohydrodynamics biphasic model on the magnetic fluidized bed.

Simulation setup

Geometry

Considering the flatness of the system (50µm thick), we decided simplify the model in a 2D simulation. The inlet channel is 100µm wide, after which the chamber widens with an angle of 13°.

Initial and boundary conditions for fluid simulation

To be comparable to what is typically used in the experiments (see Figure 49), we set an inlet velocity from 1.667 to 6.667mm/s, corresponding to 0.5 to 2 µL/min respectively. The outlet was set as zero pressure.

The initial particle distribution is shown on Figure 50, we set ï ∏ = 0.4 in a 3mm long region in order to have a total particle mass ∭ $ ∏ ï ∏ BD of 5µg. Note that on the 2D geometry, we integrate on the surface and then multiply by the thickness 50µm. For M270 (ThermoFisher) beads, we have

$ ∏ = 1800 kg/m 3 .
Boundary conditions at the walls is no slip for the continuous phase (% ñ = 0) but slip velocity is allowed for the dispersed phase (% ∏ ≠ 0).

Magnetic field simulation

A powerful permanent magnet (2´2´3cm, Br=1.43T) is positioned at 2mm from the bottom of the chip. The magnet is however not centered in z compared to the microfluidic channels but is placed on the glass slide holding the chip.

To avoid us to perform a 3D simulation, we computed the magnetic field in the chip following an analytical solution, derived by Gou et al. 379 , who proposed formulas that describe the magnetic field distribution around rectangular permanent magnets (see Appendix J). The computed field is shown on Figure 50. As we didn't consider any modification of the field by the magnetic particles, we could use R = Q ' K ⁄ to calculated the magnetic force as in Eq. 42.

The magnetization of the beads was calculated with Eq. 39, using the properties of the M270 (Ther-moFisher) beads: T `= 10emu/g.

Drag coefficient estimation

This 2D simulation is quite far from reality where particles form columns and aggregates that considerably affects fluidization. We had to modify the drag coefficient to take into account aggregation. In practice, we modified the product 2ø in Eq. 31 and 32, which correspond to the hydrodynamic diameter of the particles, where 2 is the diameter of an equivalent volume sphere for a column or aggregate, and ø a sphericity parameter between 0 and 1.

For columns of height ℎ and diameter B, we calculate estimate the 2ø product as follows. We define 2 so that the column volume MℎB , is equal to the volume of a sphere of diameter 2. Eq. 48

The sphericity can have different definitions. We use the one of Sobieski 359 :

ø = 5 B √Bℎ 8 6/,
Eq. 49

Optimization

As for the previous part, a grid and tolerance factor convergence study were performed to optimize the computational cost (see Appendix I). The calculation was then run on a Dell Precision 5820

Tower equipped with an Intel Xeon W-2155 CPU (3.30 GHz), and 64 GB of RAM. Approximately 2 hours were needed to simulate 2 seconds of fluidization.

It is known that the presence of sharp interfaces in problems that include convection are subjected to numerical aberrations. In our example, we observed an abnormal advancement of the bed front, resulting in an aberrant increase of the total particles quantity. This kind of problem is generally solved by adding a small artificial diffusion, that smooths sharp interfaces 357,380 . This approach, called "inconsistent stabilization" is readily available in COMSOL. A tuning parameter between 0 and 1 has to be set to determine how much diffusion we introduce in the system 380 . As recommended in the COMSOL manual 350 , we chose 0.25, which could effectively solve our problem, and didn't show any abnormal or excessive diffusion.

Results

In the previous part, for the micro-magnetic-tweezers, we didn't have to increase the drag coefficient. Considering that 2 corresponded to the particle size, with ø = 1 (no sphericity), provided good results. Unfortunately, it did not give nice results in the present simulation: all the particles were flushed away with the flow. The formation of columns and aggregates seems to have a great influence on the fluidized bed stability. Pereiro et al. 375 showed notably that modifying the height of the external magnet modifies the columns angle, changing significantly the bed expansion. Such phenomenon cannot be modelled directly in our 2D simulation, and adjusting the value of the product 2ø seems to be the easiest way to correct our simulation.

We ran transient simulations, with the initial values as mentioned previously. Video 4.3 shows the bed opening for a simulation with 1 µL/min and 2ø = 15.39, corresponding to bead columns of 105µm high and 11.2µm thick. The inlet velocity is turned on only after 1s of video. Figure 51 shows the same results at 10s.

We see that during the first second, when there is no velocity yet, the particles are attracted toward the magnet. Then, after the inlet velocity has been switched on, the bed opens and stabilizes in a steady state after 3s. The white arrows symbolize the direction of the particle velocity ∫ ∏ , showing similar recirculation patterns to experiments (as in Figure 49). Different flow rates and values for 2ø were also tried out, Figure 52 shows the results for the different tested conditions at 9s (after bed stabilization). Video 4.4 shows the same data over time. We first see that, as expected, the bed expands with velocity. Also, it expands less with bigger hydrodynamic diameters 2ø. This behaviour is in good agreement with the theoretical parameters that we derived in the previous Chapter (see Eq. 3 in Chap. 3) where we showed that bigger particles increases the ratio F mag F drag ⁄ , promoting magnetic attraction against drag. Ultimately, with small particles or columns (2ø = 4.34) and high velocity (2 µL/min), the particles are flushed out of the chip. Another thing that could be noticed is the eventual formation of a preferential path of higher velocity and lower particle density. This effect -called channeling -is well known in fluidized bed systems, it indicates a poor exchange between phases and must be avoided. This can be due to poor mixing, high inter-particles interaction or a too fast fluidization 260 . This channeling effect could be avoided by increasing the particle size (Figure 52). Note that this channeling effect is also observed experimentally when the velocity is too high.

Our simulation provides results that are qualitatively very close to the experiments. However, our best results were obtained with 2ø = 15.39, and were calculated by considering a column of dimensions ℎ = 105µm, B = 11.2µm, which might be far from the size of observed columns (Figure 49d). And even if we see a bed expansion with velocity, it does not seem to correspond to the experimental data (Figure 49c). These results are preliminary, and a further analysis must be carried out to put them in contrast with experiment, and also to optimize the different input variables.

Free antigen:

©Â (mol/m Eq. 52

After having solved the fluidized bed opening, the flow remains steady. If we consider that binding/release does not interact with the fluid flow, we can solve it separately, using the results of the steady state flow as an input.

This model would be useful in the future to study the mechanisms of biomolecule capture in the bed, to predict its saturation, or even to optimize the chip geometry.

Chapter conclusion

In this chapter, we developed a new approach for modelling dense flows of magnetic particles in microfluidics. Unlike most numerical simulation found in the microfluidics literature, we used a continuous approach, where the particles are considered as a second phase that interpenetrates the continuous phase. The presence of particles in then determined everywhere by a scalar field: the particle volume fraction ï ∏ .

The method used for such multiphase flow was the Euler-Euler method, where both phases have their own set of Navier-Stokes equations, and the interaction between them is described by a momentum exchange term. This term accounts for the drag forces, and can be calculated following different models. We used the Gidaspow model, which is recommended for fluidized beds, or for systems where particles can be in all the states from highly dilute to packed.

We computed the magnetic force applied on the particles following Rosensweig's ferrohydrodynamics theory. Finding the right expression for the force applied on an arbitrary magnetizable volume is not straightforward, and was detailed in this chapter. To avoid a prohibitively costly coupled computation, we had to assume that the particles does not modify the external field. The remaining term is called the Kelvin body force density, and is expressed ' K T∇R where H is the external field and M is the local magnetization, which depends on the magnetization curve of the particles, the external field and the local particles fraction.

This simplified formulation provided consistent results with respect to experimental observations.

We successfully modelled the particles aggregation process in the micro-magnetic-tweezers (as described in Chapter 3), and the complex particles recirculation in a microfluidic magnetic fluidized bed. Though needing some strong assumptions (demagnetizing fields neglected) and some fitting parameters (drag coefficient) to give results close to experimental, we could reproduce accurately main the mechanisms that are experimentally observed.

We believe that such simulation approach would facilitate researchers to design microfluidic devices involving dense magnetic-particles-laden flows. We will also in the near future implement a binding/release chemical model, completing this approach to model a complete Lab-on-a-Chip.

CHAPTER 5

Physical separation of mRNA and gDNA

The work presented in this chapter was carried out in tandem with Mathilde Richerd, PhD student in the team, with whom I had the chance to share an office, and some epic fights against noncooperative droplets and DNA. I would also like to thank Fanny Cayrac, Aude Battistella and Fahima Di Federico who introduced us to cell culture and molecular biology.

We aim at providing new tools based on droplet microfluidics and magnetic particles to perform multimodal single-cell analysis. When looking at the state-of-the-art in single-cell multi-omics, there are a very few integrated platforms. While droplet microfluidics has recently been used to perform transcriptomics/proteomics studies (Abseq 5 , see Chapter 1, Part 3.8), there is at our knowledge no droplet-based techniques to combine transcriptomics with genomics or epigenomics yet.

An existing protocol that took up our attention, and would be a good candidate to be implemented in our magnetic-tweezers platform was G&T-seq 229,384 (see Chapter 1, Part 3.8). This protocol is based on magnetic bead separation of genomic DNA (gDNA) and messenger RNA (mRNA), followed by sequencing. G&T-seq however still requires many delicate manual operation, and remains limited to the microtiter format. We believe that our magnetic-tweezers platform, either in its already established version, or in the new integrated one presented in Chapter 3 of this manuscript (which is still under development), would be useful to automatize, decrease reaction volumes and increase throughput of protocols such as G&T-seq.

But prior to do such single-cell sequencing experiment, we needed to show that we are able to separate mRNA and gDNA in our system. This chapter will present some experiments done with the already established "macro" magnetic-tweezer platform, aiming at separating mRNA from gDNA, and at measuring the efficiency of this extraction process.

In the first part we will present an attempt to develop a one-step assay to assess the presence and quantity of mRNA compared to gDNA. This assay would allow us to characterize the efficiency of separation in our system, its specificity, and eventual loss of information.

The second part describes our first experiments of physical separation of mRNA and gDNA using the magnetic-tweezers platform, whose efficiency is compared to conventional bead-based manual separation.

1 Attempt to develop a one-step multiplex mRNA/gDNA qPCR assay Two main methods for detection are available:

• Intercalating probes are molecules that can insert in DNA, delivering fluorescence. The fluorescence of a sample containing such probes then rapidly increases with the quantity of DNA. The most commonly used intercalating probe is the SYBR Green.

• Dual-labelled probes (or hydrolysis probes) are single-stranded oligonucleotides, designed to be specific to a targeted sequence. They have a fluorescent reporter at their 3' end and a quencher at 5' end. They bind on the target sequence, and are eliminated during amplification, delivering their fluorescence. Thus, they allow the quantification of a specific sequence in the sample. The most known dual-labelled probes are the TaqMan, commercialized by ThermoFisher, but the other suppliers propose equivalent products.

As PCR works only with a double stranded oligonucleotide, so an additional reverse-transcription (RT) step has to be added to enable the quantification of gene expression. This is performed with a reverse-transcriptase enzyme that synthesises the complementary strand of RNA, resulting in a double-stranded oligo called complementary DNA (cDNA). Unlike, PCR, the RT reaction is isothermal and is processed at a lower temperature, typically 50°C, allowing us to do it immediately before PCR cycling in the same reaction mix.

In our project, we aim at quantifying gDNA and mRNA simultaneously form and in the same sample, to assess the bioseparation capability of our magnetic-tweezers platform. An easy method would be to split the sample into two parts, to perform an intercalating probe based qPCR on the first part to detect gDNA, and an RT-qPCR on the second part using a TaqMan probe targeting an exon-exon junction. Such exon-exon junctions exist exists only after splicing -an intron removing step occurring after RNA transcription -and are thus specific to RNA. They are not expected to be present in gDNA, that still contain the introns.

However, splitting a single-cell sample unavoidably results in information loss, especially for gDNA for which each gene is present only in one or two copies per cell. For this reason, we developed a one-step multiplex qPCR targeting both gDNA and mRNA in the same reaction. Multiplex Unfortunately, this assay did not provide the expected results, and could not be successfully used.

In the next paragraphs, we describe in details our method, results, and why we think it did not work.

Material and methods

Fluorescent probes were bought from Integrated DNA Technologies (IDT), and designed with the PrimerQuest tool proposed on their website 385 . After entering a sequence, PrimerQuest proposes different combinations of primers/probes that would be suitable for PCR, with an appropriate GC%, amplicon length and melting temperature.

For the gDNA specific probe, we entered the sequence of intron 2-3 of the housekeeping GAPDH human gene, taken on the Ensembl.org database 386 . We chose this specific intron because it is long enough (1,632 bp) not to be amplified with the primers for cDNA (see Figure 53), a polymerase starting from a cDNA primer will not have enough time in a PCR cycle to travel all along the intronic sequence. Introns can sometimes remain included in mRNA, this phenomenon is called "intron retention" and is well described 387 , we have access in Ensembl to the regions that are frequently kept in mRNA, and we carefully chose our probes outside of these regions. The selected sequences are given in Appendix K. The dye reporter for this probe was FAM (Fluorescein), which is the most used for qPCR.

The mRNA specific probe was chosen in the exon 2-3 junction of the same gene. As for the previous one, PrimerQuest was used to find appropriate primers. The dye reporter was YakimaYellow®, which is an alternative to the ThermoFisher licensed VIC, compatible with our qPCR machine.

The samples used for assay tests consisted in a mix of purified DNA and RNA at a desired ratio in nuclease free water. They were obtained by extraction from cultured human breast cancer cells (MDA-MB-231 cell-line) using spin columns-based kits: NucleoSpin (Macherey-Nagel) for DNA and RNeasy Mini Kit (Qiagen) for RNA. Purified samples were analysed with a NanoDrop spectrophotometer (ThermoFisher) and QuBit fluorometer (ThermoFisher) to estimate the final quantity of product.

All the RT-qPCR were performed in a QuantStudio 3 (Applied Biosystems) machine, with reagents from Invitrogen (CellsDirect kit with SuperScript® III RT/Platinum® Taq Mix). A reference dye (ROX, Invitrogen) was added in the mix to normalize the amplification curves between the different tubes. All the quantities, reagents concentrations and PCR programs are given in Appendix K.

After the reaction, the PCR data were transferred to the QuantStudio software to normalize the signal with ROX and extract the Cts.

Results

We first performed RT-qPCR on a sample at different known concentrations of RNA to produce a calibration curve (or standard curve). Such curve allows us to corrleate the measured Ct with initial RNA concentration as well as to estimate the efficiency of the reaction. These RT-qPCR were performed first with each probe separately (singleplex) and then with both probes in the same reaction mix (Multiplex). Figure 54 shows the obtained standard curves. We obtained the same Ct for singleplex and multiplex assays, showing that the presence of two probes in the mix does not affect the amplification, nor the detected signal.

It is not common in the literature to use intronic probes, so we wanted to ensure that they are specific to gDNA and do not measure RNA. To do that, we performed two assays with the intronic probe on two samples: with and without RNase treatment. We used RNase A, which is an enzyme that cleaves single-stranded RNA, but keeps DNA intact. The treated sample is supposed to contain only gDNA while the other one still contains RNA. If the probe is specific to gDNA, it should not detect RNA and both samples should have the same Ct. A control experiment without RT and using SYBR Green instead of the intronic probe was performed to check that gDNA was not damaged during RNase treatment. The results of this experiment are shown on Figure 55a for a sample that contains 39ng/µL of DNA and 164ng/µL of RNA (NanoDrop measurement). We see that in the no-RT control (SYBR Green), there is no significant change between the sample that was RNase-treated and the other, indicating that gDNA was not damaged and is still present in the same quantity after treatment. With our intronic probe however, we obtained a significantly higher Ct with the RNase-treated sample. This indicates a higher quantity of intron in the sample when RNA is present in the sample.

We know that mRNA accounts for only 1 to 5% of the total RNA in a cell, we decided to perform the assay in mRNA only to see if it possesses the intronic sequence as well. To do that, an magnetic bead-based oligo dT purification was carried out using a Dynabeads Oligo(dT)25 kit (Invitrogen).

We then performed the RT-qPCR assay in singleplex and multiplex on the oligo dT purified sample, as well as in the raw sample before purification. The raw sample used in this experiment contained 22ng/µL of DNA and 40ng/µL or total RNA. The oligo-dT purified sample is supposed to only contain mRNA, which accounts for 3% of total RNA. The results of these experiments are shown on Figure 55b. As in the calibration curve, we see no big difference between the results in single and in multiplex. We obtained a slightly higher Ct (+2.1) in the purified sample for the exon probe, indicating that a few mRNA have been lost during the purification. With the intronic probe, we obtained higher Ct (+3.15) in the oligo-dT purified sample. It suggests that there are less intronic sequence in the oligo-dT purified sample compared with the raw sample. However, with the oligo dT purification, we were expecting to completely get rid of the introns completely by selecting only mature and fully spliced mRNA, that should have resulted in much higher Cts for the intron (typically above 30), and as shown in Figure 55b, it is absolutely not the case.

We assume that the presence of intronic sequences in the purified sample comes from pre-mRNA molecules, which is a transition state of RNA between transcription and splicing. Such pre-mRNA are polyadenylated before the process of intron removal, justifying why we can capture them on oligo dT beads, and amplify intronic sequences.

We did an additional control experiment without RT using SYBR Green (KiCqStart SYBR Ready-Mix, Merck)and the intronic primers to ensure that the intron was present on RNA. We obtained at Ct of 24 in the raw sample and 34 in the purified one. The high Ct value in the purified sample shows that gDNA is almost absent after oligo dT purification. The intronic sequence is however well present in the raw sample. It confirms that the signal measured in the purified sample does not come from gDNA, but certainly from pre-mRNA.

Finally, this assay cannot be used to differentiate mRNA from gDNA in a single step. We think that pre-mRNA containing introns can be reverse transcribed, and are then identified as gDNA during qPCR. The only simple way to discriminate them would be to remove the RT step for gDNA, but this implies the necessity of splitting the sample.

Separation in tubes with conventional bead-based method

The DNA/RNA physical separation was first performed with an initial solution of purified oligonucleotide, and in a second step with cell lysate as initial sample. As shown in Figure 56, all the resulting solutions were analysed through (RT)qPCR, as well as the different washing buffers used for the separation. The obtained Ct were reported on a calibration curve (Appendix L.3) to estimate the DNA/RNA quantity in each solution. From this, we can calculate the percentage of detected material in each solution.

Figure 57 shows the results obtained for the in-tube purification of different DNA/RNA samples.

The samples were obtained from cells through conventional spin-column purification (see Appendix L for complete protocols) and then diluted at different concentrations: from 0.32 to 40ng/µL of DNA and from 0.016 to 2ng/µL of total RNA. We see that 84-93% of mRNA was captured on oligo dT beads, while the rest is mainly captured on the AMPure during the second step. Almost no mRNA remained in the supernatant. For DNA, we can estimate that up to 20% are captured by the oligo dT in the first step, and 49-85% are captured by the AMPure. Up to 30% can remain in the supernatant. As mentioned above, AMPure purification is a non-specific method, and these results

correspond to what was expected, and it seemed to work slightly better at higher concentration.

These experiment however need to be reproduced to provide error bars and more accurate results, that would help us to decipher the influence of sample concentration on extraction. 56). One should note that here 100% correspond to the total detected quantity, and not the total quantity present in the initial sample. So eventual loss of material (on the pipette cones or tubes) are neglected. Each measurement was done in triplicate, on 4 samples at different concentrations of DNA/RNA, as indicated on the xaxis.

Figure 58 shows the results for a similar experiment, but with a cell lysate as starting sample. The capture is less efficient for mRNA for which only 58% was extracted with the oligo-dT beads. More mRNA remained in the initial sample compared to the previous experiment where more than 80%

was achieved. But we can also note that the mRNA amount captured by AMPure in the second step is similar than the one obtained previously. The DNA quantity captured by the AMPure is comparable to what we had previously. We can note that, unlike in the previous experiment, almost no DNA was captured on oligo dT. Finally, except a lower efficiency for mRNA capture on oligo dT, this first result with a lysate is very comparable to what we obtained with purified DNA/RNA.

Separation in droplets with the magnetic-tweezers platform

As a reminder from Chapter 1, Figure 59a-b describes the magnetic-tweezers platform used for the experiments presented here, this is a well-established technology developed in our group [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF][START_REF] Ferraro | Microfluidic platform combining droplets and magnetic tweezers: application to HER2 expression in cancer diagnosis[END_REF][START_REF] Mai | Single-step immunoassays and microfluidic droplet operation: towards a versatile approach for detection of amyloid-β peptide-based biomarkers of Alzheimer's disease[END_REF]270,285 .

It allows magnetic bead extraction in small volumes (»100nL), with high purification rate, while minimizing the sample loss.

In the experiment presented here, and illustrated in Figure 59c-d As previously, the beads are then transferred into a water droplet that is collected in a tube.

After 5min of binding in the droplet, the beads are removed with the tweezers, redispersed in a washing buffer droplet and then in a water droplet. This droplet containing purified mRNA on beads, as well as the washing buffer droplet, are collected in separate PCR tubes. The droplet containing the sample, now depleted from mRNA, is however kept in the capillary.

Unlike with oligo-dT, we cannot just introduce AMPure beads in the sample droplet to capture DNA, as PEG is also needed to trigger DNA precipitation on the beads. The simplest way was to merge the sample droplet with an AMPure XP solution, that already contains the beads, and the other needed reagents for DNA precipitation. This way, the same ratio between sample and AM-Pure solution is kept compared to the experiment in tubes. While keeping the sample droplet in the capillary, close to the tip, a droplet containing AMPure XP solution is pipetted in the capillary (Figure 59d). The droplets merge spontaneously because they advance at different speed in the capillary. This phenomenon arises from their difference of surface tension and viscosity, a phenomenon recently described by our team [START_REF] Baroud | Dynamics of microfluidic droplets[END_REF] . The PEG ratio in the final droplet can be tuned by controlling the size of the AMPure droplet compared to the sample droplet. After 5 minutes of incubation, AMPure beads are transferred into a water droplet, which is collected in a PCR tube.

Experimental details for the magnetic-tweezers platform operation are given in Appendix L.2

The content of each PCR tube is split into two parts and (RT)qPCR analysis is performed to detect DNA and mRNA, as described in the previous part, and in Appendix L.3.

Figure 60 shows the results for two samples initially containing purified RNA and DNA at two different concentrations. We obtain results comparable to the same experiment done in conventional pipetting. More than 70% of mRNA is captured on the oligo dT beads. The 30% of remaining mRNA is either captured on AMPure during the second extraction step, or remain in the supernatant. Up to 73% of DNA was captured on AMPure. Almost no DNA was captured on oligo dT, which indicates a high specificity of purification for mRNA. AMPure were less performant because up to 40% of DNA remained in the droplet.

These results are consistent with what was obtained with conventional techniques, suggesting that the magnetic-tweezers can reliably separate mRNA from DNA. Additional experiments will be done in the future, first on lysates, then on single cells in droplets. These experiments are our first step toward multimodal single-cell analysis. They are still under development, and an updated version of this project will be presented in Mathilde's PhD thesis on the next year. 56). As in Figure 57 and Figure 58, 100% correspond to the total detected quantity. Each experiment was done in triplicate.

Chapter conclusion

In this chapter, we presented preliminary results for the physical separation of "omics" on magnetic beads using the magnetic-tweezers platform. Inspired by the G&T-seq protocol, in which mRNA from single-cells is separated from gDNA with magnetic beads, we wanted to start with mRNA/gDNA separation.

We attempted to develop a one-step multiplex qPCR assay to quantify gDNA and mRNA in a unique compartment. Unfortunately, we couldn't quantify intronic sequences, specific to gDNA, without measuring pre-mRNA as well. This assay must be reshaped completely if we want to quantify gDNA and mRNA in a single step. For the next experiments, we decided to split each sample to perform two separate qPCR, one for gDNA, the other for mRNA. The one for gDNA is done without RT to remove the risk of amplifying pre-mRNA. Though this splitting approach was appropriate for our preliminary experiments with oligonucleotide solutions and lysates as starting samples, it will not be considered in the future for single-cell samples, for which the loss of material will be too important.

As a first test for physical separation, and similarly to G&T-seq, we performed an oligo dT extraction for mRNA, followed by a DNA precipitation on AMPure beads for gDNA. This was done first on purified oligonucleotide samples, and then in cell lysates. Though the protocol, buffers and concentrations, could be optimized, we obtained some promising results, with satisfactory separation rates. The experiment was then integrated in the magnetic-tweezers platform, for which similar separation rates were obtained.

In the future, such physical separation would have to be done on single-cell droplets. The micromagnetic-tweezers presented in Chapter 3 of this thesis, by facilitating cell encapsulation and increasing throughput, may be an appropriate tool to perform such single-cell analysis.

CHAPTER 6

Integration of the micro-magnetictweezers in a droplet microfluidic workflow

In parallel to the development the micro-magnetic-tweezers, we had to think on how to integrate them along with droplet manipulation in a complete microfluidic workflow. Questions about droplet generation, fusion and sorting were put forward.

Our previous magnetic-tweezers platform relied on a pipetting robot to generate the droplets in a capillary. This method allowed us to produce complex droplet sequences, which is perfectly suited to the magnetic-tweezers approach where magnetic beads have to be transferred from droplet to droplet. Although very versatile, the pipetting robot cannot be applied for nanoliter scale droplet microfluidics, the precision limit of syringe pumps being overpassed, and the required capillary diameter being too small. Common nanoliter or sub-nanoliter scale droplet microfluidic methods are based on a continuous droplet generation, which allows high-throughput (up to kHz) but is limited to the generation of many droplets of the same composition.

Nevertheless, several techniques have been developed to allow sequential generation of droplets, they are often classified under the name "droplet-on-demand". We adapted one of them to our system.

Unlike in our previous magnetic-tweezers platform, droplets at nanoliter scale need to be stabilized by fluorosurfactants which prevents them from merging. As a consequence, it also prevents the cluster of magnetic particles to be reinjected into the following droplet. To tackle this, we have as already described in Chapter 3 developed an approach to release the magnetic particles cluster in the absence of merging thanks to the force exerted by the following droplet, we also had to implement an electro-coalescence step in our device to merge the magnetic cluster with this "pushing" droplet.

Once these elementary operations integrated, the question of droplet collection was also put forward. While in our previous platform, we could collect the droplets individually at the outlet of the tube, it would be very difficult with sub-nanoliter droplets. We implemented in our chip a continuous droplet generation (100Hz-10,000Hz). We provide here a quick review of some selected DoD methods.

Earliest DoD devices were based on integrated microvalves. These valves, often called Quake formation 398 . In a general manner, the microvalve approach allows minimal dead volume, and droplets as small as 1pL can be produced.

Another common method for DoD is to used sequential pipetting. This is the method used in our magnetic-tweezers platform which has already been extensively described in this manuscript (see Chapter 1 part 4.3, Chapter 3 part 2.3 and Chapter 5 part 2.2). The same approach was integrated in a fully automated device, using a rotating rack compatible with standard tubes 388 . This method is very versatile, but is limited to pipetting robot capabilities, namely low throughput (~1Hz), and quite big droplets (typically >100nL).

An alternative approach was reported by Teo et al. as shown on Figure 62c, they use a simple Tjunction with a tapered neck. The outlet is pressurized until the droplet generation stops, the meniscus remains in a stable state at the junction. Then, a negative pressure pulse can be applied by decreasing momentarily the outlet pressure. They were able to produce droplets as small as 100pL at frequencies up to 50Hz.

The last main approach is the use of external valves. It was originally developed in the lab of Piotr Garstecki in a series of publications starting from 2010. Unlike with Quake valves, the use of external valves does not require the microfluidic device to be soft, Churski et al. 391 developed an external electromagnetic valve with low dead volume (<20nL) that allows to start and stop the flow at Tjunction in a stiff polymeric device. When opening momentarily the valve (20-40ms), they were able to produce droplets of 100-500nL. This method is limited to large volume droplets because of the dead volume in the valve, which is defined as the displaced volume during the valve actuation, preventing us from closing the valve without expelling this volume in the chip. et al. 394 . The pressure is adjusted so that the interface is pinned in the constriction (i). By closing and reopening quickly an external valve placed at the injection tubing before the chip, a pressure pulse is generated, resulting in droplet delivery (ii-vi).

The same authors later proposed a method using inexpensive electromagnetic valves with large dead volume (>10µL) to accurately produce small droplets of around 1nL 392 . This was achieved by a drastic disproportion between the hydraulic resistance before and after the valve. A steel capillary (I.D. 0.2mm, Length 10cm) was added after the valve in a way that when closing, most of the displaced volume goes backward. With such huge resistance however, a very stiff fluidic circuit is needed to keep a responsive enough control.

Ferraro et al. 393 developed in our group a valve with a dead volume as small as 2nL, providing a very low back flow. This valve is based on the pinch-valve concept, where a very thin 3D printed tip pinches a soft and thin tubing.

Zhou et al. 394 had the smart idea to take at their advantage the generally undesired displaced volume to form the droplets. Here, the valve is normally open, as shown on Figure 62d, the pressure in the injection channel is set to pinch the interface at a constriction. Closing momentarily the valve creates a pressure pulse that results in droplet formation. This method has the advantage of allowing small droplet (<1nL) formation on PDMS devices with standard low cost electromagnetic valves. We decided for this reason to adapt this approach in our device. The involved physical mechanisms and operation are detailed in the following part.

Working principles of droplet generation

The device relies on the same principles than the one of Zhou et al. 394 . The applied pressure at the injection channel is adjusted in a way to pin the interface at a constriction, as shown on Figure 63a.

In this state, because there is no flow in the water channel, the inlet pressure before the valve Pw is equal to the one at the constriction Pi. A pressure barrier due to capillary forces prevent the droplets to be formed at the constriction. This pressure barrier can be estimated by Laplace pressure:

∆ò = 3 5 1 ! 6 + 1 ! , 8
Eq. 53

Where ! 6 and ! , are the principal radii of curvature of the interface. In our chip, similarly to Zhou et al. 394 , the constriction is 20µm wide and 35µm high, so the radii of curvatures are 10µm and 17.5µm. 3 ~ 3mN/m is the interfacial tension between oil (Novec-7500 + 0.5% Picosurf) and water.

As illustrated on Figure 63b, a droplet is released as soon as the pressure in the injection channel overpass this barrier. This additional pressure is delivered when the valve is briefly actuated: its closure expels the valve dead volume which increases the pressure. The valve is however not necessarily dedicated to microfluidics and can have a huge dead volume compared to the desired droplet size. So an important hydraulic resistance (~ 4 Pa×s×m -3 ) must be added between the valve and the chip to avoid the channels to be flooded after valve actuation. Though this system relies on a hydraulic resistance as in Churski et al. 391 mentioned before, it does not need a particularly stiff fluidic circuit, and allows sub-nanoliter droplet generation. Their fundamental difference resides in the fact that here the valve is only used to generate a pressure pulse and not to stop the flow, which is done by the capillary pinning at the constriction.

In this work, we reproduced the system of Zhou et al., but not without difficulties. Indeed, they used mineral oil (density 840 kg/m 3 , viscosity 30 mPa×s) with no surfactant, resulting in a surface tension of 38 mN/m, which is ten times higher than what we have with fluorinated oils and surfactants. It results in a highly deformable interface and thus a more delicate pinning at the constriction. To illustrate, the barrier pressure can be calculated with Eq. 53. In the case of Zhou it is around 40 mbar while it is only 3 mbar for us. A good pinning of the interface occur only if Pi > Po but the difference Pi -Po must be below the barrier pressure to avoid spontaneous dripping. (see Figure 63a-b) We have thus in our system a working range of 3 mbar to obtain a good pinning without dripping, which requires a very precise control in pressure.

device was fabricated to control the valves through a LabView program. They are described in Appendix M.

Experiments were carried out to measure the droplet size at different conditions. The LabView program allowed us to activate the valve at prescribed times for prescribed durations. For all the experiments described in this part, short pulses were automatically applied every 2 second. The pulse duration (i.e. time on which the valve is closed) was varied between 10 to 120 ms. The program automatically released droplets and took pictures for further image analysis. Different conditions were tried out to see the influence of inlet pressures and hydraulic resistance on the droplet sizes.

The images were analyzed with a MATLAB script using the function imfindcircles after thresholding to detect the droplets outline and measure their size.

Results

We had to fix some problems prior to characterize the system. Because of the reasons explained above, we had a very small pressure range to effectively pin the interface in the constriction, and spontaneous dripping was often observed even before applying the pressure pulse. We also noticed a discrepancy in droplet size over time. A few points had to be considered:

• We noticed that Novec-7500 was less subject to unintentional dripping than FC-40. This is because of its lower viscosity, that increases the Capillary number. As Zhou et al. observed, high capillary number promotes droplet deformation and breakup, and thus facilitates dripping.

• An aqueous phase that contains magnetic particles is more difficult to keep pinned at the constriction. This is explained because of a surfactant, Pluronic F217, that is contained in the magnetic particles solution. This effect is lowered after several washing of the particles, but still remains a bit. The particles themselves might also modify the interface properties.

• We tried to use a narrower constriction of 10µm width. It seemed to improve the pinning mechanism, but also caused droplet breakup problems. When a droplet was released, it broke up into very small droplets, and producing droplets of around 1nL did not seem possible.

• We observed a droplet size decrease after long periods of time. Since all our system is controlled by pressure, and that very low pressures are involved, hydrostatic pressure in the reservoirs had a great influence on the flow rate. Over time, the reagent reservoirs are emptied while the waste reservoir fills up. Better stability was obtained when the outlet

Perspectives

This work on DoD was carried out during my first year of PhD, we wanted to reproduce the workflow of our previous magnetic-tweezers platform. Unfortunately, it turned out to be very difficult to accurately introduce magnetic particles in the system. This DoD system is by nature a lowthroughput device, and the aqueous phase in the injection channel, as well as in all the upstream fluidic circuit is almost immobile. The magnetic beads have plenty of time to sediment in the tubings, in the injection channel or in the reservoir. Also, they can aggregate in the very thin hydraulic resistances (25µm I.D.) that often clogs the circuit. The presence of an external magnet close to the chip to actuate the micro-magnetic-tweezers made those problems even worse, the particles aggregate even more and can sediment magnetically.

As a result, we never managed to have a controlled and stable concentration of magnetic particles in the generated droplets. They got generally quickly accumulated in the hydraulic resistance. For this reason, we though that it would be more convenient to reinject premade droplets that already contain the particles. They could be generated at high throughput, limiting sedimentation problems, and stored off chip before being used. We thus considered the paired reinjection technique, that seemed to be much simpler that DoD, and after a few tries, we decided to go in this direction.

The paired reinjection method is detailed in the next part of this chapter.

The DoD device presented here will most likely not be used for the micro-magnetic-tweezers, but can maybe find some other applications.

Paired reinjection

Production of droplet pairs appeared at the early times of droplet microfluidics. Zheng et al. 399 simply put two T-junctions from each side of a channel and paired droplet train is generated if both inlets have the same flow rate (Figure 65a). Another geometry was proposed by Frenz et al. to produce droplet pairs in a stable manner over a wide range of droplet size and frequency. Two nozzles were hydrodynamically coupled, meaning that the release of a droplet in the first nozzle will induce the one in the second. Their specific geometry tolerates a difference in size between the droplets (up to 1:5 ratio on 50-250pL droplets), while keeping a reliable pairing. Similar approaches were demonstrated by Barbier et al. 400 ,Phan et al. 401 ,and Hong et al. 402 .

Alternatively, it was shown that a ladder-like channel network can be used to synchronize two trains of preform droplets (Figure 65b) 403 . This particular geometry allows for the oil to circulate between the two parallel channels, until the pressure in both channels is balanced. But the droplets need to be the same size for a perfect pairing.

Thanks to fluorinated surfactants (see Chapter 1, part 1.3), emulsions can be stored for extended times (days to months) off-chip in a tube, without merging and cross-contamination, and then possibly be reinjected in a microfluidic chip for further analysis [START_REF] Clausell-Tormos | Droplet-Based Microfluidic Platforms for the Encapsulation and Screening of Mammalian Cells and Multicellular Organisms[END_REF] . To be exploitable, the droplets generally need to be reintroduced as a close-packed emulsion to allow a regular droplet delivery. This is generally done by injecting the emulsion in the microfluidic device with a syringe pump placed vertically, the droplets being lighter than the oil, they are introduced first, and as a packed emulsion. The reinjected droplets can be then spaced with an oil cross-flow and synchronized with another droplet train to form droplet pairs [START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF] . Lee et al. [START_REF] Lee | Synchronized reinjection and coalescence of droplets in microfluidics[END_REF] (Figure 65c) demonstrated a synchronous reinjection of two emulsions with a single oil inlet. As shown on Figure 65c, two T-junctions, from which droplets are reinjected, are facing each other. The pressure driving both droplet reinjection have to be equal, and finely adjusted, to obtain a perfectly paired reinjection. This was achieved by monitoring the height of the emulsion reservoirs, allowing a fine adjustment of hydrostatic pressure. According to the authors, the synchronization also results from a complex interplay between the droplets and the cross oil flow, leading to a coupling between the nozzles. A high synchronization error-rate, no less than 10%, was however obtained. Dressler et al. 404 proposed another approach to reduce the synchronization error-rate (Figure 65d). It is known that a close packed 2D

emulsion exhibit an hexagonal auto-arrangement when confined (as in Figure 65c-d), to minimize the surface of contact between the droplets. As shown on Figure 65d, this phenomenon was exploited to allow a highly reliable paired rearrangement of the droplets. It demonstrated a good robustness against input frequency changes, and an error rate less than 0.2% could be achieved at a rate of 33 Hz. A better synchronization efficiency was obtained when both emulsions have the same droplet size.

We reproduced the design of Dressler et al. (Figure 65d) to reinject alternatively droplets with and without magnetic particles (same dimensions were used). For droplet generation and reinjection, methods are similar than exposed in Chapter 3, Part 3.1. The reinjection was done with the reservoirs made from pipette cones, pressurized from 40 to 140 mbar by an MFCS Fluigent (Figure 66a).

A satisfactory reinjection could be obtained when both reservoirs were set at the same pressure, but it was never perfect. The two emulsions always have slight differences in droplet size, surface tension (if particles are inside), or packing, and a fine adjustment of pressure is always needed to equalize the droplet flow rate. The central region (Figure 66b, Video 6.2), where the droplets rearrange in an organized way, provided a good visual control for pairing, the pressure of one emulsion could be easily readjusted if droplets were in the wrong line. After droplet pairing, they can be spaced with a cross oil stream (Figure 66c, Video 6.3). The error-rate was experimentally quantified. The pressure was changed from 40 to 140mbar, and we took movies of 25 to 40 seconds to count the number of pairing errors. Before taking picture, the pressure was adjusted (±0-10mbar) thanks to our pressure controller (that has a precision below 0.5mbar) to obtain visually a good pairing as on Figure 66b. Table 6 shows the obtained results. For each movie, the error-rate remains quite low, 1.72% in average (1.35% standard deviation). We should however note that there is no particular dependency between the error rate and the applied pressure, which could have been better adjusted for movies with an error rate over 2%. (40-140mbar), we took movies and counted the number of pairing errors. Each row correspond to one movie. Note that for each row, the pressure of one of the inlet was finely adjusted (±0-10mbar) to achieve a good pairing, but could have been even better adjusted for some movies.

Electrocoalescence

At the beginning of my PhD project, we planned to redisperse the cluster of particles in a passive way, directly in the tweezers region as we were used to do with our previous magnetic-tweezers platform. This approach however brought two major constraints: i. Standard microfluidics PFPEbased fluorosurfactants cannot be used because they prevents the droplets to merge, and thus the cluster to be reintroduced. ii. The magnetic field needs to be turned off after cluster redispersion, otherwise the cluster is extracted again.

After a few tests with Krytox 157 FSH as a surfactant (which does not prevent from merging) and a Thorlabs programmable moving stage to pull away the external magnet after redispersion, we realized that a cluster that has roughly the size of the channel can be pushed by the following droplet (Figure 67a-b). We decided to use this phenomenon to release the magnetic cluster and thus to relocate the merging in a subsequent electrocoalescence step (Figure 67c-d). This approach would allow us to use standard and biocompatible fluorosurfactants, and to prevent us from using a moving stage that has to be synchronized with the droplets, and for these reasons, would allow higher throughput.

Electrocoalescence in droplet microfluidics is now a well-established technology. One of the first work demonstrating electricity actuated coalescence in a channel was conducted in 2005 in our group by Chabert et al. [START_REF] Chabert | Droplet fusion by alternating current (AC) field electrocoalescence in microchannels[END_REF] . An AC electric field was produced by electrodes placed around a PTFE tubing filled by fluorinated oil that contains confined droplets. The electrodes are not in direct contact with the liquids, preventing cross contamination. Electrocoalescence occurs when high conductivity droplets, stabilized by surfactants, are immersed in a low conductivity carrier oil. The AC field then creates dipolar forces that destabilizes interfaces, and ultimately leads to coalescence of droplets.

This approach was integrated in a chip by using physical vapor deposition (PVD) to pattern ITO 405 or gold 406 electrodes on the glass slide. Simultaneously, microsolidics [START_REF] Siegel | Microsolidics: Fabrication of three-dimensional metallic microstructures in poly(dimethylsiloxane)[END_REF] was developed as a method to rapidly produce electrodes by introducing molten solder in a channel, without the need of complex microfabrication steps like PVD or lift-off. Since then, the method has been extensively used for electro-coalescence [START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF][START_REF] Mazutis | Droplet-Based Microfluidic Systems for High-Throughput Single DNA Molecule Isothermal Amplification and Analysis[END_REF][START_REF] Frenz | Droplet-based microreactors for the synthesis of magnetic iron oxide nanoparticles[END_REF] and became the gold standard. An alternative to microsolidics is to fill electrode channels with salt water instead of liquid metal, avoiding the use of expansive indiumbased solder 407 . Salt water electrodes are however subject to evaporation, and can be more difficult to manipulate.

We decided to use the "microsolidics" approach to produce our electrodes. This technique is well documented, and a detailed protocol was published in Nature Protocols by Mazutis et al. [START_REF] Mazutis | Single-cell analysis and sorting using droplet-based microfluidics[END_REF] . Briefly, a glass-PDMS chip is fabricated following the standard soft lithography protocol. The channels that are meant to become electrodes can be treated with 3-mercaptopropyltrimethoxysilane diluted at 0.1M in acetonitrile to promote liquid metal wetting. This step however does not seem to be mandatory as it is mentioned only in the original microsolidics publication [START_REF] Siegel | Microsolidics: Fabrication of three-dimensional metallic microstructures in poly(dimethylsiloxane)[END_REF] . The chip is placed on a hotplate at 90°C, after which the low temperature melting solder (51In, 32.5Bi, 16.5Sn, Indium

Corporation) is carefully pushed, it immediately melts and fills the channel. When the channel is fully filled by solder, metal pins are introduced in the holes, and electrical conductivity is checked with a multimeter. The electrodes solidifies quickly when the chip is cooled down. We decided to use a similar approach except that we implementd another micro-soft-magnet at the sorting junction, in order to increase the local magnetic force and have a faster and more controllable sorting. This second micro-magnet was be fabricated using the same electroplating workflow simultaneously with the micro-magnetic-tweezers, and no additional microfabrication step was needed.

Figure 69 shows droplet being sorted in our system, and Video 6.4 shows the same scene in motion.

We fabricated a square micro magnet to attract the magnetic particles toward the corners, as the red arrows show on Figure 69. As expected, the particles present in the droplets aggregate and are attracted by the magnet. The magnetic force is however not strong enough to break the droplet, resulting in a simple deflection of the droplet toward the secondary channel. We didn't characterize yet this system and we didn't try different configurations to push it to its limits. However, it seemed to work perfectly in all the flow rate range we usually work in (0-30 droplets/s). With the geometry shown on Figure 69, we didn't observe any sorting error at inlet pressure from 40 to 200mbar, and we generally work below 100mbar. This way, we were able to efficiently sort up to

Chapter conclusion

In this chapter, we developed and characterized different microfluidic modules to be used for a further integration of the micro-magnetic-tweezers in a complete microfluidic workflow.

A droplet on demand system was first developed. Inspired by Zhou et al. 394 , it allows us to generate droplets from 0.5 to 2 nL with a good accuracy. It enables the generation of complex droplet trains.

This system however was hardy applicable to the micro-magnetic-tweezers, indeed, introducing magnetic particles in such a system is difficult because of undesired particles sedimentation, magnetophoresis and aggregation.

For this reason, we decided not to use the DoD approach, and a paired reinjection was preferred.

Here, we initially produce droplets at high throughput using a standard flow-focusing device, and we store them off-chip. Such emulsions are stabilized by fluorosurfactants and can remain stable for days to months. We then reinject them in a chip as a close-packed emulsion. Packed emulsions have great auto-arrangement properties, facilitating their organized reinjection. Inspired by Dressler et al. 404 , we used this property to reinject two emulsions in a paired manner. The first emulsion contains the magnetic particles to extract, while the second one is meant to receive the particles.

Then an electrocoalescence module was added to merge the extracted cluster with another droplet free of particles. Such electrocoalescence of droplets in microfluidics is well described, and we successfully used the gold standard method that uses electrodes fabricated from molten solder, according to the "microsolidics" fabrication method.

At the outlet of the chip, a magnetic sorting module was implemented to separate droplets with magnetic particles from the ones without. We added another micro-magnet, fabricated at the same time than the micro-magnetic-tweezers, to attract the droplets that contains particles into a secondary channel, while the empty droplets will continue their way in the main channel. We were able to magnetically sort droplets at frequencies from 1 to 30Hz with no error, which is better than what was done in the literature.

Although every module seems to be working well, we never manages so far to perform all of them simultaneously in the same chip. The optimization process of each one of these modules is long, changing a simple geometrical parameter requires to print a new lithography mask, to fabricate a new mold, and a new electroplating. We still need to modify some geometrical parameters (and particularly for the electrocoalescence module as mentioned previously) to have a stable and reliable chip that would work at our desired throughput and droplet size. There is a priori no particular technological obstacle, and we think that the system would be able to work properly in a few more months.

CHAPTER 7

Magnetic-hydrogel-beads: a new class of solid support for bioseparation in droplet microfluidics

This part reports the results of two consecutive 4 months internships, carried out by Elina Gilbert and Grégoire Lemahieu, who I had the chance to supervise during my last year of PhD.

Hydrogels consist of a network of polymer chains that are cross linked together. They differ from other polymers by the high hydrophilicity of their chains, which allows for water to penetrate into the network, making them highly absorbent materials that can contain up to 99% of water when swollen. They are fabricated by cross linking solubilized polymer chains, which can be achieved by radical polymerization, triggered by a photo or thermal initiator. They offer unique properties such as transparency, high elasticity, controlled porosity, and can easily be grafted with various functional chemical groups.

With polymers such as collagen, agarose, or fibrin, they have become used to fabricate bioinspired materials, but one of their main field of application resides in analytical biochemistry where they are used to perform gel electrophoresis, in which macromolecules migrate within an agarose or polyacrylamide network. Hydrogels are also encountered in the food industry (gelatin) and are the material constituting contact lenses (silicone hydrogels) 409 .

Micrometric hydrogel beads (HBs), sometimes referred to as "microgels" become increasingly used for bioanalytical applications 410 . By grafting an appropriate chemical function on the polymer chains, they can be used to trap biomolecules much more effectively than hard polymer beads, because their high porosity greatly increases the surface of interaction between the liquid and the polymer.

Such HBs have been encapsulated in droplets to conduct single-cell transcriptomics studies. Notably in the well-known inDrop protocol [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] , where HBs are co-encapsulated with cells and serve as a DNA barcode carrier to index cell content prior to sequencing. Such HBs were also used to directly capture single-cell compounds in the polymer network 101 . Besides the functionalization aspect, their remarkable deformability enables their close-packed reinjection in a microfluidic device, allowing deterministic HB delivery [START_REF] Abate | Beating Poisson encapsulation statistics using close-packed ordering[END_REF] .

We aim at developing a new class of HBs allowing their magnetic manipulation. These magnetic hydrogel beads (MHBs) are meant to be magnetically extracted from droplets passing through the micro-magnetic-tweezers. By replacing the commercial magnetic particles in the droplets by a single MHB, we would be able to get rid of the limitations described in Chapter 3 and 4, where a magnetophoretic time was needed for the particles to form a compact cluster, before being extracted. Besides increasing significantly the throughput of our system, this approach would also highly facilitate single-cell indexing, as barcoding of HBs is an already well-established technique.

In addition, the porous nature of the mesh allows us to keep a high surface/volume ratio to maximize the interaction between the liquid and the solid phase.

In this chapter, we will first provide a short review of the main applications of hydrogel beads in microfluidics. Then we will review the different methods for MHBs production, as well as their applications. In the following part, we will present the protocols that we developed to produce MHBs. Finally, preliminary results and perspectives will be provided.

1 Hydrogel beads (HBs) in microfluidics

HBs production

Traditional techniques to produce polymer micrometer-scale particles were based on nucleation, complexation or emulsification. They were mostly suited to particles below 1µm, and generating particles of diameter over 50µm often required complex multistep methods 411 .

Droplet microfluidics provided a robust and versatile method to produce HBs. The idea is to produce monodisperse droplets made of a prepolymer in a flow-focusing or T-junction microfluidic device, and to induce their cross-linking. A first pioneering work using this idea was proposed by Nisisako et al. 411 , three years after the first introduction of droplet microfluidics by Thorsen et al. 38 They were able to produce acrylic beads of 30-190µm by cross linking droplets of hexanediol diacrylate in a polyvinyl alcohol aqueous carrier phase 411 . They could successfully obtain beads by both thermal and photo polymerization.

In the following years, different authors used the same approach to produce HB with various polymers including poly-n-isopropylacrylamide (polyNIPAM) 412,413 , dextran-hydroxyethyl-methacrylate (DEX-Hema) 414 . Among the most commonly used polymers today, there are polyacrylamide [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] , polyethylene glycol diacrylate (PEGDA) 415 , alginate 416 and agarose 417 .

The group of P.S. Doyle developed an on-chip technique to produce HBs. As shown on Figure 70a, they use a UV lamp mounted on a microscope to allow fast photopolymerization of PEGDA 418 or Norland Optical Adhesive (NOA) particles 419 . Curing occurs rapidly in the channels, in a way that the droplets keeps their confined shape, enabling non-spherical beads production (Figure 70a).

The same team then developed a technique called "stop-flow lithography" where a photomask is used in between the UV light and the objective to perform curing only in a specified region 420 . In this monophasic condition, where the channel is entirely filled by PEGDA, oxygen diffusion through PDMS walls inhibit cross-linking at the walls, thus keeping a lubrication film between the particle and the channel, allowing for the particles not be remain stuck in the channel. They were able to fabricate PEGDA beads of arbitrary shape such as triangles or squares, but more importantly, they could produce graphical barcodes on particle [421][422][423] (Figure 70b). If the particles are made in a laminar cross-flow, it is possible to create hydrogel particles with stripes of different functionalization (Figure 70c). These particles show great promise for biosensing applications, which are described below.

HBs for biosensing

Aliberti et al. provided a comprehensive review of the biosensing applications of HBs 410 . They put forward that hydrogel most attractive characteristics relies on their flexibility synthetic approach to design multifunctional particles, with encoding and sensing capabilities. They can target pollutants, biomarkers, or any other relevant molecule. According to the authors, many parameters have to be considered for a good capture efficiency. It can be hindered by a difficult diffusion because a small pore size, in contrast, a swollen gel can shrink when changing environmental conditions (pH, temperature) to trap big molecules. The capture can also be done on specific probes such as antibodies or oligo-dT that are cross-linked on the mesh, a proper diffusion has to be ensured, and a sufficient probe density is required. We will provide here a short and non-exhaustive review of HBs in a biosensing context, but a more comprehensive review can be found in Aliberti et al. in diameter as a scaffold for cells to grow (Figure 70d). The beads are mixed with cells and poured in a mold, after which the beads can be covalently linked together thanks to an enzymatic reaction.

Another approach is to encapsulate single-cells in HBs before using them as building blocks 102 .

Single-cell encapsulation in alginate has been demonstrated for the first time in 2007 by Tan et al. 100 It has been done similarly in other physiologically relevant hydrogels including collagen-gelatin 431 , fibrin 432 and matrigel 433 . Kampermann et al. [START_REF] Kamperman | Single Cell Microgel Based Modular Bioinks for Uncoupled Cellular Microand Macroenvironments[END_REF] encapsulated single-cells in PEGDA beads with a

Poisson distribution before being FACS sorted. The recovered beads contain a single-cell, and were used as bio-ink to construct 3D tissues. Mao et al. 434 obtained single-cell HBs without the need for FACS sorting by fixing the cross-linker precursor on cells, so that only cell-containing droplets will polymerize.

Polymerizing cell in the presence of cells can however be challenging because of the eventual cytotoxicity of precursors, or the need for heating or UV curing that can damage the cells. Henke et al. 435 developed an enzymatic crosslinking of dextran-tyramine microgels that showed better cell survival-rate than PEGDA or alginate.

Besides 3D cell culture, HBs can be of great interest for medicine as they can be injected in vivo 436 .

Injectable cell-containing HBs can be used for tissue regeneration 107 . Singly encapsulated marrow stromal cells were successfully injected into mice 435 .

HBs for single-cell omics

Hydrogel beads are widely used for droplet microfluidics based single-cell omics. The first singlecell omics study relying on HBs was carried out by Novak et al. 101 in 2011, who co-encapsulated cells with primer-functionalized beads in agarose droplets. The advantage of such HBs is that the genome of individual cells, imprisoned in the HBs mesh, could be manipulated in bulk without mixing the genetic content of the different cells. They performed PCR on the gels in a way that the amplification product binds on the primer-functionalized beads. The beads are then analyzed by fluorescence with FACS to detect several genes. Similar studies were conducted the following year where DNA 178 or mRNA 437 were amplified in liquid state, after which the droplets were polymerized and analyzed through flow cytometry.

Biomolecules from single-cells can also be detected directly on the HBs without the need for flow Abate et al. [START_REF] Abate | Beating Poisson encapsulation statistics using close-packed ordering[END_REF] showed that a close-packed HB solution can be reinjected in a chip, allowing a periodic delivery of HBs, that can be synchronized with droplet generation to obtain a sub-Poisson encapsulation in droplet (which is often called mistakenly super-Poisson encapsulation). Such deterministic reinjection is one of the main features of the inDrop 3 protocol, in which HBs carrying barcoded primers are co-encapsulated with cells in droplets (see Chapter 1, Part 3.3). The primers can be released from the gel in the droplet and bind with the lysed cell mRNA, resulting in the barcoding (or indexing) of the cell mRNA. A similar platform commercialized by 10X Genomics (Chromium) is also available, which has recently been improved to reinject both barcoded primers and cells in two HB streams, reducing even more the probability of an empty droplet 181 .

More recently, Lan et al. introduced SiC-seq 180 , which was the first droplet-based whole genome sequencing platform. Here, each cell is labeled with a unique DNA barcode by merging single-cells lysis encapsulated in agarose beads with droplets containing barcodes. The advantage of using agarose beads is that they allow for small molecule to diffuse, but not for DNA which remains trapped in the mesh, allowing for different batch processing such as detergent washing or protease treatment.

Inspired by inDrop [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF] and SiC-seq 180 , Li et al. 424 developed recently polyacrylamide beads containing customized 5'-Acrydite modified oligonucleotides which are covalently bound to the mesh. As in inDrop, the acrydite-modified primers are used for barcoding, but they are also used to capture the content of encapsulated cells as in SiC-seq. However, unlike in SiC-seq where agarose beads were used to mechanically trap DNA, polyacrylamide allows for diffusion, and the capture is done by specific hybridization on the primers. They demonstrated capture and barcoding of DNA or RNA from single-cell, but this method could be extended to other analytes or to multi-omics.

Wang et al. 440 recently presented a method to easily dissolve polyacrylamide hydrogel beads in droplets, offering more efficient primer release. They replaced the usual bisacrylamide cross-linker by a bis(acryloyl)cystamine, that has disulfite bridges, and can therefore easily be cleaved by the addition of dithiothreitol (DTT). Gels could be dissolved in less than 3 minutes, and did not influence RT nor PCR reaction.

2 Magnetic hydrogel beads (MHBs)

Magnetic hydrogels

There is a very rich literature on hydrogels incorporating magnetic nanoparticles (MNPs). These materials, often referred to as 'ferrogels' bring together the unique properties of hydrogels and ferrofluids. Introducing MNPs (e.g. magnetite Fe3O4, maghemite g-Fe2O3, cobalt ferrite CoFe2O4) in hydrogels allows their quick mechanical response to an external magnetic field, enhancing their controllability.

In a comprehensive review, Li et al. 441 listed the main applications of magnetic hydrogels, they include:

• Tissue engineering, where they are used as scaffolds for cells to evolve. They can be magnetically actuated to produce stimuli. It was also shown that MNPs present in the scaffold promotes cell adhesion 442 .

• Cell/drug delivery, where magnetic hydrogels can be remotely controlled to enable targeted drug delivery. They can release a drug on-demand by applying an alternative magnetic field, causing rapid swelling and deswelling, that enhance delivery of HB content.

• Hyperthermia cancer therapy where MNPs introduced in the body and heated remotely with a strong alternative magnetic field. This localized temperature increase is used to treat tumor tissues. MNP-containing hydrogels can be used to better control the particle distribution, and can be combined with heat-induced drug delivery.

• Soft actuators can also be fabricated by using a magnetic hydrogel able to controllably deform under a magnetic field.

Li et al. 441 also distinguished three different approaches to integrate the MNP into the hydrogel mesh, and give several references for each one of them:

• The blending method (Figure 71a) consist in mixing together the gel precursor with MNPs that were made separately. This method is easy since both gel and MNPs preparation can be optimized separately, and the quantity of MNPs in the gel is easily controlled. It is however challenging because the particles can diffuse out of the gel. Particle size, pore size and aggregation of MNPs are then critical parameters.

• The in situ preparation method (Figure 71b). In this method, the MNPs are synthetized by co-precipitation directly with the polymerized gel. The gel is first swollen with a solution of Fe 2+ and Fe 3+ ions, after which an alkali precipitating agent (NaOH, HN3×H2O) is added, resulting in immediate precipitation Fe3O4 NPs. This method is simple and low cost, and does not require to modify a preexisting hydrogel fabrication protocol. It however requires that the gel and its content are resistant to the strong alkali solution, limiting its biological applications. In addition, the yield of MNPs can be limited to gels that have a negatively charged ligand that can react with iron cations. As in the blending method, the question of particles diffusion has to be assessed.

• The grafting-onto method (Figure 71c) uses the MNPs as a crosslinker, enabling a covalent bonding of the particles into the mesh. They prevent any MNPs escape from the gel and provide very stable properties. They require however a more complex fabrication process, involving several steps of surface functionalization to graft the crosslinker onto the MNPs.

As an example, Messing et al. 443 They provide a detailed protocol to produce their highly concentrated magnetite ferrofluid. On Figure 72b are shown their alginate-magnetite MHBs, they effectively align under a magnetic field.

Janus MHBs

By means of a rapid polymerization of droplets made from a co-flow of two alginate solution, with one containing ferrofluid, Zhao et al. 451 were able to produce janus MHBs. Janus alginate droplets are produced at a flow-focusing junction with two inlets, they are then merged with CaCl2 droplets to induce their fast gelation before homogenization of the ferrofluid within the Janus droplets. According to the authors, such Janus particles have biochemical application potential, where the magnetic hemisphere is used for HB manipulation while the other hemisphere is used as a carrier of cells or biochemical substances. Similar Janus MHBs were produced by sedimentation of MNPs in the prepolymer droplets before gelation 452 .

In situ precipitation

In situ precipitation of MNPs in HBs was demonstrated before the emergence of droplet microfluidics. Kawaguchi et al. 453 prepared HBs by precipitation polymerization of acrylamide, methylenebisacrylamide and methacrylic acid. The HBs were then swollen with an aqueous solution of FeCl2 and FeCl3. After a few hours of incubation, the particles are immersed in an alkali solution to precipitate magnetite (Fe3O4) NMPs in the gel following the reaction:

Fe ,± + 2Fe l± + 8OH O → Fe 3 O 4 (s) + 4H 2 O
Eq. 55

Figure 72c shows a thin section of a HB containing magnetite MNPs. They measured a magnetization at saturation of 50 emu/g for the MNPs and 10 emu/g for the composite MHBs.

In a recent study, Seyfoori et al. 456 produced poly(NIPAM)-co-acylic acid HBs by a two-step emulsification stirring method in which they precipitated magnetite MNPs as described above. MHBs were then functionalized with anti-EpCAM protein to capture circulating tumor cells.

Core shell

Another fabrication approach is surprisingly not described in the review of Li et al. 441 , and consists in polymerizing the hydrogel around a magnetic core. Luo et al. 454 prepared MNPs nanoclusters of controlled sizes between 90 and 260 nm (Figure 72d,i). The nanoclusters were then treated with tetraethyl orthosilicate (TEOS) to coat them with a silica shell, a second treatment with a methacrylate-functionalized silane was performed to promote subsequent poly(NIPAM) precipitation polymerization. Figure 72d,ii,iii shows such multifunctional MHBs. The MNPs nanoclusters and the composite MHBs had a saturation magnetization value of 75.8 and 41.6 emu/g respectively.

Another smart approach to produce core-shell MHBs was proposed by Chen et al. 455 in 2009. As shown on Figure 72e, they prepared a double-emulsion of an oil-based ferrofluid in hydrogel precursor in fluorinated oil. The inner magnetic phase was composed of styrene, divinylbenzene and EFH1 ferrofluid (Ferrotec), the outer hydrogel phase was composed of acrylamide and methylenebisacrylamide. UV photopolymerization was performed thanks to a photo-initiator present in both phases. The core phase being opaque, a thermo-initiator had to be added to complete the cross-linking of styrene and divinylbenzene at the center of the beads. A particular difficulty was to make the channels hydrophobic everywhere except where the hydrogel solution is flowing to allow ferrofluid droplet formation. This was done by a sol-gel reaction on the channels surface induced by localized UV-light to coat specific regions with a fluorinated silane.

e jgk = $ [ ï [ D '¨T[ ∇Q Eq. 58
Where $ [ (kg/m 3 ) is the density of MNPs, and D '¨ (m 3 ) is the HB volume.

Saturation magnetization of magnetite MNPs from 60 to 100emu/g has been reported, with a typical value around 92emu/g for commercial ferrofluids 450,457,458 , we took this value for the following calculation. The density of magnetite 459 is 5200kg/m 3 . If we take the same value of magnetic gradient ∇Q = 5 × 10 l T/m than in Chapter 3 (Part 2.4), the same surface tension 3 = 3mN/m, a channel size of R = 35µm, & = 30µm, and a HB of diameter 30µm (D '¨= 14.1pL), we can estimate the required MNP quantity in terms of total mass or volume fraction as follows:

ó = 23(R + &) T `∇Q ~ 0.85 ng Eq. 59 ï [ = 23(R + &) $ [ D '¨T`∇ Q ~ 1.15% Eq. 60
Hence, a MNP quantity as small as 0.85ng per HB would be sufficient to allow its extraction from the droplet, and this quantity would occupy only 1.15% of the HB volume. Note that we assumed here that the MNPs were made of pure magnetite, but eventual maghemite or hematite can modify the values for density and saturation magnetization.

Production of MHBs

In this project, we aim as using MHBs for single-cell analysis in droplet microfluidics. For this reason, we decided to base our initial protocol on inDrop 3 , which is standardized and well documented. Amandine Trouchet, who works at the single-cell platform of Institut Curie could train us on the polyacrylamide HBs synthesis.

Unlike in inDrop, we aim at extracting the HB out of the droplet. As the HB is porous and filled by liquid, such extraction will inevitably result in sample loss. We need for this reason to minimize the volume occupied by the HB compared to the total droplet volume. Working with AE60µm HBs in 1nL droplets, as in inDrop, would result in a loss of sample of around 11%. For this reason, we decided to scale our HBs down to AE50µm or AE40µm, to reduce the sample loss to 6.5% and 3.3% respectively. As it will be shown in this part, we could change the HBs size by using another flowfocusing chip, and downscaling them to ~AE40µm worked well without having to change anything else in the protocol.

Polyacrylamide HBs production

Prior to fabricate MHBs, we reproduced the protocol of inDrop 3 to synthesize polyacrylamide HBs.

Zilionis et al. [START_REF] Zilionis | Single-cell barcoding and sequencing using droplet microfluidics[END_REF] published a more detailed version of the protocol in Nature Protocols, on which we based our protocol. Briefly, aqueous droplets of diameter 40-60µm containing acrylamide monomers, the cross-linker methylenebisacrylamide (Bis) and ammonium persulfate (APS) were generated in a flow-focusing microfluidic chip. The exact composition of the aqueous droplet phase is given in Table 7. The carrier oil was Novec-7500 with 1% w/v FluoSurf (Emulseo) fluorosurfactant and 0.4% v/v TEMED. Cross-linking is initiated by the presence of both APS and TEMED, so that it is triggered only after the droplets are formed. The polymerization reaction of acrylamide is represented on Figure 74a.

The droplets were collected in Eppendorf tubes containing Novec-7500 with FluoSurf 1% w/v to prevent their coalescence, an upper layer of light mineral oil was added to the tubes to prevent evaporation, after which the tubes were incubated overnight at 65°C for the polyacrylamide gelation to occur.

Reagent Volume for 1mL

Water 620µL

TBSET buffer (Tris Buffered Saline EDTA Triton)

• 10mM Tris-HCl (pH 8.0)

• 137mM NaCl • 2.7mM KCl • 10mM EDTA • 0.1% v/v Triton-X100 100µL
4

´ AB solution For 1mL Several washing steps were needed to transfer the HBs from their oil phase to an aqueous phase.

After having discarded the top mineral oil layer, perfluorooctan-1-ol at 20% in Novec-7500 was added to the tubes to break the emulsion, and TBSET buffer (see composition in Table 7) was also added to resuspend the HBs. After vigorous vortexing and centrifugation, the HBs were located in the top aqueous layer. The bottom oil layer was discarded and this step had to be reproduced at least 4 times to completely remove the oil and surfactants present around HBs. A second round of layer was discarded and sodium citrate 0.5M was added to make the particles stable in water. After vigorous mixing and centrifugation, the particles can be magnetically isolated and collected in small tubes. Note that we did not characterize the obtained ferrofluid at this stage of development.

At first, the blending method was tried out because it appeared to us to be the most natural way to proceed. The ferrofluid was mixed with the aqueous droplet phase (Table 7) to be introduced in the microfluidic chip. Unfortunately, we observed a spontaneous gelation of the solution after the addition of ferrofluid, preventing us from making droplets, while it worked well without ferrofluid. It can be hypothesized that the presence of citrate or any other interfering molecules in the solution could affect the polymerization.

We then decided to explore the in situ precipitation method on already polymerized gels as shown on Figure 74b. We based our protocol on Kawaguchi et al. 453 , the gels were swollen with an iron II and III solution (same concentrations than above: 64g/L FeCl2, 151g/L FeCl3) and were left to incubate overnight for the solution diffuse and homogenize in the mesh. They were then treated with ammonia to precipitate the iron in situ into magnetite. Kawaguchi and colleagues also added dextran (100g/L) to minimize the formation of iron oxide in the aqueous phase outside of the gel. This method showed promising results immediately after the first try, as we could see some magnetically responsive HBs, so we decided to try to optimize it.

The use of dextran was rapidly abandoned in favor of successive rinsing and centrifugation to get rid of the precipitate outside of the beads. Indeed, big aggregates seemed to appear around the beads in the presence of dextran as shown of Figure 75a. After magnetite precipitation, the gels were magnetically isolated and the supernatant was discarded, this step was repeated until the supernatant was colorless. Finally, 500µL of sodium citrate 0.5M was added to the tube to avoid attractive forces between the MNPs. The obtained MHBs appeared to be clear under microscope (Figure 75b) but they macroscopically showed a brownish tone, and were magnetically responsive (Figure 75c). However, we can notice on Figure 75b that some iron oxide clusters appear as black spots around the MHBs and are difficult to get rid of, we think that they have similar mass and magnetization compared to MHBs and that neither centrifugation nor magnetic decantation can exclude them. Nevertheless, these results suggest an effective but low MNPs loading, that would be sufficient to magnetically manipulate the beads, but maybe not to extract a single MHBs from a subnanoliter droplet. These experiments were preliminary test of feasibility, but we need to perform further characterization of the MHBs obtained with this method.

We thus tried to extract clusters of MHBs in the macroscopic magnetic-tweezers. As shown on Figure 75d, we were able to deflect the droplet interface, leading to extraction of the cluster of MHBs. We couldn't try at this stage to extract them with the micro-magnetic-tweezers (see Chapter

3) because we did not have already the chips for HBs reinjection and encapsulation, and that the gels were not clean enough at this stage to be reinjected in a microfluidic chip.

Blending method with commercial ferrofluid (Grégoire

Lemahieu)

A second internship was carried out on this subject by Grégoire Lemahieu from April to August 2020. In this internship, we decided to focus more on the blending method (Figure 71a) that was quickly abandoned before. This decision was motivated by two main factors: i. the in situ precipitation method seemed to have some limitations in terms of MNPs loading, and ii. we received in April some ferrofluids by Ferrotec that have good magnetic properties, MNPs monodispersity and stability in water, and we wanted to try the blending method with them.

Three different water-based ferrofluids of which physical properties are given in Table 8 were tried out, they differ mainly by the nature of their surfactants. Like with our homemade ferrofluid described in the previous part, we faced the problem of spontaneous gelation when the ferrofluid was directly added in the gel precursor. We realized that it occurred only in the presence of both ferrofluid and APS. To tackle this, we decided to remove APS from the initial mix, and we introduced it in the microfluidic chip just before the flow-focusing junction, as shown in Figure 76. Experimental details are given in Appendix N1. Droplet generation worked properly for EMG 700SP and PBG 600 while for EMG 601P, the formation of a precipitate was observed when the ferrofluid entered in contact with APS. This precipitate eventually clogged the chip. The physical properties of each ferrofluid can be found in Table 8.

In these optimized conditions, we were able to generate properly the emulsions without early gelation with the anionic EMG 700SP (Figure 76a), and with the non-ionic PBG 600 (Figure 76c) ferrofluids. However, with the cationic ferrofluid EMG 601P, what resembles to a dark precipitate, or MNPs aggregates, appeared at the junction between the ferrofluid gel precursor and the APS solution (Figure 76b), and could eventually clog the chip. It might be due to APS complexation on the cationic nanoparticles. The droplets were collected, baked and washed as in part 4.1 of the current chapter. Unexpectedly, the droplets containing the cationic ferrofluid EMG 601P did not seem to polymerize, and no HBs were collected at all. In contrast, the anionic and non-ionic ferrofluid did not interfere with the gelation reaction, and we obtained HBs that obviously contained MNPs, as shown on Figure 77.

Several observations must be noted:

• No hydrogel debris nor iron oxide aggregates are visible around the MHBs.

• The swelling ratio was reduced from ~40% to ~20% when ferrofluid was present in the prepolymer solution.

• For both EMG 700SP and PBG 600, several additional washing with TBSET were required for the supernatant to appear clear, suggesting that some MNPs were able to escape the gel matrix. Further studies must be conducted to assess if the MNPs remain well in the HBs for extended times.

• The MNPs appear as black dots in the gel. Considering their small size of around 10nm, they should appear as a homogeneous grey medium with our 10X objective. This might suggest that they form small aggregates that are visible under microscope, that would explain why the MNPs remain trapped in the mesh and do not seem to diffuse a lot out of the beads.

• MHBs containing non-ionic ferrofluid were difficult to manipulate because of the absence of repulsive interaction between the beads. They sometimes stick together, are displaced as a whole, and are difficult to pipette or to reinject. In contrast, anionic ferrofluid-containing MHBs are more convenient to handle as they don't form aggregates.

For these reasons, the most promising MHBs were obviously the ones containing the anionic EMG 700SP ferrofluid (Figure 77a). Moreover, anionic functions are more interesting in a biomolecular context as they will avoid non-specific adsorption of nucleic acids. They are the ones we decided to optimize in the future.

MHB encapsulation and extraction

Encapsulation

Once synthesized, washed and filtered through a cell strainer (70µm), the MHBs could be reinjected into a microfluidic chip for their encapsulation. To reinject the HBs in a close-packed manner, we proceeded as in Zilionis et al. [START_REF] Zilionis | Single-cell barcoding and sequencing using droplet microfluidics[END_REF] . The beads were first packed in Eppendorf tubes by centrifugation, then a PTFE tubing (I.D. 0.3mm) was dipped into the gels that were aspirated by a syringe placed at the other end of the tubing. The tubing filled with HBs was cut and connected to a 50µL glass syringe filled by Novec-7500.

The main difficulty for encapsulation of HBs is to ensure a proper close-packed reinjection. This close-packed reinjection is of absolute necessity to achieve stable and continuous gel release and monodisperse droplet formation. Figure 78 shows the reinjection process of MHBs. Noticeably, MHBs seemed to be more difficult to get close-packed with high MNPs loading. This might be due to a lower HBs deformability due to MNPs 445 , making them more difficult to get packed.

Figure 78a and Figure 78b show the gels being reinjected in the chip, that were loaded respectively with 1.85% and 0.46% of MNPs (v/v). The MNPs loading was controlled by diluting the right amount of ferrofluid EMG 700SP (that has 5.8% v/v of MNPs, see Table 8) in the gel precursor. In both cases, the beads were centrifuged for 1 minutes at 5,000g, the supernatant was carefully aspirated, prior to being loaded in the tubing. Even if it is not obvious on a single picture, we could clearly observe that the gels were more packed with low MNPs loading, and that the flow of beads was smoother. In contrast, high MNPs-loaded MHBs exhibited a less packed state, and a more erratic, pulsatile reinjection. This behavior might be explained by several factors such as, electrostatic repulsion between gel beads, increased friction between beads due to the presence MNPs, but also by an increased stiffness of the gels due to MNPs.

We were able to improve gel packing by applying stronger centrifugation before gel loading. Same conditions that in (a) but with 0.46% v/v loading (4 times less). Packing was better and the beads flow was smoother. Note that a dust is present on the top right corner of the picture but didn't interfere to the MHBs reinjection. c. MHBs encapsulation. The MHBs contained 1.85% v/v of MNPs and were packed by 1min centrifugation at 5,000rpm. We see important gaps between the MHBs (red arrow) that lead to instabilities, double gel encapsulation and polydisperse droplet sizes. d. After 1min centrifugation at 9,000rpm, the gaps were reduced and the encapsulation was more stable. For (c) and (d), the flow rates were 400µL/h for carrier oil (Novec-7500 + 1% w/t FluoSurf), 500µL/h for water (PBS) and 20µL/h for MHBs, leading to a 100Hz production of ~1.4nL droplets.

With a microfluidic device very similar to the one used by inDrop [START_REF] Klein | Droplet Barcoding for Single-Cell Transcriptomics Applied to Embryonic Stem Cells[END_REF][START_REF] Zilionis | Single-cell barcoding and sequencing using droplet microfluidics[END_REF] (visible in Figure 78c-d), we were able to encapsulate MHBs (Ø49µm) in ~1.4nL droplets at a rate of around 100Hz with flow rates of 400µL/h for carrier oil, 500µL/h for water (Phosphate Buffered Saline) and 20µL/h for MHBs. Though we observed several empty droplets or droplets containing two MHBs, most of the droplets contained a single MHB. This device has not been properly characterized yet, and some optimization are still needed.

Extraction

We aim at extracting MHBs from the droplets to perform physical separation of analytes. An important parameter to consider is the size of MHBs compared to the one of the droplets. During the extraction, the sample volume contained inside of the bead is "lost", so one must minimize the bead size compared to droplet size. In our case, we generated Ø49µm MHBs, corresponding to a volume of 62pL. In a 1.4nL droplet as we generated in the previous part (Figure 78d), MHBs occupies 4.4% of the droplets volume. Note that the actual sample loss is not 62pL but only the volume occupied by liquid in the polymer mesh, so we can expect the sample loss of less than 4.4%.

Droplets containing MHBs were reinjected in a micro-magnetic-tweezers chip as described in Chapter 3, Part 3.1. The central channel was 35µm high and 30µm wide, the tweezers were ~35µm thick trapezoid with an 80µm flat side facing the channels (as shown in Figure 79). They were magnetized with a 1cm 3 neodymium magnet (Br=1.31T) placed at 3mm away from them.

We reinjected the droplets as slowly as possible (~3mm/s) to observe the extraction process. Unlike in Chapter 3 where magnetic microparticles needed time to form a cluster, the extraction efficiency should be here independent, or less dependent, to droplet velocity. The MHBs we used in this experiment contained EMG 700SP with a final MNPs concentration of 1.85% v/v. According our theoretical calculated provided in Part 3 of this chapter, this MNPs loading is in a range enabling extraction. Unfortunately, and as shown in Figure 79, the MHBs were not extracted after being passed through the micro-magnetic-tweezers. We will try in the future to redo the experiment with an even higher MNPs loading.

This inability of capturing the MHB can also result from an increased pressure due to gel deformation. The gel being larger than the channel, it is deformed (as shown in Figure 79) and acts as a plug occupying the whole channel cross section, narrowing the gutters which are needed for the flow of oil, which ultimately leads to an increased pressure before the gel. This additional pressure then pushes the MHBs in the flow direction. We need to reproduce the experiment with smaller MHBs (Ø30µm instead of Ø49µm) that would not clog the channel. Interestingly, we can see on Figure 79 that the MHBs remain at the droplet rear. This is explained by the z-confinement of the bead which cause friction of MHBs on the walls, making them slowing down. This behavior was not observed when the channels were thicker than the MHBs diameter.

In the meantime, we found other methods to passively extract HBs and MHBs from droplets at high throughput that would not need the micro-magnetic-tweezers. We do not detail them in this manuscript because we are currently studying the possibility of patenting this technology.

Functionalization and biocapture

Another specification for these MHBs to be used in the context of single-cell analysis relies on their ability to capture biomolecules. To begin with, we decided to graft oligo-dT primers in the gel mesh to specifically capture mRNA.

As already described in inDrop, and more recently in Li et al. 424 , so called acrydite-modified primers are commercially available and allow for custom primers to be incorporated in the polyacrylamide gel. Such primers, first introduced in 1998 by Kenney et al. 460 , consist of a custom oligonucleotide grafted with a methacryl group at its 5' end (Figure 80). The methacryl group is incorporated in the mesh by free radical polymerization, simultaneously with acrylamide.

Figure 80: Structure of the acrydite-modified primers. The oligonucleotide is grafted from its 5' end to a methacryl group. This methacryl group can be incorporated in the polyacrylamide mesh by free radical polymerization.

Considering the extensive use of these primers in the literature, we were quite confident in the fact that polyacrylamide HBs embedding acrydite-modified oligo-dT primers would enable mRNA capture. But we needed to determine if the presence of iron-oxide MNPs has an effect on the capture. To assess the influence of MNPs on capture, we performed capure tests on four batches of HBs: with and without MNPs, and with and without acrydite-modified primers. Note that:

• The two batches without primers were used as negative control to ensure that no nonspecific binding occurs with and without MNPs.

• The two batches without ferrofluid were used as negative control to see if ferrofluid affects the capture.

We chose the primer concentration so that a single-gel can capture the whole mRNA of a singlecell. The primer concentration in the gel precursor was set to 28.4µM, so that each prepolymer droplet (of 40µm in diameter) contained around 570 million primers. Knowing that a cell contains around 360,000 mRNA molecules, a single HB has 1.5k times more oligo-dT primers that a cell has mRNA molecules to be captured. In principle, such HB would be largely able to capture all the mRNA of a single-cell. It might be therefore hindered by a limited mRNA diffusion in the gel mesh, and by a low accessibility of the HB central region for long molecules such as RNA. For this reason, we decided to put the oligo-dT primers in large excess. Note that the inDrop protocol uses 1 billion primers per gel, which is even more, we do not know if it is absolutely necessary, but considering the high cost of acrydite-modified primers, we believe that it was. In our case, an optimization of required primer quantity to keep good capture rates could be done in the future. Detailed protocols for the four HBs batches synthesis, as well as exact sequences of acrydite-modified primers and poly(A) fluorescent probe are provided in Appendix N2.

We took care of synthesizing these four batches with nuclease-free reagents to avoid any primer degradation, except for ferrofluid which was not nuclease-free guaranteed.

To assess the efficiency of capture for each batch of beads, we used a probe that consists in a poly(A) oligonucleotide, grafted with a fluorescent molecule (fluorescein) at its 5' end. The poly(A) tail is meant to hybridize on the oligo-dT, making the binding directly visible by fluorescence. The beads were diluted in a binding buffer supplemented with the poly(A) fluorescent probe. The concentration of probe in the tube was 100nM, and the beads occupied approximately 50% of the total volume, this way, we have 100 times more of oligo-dT primers than of probes in the reaction mix. This condition is largely unfavorable compared to the 1.5k excess mentioned in the previous paragraph, but was chosen to stay in a good range of detection of our QuBit fluorometer (See Appendix N3).

HBs and probes were incubated together under agitation for 30min at room temperature to let the binding to occur, the solution was then filtered through a Costar Spin-X 0.45µm cellulose acetate filter column to get rid of the beads, after which the fluorescence of the supernatant was measured on a fluorometer as indirect measurement of the beads capture efficiency (QuBit, Thermofisher).

Fluorescence values were converted into concentration thanks to a calibration curve provided in Appendix N3. A more detailed protocol, as well as raw fluorescence data, are given in Appendix N3.

Figure 81 shows the measured fluorescent probe concentrations in the supernatant for the four batches of beads. We clearly see that the fluorescence in the supernatant for the beads that does not contain primers was very close to the initial concentration (100nM), suggesting that the probe was not captured in these HBs. One can note that for the HBs without primers nor MNPs, we measured a value of 101.2nM, which is higher than the initial value of 100nM in the reaction mix. This is explained by the fact that the volume occupied by the polymer mesh decreased the total liquid volume, and the concentration in the liquid supernatant could consequently be over 100nM. A 'corrected' concentration that takes into account the solid volume fraction would be difficult to estimate, because the solid volume fraction highly depends on many factors such as HB composition or swelling ratio. We can also notice that the value is ~10% lower with the MNPs-containing HBs, which would suggest a slight non-specific binding on the MNPs. We must however be careful with this result because we observed that the supernatant for MNPs-containing HBs was slightly yellowish, suggesting that MNPs were extracted from HBs during centrifugation filtering. The presence of MNPs in the supernatant might affect the fluorescence signal.

Most importantly, when oligo-dT primers were present in the beads, the fluorescent probe concentration was decreased by ~90%, with and without MNPs in the gel, showing that the probe remained in the polyacrylamide mesh after filtering. This very promising results demonstrate that our HBs would be able to capture mRNA, and that it is not affected by the presence of MNPs in the gel. In the future, we will reproduce this experiment with real mRNA, which are much longer molecules for which it is more difficult to diffuse in the polymer mesh, and to quantify them by RT-qPCR, and then in droplets.

Chapter conclusion

We demonstrated in this chapter the synthesis of magnetic-hydrogel-beads (MHBs), their encapsulation into nanoliter droplets, and an attempt of extraction through the micro-magnetic-tweezers.

The HBs were successfully produced by polymerization of polyacrylamide droplets generated by a flow-focusing microfluidic device, as in the inDrop 3 protocol. Two approaches were tried to magnetize them: i. the in situ precipitation method where MNPs were precipitated from an iron solution into the gel and ii. the blending method, where ferrofluid was added in the gel precursor.

Despite a few difficulties, the blending method provided more promising results. Ferrofluid was added into the acrylamide solution. The polymerization initiator, ammonium persulfate, had to be introduced in a junction placed just before the droplet formation to avoid spontaneous polymerization of the gel precursor in the syringe.

We tried three different ferrofluids that are stabilized with different surfactants that can be either, anionic, cationic or non-ionic. The anionic-surfacted ferrofluid (EMG 700SP, Ferrotec) provided the best results as they were easier to manipulate than the non-ionic one (PBG 700), where the beads were forming aggregates. The cationic-surfacted ferrofluid (EMG 601P) however inhibited polymerization.

The MHBs were then encapsulated into nanoliter droplets. We faced a problem of non-perfect close-packing, which caused instabilities and polydisperse droplets. This problem was solved by centrifuging strongly (5min 15,000rpm) the MHBs before loading them into the chip. Unfortunately, we weren't able to extract the MHBs from droplets with the micro-magnetic-tweezers. This is probably due to an insufficient MNPs loading in the beads, and further experiments will be carried out in the future. During the course of this project, we found a passive method for highthroughput MHBs extraction from droplets. This technique will maybe be patented, and is not shown here for this reason.

To ensure that the MHBs can be used for bioseparation purposes, we performed preliminary tests with our MHBs in a simple biocapture experiment. Acrydite-modified oligo-dT primers were polymerized with the acrylamide into the beads. We showed that such functionalized beads were able to capture specifically a poly(A) fluorescent probe, and more importantly, that the presence of iron oxide did not perturb the capture process. In the future, we will need to assess the efficiency of capture on real mRNA, and then on real biological samples and then in droplet format. For multiomics purposes, capture of other biomolecules can be tried out.

To improve the MHBs properties, several approaches can be followed: we could increase the MNPs quantity by increasing the ferrofluid proportion in the initial mix, or by using other commercial MNPs. Besides the Ferrotec ferrofluids, MNPs functionalized with carboxyl acid or amin groups are commercially available, which would allow us to add further functionalization onto the MNPs, such as an methacryl group, that would allow us to covalently integrate the MNPs into the polyacrylamide mesh.

Many characterization of the objects will have to be done in the future to measure the magnetization, stiffness, or iron content.

We believe that this technology would enable simplified bioseparation in droplet microfluidics at high-throughput, enabling new single-cell multi-omics studies.

CONCLUSION AND PERSPECTIVES

roplet microfluidics has become an established technology to study transcriptomics, genomics, proteomics and epigenomics within single-cells [START_REF] Matuła | Single-Cell Analysis Using Droplet Microfluidics[END_REF] . However, these technologies are generally limited to only one modality, and studying several "omics" from the same cell remains challenging. Such "multi-omics" studies often need a physical separation of analytes 236 , making them difficult to implement in droplet microfluidics.

In multimodal single-cell methods, physical separation can be achieved either by isolating nucleus from cytosol 222 , or by performing specific capture of biomolecules on superparamagnetic microparticles 229 . So far, magnetic separation steps have been mostly executed manually, limiting throughput and automation potential of such experiments. Besides, magnetic particles separation steps have been implemented in droplet microfluidics with electrowetting, or asymmetric droplet splitting [START_REF] Serra | The power of solid supports in multiphase and droplet-based microfluidics: towards clinical applications[END_REF] . However, these approaches remain limited to, respectively, low throughput and poor purification rate.

Our group proposed another method using magnetic tweezers to extract and redisperse high loads of particles with high purification rates from droplets flowing in a PTFE capillary [START_REF] Ali-Cherif | Programmable Magnetic Tweezers and Droplet Microfluidic Device for High-Throughput Nanoliter Multi-Step Assays[END_REF][START_REF] Ferraro | Microfluidic platform combining droplets and magnetic tweezers: application to HER2 expression in cancer diagnosis[END_REF] . Despite the efficiency of this technology, it does not allow for the manipulation of droplets smaller than 100nL, and therefore needs to be reduced by 2 or 3 orders of magnitude to be compatible with highthroughput state of the art systems.

Downscaling the system leads to preponderant interfacial forces, and thus require much stronger magnetic forces to enable magnetic particles extraction from a droplet. Our strategy is to fabricate the micro-magnetic-tweezers by means of an electroplating protocol 286 to obtain NiFe structures that are highly magnetizable. Placed from either side of a microfluidic channel, the micro-magnetic-tweezers are able to trap and extract magnetic particles from sub-nanoliter droplets.

The micro-magnetic-tweezers device (Figure 82) is able to extract and reintroduce magnetic particles in sub-nanoliter droplets. This project aim at providing a tool to selectively separate analytes from single-cells in encapsulated in droplets, offering new opportunities for high-throughput multimodal single-cell profiling. This project was very pluridisciplinary, and the different aspects could be treated separately, but were all interdependent. We summarize here these different aspects, each corresponding to a chapter.

D

• The cluster release stage occurs when another droplet arrives in the channel and pushes the trapped cluster. To avoid clogging, it is important that the force applying by the pushing droplet is higher than the magnetic force.

Each stage was studied, but only the cluster formation stage turned out to be problematic, because it greatly limited the capture efficiency when increasing droplet velocity. On the early versions of the chip, the capture efficiency was ~80% at 3mm/s and dropped to ~45% at 12mm/s. Thanks to numerical simulations, we were able to optimize the tweezers design to maximize the magnetic field gradient. In their last version, the tweezers can capture up to 100% of the magnetic particles at velocities below 12mm/s, but this capture rate still decreases slowly at higher velocities.

Though the design can be further optimized, this is a real limitation in terms of throughput, allowing 100% extraction at a rate not higher than 7 droplets/s, which will limit the device applicability in a real single-cell workflow, where most of the droplets are empty due to Poisson statistics, and hundreds of thousands of droplets are generally formed in a single experiment.

Numerical simulations

Besides the experimental part, we developed a FEA (Finite-Elements Analysis) model to simulate dense magnetic particles-laden flows, applicable to microfluidics (Chapter 4). We aimed initially at providing a numerical model for the above-mentioned cluster formation stage in the micro-magnetic-tweezers only, but we realized that it was also applicable to another magnetic particles-based device developed in our group: the microfluidic magnetic fluidized bed, and that this model can be extended to various microfluidic devices involving dense magnetic particles-laden flows.

Simulations of discrete magnetic particles and magnetophoresis in microfluidic devices has long been established, but is not adapted to model collective behaviors of thousands of particles. Such flows are particularly difficult to model because they include coupling between the dispersed and the continuous phase. In other words, the particles distribution at any moment modifies the flow, and the flow modifies the particles distribution.

Our model is based on a Euler-Euler approach, where both continuous and dispersed phases are modelled as interpenetrating continuum with a Navier-Stokes equations set for each. Unlike previous similar works 357 , our model is based on the Gidaspow model for fluidized beds 350 , and is therefore able to capture all dilute, dense and packed situations. The magnetic part is inspired by the ferrohydrodynamics theory of Rosensweig 12 , where the magnetic force is calculated everywhere as a body force density that depends on the local magnetic particles concentration and magnetic field gradient.

We were able to qualitatively model the cluster formation stage in the micro-magnetic-tweezers, as well as the fluidization state of the microfluidic magnetic fluidized bed. This model could be in the future a useful tool to simulate different lab-on-a-chip involving dense to packed magnetic particles flows.

Molecular biology

As the final goal of the micro-magnetic-tweezers is to perform bioseparation in single-cells, we wanted to start developing molecular biology tools to show that it would be feasible. In collaboration with Mathilde Richerd, we tried to adapt the G&T-seq 229 protocol of mRNA/gDNA separation on our magnetic tweezers platform. This protocol makes used of two rounds of magnetic beads separation on single-cells, the first with oligo-dT beads, the second with AMPure beads, to separate selectively mRNA, and gDNA, respectively.

We performed such two-step separation, first in tubes, then in 100nL droplets with the magnetic tweezers, on samples of DNA/RNA at single-cell concentration, and then on cell lysates. Thanks to qPCR quantification of our separated samples, we showed that for both tubes and droplet experiments, around 70% of mRNA was captured during the first oligo-dT round, and from 55 to 70% of gDNA was captured by the AMPure beads. These results are very encouraging, and

Mathilde is currently actively working on the protocol optimization, and she is now working on cell encapsulation in droplets before bead-based separation. We will in the near future try to find and develop multi-omics applications of the magnetic tweezers, with the collaboration of biologists in Institut Curie.

In parallel, we tried to develop a one-step qPCR-based assay to quantify gDNA and mRNA without needing to split the sample. This assay, based on multiplex RT-qPCR was unsuccessful, we think that it is because we weren't able to discriminate between gDNA and pre-mRNA.

Microfluidics integration

We integrated the micro-magnetic-tweezers in a compete microfluidics workflow.

First, we wanted to develop a droplet-on-demand module, inspired by Zhou et al. 394 , to generate complex droplet sequences. An important part of my first year of PhD was spent to develop and characterize this system, but we realized that it was not well adapted to our needs because of the difficulty to introduce magnetic particles in the droplets. Problems of sedimentation and magnetophoresis prevented us from generating droplet with controlled magnetic particles loading.

We then decided to replace it by a paired reinjection module. Droplets are first generated at high throughput through a flow-focusing device, allowing a better control of particles loading. They are then reinjected in the chip in a paired fashion with a channel design taken from Dressler et al. 404 Then an electro-coalescence module was added to redisperse the magnetic particles cluster into another droplet. As it is commonly done in microfluidics, we used microsolidics [START_REF] Siegel | Microsolidics: Fabrication of three-dimensional metallic microstructures in poly(dimethylsiloxane)[END_REF] to produce electrodes that are very close to the microfluidic channel, and by applying a strong DC voltage (500V), we were able to destabilize the droplet interfaces, leading to their merging.

Finally, a magnetic sorting module was implemented to sort the droplets. Another microfabricated soft-magnet was added at junction to sort droplets that contain, or not, magnetic particles.

Though we have shown that each step can operate properly, we never managed to make them work together simultaneously. The final device is still under development because some modules still need optimization, it can take time because of the complex fabrication, but we are not facing any particular technical obstacle and it should be ready in a few months.

In the short-term future, we plan to finish the development of the fully integrated device, and then to perform a mRNA extraction on cell lysates as a proof-of-concept to show that our device can selectively extract analytes. In the long-term future, we will have to think about eventual singlecell applications, but we are facing the problem of low throughput, and a cell indexing strategy has to be found.

Magnetic hydrogel beads

During the last year of my PhD, I supervised Elina Gilbert and Grégoire Lemahieu for their internship on a project aiming at developing magnetic hydrogel beads (MHBs) as a new class of solid support for bioseparation in droplet microfluidics.

Hydrogel beads (HBs) are already widely used in droplet microfluidics, notably in inDrop 3 , as barcoded primers carrier for single-cell indexing. They have the advantage of being deformable, allowing their deterministic encapsulation in droplets, and they can also be manipulated off-chip, allowing them to be barcoded through the split & pool method.

Our purpose in this project is to fabricate MHBs that can be used to selectively capture analytes from a single-cell lysed in a droplet, after which they can be extracted from the droplet, or passed from droplet to droplet, in order to carry out complex, multi-step, and multi-omics studies. Using such MHBs instead of magnetic microparticles in our micro-magnetic-tweezers would have great interest, avoiding the cluster formation step that is the main limitation of our system, and facilitating cell indexing as HBs barcoding is already well established.

We synthesized polyacrylamide HBs following the inDrop protocol [START_REF] Zilionis | Single-cell barcoding and sequencing using droplet microfluidics[END_REF] , by polymerizing droplets of prepolymer generated through a flow-focusing microfluidic device. A ferrofluid was added in the prepolymer mix to render them magnetic. We observed a decreased swelling ratio, and some aggregation of iron-oxide nanoparticles, preventing them from escaping through the polymer mesh.

Ferrofluid stabilized by anionic surfactants provided better manipulability compared to non-ionic where aggregation of MHBs was observed.

We functionalized the MHBs by adding acrydite-modified oligo-dT primers in the prepolymer mix. Then we tested the functionalization by capturing a poly(A) fluorescent probe in the beads.

With a ratio of one fluorescent probe for 100 oligo-dT primers, we achieved a capture efficiency of ~90%. If the beads did not contain the primers, the efficiency was reduced to ~10%, suggesting a low non-specific binding. No significant different was observed with non-magnetic HBs, showing that the presence of ferrofluid does not interfere to the capture.

So far, we were not able to extract the MHBs with the micro-magnetic-tweezers. This might be due to i. a too low magnetic material quantity in the beads, or ii. to the fact that the gels were too big, they obstructed the channel and thus a high pressure was applied on them, preventing them to be stopped by the magnetic force. In the near future, we will try again this experiment with higher magnetic nanoparticles loads, and with smaller MHBs.

In parallel, we developed a passive device to extract MHBs from droplets, which is not discussed here because it might be patented in the near future.

In the middle-term future, we will think of developing single-cell methods with MHBs extraction from droplets. This approach should be much easier to integrate in a complete single-cell droplet microfluidics workflow than the microparticles-based micro-magnetic-tweezers, as it needs mostly well-established techniques such as HBs synthesis, barcoding and co-encapsulation with cells. The novelty is the ability to extract a specific analyte on the beads, while keeping the remaining supernatant for further analysis.

K.4 RNase treatment

RNase treatment is done by adding 1µL of RNase A (PureLink RNase A, Invitrogen) in 20µL of sample. After a 1h incubation at 37°C, the sample does not contain RNA anymore.

N.2 MHBs with acrydite-modified primers synthesis protocol

The primers were bought from Integrated DNA Technologies (IDT), the sequences are given in Table 1 below:

Acrydite-modified oligo-dT primer TBSET, 4×AB solution, carrier oil composition and flow rates are the same as in Appendix N.1

N.3 Capture of poly(A)-fluorescein probe on the gels

To know the working range of our QuBit (Thermofisher) fluorometer for our poly(A) fluorescent probe, we prepared successive dilutions of the probe in water and in a buffer obtained by mixing at a 1:1 ratio TBSET and a Lysis/Binding buffer taken from a commercial oligo-dT beads mRNA extraction kit (Dynabeads mRNA DIRECT). Figure 1 shows the measured fluorescence against probe concentration. We observed an important difference between the fluorescence in water and the one in buffer. This is because the light intensity emitted by fluorescein can vary a lot with the pH.

Chapter 7 -

 7 Magnetic-hydrogel-beads: a new class of solid support for bioseparation in droplet microfluidics ....................................................................production .................................................................................................................... 1.2 HBs for biosensing ............................................................................................................... 1.3 HBs for 3D cell culture and regenerative medicine ........................................................ 1.4 HBs for single-cell omics ....................................................................................................

Figure 1 :

 1 Figure 1: Stages of magnetic particle capture in the micro-magnetic-tweezers. a-b. Cluster formation. cd. Droplet breakup. e-f. Cluster release. Experimental details are given in the experimental part of this chapter.

Figure 3 :

 3 Figure 3: A microfluidic chip (Source: Wyss Institute)

Figure 7 :

 7 Figure 7: inDrop cell/gel bead co-encapsulation. A. Chip design used for inDrop. B. Micrograph of the chip in process. Red and blue arrows show respectively the cells and hydrogel beads being co-encapsulation in droplet. C. The gels are reinjected in a close-packed manner to allow sub-Poisson loading. The cells encapsulation still follows a Poisson distribution. Taken from Klein et al.3

Figure 9 :

 9 Figure 9: a. Production of multi-layer capsules for drug delivery. Adapted from Amstad 2018. 104 b. Hexagonal prismatic hydrogel sheet. Adapted from Du et al. 2018. 106 c. Multiscale tissue-engineering. i: Single-cell microgel generation and cross-linking. ii: Macrogel matrix production. iii: Injection and crosslinking of the material. Adapted fromKamperman et al. 2017. 99

  Figure 10: a. Microvalves system to produce droplets libraries on demand. 117 b. Drug screening at single-cell level by Brouzes et al. (i) Coded library generation. (ii) Library and cell combination. (iii) Incubation. (iv) Live-dead assay and coding readout, Brouzes et al.[START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF]

  early times, single-cell assays such as immunofluorescence, fluorescence in situ hybridization (FISH) and single-cell PCR allowed only for the detection of certain molecular markers at lowthroughput. In the recent years however, tremendous advances on technologies such as next-generation sequencing (NGS) and mass spectrometry (MS), combined with new cell isolation tools, are enabling the study of single-cells at different levels including: genomics, transcriptomics, proteomics, epigenomics or metabolomics. They allowed for the emergence of a new field of research:

Figure 11 :

 11 Figure 11: Analyzing a tissue at the single-cell level reveals heterogeneity and sub-populations of cells that are masked in bulk analysis. Source: biocompare.com

  primers followed by universal PCR and SMART (Switching Mechanism At RNA Termini) which is based on template switching 160 . SMART amplification was used on single-cells prior to their sequencing (SMART-seq) 161 . Another method, called in vitro transcription (IVT), can reduce the exponential amplification bias by replicating new RNA always from the original molecule. It has a better accuracy than PCR-based techniques but also require five days of reaction. CEL-seq (Cell Expression by Linear amplification and Sequencing) was developed in 2012, it is a protocol exploiting IVT amplification with barcoded poly(T) primers on single-cells isolated in microtiter-plates prior to sequencing 162 . Other techniques were developed such as the IVT-based Quartz-seq and others based on the Phi29 polymerase 160 . The first transcriptomics experiments in microfluidics were based on RT-qPCR to perform targeted gene expression analysis. It was achieved with valves 163 and wells 164 . But microfluidics was soon used to integrate single-cell sequencing protocols like CEL-seq or SMART-seq. It was in particular enabled by the valve-based Fluidigm C1, and several scRNA-seq papers were published between

Figure 14 :

 14 Figure 14: Abseq workflow. a. Cells are immunostained with antibodies tagged with a barcode. b. They are encapsulated in droplets. c. Cell-barcode droplets are produced to index cells. d. Cell and barcode droplets are merged together with PCR reagents. For each cell, the Ab-barcode is combined with the Cell-barcode and is amplified. e. Emulsion is broken and prepared for sequencing. By reading Cell and Ab barcodes, we know what antibodies were on each cell. Reprinted from Shahi et al.5

Figure 17 :

 17 Figure 17: a. Physical separation the omics from a single-cell lysate with functionalized beads b. Physical separation of the nucleus from the cytosol. c. One-step assay without separation. d. Sample splitting to perform two separate assays. Reprinted from Chappell et al. 236

Figure 20 :

 20 Figure 20: a. Sandwich ELISA on chip. (i-ii) Magnetic beads coated with antibodies are immobilized on electromagnets. (iii-iv) Sample containing antigen is flown in the chamber. The target binds on the beads whereas the other molecules are washed away. (v-vi) Secondary antibody binds on immobilized antigen and is detected by electrochemical sensors. (vii) Beads are released for further analysis or to reuse the chip. Adapted from 255 b. Sandwich ELISA on chip with a bead moving through the different buffers of the bioassay in a co-laminar stream. Adapted from 265 c. Magnetic plug in a continuous flow for protein digestion. Adapted from 258 d. Magnetic microfluidic fluidized bed. Adapted from 260 e. Digital ELISA assay. Adapted from 266

Figure 21 :

 21 Figure 21: Strategies for magnetic particles extraction in multiphase microfluidics: a. IFAST system. Three reservoirs are connected together by narrow constrictions. A lysis and an elution buffer coexist with an immiscible oil phase placed in between them in the central reservoir. Magnetic particles are put together with the sample (i). They spontaneously form a cluster in the presence of an external magnet. It can then be extracted from the initial reservoir, passed through the oil (ii) and redispersed into the third one for elution (iii) 271 . b. A digital microfluidic based magnetic extraction. The magnetic particles are aggregated and kept immobile under the action of a permanent magnet. The droplet is then displaced thanks to EWOD, leading to the extraction of the particles 272 . c. Particle separation following the splitting approach proposed by Lombardi and Dittrich 274 . d. Extraction and washing step implemented by Lee et al. 277 e. Optimized asymmetric geometry by Brouzes et al. 278 f. The Car-Wash system. Particles in droplets are washed in a buffer stream before being re-emulsified 283 .

Figure 22 :

 22 Figure22: a. Magnetic particles extraction in the DropLab system. The preformed ferromagnetic cluster remains immobile in the channel (i). After the merging of the droplet with the cluster, the magnetic particles present in the droplet are attracted by the cluster (ii) and are extracted (iii,iv). Adapted fromGu et al. 284 b. Magnetic tweezers technology (i). A droplet is approaching the magnetic tip (ii). The magnetic field is turned on, leading to the accumulation of particles close to the tip (iii) and to the extraction of the magnetic cluster (iv). Adapted from Ferraro et al. 9 c. mRNA extraction with the magnetic tweezers. Oligo(dT) beads are first captured (i-ii) and extracted (iii). A droplet containing total RNA is approaching (iii) and merged with the cluster of Oligo(dT) beads (iv). After binding of mRNA to the beads, the cluster is captured again and passed in a washing buffer droplet (v) before being released into an RT-qPCR mix (vi). Adapted from Ferraro et al. 9 d. Modified magnetic tweezers with integrated soft magnetic elements. The particles are attracted between the two soft magnets (i-ii), deforming the droplet interface (iii). The droplet is then broken by shear force (iv), while keeping the particles in the magnetic region (v). Adapted from Serra et al.[START_REF] Serra | Integrated droplet microfluidic device for magnetic particles handling: Application to DNA size selection in NGS libraries preparation[END_REF]

Figure 23 :

 23 Figure 23: a. Principle of electroplating. An electric current makes cations move from the anode to the cathode, resulting in a metal deposition on the cathode while the anode is dissolved. b. As many 19 th century sculptures, L'Harmonie by Charles Guméry (1869), crowning the Opéra Garnier in Paris, is actually a copper electrotype. (source: Wikipedia) c. Example of a small-scale electroplating equipment, here on a silicon wafer to produce nickel microstructures. (source: yamamoto-ms.co.jp) d. Example of an industrial large-scale zinc plating (source: Gatto Industrial Platers, Inc.)

Figure 24 :

 24 Figure 24: a. Micro magnetic stirrer in a microfluidic chip. Adapted from 314 b. Micro magnetic tool that can be actuated with magnetic needles. It can serve as a gate in a microfluidic circuit. Adapted from 316 c. Micro electromagnet. The coil is made of electroplated Cu while the core is made of electroplated permalloy. It is placed next to a microfluidic circuit embedding permalloy lines to guide magnetic particles. Adapted from 318 d. Array of permalloy posts to trap magnetic particles. The soft magnets are actuated by external permanent magnets. Adapted from 321 e. Substrate patterned with micro-magnets to attract nanoparticles within cells. Adapted from 286 . f. Flexible and stretchable PDMS substrate patterned with permalloy elements. Adapted from 328 .

Figure 26 :

 26 Figure 26: a. Micrograph of an electroplated permalloy structure on glass. b. Permalloy magnetization curve measured with VSM. c. SEM micrograph of microfabricated permalloy tweezers.

Figure 27 :

 27 Figure 27: a. Alignment and bonding method byCottet et al. 332 . i. General overview of the MJB4 mask aligner. A binocular microscope is integrated in the machine to see the alignment. X, Y, Z and rotation of the substrate holder can be finely adjusted. ii. The PDMS slab is placed on the mask holder and the substrate is placed on the MJB4 chuck. iii. After alignment, the chuck can be moved up until contact with the PDMS. When we move down the chuck again, the substrate remains on the PDMS slab.

Figure 28 :

 28 Figure 28: Stages of magnetic particle capture in the micro-magnetic-tweezers. a-b. Cluster formation. c-d. Droplet breakup. e-f. Cluster release. Experimental details are given in the experimental part of this chapter.

  e mag,C = $ [ ïD ñ T [ ∇Q Eq. 13 Alternatively, it can be expressed in function of the total mass on beads ó = å$ [ D [ in the cluster: e mag,C = óT [ ∇Q Eq. 14 In a squared cross section channel (R = &) and with a cluster of the same size (D ñ = M& l /6), the magnetic force scales with ∝ & l while it only scales with ∝ & for the capillary force. It suggests that smaller dimensions will make the extraction harder. The ratio between the two forces is: e mag,C e cap = $ [ ï& , T [ ∇Q 243

Figure 33 :

 33 Figure 33: Simulation of the magnetic field. a. Simulation geometry. A cubic (5mm3 ) neodymium magnet (Br=1.43T) generates the magnetic field. The magnetic tweezers are placed 3mm apart from it. They are magnetized by the external field according to the material properties (Chap. II Fig.4b). The surrounding air and the channel are non-magnetizable and does not interact with the field. b. The magnetic field lines are focused by the tweezers. We observe an increase in magnetic field strength between the two tips. c. Magnetic field strength in the middle plane (z=0) of the channel. d. Magnetic field gradient in the middle plane in x (left graph) and in y (right graph). The channel is 30µm wide and 35µm high.

Figure 34 :

 34 Figure 34: Interfacial tension between fluorinated oil and water. Three surfactants were tried out: the ionic Krytox 157FSH is shown in blue, the non-ionic dSurf in red and Picosurf in green. The surfactant was diluted at different concentrations in Novec-7500 and the interfacial tension was measured for pure water and PBS. As a comparison, we show a measurement made by Rashmi Ramesh (in light blue) of the interfacial tension of PBS with FC-40, another commonly used fluorinated oil.

  possible (in the mm/s order of magnitude)Channel size (&)As small as possible (from 10 to 100 µm)

  Figure 28. Images of the droplets before and after extraction are taken during the experiment, and the capture efficiency is calculated through image analysis.

Figure 40 :

 40 Figure 40: Workflow of the MATLAB program to analyse the images. The raw images are first read by the program (1).Then, an image taken at the same place without droplets is subtracted to remove the background(2). The program is able to detect droplets outline of and to measure the intensity within the selected region. This is done for droplets before (B) and after (A) extraction, as well as for empty droplets (E). The efficiency of capture is then calculated based on 15 measurements for B, A and E with the formula(3). Finally, the standard deviation of the capture efficiency is calculated by considering uncertainties propagation.

Figure 41 :

 41 Figure 41: The percentage of capture are plotted against velocity for different conditions. Each point corresponds to an average over 15 droplets. Error bars correspond to standard deviation for both capture percentage (vertical) and velocity (horizontal). All experiments were performed with 450pL droplets flowing in a 35µm thick, 30µm wide channel, and with 35µm thick micro-magnets. For experiment a and b, we show simulation results of the magnetic field and magnetic gradient along the channel. a. Influence of micro-magnet size. Experiment conditions: 22.5ng of Masterbeads per droplet, and external magnet placed at 5mm from the chip. b. Influence of external magnet distance. Experimental conditions: 18ng of Masterbeads per droplet, micro-magnet of 400µm. c. Influence of beads concentration. Experimental conditions: External magnet placed at 3mm, micro-magnet of 400µm. d. Influence of Masterbeads/MyOne ratio. Experimental conditions: External magnet placed at 3mm, 18ng of beads per droplet, micro-magnet of of 400µm.

Figure 43 :

 43 Figure 43: Characterization of the flat tweezers. Capture percentage was measured on three chips: type A refers to the triangle shaped magnets, type B and C refer to trapezoids with flat sides of 40µm and 80µm respectively. All the experiment presented in this figure were performed with 450pL droplets containing 18ng of particles, and flowing in a 30µm×35µm channel. a. The left panel shows the experimental results in terms of capture efficiency for the three types of tweezers. The right panel shows the simulated magnetic field and gradient. In orange are shown the results for type A, in light blue for the type B and in dark blue for the type C. b. Micrograph showing the capture process of 18ng of MyOne in a 450pL droplet for tweezers type B and C. These micrographs were all taken at a low velocity (around 8mm/s) with a high-speed camera (Phantom). Arrows show the flow direction. Videos are provided in supplementary data. c. Experimental and numerical results with different external magnets. This experiment was performed with 18ng of MyOne per droplet and with the 80µm side flat trapezoidal tweezers.

Figure 45 :

 45 Figure 45: Fluidization process. a. Standard fluidized bed. The fluid is pushed from the bottom, resulting in an equilibrium between drag and gravity for the particles. b. Chaotic bubbling in a fluidized bed reactor. c. Magnetically stabilized fluidized bed. Figure adapted from Rosensweig 12 .

around 1

 1 hour to solve on a Dell Precision 5820 Tower equipped with an Intel Xeon W-2155 CPU(3.30 GHz), and 64 GB of RAM.

Figure 46 :

 46 Figure 46: Simulation setup. a. Geometry of simulation. The channel is 30µm wide, 35µm high and 1mm long. The tweezer is a trapezoid of 400µm base and height, the side close to the channel is 80µm long. The geometry shown here is actually only a quarter of the total geometry because symmetry allows us to model only a part of the total problem. There are two planes of symmetry: the first is the xy plane cutting the channel and tweezers in half, the second is the yz plane cutting the channel in half. b. xy-cut plane showing initial conditions for the particles density. It has been set to ï ∏ = 0.111 in a channel portion of length 200µm to have a particle plug of 18ng in total mass. Note that the symmetric part, though not computed, can be reconstructed for display. c. Results of the magnetic field simulation performed before the fluid simulation.

Figure 47 :

 47 Figure 47: Examples of results of the simulations. a. Capture of 18ng of particles through the micromagnetic-tweezers (trapezoid with 40µm flat tip) at a flow velocity of 5mm/s. The results are shown on the central xy-cut plane. Colors indicates the particles volume fraction, where white is ï ∏ = 0 (no particles) and black is ï ∏ = 0.5 (packed bed). b. 3D view of the particle plug after capture in the micromagnetic-tweezers (triangles). Flow velocity is 5mm/s. The black volume is defined by ï ∏ > 0.3, and shows the packed region. Streamlines show the flow direction, for which colours relates to the continuous phase velocity % ñ . Around the cluster, the velocity can reach up to 45mm/s, while the fluid percolating inside the cluster is around 0.5mm/s. c. Top view of the same picture. d. Front view of the same picture.

Figure 49 :

 49 Figure 49: General overview of the microfluidic magnetic fluidized bed. a. Device overview. The diamond-shaped chip is placed at 1mm from a powerful neodymium external magnet. The chip is 50µm high, and 100µm wide at the inlet. Since the magnetic force decreases with the distance from the magnet, a widening chamber was designed to decrease the flow velocity and thus to keep the balance between drag and magnetic forces. An optimal angle of 13° was determined experimentally. b. Fluidization process for 50µg of ThermoFisher M270 (AE2.8µm, T `= 10emu/g). Without flow, the particles are packed in the bottom of the chamber. Fluidization occurs with a flow, resulting in a homogeneous distribution of particles that continuously recirculates as shown by the arrows. Scale bar = 1mm. c. Bed opening length increases with flow rate. d. Details of the magnetic particles columns. Scale bar = 200µm. Figure is taken from Pereiro et al. 260

Figure 50 :

 50 Figure 50: Simulation setup. Top panel shows the distribution of the magnetic field calculated following Gou et al.. The bottom panel shows the initial particles distribution. It was set to have a total particle quantity of 50µg.

Figure 51 :

 51 Figure 51 : Simulation results after bed stabilization (t=10s). The conditions for this simulations are 1 µL/min and 2ø = 15.39. Black color corresponds to dense regions where ï ∏ ≥ 0.5 and white regions corresponds to ï ∏ = 0. White arrows indicates the direction of particles velocity, showing recirculation patters as in experiments. Watch Video 4.3 to see the establishment of the fluidized state in this particular condition.

  qPCR are already quite common, they use several TaqMan probes with a specific dye each that target different sequences. As shown on Figure53, we designed a TaqMan assay with two probes: one is placed on an intron, and is thus specific to gDNA, the other one is placed on an exon-exon junction, which exists only in RNA. Both TaqMan probes use different dyes, and a different set of PCR primers.

Figure 53 :

 53 Figure 53: Design of the multiplex qPCR assay. gDNA can be differentiated from mRNA because it possesses introns. mRNA, which was reverse transcribed and amplified into cDNA, can be recognized by the presence of exon-exon junctions that are present because intron removal (splicing) during RNA transcription.

Figure 54 :

 54 Figure 54: Standard curves for the exon probe that targets mRNA (left) and the intron probe that targets gDNA (right). The RT-qPCR were performed in singleplex and multiplex, on 4 samples that contains purified DNA and RNA. The most concentrated sample contains 37.3ng/µL of DNA and 174.3ng/µL of RNA (NanoDrop measurements). Three successive dilutions by a factor 10 were done a obtain the three other samples. Negative control experiments were performed, in which all the reagents are present but the sample is replaced by nuclease free water. All the negative control experiments didn't show any amplification. Every reaction was done in triplicate, the Ct values are given in Appendix K. Note that the three values are very close to each other for each concentration, and that the points shown on the graph overlaps.

Figure 57 :

 57 Figure 57: RNA/DNA proportion in the different solutions after physical separation. The red bars correspond to the proportion of material captured on oligo dT, the green bars to the one captured on AM-Pure and the blue bars to the remaining material in the initial sample (see Figure56). One should note that here 100% correspond to the total detected quantity, and not the total quantity present in the initial sample. So eventual loss of material (on the pipette cones or tubes) are neglected. Each measurement was done in triplicate, on 4 samples at different concentrations of DNA/RNA, as indicated on the xaxis.

Figure 58 :

 58 Figure58: RNA/DNA proportion in the different solutions after physical separation from the lysate sample. The red bars correspond to the proportion of material captured on oligo dT, the green bars to the one captured on AM-Pure and the blue bars to the remaining material in the initial sample (see Figure4). Yellow and pink bars show the DNA and RNA that was measured in the washing buffers. As in Figure5, 100% correspond to the total detected quantity. Each experiment was done in triplicate.

Figure 59 :

 59 Figure 59: Magnetic-tweezers platform. a. General view of the platform. A robotic arm (i) places a PTFE capillary, beforehand filled by oil, alternatively in different wells. A syringe pump (iii) is then actuated to aspirate desired volumes in the well. The robotic arm and syringe pump are synchronously programmed (with the software Qmix) to produce a train of droplets of desired sizes and composition in the capillary. A permalloy tip (ii) placed in a coil serves as a magnetic tweezer to extract and redisperse magnetic particles from droplets. b. Magnetic particle capture process. (i) Device overview. (ii) A droplet containing magnetic particles approaches the tweezer. (iii) The tweezer is actuated, attracting the particles.(iv) The previously formed cluster of particles is extracted from the droplet, and can be redispersed in the next droplet. c. Graphic representing the mRNA extraction with oligo dT beads from a sample containing DNA and RNA. Magnetic beads are successively transferred in the sample to capture mRNA, then in a washing buffer, and finally in a water droplet that is collected in a tube for further PCR. d. For DNA purification, starting from the same sample that was depleted from mRNA in the previous step, an AMPure XP solution droplet is added in the capillary and merged with the sample. As previously, the beads are then transferred into a water droplet that is collected in a tube.

Figure 60 :

 60 Figure 60: RNA/DNA proportion in the different solutions after physical separation from the sample droplets are two different concentrations of the initial DNA/RNA sample. The red bars correspond to the proportion of material captured on oligo dT, the green bars to the one captured on AMPure and the blue bars to the remaining material in the initial sample (see Figure56). As in Figure57and Figure58, 100% correspond to the total detected quantity. Each experiment was done in triplicate.

  valves were first introduced by Unger et al. in Quake's lab153 . They are made of a two layered microchannel circuit, the first layer being for the fluid itself, and the second one for control channels that are pressurized on demand to deflect a membrane, closing or opening the fluidic channel. Lin and Su 397 added such a valve on a T-junction droplet maker (Figure62a), and by periodically opening and closing it, they were are to produce 0.5-400pL droplets of controlled size at controlled intervals (0.4-20Hz). Soon after, multiple valves were integrated as shown on Figure62bto produce droplets with different composition117,396 . Though such microvalves are generally actuated by pressurized air, Bransky et al. developed a chip embedding a piezoelectric actuator to trigger droplet

Figure 62 :

 62 Figure 62: Different DoD devices. a. Sketch of an integrated pneumatic microvalve used by Lin et al. 397 to produce picoliter droplets. Adapted from Zeng et al. 396 b. Similar valves used to produce droplet sequences. c. Negative pressure pulse formed droplets as proposed by Teo et al. 389 . The duration of the pulse can be modified to adjust the droplet size. d. External valve based DoD device proposed by Zhou et al.394 . The pressure is adjusted so that the interface is pinned in the constriction (i). By closing and reopening quickly an external valve placed at the injection tubing before the chip, a pressure pulse is generated, resulting in droplet delivery (ii-vi).

Figure 65 :

 65 Figure 65: Droplet pairing methods from literature. Taken from Zheng et al. 399 a. Paired droplet generation with two T-junctions facing each other. b. Ladder-like channel to synchronize two droplet trains. Taken from Ahn et al. 403 c. Paired droplet reinjection by two T-junctions facing each other. Taken from Lee et al. 61 . d. Droplet reinjection exploiting the capacity of packed emulsion to auto-organize into an hexagonal lattice. Taken from Dressler et al. 404

Figure 66 :

 66 Figure 66: Droplet reinjection. a. Setup used for droplet reinjection. (i) Microfluidic chip. (ii) External permanent magnet. (iii) Pressurized reservoirs containing the emulsions. b. Micrograph of the reinjected droplets in the microfluidic chip. Packed droplets auto-organize into an hexagonal lattice. c. After being paired, the droplets are spaced by oil.

Figure 67 shows

 67 Figure67shows the cluster being pushed by the following droplet (a-b), after which they are merged together (c-d). The deconfinement is here to slow down the droplets and force them to enter in close contact. The electrodes are visible on the picture in black, one is connected to the ground, and the other one to a high voltage generator (LabSmith), delivering ±600V at 40Hz.

Figure 68 :

 68 Figure 68: Magnetic sorting approach of Zhang et al. 408 . Without external magnets, the droplets are not deflected and are transported toward outlet 1 (a,b). When adding the magnet, only droplets that contain superparamagnetic nanoparticles are deflected toward the bottom outlet 3 (c,d). The magnet can be moved to decrease the distance where magnetophoresis occur, leading the droplets toward the intermediate outlet 2 (e,f).

Figure 69 :

 69 Figure 69: Magnetic sorting. The particles in the droplets are attracted by the micro-soft-magnet fabricated close to the microfluidic channel. This results in the deflection of particles-containing droplets toward the bottom channel. Video 6.3 shows the same scene in motion. The droplets are here 450pL PBS droplets, containing, or not, 18ng of MyOne particles. The carrier oil is Novec-7500 with 2% Picosurf. The pressure is 110mbar, corresponding to a sorting of ~30 droplets/s. Red arrows show the direction of the magnetic force, pointing the micro-magnet.

1 . 3

 13 410 .While bead-based assays (such as ELISA) are already well-established, multifunctional HBs provide a higher degree of complexity and facilitates multiplex assays.Appleyard et al. 422 performed a multiplex sandwich ELISA on barcoded hydrogels as detailed before (similar to Figure70,b-c), where the barcodes indicate what antibody has been grafted on each hydrogel. After doing the ELISA reaction in batch, the particles fluorescence and barcodes are read one-by-one in a microfluidic chip Similar protein assay were performed on HBs with different types of encoding based on photonic crystal relfection 425 , dyes (Luminex technology) or quantum dots (semiconductors nanoparticles) 426 . Analogous assays have been done to detect oligonucleotides. Aliberti et al. 427 developed an on-gel assay consisting in a quenched DNA probe that delivers fluorescence when a complementary strand binds on it. By focusing the fluorescent signal on the gel, the authors claim a 10 5fold enhancement of the assay sensitivity. Similarly, the approach of Appleyard et al. described above has been adapted to microRNA detection 428 , which can be a relevant circulating biomarker of cancer. HBs for 3D cell culture and regenerative medicine Thanks to unique mechanical properties, biocompatibility and potential of chemical/biochemical modifications, hydrogel beads have also been used as a support for 3D cell culture. Hydrogels are already widely used in the organ-on-chip community to mimic extracellular-matrix (ECM), in which cells can grow and feed 429 . While hydrogel containing cells is generally molded and cross-linked directly in the tissue chamber, it has been found interesting to use HBs instead of bulk hydrogel. In a pioneering work, Matsunaga et al. 430 used collagen beads of 50-300µm, preformed on a flow-focusing device, as a cell-culture substrate. Once the beads were covered by cells, they could be manipulated in bulk and be used a building blocks to construct a 3D tissue. Thick (several millimeters) artificial tissues were fabricated with a high uniformity in cell density, and leaving cavities between beads to allow efficient nutrient supply. More recently, de Rutte et al. 108 used PEG-based polymer beads of 50-100 µm

  cytometry. An example is shown on Figure70f. Here,Rakszewska et al. 438 encapsulated single-cells in HBs that contain a lysis buffer and primers for rolling-circle-amplification (RCA). Such amplification is used to generate a detectable, local fluorescent dot where a targeted RNA or DNA sequence has been immobilized. We can then quantify the initial number of molecules that have the targeted sequence by counting the number of fluorescent dots in the HB. A comparable approach has been used to quantify secreted proteins with microparticles trapped in the HB on which a fluorescent ELISA is performed. The proteins were quantified by counting the number of fluorescent particles 189 . A similar approach has also been used to quantify lipids in encapsulated microalgaes 439 .

Figure 72 :

 72 Figure 72: Various MHBs produced with different approaches. a. PEGDA particles embedding iron oxide particles. Scale bar is 30µm. Adapted from 418 . b. Alginate beads embedding high loads of magnetite nanoparticles. They show a superparamagnetic behavior, and can align into columns in the presence of a magnetic field. Adapted from 450 . c. Hydrogel bead in which magnetite was precipitated in situ. Scale bar is 200nm. Adapted from 453 . d. Preparation of multi-composite MHBs. (i) Iron oxide core shell (ii,iii) Cores shells are then coated with poly(NIPAM). Scale bars are 200nm. Adapted from 454 . e. Core-shell composite MHBs prepared by double emulsion of ferrofluid in polyacrylamide in fluorinated oil. Scale bar is 50µm Adapted from 455 .

Figure 75 :

 75 Figure 75: MHBs done by Elina Gilbert. a. MHBs obtained with the presence of dextran in the solution. Undesired clusters appeared around the HBs, which are suspected to be dextran aggregates. b. MHBs obtained without dextran in the solution. We observe less unwanted aggregates, but iron oxide clusters seem to be present around the HBs. c. The MHBs shows a brownish color and are magnetically responsive. d. A cluster of MHBs is extracted from a droplet in the macroscopic magnetic-tweezers. Outlines of the droplet are highlighted in red. The droplet is moving from right to left, the MHBs being at the rear. We see the deflection of the interface, which ultimately lead to droplet breakup. Carrier oil is FC-40 + 2% Perfluorodecanol. Droplet velocity is 0.15mm/s

  ) and mass magnetization (emu/g). The conversion can be done by multiplying the first one by 10 l 4M$ ⁄ where $ is the density of the ferrofluid.

Figure 76 :

 76 Figure 76: MHBs generation embedding three different ferrofluid: the anionic EMG 700SP (a), the cationic EMG 601P (b) and the non-ionic PBG 600 (c).A secondary nozzle is present to add an APS 2.5% w/v solution separately from the gel precursor to avoid early gelation before the flow-focusing junction. Droplet generation worked properly for EMG 700SP and PBG 600 while for EMG 601P, the formation of a precipitate was observed when the ferrofluid entered in contact with APS. This precipitate eventually clogged the chip. The physical properties of each ferrofluid can be found in Table8.

Figure 77 :

 77 Figure 77: MHBs after polymerization and washing. a. HBs containing the anionic ferrofluid EMG 700SP. If we do not loose MNPs, the theoretical MNP volume fraction in the gel is 1.02%. b. HBs containing the non-ionic ferrofluid PBG 600. Theoretical MNP volume fraction is 2.07%. Note that the droplets with the cationic ferrofluid EMG 601P did not polymerize.

  Figure 78c and Figure78dshow reinjection and encapsulation for MHBs that were beforehand centrifuged for 1min at 5,000g and 9,000g respectively. An extended centrifugation of 5min at 15,000g provided even more efficient packing (data not shown because of lack of pictures).

Figure 78 :

 78 Figure 78: Reinjection and encapsulation of MHBs. a. MHBs loaded with 1.85% v/v of MNPs are reinjected in the chip.We can see here that packing is not perfect and gaps exist between the MHBs. b. Same conditions that in (a) but with 0.46% v/v loading (4 times less). Packing was better and the beads flow was smoother. Note that a dust is present on the top right corner of the picture but didn't interfere to the MHBs reinjection. c. MHBs encapsulation. The MHBs contained 1.85% v/v of MNPs and were packed by 1min centrifugation at 5,000rpm. We see important gaps between the MHBs (red arrow) that lead to instabilities, double gel encapsulation and polydisperse droplet sizes. d. After 1min centrifugation at 9,000rpm, the gaps were reduced and the encapsulation was more stable. For (c) and (d), the flow rates were 400µL/h for carrier oil (Novec-7500 + 1% w/t FluoSurf), 500µL/h for water (PBS) and 20µL/h for MHBs, leading to a 100Hz production of ~1.4nL droplets.

Figure 79 :

 79 Figure 79: A MHB-containing droplet pass through the micro-magnetic tweezers (a). When the MHB is in the central region (b), it is squeezed because of confinement, but the magnetic force is not strong enough to break the interface and the MHB remain in the droplet (c). The droplet shown here is moving at 3mm/s in Novec-7500 + 1% w/t FluoSurf. The MHB contains 1.85% v/v of MNPs.

Figure 81 :

 81 Figure 81: Concentration of poly(A) fluorescent probe measured in the supernatant of four reaction mixes that contained: the probe, and HBs with and without oligo-dT primers, and with and without MNPs. Higher values are obtained when HBs did not contain primers, revealing a low capture rate, while the lower values for primer-containing HBs reveals an efficient capture. The presence of MNPs in the gel did not seem to reduce the capture efficiency more than 10%.

  Figure a shows the calculated deflection of light rays starting from different D E . Figure Figure 2Eb shows the deflection function & E (D E ).

Figure

  Figure 2E: a. Delfection of light rays for different starting x coordinates. The parameters are r=300µm, R=600µm, n0=1, n1=1.315 (PTFE) and n2=1.29 (FC-40 oil). b. Deflection function & E (D E ) allows us to calculate how to deform the picture by applying linear interpolation. Linear interpolation using the interp1 function of MATLAB is then used to deform the original picture following the deflection function & E (D E ).

K. 5

 5 Olido-dT magnetic beads mRNA purification 200µL of DynaBeads (1mg) was washed three times with binding buffer (10mM Tris-HCl pH 7.5, 500mM LiCl, 1mM EDTA) and resuspended in 100µL of the same buffer. 200µL of sample was heated at 65°C for 2 min to disrupt secondary structures, and added to the beads. We let 5 min under agitation at room temperature for mRNA to bind onto the beads. The particles are then magnetically isolated and the supernatant is transferred into a new tube. The beads are washed with Washing Buffer B (10mM Tris-HCl pH 7.5, 0.15M LiCl, 1mM EDTA). The washed beads with purified mRNA are then transferred into 20µL of 10mM Tris-HCl and incubated at 75°C for 2min for elution. The supernatant is transferred to a new tube, after which the beads are discarded.

5 '

 5 -/5Acryd/CG ATG ACG TAA TAC GAC TCA CTA TAG GGA TAC CAC CAT GGT TTT TTT TTT TTT TTT TTT V -3' Poly(A) Fluorescent probe 5'-/5Acryd/CG ATG ACG TAA TAC GAC TCA CTA TAG GGA TAC CAC CAT GGT TTT TTT TTT TTT TTT TTT V -3'

  . In this context,Debs et al. used droplet microfluidics to screen 300,000 hybridoma cells in less than a day121 . A similar study demonstrated a screening and sorting of 1 million hybridoma cells, improving considerably the performances compared to conventional antibody screening[START_REF] Mazutis | Single-cell analysis and sorting using droplet-based microfluidics[END_REF] .

Eyer et al. 122

developed a droplet-based assay -DropMap -to characterize antibody-secreting cells in mice immunized with tetanus toxoid. Single-cells were encapsulated in tens of thousands of 40pL droplets among with magnetic beads that are able to capture the secreted antibodies. The droplets are stored into a 2D array and a sandwich ELISA is performed on the beads. The chip is

  129

  environment to continuously synthesize proteins 131 . Elani et al. 132 added sub-compartments in the vesicles to mimic organelles. Besides a high potential value in fundamental research, artificial cells performing various functions could also have several clinical applications in drug development and delivery 129 .

. Liposomes able to amplify DNA and replicate themselves were reported 130 . They were also able to internalize compounds from their

Table 2 :

 2 ). Soft lithography was first introduced byXia et al. in 1998 17 and is now extensively described in the literature, and a detailed protocol is provided in Appendix C. Troubleshooting for the electroplating protocolThe PDMS part had then to be aligned and bonded with the substrate. This operation involves high precision (<3µm) and therefore cannot be done manually.Cottet et al. proposed a protocol to precisely align and bond a PDMS chip with a patterned substrate by means of a MJB4 mask aligner (Süss MicroTec, Figure

	Chapter 2

Table 4 :

 4 Evaluation methods for all involved parameters

		Symbol	Evaluation method
	Intrinsic beads properties Intrinsic fluids properties	$ [ , t [ s, 3	Provided by supplier Water viscosity: literature Interfacial tension: measured (Section 2.2)
	Magnetic field gradient Particle magnetization	∇Q T [	Simulations (Section 2.1) Particles supplier provides M(H) curves. H is the magnetic field calculated through simula-
			tion
	Channel size	&, R	Our aim is to work with sub-nanoliter drop-lets. We used L=30µm, H=35µm.
	Droplet velocity %, ò in , ò Particle packing density ï Number of beads per column å	Measured (Section 2.3) Estimated with images

out Our aim is to achieve the higher throughput as possible. Velocity is desired to be maximized.

Table 6 :

 6 If the pressure is constantly monitored, there is in principle no particular limitation in paring accuracy. Results of an experiment. For different inlet pressure

	Pressure (mbar) Video time (s) Number of droplets Frequency (Hz) Number of errors Error %
	40	40	137	3	3	2.2%
	50	35	177	5	0	0.0%
	60	30	187	6	6	3.2%
	70	30	242	8	3	1.2%
	80	30	300	10	12	4.0%
	90	30	358	12	12	3.4%
	100	30	398	13	3	0.8%
	110	30	473	16	9	1.9%
	120	25	456	18	1	0.2%
	130	25	508	20	0	0.0%
	140	25	567	23	12	2.1%

2 Magnetic hydrogel beads (MHBs) 2.2.1 Blending method

  grafted a methacrylate functionalized silane onto cobalt ferrite MNPs allowing the crosslinking of a polyacrylamide gel.Hwang et al.418 added a maghemite-based ferrofluid into PEGDA solution and formed droplets in a T-junction. After UV polymerization, they obtained MHBs (Figure72a) that were responsive to a magnetic field. The magnetization at saturation for the MNPs was measured to 64 emu/g while it was reduced to 3.3 emu/g for the MHBs. Knowing that the magnetization at saturation is proportional to the MNP loading (Eq. 54), the measurements were in accordance with the fact that the MHBs contained 5% of MNPs in weight. The same approach was used byAndor et al.

	Millimetric magnetic hydrogel beads (MHBs) were prepared by instantaneous gelation of poly(vi-
	nyl alcohol) as cleaning agent for water. Droplets containing the polymer and iron ions were
	dropped into a bath of NH4OH, resulting in their simultaneous gelation and MNPs precipitation.
	Such beads were used to capture dyes, heavy metals 446 , bovine serum albumin (BSA) 447 or ce-
	sium 448 .

2.

181

where MNPs were added in polyacrylamide beads to facilitate manual handling steps, avoiding centrifugation for the different washing steps.

Nozdriukhin et al. 449

demonstrated an on-chip magnetic sorting of polyacrylamide beads doped with MNPs.

In a recent paper, Singh et al.

450

obtained a very high magnetization at saturation value over 50 emu/g by loading alginate droplets with iron oxide MNPs at mass fractions between 65% and 88%.

Table 7 :

 7 Composition of the aqueous droplet phase

		250µL
	• 360µL of Acrylamide/Bis solution 40% (w/w) molar ratio 19:1 • 258µL of Acrylamide solution 40% (w/w) • 382µL of water
	10% w/v APS	30µL
	Total	1000µL

Table 8 :

 8 Properties

of ferrofluids from Ferrotec. Magnetization values are given in terms of volume magnetization (in Gauss

SYBR Green assay (for 20µL in a PCR tube or plate)

	Multiplex assay RT-qPCR experimental details
	K.3
	SuperScript® III RT/Platinum® Taq Mix	0.5 µL
	2X Reaction Mix	12.5 µL
	Forward primer, 10 µM	0.5 µL
	Reverse primer, 10 µM	0.5 µL
	TaqMan probe, 10 µM	0.25 µL
	ROX Reference Dye	0.05 µL
	Sample	1 µL
	DEPC-treated water	To 25 µL
	RT-qPCR program: 50°C 15 min, 95°C 2 min, 40x(95°C 15s, 60°C 30s)
	The program is given here: KiCqStart® SYBR® Green qPCR ReadyMix	10 µL
	clear all Forward primer, 22.5 µM	0.25 µL
	for k=1:1 % Loop for processing several images (1:1 means 1 image only) Reverse primer, 22.5 µM 0.25 µL
	clearvars -except k Sample	1 µL
	% Choose input and output file nameRead='I1.tif'; DEPC-treated water	To 20 µL
	nameWrite='I1-mod.tif';
	% Inner diameter r=0.3; qPCR program: 95°C 2 min, 40x(95°C 15s, 60°C 30s)
	% Outer diameter
		xxix

Ct values for multiplex assay standard curve Exon-exon probe

		Singleplex			Multiplex
	C (ng/µL)	Ct N1	Ct N2	Ct N3	C (ng/µL) Ct N1	Ct N2	Ct N3
	174	16.773	16.831	17.083	174	16.931	16.932	16.987
	17.4	20.148	20.257	20.267	17.4	20.624	20.731	20.559
	0.74	24.818	24.458	24.711	0.74	25.346	25.124	24.806
	0.174	27.866	28.355	26.562	0.174	27.886	27.918	28.088
	Intron probe
		Singleplex			Multiplex
	C (ng/µL)	Ct N1	Ct N2	Ct N2	C (ng/µL) Ct N1	Ct N2	Ct N3
	174	20.767	20.730	20.778	174	20.473	20.489	20.475
	17.4	24.163	24.167	24.227	17.4	24.157	24.076	24.054
	0.74	28.477	28.684	28.657	0.74	28.376	28.161	28.198
	0.174	31.338	31.089	31.218	0.174	30.969	31.319	31.416

Table 1 :

 1 Primers and probes sequencesFour batches of HBs were synthesized as in Chapter 7, Part 4.3, with gel precursor mixes composed as shown in Table2 below:

	Batch 1	Batch 2	Batch 3	Batch 4
	With primers	No primers	With primers	No primers
	No MNPs	No MNPs	With MNPs	With MNPs
	215µL Water	265µL Water	77.5µL EMG700SP	77.5µL EMG700SP
	50µL TBSET	50µL TBSET	137.5µL Water	187.5µL Water
	125µL 4×AB	125µL 4×AB	50µL TBSET	50µL TBSET
	solution	solution	125µL 4×AB	125µL 4×AB
	50µL Acrydite (250µM) modified primer		modified primer 50µL Acrydite solution	solution
			(250µM)

Table 2 :

 2 Composition of gel precursors for the four batches of HBs.

† Droplets were generated either on a flow-focusing device, either on a droplet-on-demand device. They will be described in Chapter 6.

ii

A. Micromagnet fabrication detailed protocol A.1 Ti-Cu Sputtering

Step 1:

Clean 50x75mm glass slides with acetone, isopropanol.

Step 2:

Cover the edges and the back of the slides with scotch tape to prevent plating in the edges.

Step 3: Plasma cleaning: Ar 30sccm, O2 10sccm, Power 50W. Throttle valve 6mtorr. 5min.

Step 4: Titanium: Ar 30sccm. Throttle valve 9mtorr. Power 75W. 6min.

Step 5:

Copper: Ar 30sccm. Throttle valve 9motrr. Power 100W. 6min.

Step 6: Note: Each step of sputtering is preceded by a 5min pre-sput to clean the target.

A.2 Photoresist processing

Step 7: Substrate cleaning: ACE, IPA, desyhdration bake at around 100°C for 3min. Do not bake too much to avoid oxidation of copper.

Step 8: Spin coating of TI Prime as an adhesion promoter for photoresist 300rpm 5s, 4000rpm 30s.

Step 9: Bake at 100°C for 1-3min, let it cool down.

Step 10: Spin coating AZ125nXT 300rpm 5s, 2600rpm 2s, 2500rpm 8s to reach thickness of 40-50µm.

Step 11: Soft bake 4min 95°C, 10min 125°C, let it cool down.

Step 12: Exposure 1500-2000mJ/cm2 in soft contact mode. The resist is still a bit tacky and sometimes sticks on the mask.

Step 13: Development in AZ826 MIF or AZ726 MIF 1min.

Step 14: Rinse with DI water and dry.

Step 15: Measure the depth of a hole on your substrate before plating with a profilometer. It will give you a reference value for deposit height measurement.

iv

The bottle should be above 25°C to re dissolve the eventual solid precipitate. It can be then filtered.

The best is to keep it at 40°C a few hours before plating.

Step 16: Pour around 800mL of plating solution in a 1L beaker, set the hotplate at 40°C with stirring (but with no bubbles appearing, 250rpm with a 3cm stir bar is good).

Step 17: Connect the pure nickel anode in the bath to the positive outlet of the generator.

Step 18: Perform UV ozone cleaning for 15 minutes to improve wetting of the substrate in the bath.

Step 19: Connect the substrate with the crocodile clip and copper tape to the negative outlet of the generator.

Step 20: Turn on the generator and set a direct current of 7mA/cm2 (7mA per square centimeter of area where the metal is deposited. The plating surface can be measure with CleWin: CTRL+A). The growth rate should be in between 2.5um and 4.5um per hour.

It is worth to adjust the current before on a test substrate (e.g. copper tape) to avoid high current peak on your substrate during generator tuning. To avoid detachment of magnets from the substrate, we do the deposition in several steps as follow:

5min deposition -> 10min pause -> 30min deposition -> 30min pause -> 3h deposition -> 30min pause -> 3h deposition -> 30min pause -> 2h deposition.

For pause steps, wash the substrate with H2O + SDS 1g/L and keep it in H2O. The substrate must remain wet because cracks in the resist can appear if it is dried. If a long pause step is needed (e.g. overnight), the water should be bubbled with N2 to remove dissolved oxygen that can oxidize the permalloy deposit.

Step 21: Two substrates can be plated together (see Figure A below): the current delivered by the generator must be doubled. Use ammeters to check that both substrates have the same current density. If not, try to reconnect the alligator clips, increase stirring, check that the copper tape and alligator clip are not wet, or wait a few minutes.

During pause step, you can check the thickness of the substrate with a profilometer.

In these conditions, water evaporates at a rate of around 4mL/h. You can add water in the bath during or after the process.

vi

Step 28: Ultrasonic bath can be beneficial to remove photoresist residues, but is not always necessary.

Step 29: Wash substrates with Water and IPA to remove the stripper, dry with N2.

A.6 TEOS functionalization, or SiO2 sputtering

Because titanium was not etched during the previous step, a surface treatment is needed to allow bonding and silanization. We apply TEOS, but SiO2 sputtering also provided good results.

For TEOS:

Step 30: Clean the substrate with Acetone, Isopropanol and dry them.

Step 31: Perform O2 plasma cleaning.

Step 32: TEOS is applied by vapor deposition. Put the substrate under vacuum desiccator, in the presence of liquid TEOS during 20min. Then heat the substrate at 95°C for a few minutes to evaporate unbounded TEOS. Rinse with isopropanol and N2 dry.

For SiO2 sputtering:

Step 33: Clean the substrates with Acetone and Isopropanol and dry them before putting them in the sputtering machine.

Step 34: Plasma cleaning: Ar 30sccm, O2 10sccm, Power 50W. Throttle valve 6mtorr. 5min.

Step 35: SiO2: Ar 30sccm, O2 5sccm, Power 150W. Throttle valve 6mtorr. 30min.

A.7 Fabrication of PDMS chip with standard soft lithography

Soft lithography is detailed in Appendix 3, however PDMS particular attention has to be paid for PDMS moulding. To allow successful alignment, the PDMS chip must be as flat as possible. Place the wafer fabricated by soft lithography in a big petri dish. Add scotch tape to maintain it at the bottom. Pour the PDMS with curing agent (10:1), degas it and let it cure overnight on a flat optical table. Finish the curing in an oven at 70°C for at least 2 hours.

Step 36: Punch the inlet with a 0.75mm biopsy puncher for the fluidic circuit and with a 0.5mm biopsy puncher for the electrodes.

A.8 Alignment and bonding with MJB4

Step 37: Clean PDMS chips with IPA in ultrasonic bath and dry them. Clean substrates with ACE and IPA.

Step 38: Follow the protocol: Cottet, J., Vaillier, C., Buret, F., Frénéa-Robin, M., & Renaud, P.

(2017). A reproducible method for µm precision alignment of PDMS microchannels with on-chip electrodes using a mask aligner. Biomicrofluidics, 11 (6).

Micromagnet fabrication detailed protocol vii

Step 39: For PDMS bonding, use the plasma in clean room: fill it with O2, then 0.6mbar, 90% power, 0.3min

A.9 Channels silanization

Step 40: Make a solution of 1% v/v Trichloro(1H,1H,2H,2H-perfluorooctyl)silane in filtered Novec-7500 in an Eppendorf tube (100µL is generally enough). The solution must be fresh and can't be stored for an extended time.

Step 41: Flow the silane solution in the chip with a syringe in the microfluidic channels. It is also possible to put a pipet cone in an inlet of the chip and let it fill by capillarity.

Step 42: After 1 or 2 minutes, bow pressurized air or N2 in the chip to dry it and put the chip on hotplate at 95°C for 10min to evaporate remaining silane. Do not keep the silane too long in the channels.

Step 43: Cover the chip with a scotch tape to protect it from dust, it can be stored for weeks or months.

Step 44: The channels for the electrocoalescence electrodes should be silanized following the same protocol but with (3-Mercaptopropyl)trimethoxysilane diluted in acetonitrile at a 1:10 ratio.

A.10 Electro-coalescence electrodes fabrication

Step 45: Put the chip on a hotplate at 90°C and wait few minutes for the chip to warm up.

Step 46: Fill a hole with low temperature melting solder (In51 Bi32.5 Sn16.5, Indium Corp. of America), it should melt immediately.

Step 47: Push the melted solder with a metal tip (an electronic component pin is good) to make it fill the channel. Keep the metal tip in the chip, it will be used as a connector.

Step 48: You can also push another metal pin in the second hole of an electrode, it allows to control the electrical connection with an ohmmeter.

Step When a magnetizable object is subject to a magnetic field, it will produce its own magnetic field, which is opposed to the external field. As a result, the measured value of H can be lower than the actual H in the material. H needs to be corrected following & ,-. = & -04$% (in cgs) where N is a demagnetizing factor. It has an analytical expression for a disk: 0 = x

C.Soft lithography detailed protocol C.1 SU-8 lithography

Step 1: Clean wafer with isopropanol, N2 dry

Step 2: Dehydrate wafer on a hotplate at > 200°C for at least 15min

Step 3: Put wafer in the spin-coater on the dedicated chuck and pour a few mL of SU-8 resist (Microchem)

Step 4: Run spin coater program. The film thickness is adjusted by spin speed and resist viscosity. For example, to achieve 35µm, we used SU-8 2035 with the following spincoating program: 10s 500rpm, 30s 3000rpm.

Step 5: Perform soft bake on hotplate. For 35µm thickness, it is 3min 65°C, 5min 95°C.

Step 6: Put the wafer in the MJB4 mask aligner (Süss). Place the chromium mask in the mask holder. Put the wafer in contact with the mask (in WEC mode). Insulate the wafer through the mask with the following settings: i-line filter (bandpass 365nm), 9s insulation, hard contact mode. The required time of insulation vary with the lamp power, it can be calculated knowing the total insulation energy, which is 160mJ/cm 2 for a 35µm thick SU-8 film.

Step 7: Post exposure bake (PEB) on hotplate. For 35µm: 1min 65°C, 5min 95°C. During PEB, the patterns should appear under the resist.

Step 8: Development under agitation in a beaker filled with PGMEA during 5min.

Unexposed resist is dissolved.

Step 9: Wash the wafer with isopropanol to stop development reaction. Then check the pattern dimensions under microscope and with profilometer. Cracks should appear in the film, they will disappear during the hard bake.

Step 10: Hard bake at > 150°C for 5 to 30min. It will improve the resist adhesion and remove undesired cracks in the film.

C.2 Wafer silanization

Wafer silanization is needed to make it hydrophobic. It will prevent PDMS to stick on the patterns, making easier demoulding.

Step 11: Perform O2 plasma cleaning on the mould

Step 12: Place the mould under vacuum in a desiccator in the presence of a few drops of liquid Trichloro(1H,1H,2H,2H-perfluorooctyl)silane. Wait 20min.

Step 13: Clean the wafer with isopropanol and N2 dry.

Soft lithography detailed protocol xi

C.3 PDMS moulding

Step 14: For one wafer, prepare 40g of PDMS in a disposable beaker and add 4g of curing agent. Mix well and put it under vacuum to get rid of bubbles.

Step 15: Put aluminium foil around the wafer to avoid liquid PDMS spill-overs.

Step 16: Pour PDMS onto the wafer.

Step 17: Put it in oven at 70°C for at least 2h. Longer bake results in stiffer PDMS. For most applications, it is not a problem to let it overnight.

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D. Magnetic field simulation implementation

We used the Magnetic Field No Currents (mfnc) module of COMSOL.

Geometry:

Tweezers were modelled as triangles of base 600µm, height 600µm and thickness 35µm, which are spaced from 75µm apart. The microchannel passing through the tweezers is 30µm wide (y direction) and 35µm thick (z direction). External magnet was 5mm3 cube placed at 3mm away from the tweezers. A boundary sphere of 40mm delimited the geometry. Thanks to an axial geometry, we could cut the geometry in half to reduce computation time. (Figure below,a)

Mesh:

The mesh was set as 'fine' settings everywhere. It was even more refined in the tweezers and channel region with a maximum element size of 7µm. (Figure below,b)

Boundary conditions:

The MH curve measured in Chapter 2 was applied in the tweezers. A constant magnetization was set in the external magnet, which was set by giving a remanent flux density of 1.43T. In the surrounding air, the field validated the equation @ = < = A, meaning that it is not interacting.

Magnetic insulation was set at the sphere boundary, which is usually satisfying if the sphere is big enough. The same condition was set for the symmetry plane, which forces the magnetic field vector to be tangential to the plane.

F. LabView program for droplet generation

We developed a LabView program to measure the size of droplets during generation. We do not provide the code here, but it works in the same principle than in Chapter 3, Part 3.2.1.

We use the "Vision" module, with IMAQdx , to make the camera (Basler) communicate with LabView. The software acquires the pictures that can be treated in real time.

Prior to generate droplets, we take a picture of the channel without droplets inside. This picture is stored in LabView and will be our background picture, and now the chip shouldn't be moved. LabView takes pictures in real time, it subtracts the background to the images. Then a threshold is applied to detect the droplet outlines. The gaps are filled, so that droplets appear as white disks in a black background. We use the "particles analysis" function to measure the area of these disks.

Then, by calculating the droplet volume with this area, we can monitor in real time the volume of generated droplets, which is displayed on the LabView window.

G. Labview program to take pictures of droplets

To avoid taking movies, that would be very heavy, we decided to only take a picture when a droplet is passing in the channel.

On a LabView program which is acquiring pictures in real time, we draw a rectangle ROI (Region Of Interest) on the acquired picture. The ROI is placed on a side of a channel, and we monitor in real time the mean intensity in the ROI. We place it in a way that the intensity signal has a peak when the droplet passes. Then, we define an intensity threshold above which we save the pictures. This way, a picture is taken only when a droplet is passing through the ROI.

H. MATLAB program for capture efficiency calculation and velocity measurement H.1 Capture efficiency

The main idea of the program is detailed in Chapter 3, Part 3.2.1. The program is semi automatic: it does all the treatment (background removing, threshold, finds the droplet outline, measure intensity) and then shows the picture and the outlines to the user, who can validate or not the measurement, and have to say if it is a droplet the contains particles or not (to calculate E, or A).

We did this because there were many errors for outline detection. There are two programs, the main one for picture screening and user decision. And a function analyzePicture that actually does the image treatment.

Main program:

Folder='20191030\Chip

H.2 Velocity measurement

Velocity measurement program is based on circle recognition using the function imfindcircles, then knowing frame rate and circles coordinates, the velocity can be easily calculated for each droplet by calculating the slope of position in function of time. Outliers are removed to get rid of errors due to image analysis. An average is then done on each measured velocity and standard deviation is calculated.

x(i)=centers (1,1); y(i)=centers(1,2); end end % X signal looks like a sawtooth line. We divide it signal into several lines j=1; k=1; absdiffx=abs(diff(x)); absdiffy=abs(diff(y)); bool=0; for i=1:length Computation times were prohibitively long, it took very small time steps, and we couldn't any differences in the results between two consecutive time step. We decided to increase it, and to try with two different meshes, as shown on the table below. The physical separation was performed on a purified DNA/RNA solution and then on a cell lysate.

L.1.1 Oligo-dT beads mRNA separation

From purified DNA/RNA solution

The starting sample was obtained by mixing purified DNA and RNA solutions, each obtained from cultured MDA-MB-231 human breast cancer cells, and spin-column-based purification kits (Macherey Nagel NucleoSpin for DNA and Qiagen RNEasy for RNA). The physical separation was then performed on four samples of concentrations varying from 2ng/µL to 16pg/µL for DNA, and 40ng/µL to 32pg/µL for total RNA (NanoDrop measurements).

100µL of oligo dT beads (500µg of beads) were washed 3 times in binding buffer (10mM Tris-HCl pH 7.5, 500mM LiCl, 1mM EDTA) and resuspended in 25µL of the same buffer. 3µL of sample was added to 27µL of binding buffer, after which 10µL of this solution was added to the 25µL of beads.

We let 5 min under agitation at room temperature for mRNA to bind onto the beads. The particles are then magnetically isolated and the supernatant is transferred into a new tube for further analysis (AMPure purification). The beads are then washed with Washing Buffer B (10mM Tris-HCl pH 7.5, 0.15M LiCl, 1mM EDTA). The washing buffer is kept to quantify the eventual DNA/RNA loss during the washing steps. The washed beads with purified mRNA are then transferred into 10µL of nuclease-free water.

From cell lysate

The lysate sample was obtained by resuspending MDA-MB-231 cultured cells in a Lysis/Binding buffer (Invitrogen) at a concentration of 1000 cells/µL. The continuous phase for generating droplets was FC-40 (3M) fluorinated oil with 2% perfluorodecanol (PFD) as a surfactant. PFD stabilizes droplets but does not prevent from merging, this class of molecules is often referred to as "pseudosurfactants".

The magnetic capture of beads was performed by means of a permalloy tip placed in a coil. When the droplet passes close to the magnetic tip, a generator is manually turned on at 1A DC to power up the coil. The particles immediately form a compact cluster that can be extracted when the droplet moves away from the magnetic tip (see Chapter 5, Figure 7b).

To collect the droplets, the robotic arm places the capillary away from the micro-titer-plate and pushed the oil until the droplet arrive at the tubing end. The droplets are then pushed carefully in PCR tubes. Some oil can be introduced in the tube, but does not perturb the PCR. The diagram below shows the circuit for two valves, but it can be expanded. The Arduino circuit was integrated in a box as shown on the picture below (right). We put six output on which we can plug valves and control them independently.

L.3 Primers

LabView allows the communication with Arduino through special blocks, to power on and off the digital outputs. We can produce a pulse on a valve by programming brief on and off switching on one of these outputs.

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N. Hydrogel beads synthesis protocol

The detailed protocol for non-magnetic HBs synthesis and washing can be found in Zilionis et al., Nature Protocols, 2017. So we describe here only what we modified from this protocol to produce magnetic hydrogel beads (MHBs).

N.1 MHBs synthesis protocol

For HBs containing ferrofluid, the gel precursor solution was obtained by mixing together:

• The carrier oil was composed of Novec-7500 with 1% w/v FluoSurf (Emulseo) and 4µL/mL of TEMED. Flow rates for droplet generation were 1500µL/h for oil, 400µL/h for gel precursor and 55µL/h for APS 2.5% w/v solution, leading to droplets of ~45µm in diameter (~53µm HBs after swelling in TBSET). The droplet size however mostly depends on the flow-focusing chip design, and the flow-rates must be adjusted if another design is used.