Keywords: general considerations, 3, 4 Core-shell Fe 2 O 3 @SiO HaloTag functionalization system, 3, 5 Ferritin-based iron oxide superparamagnetic nanoparticles, GFP nanobody system

cell . . . . 4.3.2 Magnetic response in the living cell . . . . . . . . . . . . . . . . . Establishment of a gradient of nanoparticles in living cells . . . . Recruitment of a protein of interest in living cells . . . . . . . . . 5 Results 5.1 Validation of loading techniques by electron microscopy . . . . . . . . . 5.2 Validation of intracellular targeting by electron microscopy . . . . . . . vi

Summary

This thesis work focuses on the improvements of magnetogenetics, a recently developed technology which implements the use of magnetic nanoparticles to study living cells signaling machineries. Most of the previous works targeted the cellular systems from the outside and activate singling pathways via channels' opening, receptors' clustering or thermal heating.

In this work we addressed the system from the inside, bypassing the external activation and directly altering the network from inside the cell. Our goal is to untangle the complex signaling network and understand how the information flows inside the cell and is converted in a meaningful response, that in general implies the emergence of a polarity state extended over several scales (from the nano to the micro scale).

In order to perform "thoughtful" tasks, such as moving or dividing, cells reorganize asymmetrically their constituents and functions. Their regulation is determined by a tight spatio-temporal arrangement.

An adequate way to question this intricate system is by means of the "perturbative approach": the state of a node in the network is altered, in a highly controlled fashion, and the propagation of the signal is analyzed. This work implements the perturbative approach by modifying the activity of targeted protein inside the cells via magnetic nanoparticles manipulation.

We adopted nanoparticles sufficiently small to exhibit unhindered diffusion inside the cytoplasm and we engineered their surface to recruit active proteins of interest, directly ex vivo. By approaching a magnetic manipulator we generated a dragging force, which bias the Brownian diffusion and leads to the creation of a gradient of proteins inside the cell. Then, by locating the gradient in different areas of the cell, we were able to prompt a protein perturbation highly controlled in space and time. Finally, we analyzed the signaling propagation by quantifying the cellular response both in terms of effectors' recruitment and morphological changes.

The manuscript is organized as follows:

Chapter 1 provides a general overview of the use of magnetic nanoparticles as a mean to interact with biological components. Important works on magnetic actuation at the single cell level are depicted, starting from the original conception iii towards the newest achievements in the field of neuroscience.

Chapter 2 deals with the explanation of the biological framework in which we implemented the magnetogenetic actuation. It presents a general description of the cellular "decision making" process, with particular emphasis on cell motility. In the pathway of signaling propagation, the role of key players, the small Rho GTPases proteins, is detailed and the concepts of signaling network and "signaling modules" are introduced. Finally we explained how the perturbative approach can help untangling the network and how it is exploited in this work.

Chapter 3 describes in details all the materials and methods employed. In particular, it includes background concepts on magnetic nanoparticles' properties, synthesis, functionalization and characterization. Moreover, cellular internalization techniques are described together with the cell patterning procedure, used to standardize the cell shape.

Chapter 4 covers the characterization of our magnetogenetics tool: the distinctive behavior of nanoparticles loaded in living cells as a function of their size and their surface functionalization; the quantification of the perturbation induced by the magnetic manipulator and the response of nanoparticles, both in vivo and ex vivo.

Chapter 5 presents the results obtained in terms of intracellular effectors' recruitment and manipulation of active proteins' gradients. Moreover it illustrates the demonstration of signaling perturbation at the level of the single protein induces by the generation and manipulation of a gradient of endogenous small Rho GTPase.

Chapter 6 summarizes the achievements of this thesis work and includes forthcoming and long term perspectives of magnetogenetics, in the context of single cell actuation.

List of Figures Adapted from [START_REF] Hyun | Magnetic nanoparticles for ultrafast mechanical control of inner ear hair cells[END_REF]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 β-catenin signaling pathway activation, via magnetic stimulation of UML, injected into mice colon. Adapted from [START_REF] María | Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure[END_REF] and [START_REF] Fernandez-Sanchez | Mechanotransduction's impact on animal development, evolution, and tumorigenesis[END_REF] [START_REF] Glogauer | A new method for application of force to cells via ferric oxide beads[END_REF] Behavioral responses in zerbafish and mice expressing the cation channel TRPV4 fused to the paramagnetic protein ferritin, after stimulation with static magnetic field. Adapted from [START_REF] Michael | Genetically targeted magnetic control of the nervous system[END_REF]. . . . . . . . . . . . . . . . 1.14 Remote activation of glucose-sensing neurons in mice. Adapted from [START_REF] Stanley | Bidirectional electromagnetic control of the hypothalamus regulates feeding and metabolism[END_REF]. 15 1.15 Intracellular signaling perturbation performed in a functional cytoplasm, reconstituted from Xenopus eggs and encapsulated in spherical droplets.

Adapted from [START_REF] Hoffmann | Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles[END_REF] [START_REF] Toettcher | The promise of optogenetics in cell biology: interrogating molecular circuits in space and time[END_REF]. 2.12 Genetically encoded photoactivable Rac1 by Wu et al. [START_REF] Yi I Wu | A genetically encoded photoactivatable Rac controls the motility of living cells[END_REF]. . . . . . . . . 2.13 Optogenetic control of cell protrusion, adapted from [START_REF] Levskaya | sup: Spatiotemporal control of cell signalling using a light-switchable protein interaction[END_REF]. . . . . . . . .

Magnetic nanoparticles in nanobioscience

Nanotechnology is a term that in the common knowledge rouse images of ultrasmall high-tech devices, ultra-fast computer chips, and even fictional, self-replicating nano-machines. All these devices are usually associated with the technological exploit and blending of physics, chemistry and engineering, arousing during the twentieth century.

In parallel to this emerging field, comes a recent renewed interest in biology and specially in biotechnology, a more mature discipline which bases its foundation on the great potential of human-controlled biological processes.

The convergence between the scientific disciplines of nanotechnology and biotechnology has given birth to a new field of study, which is being explored nowadays in many laboratories across the world: Nanobioscience [START_REF] Cady | MS Windows NTNanobiology[END_REF].

As a merger of interdisciplinary knowledge, nanobioscience encompasses a wide range of research topics, which can be coarsely divided into two main categories, based on their different sources of inspiration for research [START_REF] Gazit | Plenty of Room for Biology at the Bottom: An Introduction to Bionanotechnology[END_REF]:

Bionanotechnology

Biologically-inspired nanotechnologies that mimic the ability of biological system in building very complex nanostructures. It can be considered as a concrete fulfillment of biology into technological applications at the nanoscale.

Nanobiotechnology

Application of physical, chemical and engineering technologies developed at the nanoscale for better understanding and controlling the biological world. This second direction is clearly related to researchers' ability to imagine and create novel tools that can be used for biological studies. This thesis work inserts in the domain of nanobiotechnology and, in particular, it focuses on fundamental biological research both performed at the nanoscale and aided by nanoscale technologies.

CHAPTER 1. MAGNETOGENETICS

Although the way we experience the biological world in everyday life is essentially at the macro-scale, we all are aware of the hierarchy of complexity that characterizes any living entity. When we scale down to the micrometric level, we start seeing cells, smallest units of life on the order of tens of µm. Cutting down the size, we found bacteria (few µm), viruses (20-450 nm), proteins (5-50 nm), DNA (2-3 nm wide and hundreds of nm long). To fully understand how different components of biological systems work together to make living matter move, grow, interact and reproduce, great efforts in nanobiotechnology have been done in exploiting nanotechnological advances to "get close" to biological objects.

With this purpose in mind, magnetic nanoparticles seem to open up very attractive possibilities (figure 1.1). First of all, they can be synthesized with controllable size, ranging from few nanometres up to tens of micrometres. In addition, their surface can be engineered in order to interact or bind to distinct biological entities, providing a powerful tool for specific targeting. Moreover, the peculiar magnetic properties of nanoparticles make them capable to be "manipulated" by external magnetic field gradients. Last but not least, they can resonantly respond to a time-varying magnetic field, enabling an effective transfer of energy from the field to the nanoparticles [START_REF] Qa A Pankhurst | Applications of magnetic nanoparticles in biomedicine[END_REF].

Consequently, magnetic nanoparticles are valid candidates to remotely manipulate and control specific cellular components in vitro and, more importantly, in vivo. They can be used to probe the mechanical and rheological properties of cells as well as to investigate cell functions and molecular signaling pathways [START_REF] Dobson | Remote control of cellular behaviour with magnetic nanoparticles[END_REF].

Magnetic actuation, defined as the manipulation of biological objects by means of magnetic nanoparticles to induce a biological response, can be considered as a complementary technique to optical tweezers and optogenetics. It brings about the special peculiarity of allowing "action at distance", given the high penetration of magnetic fields into tissues.

Thanks to their special physical and chemical properties, magnetic nanoparticles have been and are currently used in a wide variety of applications in nanobiotechnology,

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

with particular consideration for nanomedicine, spanning from magnetic separation, drug delivery, hyperthermia treatments, magnetic resonance imaging (MRI) and tissue engineering. For a broader description, it is worth to refer to the detailed reviews [START_REF] Qa A Pankhurst | Applications of magnetic nanoparticles in biomedicine[END_REF] and [START_REF] Pankhurst | Progress in applications of magnetic nanoparticles in biomedicine[END_REF].

The following paragraphs offer an overview of magnetic actuation in nanobiotechnology, from its original conception to the newest achievements, providing the general framework of this thesis work.

Magnetic actuation at single cell level 1.2.1 Non-Specific mechanical actuation

The earliest application of magnetic actuation in cell biology dates back to the work of Siefritz in the 1920s [START_REF] Dobson | Remote control of cellular behaviour with magnetic nanoparticles[END_REF][START_REF] Seifriz | An elastic value of protoplasm, with further observations on the viscosity of protoplasm[END_REF]. He investigated the mechanical and rheological properties of the cytoplasm of a dollar-sand mature un-fertilized egg, by manipulatinga magnetic micro-particle inside it, by means of an electromagnet.

In a following attempt in 1950, Crick and Hughes, used twisted and pulled phagocytosed magnetic particles, in order to better quantify the rheological properties of chick fibroblasts in tissue culture [START_REF] Crick | The physical properties of cytoplasm[END_REF].

Afterward, during the 80s, Valgberg et al. focused on the rheology of pulmonary macrophages, isolated from lungs of hamsters, one day after the animals had breathed airborne iron oxide particles. The motions of magnetic particles, contained within organelles of the living cells, were followed by measuring magnetic fields generated by the particles. The alignment of particles was sensed magnetometrically and was manipulated by external fields, allowing non-invasive detection of particle motion as well as examination of cytoplasmic viscoelasticity [START_REF] Valberg | Cytoplasmic motions, rheology, and structure probed by a novel magnetic particle method[END_REF].

Twisting and pulling perturbation

However, according to Dobson [START_REF] Pankhurst | Progress in applications of magnetic nanoparticles in biomedicine[END_REF], the idea of using magnetic actuation to control specific cell functions, such as ion channel activation, originates form the theoretical work of Kirschvink in 1992, which explains the interaction of magnetic iron compounds found in the brain with enviromental electromagnetic filed [START_REF] Kirschvink | Magnetite biomineralization in the human brain[END_REF]. The model demonstrates how a magnetically blocked nanoparticle (a particle which retains a magnetization in absence of a field) would "twist" in response of an external magnetic field, applied at an angle to the magnetization vector of the particles. If we imagine to bind this particle sufficently close to an ion channel, the torque applied would force open and close the channel, in response to magnetic field oscillations.

Exploiting Kirschvink model, in 1990s, Wang, Buter and Ingber conceived the "magnetic twisting cytometry" (MTC), by functionalizing magnetically blocked nanoparticles with molecules that binds to integrins proteins on cell's membrane [START_REF] Wang | Mechanotransduction across the cell surface and through the cytoskeleton[END_REF]. Integrins are transmembrane receptors involved in cell-cell and cell-extracellular matrix (ECM) CHAPTER 1. MAGNETOGENETICS interactions. When triggered, integrins in turn activate biochemical intracellular signaling pathways, which results in a global cellular response, such as regulation of the cell cycle, shape, and motility.

In their approach, magnetically blocked micro-particles were coated with molecules capable of binding specific integrin receptor. After binding to the membrane, the particles were magnetized by a strong magnetic field pulse. Then, by applying a subsequent weaker magnetic field, it was possible to twist the particle in a controlled fashion and investigate the mechanical response of the cell (figure 1.2(a) [START_REF] Dobson | Remote control of cellular behaviour with magnetic nanoparticles[END_REF]). Beside twisting magnetic nanoparticles, one can also "pull" the particles specifically attached to the cell membrane, provided there is a magnetic field gradient. This attractive force, sometimes in combination with torque, can be used to measure viscoelastic parameters of adherent cells, as descibed by Bausch [START_REF] Bausch | Local measurements of viscoelastic parameters of adherent cell BIBLIOGRAPHY surfaces by magnetic bead microrheometry[END_REF], but also to actuate and control specific cellular functions, as reported in the works of Pommerenke [START_REF] Pommerenke | Stimulation of integrin receptors using a magnetic drag force device induces an intracellular free calcium response[END_REF] and Glogauer [START_REF] Glogauer | A new method for application of force to cells via ferric oxide beads[END_REF] (figure 1.2(b), extensively reviewed in [START_REF] Hughes | Magnetic micro-and nanoparticle mediated activation of mechanosensitive ion channels[END_REF]).

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

Mechanosensitive ion channels' perturbation

The most suitable candidates for this kind of perturbation, are mechanosensitive ion channels (MSCs), membrane proteins found on the cell membrane of almost all cell types, capable of initiate singling pathways that leads to fundamental development and normal functioning of tissues. MSCs are sensitive to changes in membrane tension and deformation and are involved in the intracellular transduction of mechanical stimuli (mechanotransduction). The channels vary in selectivity for permeating ions, from non selective between anions and cations, to cation selective allowing passage of Ca 2+ , K + and Na + in eukaryotes, and highly selective K + channels in bacteria and eukaryotes.

Lee at al. succeeded to magnetically modulate the gating of mechanosensitive ion channels, choosing, as a model system, inner ear hair cells, fundamental in the transduction of auditory and vestibular signals [START_REF] Hyun | Magnetic nanoparticles for ultrafast mechanical control of inner ear hair cells[END_REF]. They bound cube-shaped zinc-doped nanoparticles (50 nm) to the dissected sensory epithelia of bullfrogs and stimulated the hair cells with an electromagnet probe. With a magnetic field gradient of about 1000 T/m, they deflected the hair bundle by 10 to 100 nm. Moreover, with a pulsed More recently, Farge and coworkers attained the activation of the tumorigenic Ret/β-catenin pathway via magneto-mechanical stimulation [START_REF] María | Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure[END_REF]. They wanted to mimic the mechanical pressure exerted by tumor growth onto non-tumorous adjacent tissues. To achieve this goal, they intravenously injected ultra-magnetic liposoms (UML), containing superparamagnetic nanoparticles, into the colon tissue of mice and exerted magnetic forces in the tissue, with a 3 mm magnet (0.12 T), subcutaneously inserted in front of the colon (figure 1.4). The magnetically-induced pressure in vivo specifically activated β-catenin signaling pathway, generating an oncogenic response after 1 month of stimulation. [START_REF] María | Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure[END_REF] and [START_REF] Fernandez-Sanchez | Mechanotransduction's impact on animal development, evolution, and tumorigenesis[END_REF].

Specific mechanical mctuation: ion channel activation

A further improvement of magnetic actuation was done by binding the particles directly to the ion channel, in order to initiate controlled cellular response. Compared to the previews studies, the novelty of this approach was to control a distinct signaling pathway, at the individual protein level, using submicrometric sized nanoparticles that requires less force to be pulled (in the order of pico-Newtons). Indeed, by scaling down the interaction, a single specific ion channel can be opened per time, without necessarily deforming the whole-cell membrane and thus excluding the contribution from unspecific force-mediated signaling (figure 1.2(c)).

As a proof of principle, Hughes et al. showed the activation of TREK-1 potassium channel by manipulation of magnetic nanoparticles, targeted against the extended extracellular loop region of TREK-1 [START_REF] Hughes | Selective activation of mechanosensitive ion channels using magnetic particles[END_REF]. Whole-cell electrophysiology measurements confirmed the activation of the channel as a result of direct magnetic force applied.

Very recently the potentialities of mechanosensitive ion channel magnetics' actuation were explored by the group of El Haj, by stimulating the Wnt Frizzled (Fz) receptor to modulate Wnt signalling pathways [START_REF] Rotherham | Remote activation of the Wnt/??catenin signalling pathway using functionalised magnetic particles[END_REF]. The interest in controlling Wnt signalling pathways yields in its crucial role in human Mesenchymal Stem Cell (hMSC) fate determination and, therefore, in its promising use in stem cell-based therapy for bone and cartilage tissue engineering.

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

Receptor clustering actuation

An alternative approach to exploit magnetic actuation was proposed in 2008 by Mannix et al. [START_REF] Robert J Mannix | Nanomagnetic actuation of receptor-mediated signal transduction[END_REF].

They employed inter-particle attractive forces, generated by an external magnetic field, to promote receptor clustering on the cell membrane. Indeed, alternative pathways of cell signaling transduction are activated upon clustering of membrane receptors, induced by multivalent ligands bounding on the receptors (figure 1.2(d)).

Mannix focused on IgE-FcεRI membrane receptors of RBL-2H3 mast cells, that engage Fc portions of single IgE molecules and therefore is involved in immune surveillance in living tissues. When not activated, these receptor-antibody complexes are unclustered. Upon binding of multivalent antigens to the IgE molecules, FcεR receptors oligomerize and an intracellular signalling response is triggered, characterized by a rapid rise in cytosolic calcium influx, followed by vesicle degranulation, histamine release and initiation of a local inflammatory response. The group coated superparamagnetic 30 nm nanoparticles with dinitrophenyl antigen lysine ligand (DNP-Lys) and bound them to IgE-FcεRI membrane receptors complexes. By means of an electromagnetic micro-needle actuator, they generated a high gradient field over sub-micrometric areas of the membrane, inducing receptors clustering via inter-particle interactions, as

Magnet Off

Magnet On (a) Nanoparticles-induced oligomerization of IgE-FcεRI receptor complexes upon magnetic field application. Cheon and coworkers succeed in pushing forwards the concept of cell stimulation via magnetically induced receptors' clustering, by triggering angiogenesis in mammalian cells [START_REF] Lee | Artificial control of cell signaling and growth by magnetic nanoparticles[END_REF]. Angiogenesis is the physiological process through which new blood vessels form from pre-existing vessels. Moreover, it is also involved in the transition of tumors from benign to malignant. Critical to the activation of angiogenic processes is the clustering of Tie2 membrane receptors, induced by angiopoietin molecules. The group of Cheon used 15nm Zn 2+ -doped ferrite magnetic nanoparticles, coated with TiMo214 monoclonal antibody (mAb), to target and manipulate Tie2 receptors. Thanks to the very small size of the nanoparticles, a complete magnetical saturation could be achieved and an external magnetic field of 1.5 T was able to induce strong attractive forces between neighbors nanoparticles. The consequent clustering of Tie2 receptor caused several downstream effectors' activation and even changes in cellular morphology of human umbilical vein endothelial cells (HUVEC), as shown in figure 1.6.

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

In a following study, the group developed a "magnetic switch" for controlling apoptosis cell signaling by clustering death membrane receptors [START_REF] Cho | A magnetic switch for the control of cell death signalling in in vitro and in vivo systems[END_REF].

Apoptosis is the physiological process of programmed cell death, which is crucial to maintain homeostasis in multicellular organisms. The authors demonstrated that the switch can be applied also in an in vivo system (zebrafish), where they induced apoptotic morphological changes. Adapted from [START_REF] Cho | A magnetic switch for the control of cell death signalling in in vitro and in vivo systems[END_REF].

Dissecting mechanotransduction inputs

Consequently to the achievements presented so far, it appears evident that magnetic actuation can help dissecting segregation (clustering) to mechanical (forces) inputs in the activation of mechanosensitive ion channels.

Indeed, in a recent work conducted by Seo et al., the mechanism of Notch and E-cadherin surface receptors' activation was investigated and, in particular, the role of chemical, spatial, temporal and mechanical inputs was deciphered [START_REF] Seo | A mechanogenetic toolkit for interrogating cell signaling in space and time[END_REF].

Notch is a contact-dependent signaling molecule involved in physiological, developmental and pathological processes; its activation undergoes spatial, chemical and mechanical changes. E-cadherin is a key mediator of mechanical signaling and adhe-CHAPTER 1. MAGNETOGENETICS sion at cell-cell junctions.

The authors developed a "mechanogenetic" tool, based on synthetic magnetoplasmonic nanoparticles capable of monovalently bind the membrane receptors Notch or E-cadherin, with a high density of labeling. By regulating the force applied to the bound particles (between 1 and 9 pN) they stimulated the receptors in three different fashions: by mechanical loading only, by receptors' clustering only or by the combination of these two stimuli. Moreover, by playing with the valency of the binding, they explored the effect of nanoscale oligomerization on receptors' activation (schematic in figure 1.8(a)).

With the "mechanogenetic" toolkit, the authors confirmed that mechanical force is necessary and sufficient for Notch activation, regardless of the receptors' oligomerization and clustering; whereas for E-cadherin, they found that spatial accumulation initiates F-actin assembly, but mechanical force is needed to stabilize F-actin filamentous network's formation (figure 1

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

Thermal activation of ion channels

In parallel to the mechanical and receptors' clustering mediated actuation, a substantial progress was conducted by the group of Pralle in 2010, which demonstrated the possibility to thermally activate ion channel receptors [START_REF] Huang | Remote control of ion channels and neurons through magnetic-field heating of nanoparticles[END_REF]. They used the thermal dissipation of heat, generated inside manganese ferrite nanoparticles due to the application a radio frequency (RF) magnetic field. The particles were specifically targeted to the membrane temperature-sensitive ion channel TRPV1 (transient receptor potential cation channel subfamily V member 1) as illustrated schematically in figure 1.9(a). By using, as a molecular-scale temperature probe, the temperature dependent variations of fluorescence intensity of fluorophores, the group was able to show a highly localized temperature increase at the cell membrane (figure 1.9(b)). Moreover, they managed to detect an increase in Ca 2+ influx, to trigger action potentials in cultured neurons and to promote behavioral responses in worms. Stanley et al. extended the magnetic actuation of TRPV1 ion channel to remotely control proteins' production in vivo [START_REF] Stanley | Radio-Wave Heating of Iron Oxide[END_REF]. First they confirmed the possibility to increase intracellular Ca 2+ uptake of human embryonic kidney (HEK) 293T cells expressing TRPV1His. This happened by applying a RF magnetic field to iron oxide nanoparticles, bound to TRPV1His through anti-His functionalization. Next, calcium entry was used to trigger gene expression and proteins' production, via a peculiar Ca 2+ -dependent human insulin construct, which was engineered to provoke proinsulin release upon Ca 2+ uptake (schematic principle in figure 1.10(a) and measured proinsulin release in figure 1.10(b)). They also demonstrated that a RF magnetic field can stimulate insulin release even in a complex organism such as a mouse. Remarkably, Stanley and his colleagues reproduced the same behavior using genetically encoded ferritin nanoparticles. Ferritin is a intracellular iron storage protein produced by almost all living organisms. It has a hollow globular shape, containing iron under the form of ferrihydrite. To all intents and purposes, ferritin is a superparamagnetic nanoparticle, thus it may provide a genetically encodable source of nanoparticles for magnetic field-mediated cell actuation (more details in chapter 3).

Magneto stimulation of neuronal activity

From the non exhaustive presentation of magnetic actuation works that have been conducted in living cells and organisms it can be inferred manifestly how the great advantages of this novel technique can be exploited in the context of neuroscience, to exert a non invasive control over neuronal activity in a whole complex organism. Whereas optogenetical strategies are restricted by poor light penetration into dense tissue and chemogenetical approaches experience slow pharmacokinetics, magnetic actuation seems to represent the new generation of actuation: non invasive, accurate, rapid, reversible and long-lasting.

Based on the this principle, Chen et al. succeeded in stimulating a subpopulation of targeted neurons deep inside the brain of mice, by applying an alternating magnetic field (500 kHz) to synthetic Fe 3 O 4 nanoparticles, bound to TRPV1 ion channels [START_REF] Chen | Wireless magnetothermal deep brain stimulation[END_REF].

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

The stimulated neurons belong to the ventral tegmental area (TVA) of the brain, a region widely implicated in the drug-dependent and natural reward circuitry. Neurons' activity was stimulated only in the presence of a magnetic field and was proven by the enhancement of the activity-dependent expression of the gene c-fos, as shown in figure 1.11.

% positive neurons % positive neurons

Step1. Transfect Wait 4 weeks

Step2. Inject MNPs % positive neurons

Step3. Expose to field % positive neurons Successively, the group of Zhang could trigger muscle contraction and withdrawal behavior in C.Elegans worms [START_REF] Long | Magnetogenetics: remote non-invasive magnetic activation of neuronal activity with a magnetoreceptor[END_REF]. As magnetoreceptor, the authors used an encodable protein similar to ferritin, Isca1 (iron-sulfur cluster assembly protein 1), which is proven to cause calcium influx by membrane depolarization in HEK-293 cells and cultured hippocampal neurons, as shown in figure 1.12(a). When expressing the magnetoreptor fused either to myo-3-specific muscle cells or mec-4-specific neurons in C.Elegans, the worm exhibited controlled muscle contraction upon application of a static magnetic field (figure 1.12(b)).

Similar behavioral outputs were observed by Wheeler at al. in mice and zebrafish [START_REF] Michael | Genetically targeted magnetic control of the nervous system[END_REF]. They focused on the cationic ion channel TRPV4 (transient receptor potential cation channel subfamily V member 4), which has been reported to be responsive to pressure. The authors engineered a single-component magnetogenetic actuator, by fusioning TRPV4 to two subunits of the paramagnetic ferritin protein. They hypothesized that the application of a magnetic field would prompt a torque to the chimeric protein, sufficient to open the channel and depolarize the cells.

By applying a static magnetic field (50 mT), the authors observed an increase of calcium influx in HEK293 cells expressing the fusion protein and, moreover, neurons' firing in mice brain slices. Furthermore, they were capable to translate the magnetic stimulation of specific neuronal areas into behavioral responses, such as coiling in zebrafish and reward in mice (figure 1.13).

Surprisingly, Meister provided evidence that a torque cannot be applied to a small paramagnetic ferritin protein, because it doesn't have a permanent magnetic moment at room temperature [START_REF] Meister | Physical limits to magnetogenetics[END_REF]. Indeed, for superparamagnetic particles above the blocking temperature T B (in the order of tens of degree Kelvin), the magnetic moment can fluctuate thermally (Neel relaxation, paragraph 3.2.2). Therefore, in the experimental conditions presented, the magnetic field could not apply a torque on the nanoparticle, but only compete with thermal agitation to orient the internal magnetic moment of the core. According to Meister, neither the forces exerted by the magnetic field might be able to open the TRPV4 channel, because they fall in the range of 10 -22 N, below the required limit of pN (10 -12 N). Perhaps, the underling biological mechanism is still unclear.

MAGNETIC ACTUATION AT SINGLE CELL LEVEL

More recently, Stanley and coworkers pushed forward their approach and succeeded in regulating neuronal activity in living mice [START_REF] Stanley | Bidirectional electromagnetic control of the hypothalamus regulates feeding and metabolism[END_REF]. They were able to induce in living mice the expression of ferritin nanoparticles, bound to the TRPV1 ion channels of only glucose-sensing neurons (figure 1.14(a)). By remotely stimulating these neurons with a radio frequency magnetic field of 465 kHz, the authors measured an increase in plasma glucose's and glucagon's level, together with a decrease of plasma insulin, which stimulated mice feeding (figure 1.14(b)). Furthermore, they could inhibit the same stimuli by mutating the TRPV1 pore, which made the channel permeable to chloride.

Intracellular signaling stimulation

A corresponding great interest lies in the field of single cell behavior, raised by the potential of magnetic actuation. In fact, at present it remains almost a mystery for scientists how a single living cell can interpret chemical and mechanical cues coming from the environment and translate them in a meaningful response. Albeit many of the molecular components involved in signaling transduction has been unraveled, it remains puzzling how these pieces work in concert. Undoubtedly, beside the interest of controlling a biological response, subsequently to a controlled stimulation, it is of crucial importance to use the stimulation as a mean to perturb specific molecular players, independently one from each other, in a spatially and temporally controlled fashion. Bypassing upstream receptor-level signaling steps, this approach will allow the reconstruction of the intracellular network of signaling and the revelation of the cause-effect relationships between molecules' activation (chapter 2).

Endosomal magnetic actuation

Before entering into the details of intracellular signaling machinery perturbation, it is worth mentioning how problematic could be exploring the intracellular environment CHAPTER 1. MAGNETOGENETICS by magnetic nanoparticles. In fact, before specifically targeting intracellular components with magnetic nanoparticles, the process of internalization always underlies the overcoming of physiological endocytotic pathways, which shields the specific targeting of the nanoparticles. On the other hand, endosomal uptake, when specifically addressed, can be exploit to magnetically manipulate endosomes.

For instance, upon cell endocytosis of 10 nm cobalt ferrite nanoparticles, Wilhelm et al. observed the formation of giant paramagnetic liquid endosomes that can be stressed by means of an external magnetic field [START_REF] Wilhelm | Deformation of intracellular endosomes under a magnetic field[END_REF]. They used this approach to study the mechanical properties of organelles' membranes in relation to the surrounding cytoskeleton. In a following study, the authors pushed forward this technique for measuring the forces required to move endosomes along a microtublein vivo and gained insights into the mechanisms of intracellular trafficking [START_REF] Robert | In vivo determination of fluctuating forces during endosome trafficking using a combination of active and passive microrheology[END_REF].

Steketee at al. used endocytosed magnetic nanoparticles to alter growth cone motility and block neurite growth in both peripheral and central nervous system neurons [START_REF] Michael B Steketee | Nanoparticle-mediated signaling endosome localization regulates growth cone motility and neurite growth[END_REF]. They functionalized magnetic nanoparticles with 29D7, an anti-tropomyosinrelated kinase B (TrkB) agonist antibody, to facilitate their endocytosis into TrkB signaling endosomes. With an electromagnet, the authors were able to alter the endosomes' localization and consequently their related functions, affecting growth cone behavior and neurite growth.

Magnetic perturbation of intracellular signaling

Going back to intracellular signaling perturbation, Hoffmann and his coworkers have shown how functionalized magnetic nanoparticles, directly conjugated to regulatory proteins, can be used to artificially control signaling pathways in space and time [START_REF] Hoffmann | Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles[END_REF].

In particular, they were interested in Ran protein signaling network, which regulates microtubule assembly during cell mitosis. Ran belongs to the family of small G-Protein and acts as a molecular switch, by shuttling between its inactive (GDP bound) and active (GTP bound) state, under the control of a guanine exchange factor (GEF) RCC1 (A simplified schematic of the RCC1/Ran signaling pathways is shown in the lower part of figure 1.15(a)). The authors used superparamagnetic nanoparticles, bound either to Ran or RCC1, to prompt the signaling machinery in an in vitro model system of the cell. This system was made encapsulating functional cytoplasm, reconstituted from Xenopus eggs, in spherical droplets. The group was able to accumulate the nanoparticles at one edge of the droplet and to induce asymmetrical aster formation and microtubule nucleation, upon concentrating Ran proteins via nanoparticles' accumulation (a schema of the principle is presented in figure 1.15(a) and results in figure 1.15(b)). Moreover, when the researchers were using nanoparticles decorated with the upstrem RCC1, they could find that microtubule fibers extended over an even grater range of distances.

Magnetogenetic actuation

In our group, a great effort has been done in pushing the intracellular magnetic perturbation directly in living cells, with the work of Etoc et al. in 2013 [35]. They developed an extensive approach, named as Magnetogenetics, based on the use of functionalized magnetic nanoparticles (f-MNPs) to actuate a highly controlled and localized self-assembly of signaling complexes. They firstly implemented this novel strategy on the Rho-GTPase family of proteins, key regulators of cell morphology CHAPTER 1. MAGNETOGENETICS (chapter 2). In particular they focused on the molecular switch protein Rac1 and its upstream regulator, the GEF Tiam1.

The protein of interest was tagged to the nanoparticles directly in situ, by means of the bio-orthogonal HaloTag system [START_REF] Georgyi V Los | Halo tag: A Novel Protein Labeling Technology for Cell Imaging and Protein Analysis[END_REF], recently optimized for specific targeting of cytoplasmic proteins [START_REF] Liße | Selective targeting of fluorescent nanoparticles to proteins inside live cells[END_REF]. It is composed by two partners, a small HaloTag ligand (HTL) and an HaloTag protein (HT), which bind covalently. In our group's work, 500 nm streptavidin-coated magnetic nanoparticles were functionalized in vitro with a biotinylated-HaloTag ligand and subsequently microinjected in living cells, expressing the protein of interest fused to the HaloTag protein. Upon injection, target proteins were specifically localized on top of the nanoparticles as reported in figure 1.16(a). In particular, Etoc et al. have shown that f-MNPs decorated with Tiam1 can activate Rac1 protein all around the nanoparticles. More interestingly, when the functionalized particles were brought close to the membrane, where Rac1 can recruit effectors, the whole signaling machinery was activated. In fact, the formation of a cell protrusion

MAGNETOGENETIC ACTUATION

was observed and, moreover, a comet of actin enclosing the nanoparticles was detected (figure 1.16(b) and 1.16(c)). In conclusion, this study represents the proof-of-concept of the feasibility of intracellular magnetic manipulation for questioning and controlling the complex cellular signaling machinery.

However, a limitation of this approach was the use of big MNPs, 500 nm in diameter. From a practical point of view, they are very difficult to internalize, because they tend to clog injection pipettes. Second, they are constrained by intracellular obstacles, presumably the cytoskeletal meshwork, and therefore magnetic manipulation requires higher forces (in the order of tens of pN) and longer dynamics, not compatible with the timescale of many cell signaling events. Significantly, big nanoparticles tens to be highly localized at the cell periphery, which, although it is an ideal condition to induce a hot spot-like perturbation, cannot reproduce the physiological graded distribution of active proteins, as required for many spatially regulated processes.

This thesis work inserts in this framework with the fundamental purpose of extending magnetogenetics towards a more methodological approach, with a special consideration of systems biology. In fact a central intent of single cell biology is to understand how exterior inputs, encoded under the form of intracellular activity gradients, are interpreted by cells to accomplish "thoughtful" tasks, such as polarization, migration, or division.

By taking advantage of the pull of the biomolecular knowledge collected in the past, the goal of this work is to characterize the interactions between the component parts of biological organizational units. Therefore, to obtain a new level of understanding and capture the dynamics of large sets of interacting components, extensive quantitative experimentation and mathematical modeling are needed [START_REF] Mazzocchi | Complexity and the reductionism-holism debate in systems biology[END_REF]. The central commitment of this work is to move a concrete step in the development of a solid and flexible magnetogenetic tool able to stand these requirements.

Chapter 2 Cell Polarity 2.1 "Decision-making" process

As mentioned in chapter 1, we are interested in investigating one of the most important attributes of living cells: the ability to make decisions, such as where to go, when and how to divide. A biological system is different from any complex dynamic non-living system, due to its central capacity to elaborate the information. Cells, in fact, integrate the information coming from extracellular conditions, internal processes and their genome and elaborate a decision that determines their future actions [START_REF] Brent | Cell signaling: What is the signal and what information does it carry?[END_REF].

Cell motility

Amongst cellular processes, cell motility or cell migration is particularly interesting for its elemental importance in the development and maintenance of many organisms. For example, during embryogenesis to shape tissues, mechanisms, such as gastrulation and dorsal and ventral closure1 , involve the migration of sheets of cells, as shown in figure 2.1. Cell migration is crucial also in adult stage for tissue renewal, wound healing and to perform immune resistance. In fact, the collective migration of hematopoietic and mesenchymal stem cells contributes to tissue regeneration; fibroblasts and keratinocytes migration is required during wound healing, as shown in figure 2.2, and leukocytes' migration plays a key role in immunological responses [START_REF] Llense | Front-to-rear polarity in migrating cells[END_REF], [START_REF] Entschladen | Cell Migration: Signalling and Mechanisms[END_REF].

Beside its role in normal physiology, abnormal cell migration is at the heart of important human pathologies, such as chronic inflammatory diseases, vascular diseases, mental retardation and cancer metastasis. For example, in the case of metastasis, tumor cells retrieve the ability to migrate and leave the tissue, invading the surrounding ones. The video was provided by A*STAR Institute of Medical Biology [START_REF]See-saw' switch sends cells on the march[END_REF].

Therefore, it is evident that a deep understanding of the mechanisms implied in cell migration is crucial and may lead to the development of novel therapeutic strategies for invasive cancers.

Cells achieve active movement by different mechanisms; less complex prokaryotes

CELL POLARITY

employ flagella or cilia, whereas eukaryotes use more complex mechanisms, associated with cell shape changes, due to cytoskeleton rearrangement. In particular, our study focuses on the migration of mammalian cultured cells in the 2D environment of glass microscopy slides (hereafter referred as ex vivo). In this condition, cells preferentially undergo random motility. Yet, whatever the kind of cell migration (random as observed in an ex vivo environment or directed as it happens in vivo), a key requisite is the establishment of a polarity state [START_REF] Ridley | Cell Migration: Integrating Signals from Front to Back[END_REF].

Cell polarity

The definition of cell polarity refers to an asymmetrical spatial distribution of shape, structure and functions enabling the cell to perform a task. In particular, for cell migration, the cell needs to establish a front-to-rear polarity axis, along which it asymmetrically differentiates structural and molecular components [START_REF] Entschladen | Cell Migration: Signalling and Mechanisms[END_REF]. This symmetry breaking allows cellular processes to be regulated differentially along this polarity axis [START_REF] Li | Symmetry breaking in biology[END_REF].

Certainly, polarity is central in other cellular processes, such as morphogenesis. For example, in the case of neurons (figure 2.3(a)), the definition of the axon growth direction is crucial. Cell polarity is also critical in multicellular environments; for instance, in epithelial tissues, cells need to generate the two opposing surfaces of the epithelium with distinct functions (figure 2.3(b)) [START_REF] Nathan | Cell polarity: mechanochemical patterning[END_REF].

In this latter case, cell polarity only manifests at the molecular and functional level, whereas for neurons, for example, it is morphologically visible, with the presence of a single long axon and multiple short dendrites [START_REF] Llense | Front-to-rear polarity in migrating cells[END_REF].

CHAPTER 2. CELL POLARITY

However, it is important to underlie is that any polarized process requires an organization of the cell machinery that is hierarchical: it engages many different components and functional diversification on different scales, from molecular distributions and assemblies (nm scale) to subcellular structures (µm scale).

For the migrating cell, the polarity axis, pointing along the direction of the motion, defines two regions: a front and a rear. In the front, there is a protruding lamellipodium: a thin sheet of very dynamic cytoplasm, with a dense network of actin. Slender cytoplasmatic projections, the filopodia, extend over the lamellipodium. The region immediately behind, called lamella, is relatively flat, thin and undergoes actin retrograde flow. Adhesion to the surface is provided by focal points and occurs through the mediation of integrin proteins. In the rear of the cell, a meshwork of actin filaments is organized in thick, stable acto-myosin cables, which contract generating retracting forces. All over the cell, it extends a network of microtubules, emerging from the microtubule-organising centre (MTOC), often the centrosome, and oriented in the direction of the motion. Parallel to these structural differences, there are gradients of signaling molecules, such as the Rho GTPases [START_REF] Sit | Rho GTPases and their role in organizing the actin cytoskeleton[END_REF]. In figure 2.4 a schematic representation of the structural and molecular asymmetries in a motile cell is presented. For more details, a great description is provided in [START_REF] Llense | Front-to-rear polarity in migrating cells[END_REF].

CELL POLARITY

CHAPTER 2. CELL POLARITY

In directed migration, the establishment of a polarity axis undergoes the following steps:

External cue perception

Examples of cues are chemical gradients of soluble or non-soluble compounds, that act as chemoattractants or chemorepellants. The migration of an organism in response to a chemical stimulus is known as chemotaxis. One of the first and most characterized examples of chemical sensing is the unicellular eukaryotic ameba Dictyostelium discoideum (figure 2.5). All over the ameba's cell surface, there are receptors uniformly distributed that can interact with specific chemoattractants. In the presence of a graded distribution of chemoattractants, an asymmetric occupancy of the external receptors occurs, interpreted by the cell as a cue [START_REF] Janetopoulos | Directional sensing during chemotaxis[END_REF]. Also immune cells can sense gradients of inflammatory factors or bacterial products, while fibroblasts follow PDGF (platelet-derived growth factor) gradients. Translation and transduction of the signal External receptors activation is often coupled, more or less directly, to intracellular response. For example, G protein-couple receptors (GPCRs) are eukaryotic transmembrane proteins, that can sense molecules outside the cell and directly activate signal transduction. Upon binding with external ligands, GPCRs change their conformation and become able to activate effectors inside the cytoplasm, such as guanine nucleotide exchange factors (GEFs). GEFs in turns can trigger an utmost complex signaling machinery, which very important players are small proteins named Rho GTPases.

Symmetry breaking and cytoskeleton rearrangements

At the front of the cell, a protruding lamellipodium generates and actin polymerization pushes forwards the plasma membrane. All the protrusions along the lateral sides of the cell are suppressed. At the rear, actin depolymerizes and the contraction of actomyosin cables increases the pressure and leads to the rapid protrusion of the plasma membrane [START_REF] Llense | Front-to-rear polarity in migrating cells[END_REF].

RHO GTPASES

In the process of understanding how the information is integrated inside the cell, we mostly concentrate on the second step. In particular we aim at defining more formally the relationship between the molecular components and the flow of information.

Specially interesting is the way the signal is integrated inside the cells by means of molecular filtering, amplification and adaptation. For example, to carry out chemotaxis, bacteria perform "temporal sensing": they integrate the changes in the chemoattractants' gradient over time and move towards the direction of maximal variation. Prokaryotes, such as bacteria, are too small to detect spacial differences in the concentration over their body length, whereas eukaryotes have also "spatial-sensing" abilities and it is of fundamental importance understanding how do they work [START_REF] Tian | Gradient sensing during chemotaxis[END_REF].

At present, it is known that the signaling machinery is far from being conceived as a linear chain of transmitters that cascade signals to their target through homogeneus space [START_REF] Boris N Kholodenko | Signalling ballet in space and time[END_REF]. It is rather comparable to a tangled network in which few molecular components interact at different scales, to generate specific cellular responses.

The highly strict orchestration in space and time of these few components gives rise to the specificity of the cell behavior. The most important junctions of this interconnected network are the Rho GTPases.

Rho GTPases

Rho family small Guanosine Triphosphate (GTP)-binding proteins (Rho GTPases) are small signaling G proteins (between 20 and 30 kDa) belonging to the Ras superfamily. They are highly conserved within all eukaryotic kingdoms, including yeasts and some plants. Twenty-two genes encoding Rho GTPases have been identified in mammals, whereas for Caenorhabditis Elegans, Drosophila melanogaster and Dictyostelium discoideum respectively 5, 7 and 15 [START_REF] Raftopoulou | Cell migration: Rho GTPases lead the way[END_REF]. GTPases are molecular switches that shuttle between two conformational states: a GTP-bound state ("active" state) and a GDP-bound state ("inactive" state) upon hydrolysis of GTP to GDP [START_REF] Etienne | Rho GTPases in cell biology[END_REF] (Figure 2.6).

GAP GEF Rho-GDP Rho-GDP GDI GDP GTP Effectors Rho-GTP Plasma membrane Pi
Although Rho GTPases conformational interconversion has been largely described, CHAPTER 2. CELL POLARITY its regulation is tightly controlled [START_REF] Hall | Rho gtpases and the control of cell behaviour[END_REF]. For example, human genome codify for a family of 60 Rho GTPases activators, called GEFs (guanine nucleotide-exchange factor) proteins, that increase GDP/GTP exchange rate. Similarly, over 70 inactivators (GTPase-activating proteins, GAPs) have been identified [START_REF] Etienne | Rho GTPases in cell biology[END_REF][START_REF] Hall | Rho gtpases and the control of cell behaviour[END_REF]. Moreover, encoded in the human genome, there are proteins able to inhibit the dissociation of GDP from Rho GTPases, called GDI (guanine-nucleotide-dissociation inhibitor) [START_REF] Hall | Rho family GTPases[END_REF]. For more detail descriptions please refer to the reviews [START_REF] Bos | GEFs and GAPs: Critical Elements in the Control of Small G Proteins[END_REF] and [START_REF] Dermardirossian | GDIs: Central regulatory molecules in Rho GTPase activation[END_REF].

Rho GTPases in the GTP-bound "active" state interact with downstream effectors, including approximately 30 kinases and a large number of scaffold/adaptor-like proteins. Their complete identification is very hard, due to the fact that target proteins do not contain a single recognizable sequence motif [START_REF] Etienne | Rho GTPases in cell biology[END_REF][START_REF] Sit | Rho GTPases and their role in organizing the actin cytoskeleton[END_REF][START_REF] Hall | Rho family GTPases[END_REF].

Regulation of Rho GTPases during cell migration

In the context of cytoskeleton reorganization during cell migration, the first insights into the cellular function of Rho GTPases were provided by four pioneering works of the group of Alan Hall, conducted between 1992 and 1995 [START_REF] Ridley | The small gtp-binding protein rho regulates the assembly of focal adhesions and actin stress fibers in response to growth factors[END_REF][START_REF] Ridley | The small gtp-binding protein rac regulates growth factor-induced membrane ruffling[END_REF][START_REF] Nobes | Rho, rac, and cdc42 gtpases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamellipodia, and filopodia[END_REF][START_REF] Kozma | The Ras-related protein Cdc42Hs and bradykinin promote formation of peripheral actin microspikes and filopodia in Swiss 3T3 fibroblasts[END_REF]. They found that Rac1 regulates actin polymerization in membrane protrusions at the leading edge (lamellipodia), Cdc42 controls peripheral filopodia formation and RhoA coordinates contractility at the back of the cell (figure 2.7).

Afterwards, the most highly conserved Rho GTPases (Rac1, Cdc42 and RhoA) were the most studied ones and they are thought to be crucial players of cell signaling machinery for establishing cell polarity during migration.

Following studies have been characterized by the discovery that, in reality, the three Rho GTPases regulate many different signaling pathways in addition to the ones linked to the actin cytoskeleton. They are involved in gene transcription, cell cycle progression, microtubule dynamics, vesicular trafficking and many more cellular functions [START_REF] Etienne | Rho GTPases in cell biology[END_REF]. Moreover, some contradictory experiments have shown that cells were still able to produce respectively lamellipodia and filopodia, even upon Rac1 and Cdc42 genetic suppression [START_REF] Wheeler | Rac1 and Rac2 regulate macrophage morphology but are not essential for migration[END_REF][START_REF] Nalbant | Activation of endogenous Cdc42 visualized in living cells[END_REF].

These evidence came with the recognition that the picture of Rho GTPases signaling machinery is more complex than expected. Interestingly, the ability to govern so many different functions, in the highly dynamic cellular context, implies that Rho GT-Pases are strongly regulated at the spatio-temporal level [START_REF] Pertz | Spatio-temporal Rho GTPase signaling -where are we now?[END_REF].

Indeed, most of the initial understanding about Rho GTPases was built on "global" experimental measurements, based on the creation of dominant-positive (DP) ornegative (DN) mutants of the three canonical Rho GTPases. The injection or the overexpression of a DP Rho GTPases mutant generates the blanket activation of all the effectors, irrespective of the usual highly specific spatio-temporal regulation. This entails that, instead of gaining informations about all the functions of the different effectors, global aberrant effects are produced. The contribution of some effectors can overcome the others and thus give rise to a specific phenotype. A turning point in the filed was the development of Rho GTPases activity reporters, based on Fluorescence Resonance Energy Transfer (FRET) probes [START_REF] Aoki | Visualization of small GTPase activity with fluorescence resonance energy transfer-based biosensors[END_REF]. These biosensors specifically detect the precise cellular location, with nanometer precision, at which Rho GTPases are activated and can follow their temporal dynamics with a resolution of seconds2 . In 2000, for the first time, the group of Klaus Hahn reported the application of a Rho GTPases FRET-based probe to monitor the activation of Rac1 during cell migration [START_REF] Kraynov | Localized Rac Activation Dynamics Visualized in Living Cells[END_REF]. The study confirmed that Rac1 activity is localized at the cell periphery in lamellipodia region of fibroblasts. Similar results were observed with Rac1 and Cdc42 biosensors based on other design [START_REF] Itoh | Activation of rac and cdc42 video imaged by fluorescent resonance energy transfer-based single-molecule probes in the membrane of living cells[END_REF]. However, other findings showed conflicting results; for example Rac1 activation also emerged at the rear of chemotactic neutrophils [START_REF] Gardiner | Spatial and temporal analysis of Rac activation during live neutrophil chemotaxis[END_REF], activation of Cdc42 was found in the Golgi compartment [START_REF] Nalbant | Activation of endogenous Cdc42 visualized in living cells[END_REF] and CHAPTER 2. CELL POLARITY active RhoA was detected also at the leading edge of protruding lamellae in fibroblasts [START_REF] Pertz | Spatiotemporal dynamics of RhoA activity in migrating cells[END_REF].

RHO GTPASES

Spatio-temporal signaling module

This evidence suggests that Rho GTPases can prompt different cellular responses, depending on the distinct location of activation. In fact, according to their position, they can interact only with specific upstream regulators (GEFs and GAPs) and downstream effectors. This view pushes our understanding of Rho GTPases signaling machinery towards a "modular" conception of the network, where a macromolecular complex ("signaling module") is formed upon the interaction between a specific GEF and his target effector, through the mediation of an activated Rho GTPases. The precise spatio-temporal context, allowing the formation of a distinct macromolecular complex, gives rise to the high degree of specificity in the cellular response [START_REF] Pertz | Spatiotemporal dynamics of RhoA activity in migrating cells[END_REF].

Once identified the different signaling modules with standard techniques, the following step is to determine the architecture of the network, i.e. the connections between the different modules. Moreover, it is fundamental to understand their activation kinetics, because every module is only transiently activated during the signal propagation.

To achieve this goal, the combination of highly spatio-temporal resolved imaging techniques and powerful mathematical modelling is needed.

Correlative analysis

Form the computational side, the correlative approach enables the reconstruction of the network's connections. For example, to study the dynamic relationship between two agents in a network, one can measure the activity fluctuation of both, by FRET biosensors in a single cell, and then perform a passive correlative analysis.

Firstly, by computing the auto-correlation function (ACF), the spatial and temporal extension of data sampling can be defined, which will ensure an accurate sampling of the topology and the kinetics of information flow in the signaling network. Then, with the cross-correlation function (CCF), the strength of the linear relationship between the two nodes can be derived [START_REF] Vilela | Fluctuation analysis of activity biosensor images for the study of information flow in signaling pathways[END_REF].

In theory, the correlative analysis allows the reconstruction of a network with more than two nodes, if the CCF between each couple is measured. This approach is limited technically by the number of FRET reporters that can be loaded simultaneously in a single cell, without considerably altering the signaling machinery.

To overcome this limitation, the fluctuation activity data of different biosensors can be imaged separately in different experiments and then integrated by computational multiplexing [START_REF] Christopher M Welch | Imaging the coordination of multiple signalling activities in living cells[END_REF] (schematic in figure 2.8). Each experiment must also measure one cellular activity, common among all the experiments. This shared activity provides a "fiduciary", allowing the time series from different experiments to be correlated.

PERTURBATIVE ANALYSIS

0CV W T G4 G XK GYU/ QN GEW N CT% GN N $ K QN QI[ ∆V ∆V ∆V ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Experiment1 Experiment2 Experiment3
Correlated time series Integrated relationships Figure 2.8: Schematic of computational multiplexing. Adapted from [START_REF] Christopher M Welch | Imaging the coordination of multiple signalling activities in living cells[END_REF].

The first example of multiplexing approach for studying Rho GTPases activity during cell protrusion was the work of Machacek in 2009 [START_REF] Machacek | Coordination of Rho GTPase activities during cell protrusion[END_REF]. He measured the spatiotemporal activity of Rac1, Cdc42 and RhoA by FRET, in fibroblast undergoing directed migration, and used cell edge velocity as "fiduciary". For each experiment the cross-correlation between biosensor activity and cell edge velocity was computed and the timing of each GTPases relative to the onset of protrusion was identified. The results was the prediction of how the GTPases would be timed and spatially shifted one relative to one another (figure 2.9).

Perturbative analysis

Although the multiplexing approach can provide insights on the strength and the nature of the relationships between nodes and can predict, to some extent, the temporal organization and kinetics of these relationships, it has some limitations. First of all, the cross-correlation is not a strictly causative measure, therefore is hard to distinguish cause-effect relation between two interacting components (A causes B causes C), from a common-cause relation between two independent components (B and C are both caused by A). Secondly, the underlying hypothesis of multiplexing is that the agents in the network are linearly related; any nonlinear relation, such as a feedback loop, complicates the analysis of the outcome [START_REF] Vilela | What's wrong with correlative experiments?[END_REF].

To untangle this type of interactions, a powerful method is the perturbative approach, where the activity of a specific Rho GTPase is deliberately manipulated and the propagation of the signal through the network is analyzed. The perturbation is quite different from the ones traditionally performed by cell biologists with genetic tools, such as overexpression of DP or DN Rho GTPases or gene knockdown3 (schematic in 2.6. PERTURBATIVE ANALYSIS figure 2.10). In this case, the perturbation is implemented at the level of the single protein and is highly controlled in intensity, space and time.

Figure 2.10: Schematic of perturbative approach. Adapted from [START_REF] Toettcher | The promise of optogenetics in cell biology: interrogating molecular circuits in space and time[END_REF].

Left: cell signaling machinery comprising feedback and feed-forward loops. Middle: classical genetic perturbations that block or enhance individual nodes inducing phenotype changes. Right: perturbative inputs specifically and precisely perturb distinct nodes in the pathway.

By varying the intensity of the perturbation, one can dissect potential non-linearities in the pathway. By controlling the spatio-temporal extension of the perturbation, one can clarify the necessary and/or sufficient conditions for signaling transduction and transmission through the network (for example, what is the spatial distribution of a specific Rho GTPase able to induce a distinct cellular response? How long this distribution needs to be maintained?).

Sensitivity and robustness balance

As regards cell motility, the perturbative approach may help to clear up a delicate argument about the balance between two opposing trends which appear during the establishment of the polarity axis: sensitivity and robustness. Upon detecting an external cue, a cell integrates and translates the information carried by the cue into a cellular response. Intracellular gradients of active proteins are formed, cytoskeleton rearrangement occurs and a polarity axis is defined; then the directed motion starts. At this point, the cell needs to be still sensitive to other external cues, yet maintaining its polarity axis robust. A disequilibrium between sensitivity and robustness will cost the cell to be either too sensitive, even to noise for example, or to be too persistent in the motion.

Perturbative approach offers an effective method to interpret the constraints of this subtle compromise. In fact, by applying a perturbation highly controlled in intensity, spatial extension and temporal duration, one can determine the necessary conditions able to induce a meaningful response. In this way, the sensitivity of the network connections can be tested. On the other side, choosing a cell already polarized and CHAPTER 2. CELL POLARITY performing the perturbation, one can access the limits of robustness of a pre-established polarity axis.

Feedback and feed-forward loops

A highly important issue in dissecting cell signaling machinery is the correct identification of feedback and feed-forward loops in the network, that undoubtedly play a fundamental role in signaling amplification. Interestingly, in the domain of electronics, there is a long tradition of using time-varying input signals to identify feedbacks in complex electronic devices. By probing the system with variable inputs, one can learn its internal organization, by observing the ways in which it responds [START_REF] Toettcher | The promise of optogenetics in cell biology: interrogating molecular circuits in space and time[END_REF]. Therefore the perturbative approach seems to be the preferential approach to definitely untangle cell networks of signaling.

Optogenetics

Optogenetics is the first developed biological method enabling the possibility to perform a rapid, reversible and modular perturbation at the single cell level, with incomparable spatio-temporal control. As suggested by the name, optogenetics is the combination of genetic and optical tools to achieve the control over a specific cellular event [START_REF] Deisseroth | Optogenetics[END_REF].

Honored with the title of Method of the Year 2010, it was conceived in the domain of neuroscience under the suggestion of Nobel laureate Francis Crick in 1971, which proposed the use of light to control one type of cell in the brain, while leaving the others unaltered [START_REF] Deisseroth | Controlling the brain with light[END_REF].

The actors in optogenetics are light-sensitive proteins, discovered 40 years ago by biologists working on microorganisms able to regulate the flow of electric charge across their membranes, in response to visible light. In particular in 2002, scientists discovered that the alga Chlamydomonas Reinhardtii can swim away from light upon the activation of a light sensitive channel (channelrhodopsin-2). Blue light causes the channel to open and positive ions to flow into the cell.

In 2005, the group of Karl Deisseroth made mammalian neurons expressing channelrhodopsin-2 and used pulses of visible light to attain control over the cells' pattern of firing of action potentials, with a temporal resolution of ms [START_REF] Edward S Boyden | Millisecond-timescale, genetically targeted optical control of neural activity[END_REF]. Since then, laboratories across the world have employed optogentics to control the behavior of cells and even more complexes organisms, using different versions of the microbial opsin gene [START_REF] Lima | Remote control of behavior through genetically targeted photostimulation of neurons[END_REF][START_REF] Douglass | Escape Behavior Elicited by Single, Channelrhodopsin-2-Evoked Spikes in Zebrafish Somatosensory Neurons[END_REF].

Beyond its interest in neuroscience, optogenetics provides a transformative solution to dissect cellular network functions. Particularly interesting in this context is the possibility to genetically encode light-controllable modules and link their photoswitching to the activation of a protein of interest (such as a Rho GTPase or a GEF).

To achieve this task two main strategies have been implemented so far as reposted schematically in figure 2.11 [START_REF] Toettcher | The promise of optogenetics in cell biology: interrogating molecular circuits in space and time[END_REF]. On the left, the first strategy: upon stimulation with light, a conformational change happens and the Rho GTPase's sterical inhibition is removed, leading to its activation. On the right the second strategy: protein activity can be indirectly controlled using light-dependent translocation to the membrane.

The first exploits a light-induced conformational change to switch on-and-off the activity of a target protein. This is the case, for example, of the light-responsive light, oxygen, voltage (LOV) domain from phototropin proteins4 , which can be fused to a protein of interest in a conformation that sterically blocks or perturbs the protein function (schematic in figure 2.12(a)). Upon light shining, photoisomerization of the LOV occurs and the protein regains its functionality. In 2009, Wu and colleagues tested LOV performances by fusing LOV domain with Rac1. They created a photoactivable Rac1 (PA-Rac1), that could reversibly generate precisely localized cell protrusions and ruffling (figure 2.12(b)) [START_REF] Yi I Wu | A genetically encoded photoactivatable Rac controls the motility of living cells[END_REF]. The second strategy for regulating cell signaling is through photodimerization in which the optical control of light induces protein-protein interaction (figure 2.11).

One example is the phytochrome B (PhyB)/phytochrome interaction factor 3 (PIF3) interaction pair from the plant Arabidopsis thaliana (figure 2.13(a)). In the work of Levskaya et al., the PhyB-PIF3 system was used to precisely and reversibly translocate to the membrane active proteins, such as GEFs, with a µm spatial resolution and at CHAPTER 2. CELL POLARITY the second timescale.

In the experiment, PhyB, localized at the membrane by a CAAX motif, underwent conformational changes, catalyzed by red and infrared light. This change triggered the recruitment of PIF3, fused with a GEF protein. The light-gated reversible translocation of the upstream activators of Rho GTPases could precisely reshape and direct the cell morphology of mammalian cells (figure 2.13(b)) [START_REF] Levskaya | sup: Spatiotemporal control of cell signalling using a light-switchable protein interaction[END_REF]. Considering what has been said previously, in the challenge of dissecting the cellular signaling network via optogenetics, it is evident that the spatial control of the illumination pattern of light is crucial. In particular, nowadays light-pattern approaches are available, based on digital micro-mirrors that reflects dynamic user-controlled patterns of light onto specific regions of cells [START_REF] Pastrana | Optogenetics: controlling cell function with light[END_REF] Yet, one limitation of optogenetics in the spatial resolution of activation patterns is proteins' diffusion. In fact, after photoativation, proteins diffuse inside the cells, spreading the spatial distribution of the initial pattern (schematic in the upper part of figure 2.14). Considering the case of optogenetic activation via light-inducible dimerization for manipulating protein distribution at the plasma membrane (figure 2.11), we can assert that the spatial extension of the protein distribution is controlled by the lateral diffusion coefficient D of the protein and the dissociation kinetics constant k off of the dimer. In particular, upon a single pulse of photoactivation, the processes of binding to the plasma membrane, lateral diffusion and complex dissociation define a typical length scale λ = D/k of f for the final protein distribution.

Valon et al. have recently developed a quantitative procedure to predict and manipulate distribution of proteins of interest on the plasma membrane, by a designing a custom pattern of illumination [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF]. They provided an in-depth characterization of the biophysical processes related to CRY2/CIBN dimerizer system [START_REF] Matthew | Rapid blue-light-mediated induction of protein interactions in living cells[END_REF] and achieved high control on the level of membrane recruitment, through the modulation of the frequency of activating light pulses.

Another strategy to contrast the spreading of proteins due to diffusion is the use of double-wavelength reversible optogenetic systems: a local activation is executed by shining a pattern of light at the wavelength of activation in the region of interest and a general deactivation is performed all over the cell (figure 2.14 at the bottom).

Magnetogenetics

A parallel alternative, which is the basis of this thesis work, is Magnetogenetics, which implements the use of functionalized magnetic nanoparticles (fMNPs) to actuate a signaling perturbation with high spatio-temporal control. Our fMNPs, either synthetic or ferritin-based, are fluorescent, magnetic and with a tailorable surface. The pattern of stimulation is controlled by magnetic stimulation and the proteins of interest are tagged to the nanoparticles directly in vivo by genetic manipulation.

CHAPTER 2. CELL POLARITY

Chapter 3

Materials and methods

Nanoparticles in cell biology: definition and examples

Nano-objects are objects having at least one nanoscopic dimension (between 1 and 100 nm); they are of great interest, because they represent a bridge between bulk materials and molecules and are characterized by appreciably different properties, compared both to the corresponding bulk material and to their atomic or molecular components.

In particular, nanoparticles are quasi-zero-dimensional (0D) nano-objects in which all characteristic linear dimensions are of the same order of magnitude (below 100 nm). Due to their size, nanoparticles are the good candidates to interact with living system components like proteins, nucleic acids, macromolecular assemblies, viruses etc. Moreover, they exhibit unique optical, electrical, mechanical and magnetic properties, that can be tailored to probe or manipulate living systems.

In the context of cell biology, one of the most interesting application of nanoparticles is the tracking of individual proteins inside living cells [START_REF] Michel Lourtioz | Nanosciences and nanotechnology: Evolution or revolution[END_REF]. The intracellular environment is crowded of functional proteins, in a state of permanent movement due to thermal agitation, diffusion and intermolecular interactions. Understanding active proteins' motion is fundamental to infer the kinetics of their interactions and, therefore, their functional role.

Artificial semiconductor nanocrystals known as quantum dots (QDs) represent a revolution in this field [START_REF] Igor L Medintz | Quantum dot bioconjugates for imaging, labelling and sensing[END_REF]. With tailorable size and shape, QDs have a size-dependent fluorescence spectrum and their surface can be functionalized to target specific proteins. They are much brighter and more photostable compared to traditional organic dyes and, therefore, enable fast, sensitive and long-term imaging of biomolecules [START_REF] Pinaud | Probing cellular events, one quantum dot at a time[END_REF].

Beside their application as "observation" tools, nanoparticles can be used to manipulate and perturb biological systems at the molecular and cellular level, by exploiting their optical, electric and magnetic properties. Examples of in vitro manipulation of biological molecules include the development of optical and magnetic tweezers, in which light intensity gradients or magnetic field gradients are used to apply forces onto CHAPTER 3. MATERIALS AND METHODS particles, in the range of hundreds of pN [START_REF] Kc Keir | Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy[END_REF]. When those particles are functionalized with biological molecules, both the mechanical properties of the molecules and their interactions with other components can be tested [START_REF] Gosse | Magnetic tweezers: micromanipulation and force measurement at the molecular level[END_REF].

The ex vivo manipulation of intracellular components by the use of functionalized magnetic nanoparticles is the central topic of this thesis work and in chapter 1 the state of art in this field has been already illustrated.

Magnetic properties of nanoparticles

Magnetic nanoparticles are not Homo sapiens invention, they exist everywhere: in human brain, bacteria, algae, birds, ants but also in soils, meteorites and interstellar space [START_REF] Sergey P Gubin | Magnetic nanoparticles[END_REF]. The merit of humans was to understand how to synthetize, visualize and manipulate magnetic nanoparticles for specific purposes.

Compared to bulk magnetic materials, nanoparticles display a wide variety of unusual properties and, more interestingly, those properties can be finely tuned during the synthesis.

Magnetic features of nanoparticles arise from two main effects: the so-called finitesize and surface effects. Yet, before dealing with a detailed description of the nanomagnetism, it is worth to recall the bases of magnetic phenomena in macroscopic systems1 .

Background: macroscopic magnetism

The macroscopic material which exhibits the most impressive magnetic behavior, is iron. However, all kind of substances show some magnetic effects, although very small. According to the strength of the response to an applied external magnetic field, materials can be classified into two groups: "weak"-magnetic (diamagnetic and paramagnetic) or "strong"-magnetic (ferromagnetic, ferrimagnetic and antiferromagnetic) materials [START_REF] Sergey P Gubin | Magnetic nanoparticles[END_REF].

In "weak"-magnetic materials, the two fundamental sources of magnetism are the magnetic moment of the atomic electrons and the electron spin magnetic moment. For some substances, the electron spin and the orbital motion of each atom are exactly balanced, so that the net moment equals to zero. In this condition, an external applied magnetic field can generate induction currents inside the material, which will oppose the field, according to Lenz's law. This phenomenon is called diamagnetism and characterizes all kind of materials (figure 3.1).

Other substances exhibit a net permanent magnetic moment at zero field condition, due to the unbalance of atomic electron spins and orbits. In this case, the small mag-

MAGNETIC PROPERTIES OF NANOPARTICLES

netic atomic moments will tend to align with an external magnetic field, enhancing it. This phenomenon is known as paramagnetism and, in general, is stronger compared to the diamagnetism (always present). As a rule, the diamagnetic and paramagnetic materials have a bulk zero net magnetization at any temperature, in the absence of an external magnetic field. The justification of this evidence will be clarified afterwards in this paragraph. A schematic of diamagnetism and paramagnetism is reported in figurediamparam3.1. On the contrary, "strong"-magnetic materials can exhibit a spontaneous macroscopic magnetization in zero-field condition. The origin of this behavior, called ferromagnetism, lies in a strong long-range ordering of magnetic dipoles, that have a purely quanto-mechanical explanation (exchange force). Ferromagnetism only occurs in few substances such as iron, nickel, cobalt, their alloys, and some alloys of rare earth metals, such as gadolinium. Every ferromagnetic material has a critical temperature, the Curie temperature T C , above which it loses its ferromagnetic properties, due to the thermal tendency to destroy the magnetic order. Figure 3.2: Alignment of atomic dipoles in ferromagnets, antiferromagnets and ferrimagnets, which exists even in absence of an external magnetic field. Adapted from [START_REF] William | Materials science and engineering: an introduction[END_REF].

Ferromagnets have only one magnetic lattice composed of parallel dipoles, whereas antiferromagnets and ferrimagnets are characterized by the superposition of two sublattices, with opposite magnetic orientation. Antiferromagnets (such as MnO 2 ), in zero-field condition, display a net null magnetization and, in the presence of an exter-CHAPTER 3. MATERIALS AND METHODS nal magnetic field, tend to behave as paramagnetic material (with some deviations due to defective structures). In ferrimagnetic materials (for example the iron oxides Fe 2 O 3 and Fe 3 O 4 ) the two opposing lattices are unequal and a spontaneous magnetization remains. A schematic of ferromagnets, ferrimagnets and antiferromagnets is reported in figure 3.2.

Domain structure

Any bulk ferro(i)magnetic material, below the Curie temperature and in the absence of external magnetic fields, consists of small regions, each spontaneously magnetized to saturation, called Weiss domains or simply domains (figure 3.3). The boundaries between domains, the domain walls, are region of finite thickness in which the magnetization gradually change from the direction of one domain to the other. The magnetization directions of domains mainly depend on the crystalline anisotropy; the direction for which the magnetization has its energy minimum (maximum) value is called axis of easy (hard) magnetization. The existence of many domains can be explained by energy balance considerations: the cost of creating domain walls balances the decrease in magnetostatic energy, stored in the external field around the specimen.

Thus, in a macroscopic ferro(i)magnetics material the magnitude of the magnetization M is the vector sum of the magnetizations of all the domains2 . In general, the demagnetized state is the energetically favorable state in large ferro(i)magnetic materials, in the zero-field condition, which explains the previous statement.

The hysteresis loop

When an increasing external magnetic field H is applied to a ferro(i)magnetic material, domains with the some magnetization of the field start to grow (domain walls displacement), even if the global magnetization remains along the axis of easy

MAGNETIC PROPERTIES OF NANOPARTICLES

magnetization (inlet of figure 3.4). At higher field, the magnetization rotate towards H and it reaches the saturation M s . When the field is decreased to zero, a nonzero (remanent) magnetization M r persists. To cancel M r , a field -H C , called the coercive force, should be applied. When the negative field increases further, the saturation value is reached again. The irreversible behavior of magnetization M versus external filed H is called hysteresis and is shown in figure 3.4.

-H c

Nanomagnetism

When the size of a ferro(i)magnetic speciment is reduced down to the nanometric scale, its magnetic properties change completely and are strongly influenced by the so-called finite-size and surface effects [START_REF] Hui Lu | ??th. Magnetic nanoparticles: Synthesis, protection, functionalization, and application[END_REF]. The first one relates to the quantum confinement of electrons and the second to the symmetry breaking of the crystal structure at the boundaries.

Finite-size effect: single domain limit and superparamagnetism

As the sample dimensions reduce, the surface energy of domain walls becomes comparable to the magnetostatic volume energy needed to support a single domain state. The size at which it is energetically convenient retaining a single domain state is called critical size D C . This critical dimension can be influenced by many parameters, such as shape anisotropies, but in general lies in the range of tens of nm. A singledomain particle consists of a uniformly magnetized core, carrying a net magnetic supermoment frozen along its crystal easy direction. If D < D c the magnetization can be reversed only by a uniform rotation of the particle super-moment.

The most interesting phenomenon that happens in magnetic nanoparticles is superparamagnetism, in which the magnetization can randomly flip direction, under the influence of the temperature. This attitude is explained by energetic considerations: CHAPTER 3. MATERIALS AND METHODS the two equivalent easy direction of magnetization are separated by an energy barrier ∆E = KV , where K is the anisotropy constant and V is the volume of the sample. With decreasing the size, the energy barrier becomes comparable to the thermal energy k B T and, when k B T > KV , the system can flip randomly its magnetization, behaving like a paramagnetic material, but without hysteresis, as show in figure 3.5 [START_REF] Hui Lu | ??th. Magnetic nanoparticles: Synthesis, protection, functionalization, and application[END_REF][START_REF] Sergey P Gubin | Magnetic nanoparticles[END_REF]. The mean time between two flips τ is called Néel relaxation time and is given by an Arrhenius law:

τ = τ 0 exp ∆E k B T
where τ 0 is the characterisitic time of the material (generally between 10 -9 and 10 -12 s), ∆E is the energy barrier, k B is the Boltzmann constant and T is the temperature.

The actual magnetic behavior of nanoparticles depends, therefore, on the value of the measuring time τ m with respect to τ. If τ m τ , the relaxation time is too fast and the particle appears as a paramagnetic system, without hysteresis, but with a very high effective magnetic moment µ per particle. On the contrary, if τ m τ , the relaxation is too slow and the particle appears frozen in a specific magnetization, as if it was a ferro(i)magnets (blocked state). The temperature at which τ m = τ is called blocking temperature T B .

We can therefore distinguish two states:

the blocked state: τ m τ or T < T B the superparamagnetic state: τ m τ or T > T B

The superparamagnetic state implies that, as soon as an external magnetic field is applied, the nanoparticles behave like paramagnets (hence the name "paramagnetism"), with the one exception that they have a much larger susceptibility (hence the "super" in the name)3 .

MAGNETIC PROPERTIES OF NANOPARTICLES

When an external magnetic filed is applied to a sample of non interacting freely diffusing superparamagnetic nanoparticles, their super magnetic moments µ start to align along the field. This results in a magnetization of the whole sample different from zero. The magnetization M of the sample (net magnetic moment per units of volume in Am 2 ) in the direction of the applied field H is given by the following equation:

M (H) = nµL µ 0 Hµ k B T (3.1)
where n is the number of nanoparticles, µ is the magnetic moment of the nanoparticles, µ 0 is the magnetic permettivity in vacuum and L(x) is the Langevin equation:

L(x) = 1 tanh(x) - 1 x
Equation 3.1 will be used to determine the magnetic moment of the nanoparticles employed in this thesis work (paragraph 3.6).

In the context of magnetic actuation in living cells, superparamagnetism has fundamental consequences, because after the manipulation with an external magnetic field, the particles do not agglomerate, upon the removal of the field.

Surface effects

Decreasing the size of a specimen, will increase the surface-atoms/bulk-atoms ratio, leading to the local breaking of symmetry at outer boundaries of the particles. Under this condition, some surface and/or interface effects can occur which, as general rule, tend to increase the anisotropy of the system. Therefore the simplified concept of a super-moment breaks down and the model of a poly-nuclear molecule becames more effective. For a more in-depth description please refer to [START_REF] Sergey P Gubin | Magnetic nanoparticles[END_REF].

Physical basis of magnetic manipulation

When a freely diffusing nanoparticle with a magnetic super-moment µ is placed in an external magnetic field B = µ 0 H, it will tend to align its moment to the external field.

If the field has a gradient ∇ B, the particle will be subjected to a magnetic force

F = ∇( µ • B) ≈ ( µ • ∇) B (3.2)
where the second term simplification arises from the assumption that the moment of the particle is not varying in space [START_REF] Gijs | Magnetic bead handling on-chip: New opportunities for analytical applications[END_REF][START_REF] Qa A Pankhurst | Applications of magnetic nanoparticles in biomedicine[END_REF].

The equation 3.2 does not take into account the effect of Brownian motion, which can influence particles' motion when the diameter is sufficiently small. This critical CHAPTER 3. MATERIALS AND METHODS diameter D p can be estimated using the following criterion:

D p ≤ k B T F
where F is the magnitude of the force applied on the nanoparticles. For particles with a diameter below D P one has to solve a Fick drift-diffusion equation for the particle volume concentration C(x, t), rather than the Newtonian equation for the trajectory of a single nanoparticle [START_REF] Sattler | Handbook of nanophysics: nanomedicine and nanorobotics[END_REF]. This second scenario is the typical one we usually face during our magnetic actuation and it will described in more details in paragraph 4.3, with relative measurements in an in vitro model system.

Nanoparticles synthesis and stabilization: general considerations

Traditional "bottom-up" approaches for nanoparticles synthesis can be used for the preparation of magnetic nanoparticles. However, if the elemental composition of the particles is complex, such as in ferrites, the range of possibility narrows down [START_REF] Sergey P Gubin | Magnetic nanoparticles[END_REF][START_REF] Hui Lu | ??th. Magnetic nanoparticles: Synthesis, protection, functionalization, and application[END_REF].

The main chemical challenge consists in producing a population of magnetic grains with a very narrow polydispersity around a suitable size, fixed by magnetic requirements. Sometimes, during the synthesis, many additional steps of size separation are applied, in order to selected a rather monodisperse fraction of the particles. The second critical point is to find a simple, cheap and, more importantly, reproducible method that can be massively implemented.

On the contrary, protein-based nanoparticles such as ferritin, can be easily synthesized in a monodisperse fashion, via expression in living systems and subsequent purification. In this case, difficulties arise from the loading of a sufficiently strong magnetic core inside the protein cage.

Anyhow, a key feature during the synthesis is nanoparticles' stabilization; in fact, due to their small size, superparamagnetic particles behave as a colloid4 [START_REF] Hui Lu | ??th. Magnetic nanoparticles: Synthesis, protection, functionalization, and application[END_REF]. The stability of a colloidal suspension results from the balance between attractive and repulsive forces. According to the DLVO (Derjaguin-Landau-Verwey-Overbeek) theory [START_REF] Derjaguin | The Derjaguin-Landau-Verwey-Overbeek (DLVO) Theory of Stability of Lyophobic Colloids[END_REF], two kinds of forces influence the inter-particle potential in a colloid: 1) strong dipolar van der Waals short-range attraction, 2) long-range electrostatic repulsion due to the electric double layer. To explain this last interaction, let us consider a negatively charged nanoparticle dispersed in solution: to neutralize its charge, a first layer of positive ions (counter-ions) firmly adheres around the surface. This layer is known as Stern Layer. A second layer, the diffuse layer, also forms and is composed by less firmly

NANOPARTICLES SYNTHESIS AND STABILIZATION: GENERAL CONSIDERATIONS

associated co-and counter-ions. Stern and diffuse layers form the so-called double layer and its boundary is termed "slipping plane" (schematic in figure 3.6(a)). The electric potential at the slipping plane is the zeta-potential (ζ-potential) and represents the overall charge that a particle manifests in a specific medium [START_REF] Hui Lu | ??th. Magnetic nanoparticles: Synthesis, protection, functionalization, and application[END_REF]100]. Combining the van der Waals attraction curve with the electrostatic repulsion curve, the net interaction energy curve can be plotted, as shown in figure 3.6(b). The point of maximum repulsive energy is an energy barrier and gives an indication of the stability of the system. In order to agglomerate, two particles need to have sufficient kinetics energy to overcome the barrier. To alter this barrier, one can change the pH or the ionic strength5 of the system and the immediate effects can be followed by monitoring the ζ-potential.

Additional important contributions to this simplified description are the steric repulsion forces, for particles that have an external coating, and magnetic dipolar forces, in the case of magnetic colloids. In particular, steric stabilization is the most common strategy to stabilize colloids and usually involves the functionalization of the particles' surface with long polymers (such as PEG, polyethylene glycol).

CHAPTER 3. MATERIALS AND METHODS

Core-shell Fe 2 O 3 @SiO 2 superparamagnetic nanoparticles

The synthetic nanoparticles used in this thesis work were provided by our collaborators from the Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystémes Interfaciaux) at Pierre et Marie Curie University in Paris.

The particles have a mean physical diameter of 40 nm and consist of a magnetic core of about 8 nm and a silica shell. The core contains between two and five maghemite (γFe 2 O 3 ) superparamagnetic nano-crystals and the silica shell (SiO 2 ) has a double functionalization of amino groups (-NH 2 ) and polyethylene glycol (PEG) chains. The amino groups provide active sites for further functionalization, while the association with the PEG moieties ensures high colloidal stability. A schematic of the particles is presented in figure 3

Synthesis and characterization

The first step in the synthesis (described in details in [START_REF] Vincent Maurice | Synthesis and characterization of functionalized core-shell γFe2O3-SiO2 nanoparticles[END_REF]), is the creation of the maghemite (γFe 2 O 3 ) cores, which is done by co-precipitation of Fe 2+ and Fe 3+ ions under alkaline conditions, following the so-called Massart's process [START_REF] Bacri | Magnetic colloidal properties of ionic ferrofluids[END_REF]. The resulting nanoparticles are coated by citrate anions (C 3 H 5 O(COO) 3 3-) and dispersed in water.

Then, a first silica shell is prepared by condensation of tetraethyl orthosilicate (TEOS, Si(OC 2 H 5 ) 4 ) on the surface of the magnetic cores, in a mixture of ethanol and water and in the presence of ammonia. The silica shell functionalization is achieved in a second step by simultaneous condensation of both a silica-amino derivated compound, the (3-Aminopropyl)triethoxysilane (APTS), and a silica-PEG derivated compound, the 2-(methoxy(polyethyleneoxy)propyl)trimethoxysilane (PEOS). Different APTS/PEOS ratios lead to the synthesis of nanoparticles with variable amino functionalities on the surface. The particles chosen for this thesis work have a ratio of 1, which gives an amino surface density of 0.85 eq/nm 2 [START_REF] Fanny | Charge-based characterization of nanometric cationic bifunctional maghemite/silica core/shell particles by capillary zone electrophoresis[END_REF] and therefore a number of -NH 2 functionalities of about 5000 per particle. In order to have fluorescent nanoparticles, during the coating of the magnetic cores by silica, rhodamine APTS derivated is added [START_REF] Georgelin | Nanoparticle-mediated delivery of bleomycin[END_REF].

Amino-PEG functionalized magnetic core-shell nanoparticles (hereafter MNPs) are dispersed after washing steps in MOPS (3-(N morpholino)propanesulfonic acid) buffer at pH 7.4. A schematic of the synthesis is reported in figure 3.8. Under the appropriate conditions, the colloidal dispersion is stable per several months; however, the silica shells tends to depolymerize over time, as shown in figure 3.9. The magnetic characterization of the bi-functionalized MNPs, performed by vibrating sample magnetometry [START_REF] Vincent Maurice | Synthesis and characterization of functionalized core-shell γFe2O3-SiO2 nanoparticles[END_REF], shows a value of saturation magnetization M S of 3x10 5 A/m, similar for both citrated γFe 2 O 3 nanoparticles and PEG/amine-functionalized core-shell nanoparticles, demonstrating that the silica shell does not alter the magnetic properties of the MNPs.

Functionalization: HaloTag functionalization system

The functionalization system of MNPs is based on the HaloTag technology, recently developed for specific proteins' labeling in living cells [START_REF] Georgyi V Los | Halo tag: A Novel Protein Labeling Technology for Cell Imaging and Protein Analysis[END_REF]. It consists of a modular HaloTag protein (HT), engineered from the Rhodococcus bacteria dehalogenase (DhaA6 ), which can bind covalently to an HaloTag synthetic chloroalkane ligand (HTL). The HTL ligand can be chemically attached to a variety of functionalities, such as the amino groups of MNPs' surface, generating functionalized MNP (f-MNP). The HT protein can be expressed in living cells fused, by means of genetic modification, to a protein of interest (for example a GEF or a Rho GTPase). Therefore this technology allows the recruitment of proteins of interest on top of MNPs' surface via a rapid, specific and permanent binding, directly ex vivo under physiological conditions.

In order to functionalize MNPs' surface with HTL ligands, a powerful "click"chemistry approach has been developed by our collaborators from the Department of Biology at the University of Osnabrück [START_REF] Liße | Selective targeting of fluorescent nanoparticles to proteins inside live cells[END_REF]. In the first step of functionalization, a commercially available dibenzylcyclooctyne-PEG12-NHS (DBCO), characterized by a triple carbon bond, is linked via NHS chemistry to the primary amine on the nanoparticles' surface (step 1 in figure 3.10). Then, the azido N 3 group of a 3-azidobenzoic acid-HTL, synthesized by the collaborators, reacts with the triple carbon bond via click chemistry, covalently binding the HTL ligand

FERRITIN-BASED IRON OXIDE SUPERPARAMAGNETIC NANOPARTICLES

onto the particles (step 2 in figure 3.10). At the end, the unbound -NH 2 groups are converted into carboxyl functionalities -COOH, via reaction with succinic anhydride. This last step confers a negative ζ-potential to the particles, preventing unspecific interactions with the negatively charged cellular membrane (paragraph 4.1.2).

Ferritin-based iron oxide superparamagnetic nanoparticles

Ferritin is an iron storage protein widely express in all living systems, including plants and humans. Its function is to oxidize the highly toxic Fe 2+ into the less toxic Fe 3+ and to store it for physiological needs [START_REF] Hu | The ferritins: molecular properties, iron storage function and cellular regulation[END_REF].

Ferritin consists of an hollow protein cage (apoferritin) of about 12 nm in diameter, which self-assembles in living cells, with an 8 nm internal hole that can contain up to ca. 4500 metal ions. The cage is composed by 24 polypetide subunits, assorted between a heavy chain (HCF) and a light chain (LCF). The HCF domain contains a ferroxidase center that catalyze the oxidation of Fe 2+ , whereas the LCF domain assists in the formation of the cage.

In mammals, the ferritin's core is made of antiferromagnetic ferrihydrate 5Fe 2 O 3 .H 2 O with variable degree of crystallization, depending on the rate of iron deposition and external medium composition [START_REF] Hu | The ferritins: molecular properties, iron storage function and cellular regulation[END_REF]. By controlling the mineralization condition (temperature, pH, oxidation rate etc.) it is possible to achieve in vitro the reconstitution of many different materials inside the ferritin nanoreactor [START_REF] Fantechi | A Smart Platform for Hyperthermia Application in Cancer Treatment : Cobalt-Doped Ferrite Nanoparticles Mineralized in Human Ferritin Cages[END_REF], with the most interesting ones being the superparamagnetic maghemite Fe 2 O 3 and magnetite Fe 3 O 4 [START_REF] Meldrum | Magnetoferritin: in vitro synthesis of a novel magnetic protein[END_REF].

The interest in using ferritin as magnetic nanoparticles for magnetogenetic actuation resides in its physiological and, therefore, non toxic nature and in the possibility to functionalize the surface by either chemical and genetic modifications.

Expression and purification

D.Lisse, former post-doc in our lab, has implemented a robust approach to synthesize a "magnetoferritin" composed by a protein cage of only heavy HCF chains and a magnetic core of Fe 3 O 4 -γFe 2 O 3 . Each subunit HCF is genetically fused via its Nterminus with a single monomeric enhanced green fluorescent protein (meGFP), which does not interfere with the cage self-assembly (mEGF::HCF, 48.7 kDa). Therefore the final ferritin has 24 meGFP all around its external surface, which confer both fluorescent properties to the particles and a 24 specific targeting sites via antiGFP nanobody (detailed explanation in paragraph 3.5.3, schematic and TEM images in figure 3.11).

The plasmid DNA for mEGF::HCF was cloned in pET21a vector and the protein was transformed in bacteria E.Coli BL21-CodonPlus(DE3)-RIPL and expressed via IPTG induction. Then, the protein was purified by heat treatment (ferritin is stable up to 70°C) and washed with ammonium sulphate. Finally, the sample was loaded onto a size exclusion chromatography column for further purifications steps. To increase the colloidal stability of the ferritin in living cells, the surface was also functionalized with methoxy-polyethylene glycol 2000-NHS (PEG2k-NHS) via NHS chemistry as demonstrated in a previous work [START_REF] Liße | Monofunctional stealth nanoparticle for unbiased single molecule tracking inside living cells[END_REF].

Magnetic core loading

To reconstitute a superparamagnetic iron oxide core inside the apoferritin (empty cage ferritin), we followed a protocol developed in 1992 [START_REF] Meldrum | Magnetoferritin: in vitro synthesis of a novel magnetic protein[END_REF]. It consists in the synthetic mineralization of iron oxides inside the nanoreactor, under high temperature and controlled pH and oxidation rate.

In a jacketed vessel under constant N 2 flow, a solution of PEGylated purified apoferritin in NaCl is maintained at 65°C and pH 8.5. Next, an Fe 2+ source, in the form of ammonium iron(II) sulfate hexahydrate ((NH 4 ) 2 Fe(SO 4 ).6H 2 O) and the strong oxidant H 2 O 2 are added to the solution, with a stoichiometric ratio of 1:3 H 2 O 2 :Fe 2+ . The two reagents are loaded simultaneously under the control of a syringe pump; in fact the rate of loading is crucial to regulate the mineralization of the core. The ions H + generated during the synthesis of the core, are balanced by an autotitration system, calibrated to keep the pH stable at 8.5. At the end of the reaction (between 5 and 10 minutes), sodium citrate is added for chelating free iron ions. TEM images of the magnetoferritin cores obtained are shown in figure 3.12, with the relative measurements of the core diameter distribution (peak at 7.4 nm).

The final product has a brownish color, implying the presence of magnetite Fe 3 O 4 . However is has been generally acknowledged that the core is a mixture of magnetite and maghemite (Fe 3 O 4 -γFe 2 O 3 ) with different degree of crystallization [START_REF] Meldrum | Magnetoferritin: in vitro synthesis of a novel magnetic protein[END_REF]. Eventually, by adding cobalt or zinc ions sources, it is possible to mineralize magnetic core with partial replacement of ferrous ions, with enhanced magnetic properties of the particles.

FERRITIN-BASED IRON OXIDE SUPERPARAMAGNETIC NANOPARTICLES

Functionalization: GFP/anti-GFP nanobody system

The 24 meGFPs proteins on top of magnetoferritin can be used for in vivo recruitment of active protein via a recently developed system know as nanobody-GFP (or anti-GFP, or α-GFP) [START_REF] Rothbauer | A Versatile Nanotrap for Biochemical and Functional Studies with Fluorescent Fusion Proteins[END_REF]. It consists of a small (13 kDa) single domain fragment unit (the V H H domain), derived from Camelidae antibodies, able to specifically bind to GFP. The α-GFP binding fragment is the smallest intact antigen-binding site and is characterized by an especially high affinity with GFP (K D =0.23 nM). Moreover, it can expressed in heterologous systems, fused to any other protein of interests (such as GEFs or Rho GTPases), providing a powerful tool of intracellular proteins' targeting.

Magnetic response of MNPs and magnetoferritin nanoparticles.

C. Monzel, post-doc in our lab, has measured the magnetic response of MNPs and magnetoferritin via superconducting quantum interference device (SQUID) magnetometry and the results are reported in figure 3.13. Magnetoferritin loaded either with zinc-doped or cobalt-doped magnetite were characterized and compared with magnetite (Fe 3 O 4 ), horse spleen ferritin 7 and MNPs.

By fitting the trend of the samples' magnetization, we derived the magnetic moments µ for each type of nanoparticle (table 3

INTRACELLULAR INTERNALIZATION STRATEGIES

Intracellular internalization strategies

Before the end of the 80s, a handful of different techniques were developed to internalize biologic material into living cells [START_REF] Celis | Microinjection of somatic cells with micropipettes: comparison with other transfer techniques[END_REF]. In general, they can be classified into two main categories, according to the way macromolecules are delivered: mechanical and aided techniques. Mechanical techniques engage the disruption of the cell membrane, and include, amongst all, microinjection, bead-loading, scrape loading, syringe loading and electroporation. Aided techniques exploit biological phenomena, such as membrane fusion, encocytosis and pinocytosis, to favor the loading into the cytoplasm. Both categories of techniques are characterized by several advantages and drawbacks, that must be evaluated individually considering the specific experimental requirements (cell type, kind and amount of loaded material, number of loaded cells etc.). In the following paragraphs, the three techniques selected for this thesis work will be described in details, pointing out the specific pros and cons.

Mechanical techniques Microinjection

Direct microinjection is a relatively old technique developed in the 70s by Graessmann [START_REF] Graessmann | Microinjection of tissue culture cells[END_REF][START_REF] Celis | Microinjection of somatic cells with micropipettes: comparison with other transfer techniques[END_REF]. It consists in injecting a small volume (between 0.1 and 2 fL) of desired material (proteins, DNA, dyes, dextran, nanoparticles etc.) into adherent cells, by means of precisely designed glass pipettes.

It is an extremely versatile technique that can be implemented for any cell type and is characterized by almost no limitations in the size of the delivered content (big nanoparticles of 500 nm have been injected in living cells in our lab, without altering cell viability [START_REF] Etoc | Subcellular control of rac-gtpase signalling by magnetogenetic manipulation inside living cells[END_REF]). Moreover, only a small amount of injected material is needed (between 2 and 4 µL), which limits the waste of precious samples. However, it is remarkably time consuming and requires a long training to be performed with high efficiency (1000 cells/h injected with minimal cell death).

The first step of microinjection consists in the preparation of glass micropipettes with optimized diameter (between 0.5 and 1 µm) and taper. This was done with a P-97 Micropipette puller form Sutter Instrument. A thin-wall borosilicate glass microcapillary (outside diameter 1.0 mm, inside diameter 0.78 mm) with filament 8 is inserted horizontal into the machine, where it is heated up by an incandescent metal ribbon. While the capillary softens, its two hands are gently pulled apart in order to taper the capillary under the ribbon. Then, the heat is switch off and an overpulling is applied to break the capillary into two symmetric micropipettes. Five main parameters need to be tuned in the Sutter machine to achieve the desired conformation of the tip: pressure (air pressure during the cooling phase), heat (electrical current supplied to the ribbon), pull (force of the hard final pull), velocity (force during the soften phase) and delay (time between when the heats turn off and when the hard pull is activated) [START_REF]P-97 Operation Manual[END_REF]. Adapting the recommendations in the Pipette Cookbook provided by Sutter [START_REF] Oesterle | Pipette Cookbook[END_REF], the following parameters have been finally retained:

Pressure Heat Pull Velocity Delay 500 526 60 80 122 These parameters allow the production of hollow micropipettes with internal diameter of about 0.6 µm and relatively short taper. The diameter was calculated by measuring the pressure needed to blow air bubbles through the microcapillary inside a solution of pure methanol, according to the following relation [START_REF] Hagag | Precise, easy measurement of glass pipet tips for microinjection or electrophysiology[END_REF]:

d [µm] = 70.4 P [hP a] 1.01 (3.3)
The microinjection is performed with an inverted microscope, under phase contrast illumination onto cells adherent on microscope glass coverslips in perfect physiological conditions (with surrounding culture medium9 and warming system at 37°C). The micropipette is filled with maximum 4 µl of the loading content, dispersed either in PBS 1X or HEPES 200 mM, and is placed on top of the cell by means of a micromanipulator. Then the material is delivered with the aid of Eppendorf FemtoJet Microinjector by regulating the injection pressures (constant flow and injection pressure). Detailed protocols for microinjection are presented in [START_REF] Zhang | Microinjection technique and protocol to single cells[END_REF] and [START_REF] Komarova | Components of a microinjection system[END_REF]

INTRACELLULAR INTERNALIZATION STRATEGIES

Bead-loading

Bead-loading is a relatively simple mechanical technique, developed in 1987 for massive loading of biomolecules in living cells [START_REF] Mcneil | Glass beads load macromolecules into living cells[END_REF]. Cells adherent on glass coverslides and surrounded by a solution of the loading material, are repetitively crashed by huge glass beads, that create transient holes onto their membrane, letting the material in. Although very rude, bead-loading is a quite powerful technique, with an efficiency that can reach 70% of cell loaded per dish10 and high cell viability after the loading.

Before stating, glass beads of 100 µm in diameter are washed once with NaOH 2M (to renew the silica surface), twice with deionized water (to decrease the pH) and once with pure ethanol (for sterilization) and dried over night. Then, they are loaded into an "home-made" container with a nylon mesh-bottom exit hole (100 µm mesh size) and kept under dry atmosphere.

For the loading, the adherent cells are washed once with PBS. Then a small volume (less than 50 µl) of the loading solution is poured on top to form a thin layer. The solution contains highly concentrated (>200 nM) nanoparticles in PBS and 20% v/v of Pluronic F-68/H 2 O (1:1), a non-ionic surfactant that favors the formation of cell membrane's holes. After that, the glass beads are sprinkled over the cells and the sample is then striked against the hood tabletop, between 6 and 8 times. Subsequently, extensive washing steps with warm medium are needed to remove the loading solution and the glass beads [START_REF] Hayashi-Takanaka | Tracking epigenetic histone modifications in single cells using Fab-based live endogenous modification labeling[END_REF]. After the loading, cells need at least 1 h to completely recover. If the cell confluence is kept high (>60%) the risk of detachment is quite low. Moreover, by regulating the concentration of nanoparticles in the solution, one can adjust the amount of content loaded, without altering the efficiency of the process. A detailed standard protocol of bead loading, provided by Tim Stasevichis, is reported in appendix A [START_REF] Hayashi-Takanaka | Tracking epigenetic histone modifications in single cells using Fab-based live endogenous modification labeling[END_REF]. Examples of HeLa cells loaded either with silica MNPs or ferritin, are shown in figure 3.15.

Facilitated techniques

Pinocytic loading

Pinocytic loading is a method developed by Okada and Rechsteiner in 1982, which exploits the osmolitic lysis of pinocytic vesicle 11 to deliver macromolecules inside the cytoplasm of a large number of cells [START_REF] Okada | Introduction of macromolecules into cultured mammalian cells by osmotic lysis of pinocytic vesicles[END_REF].

Initially conceived to deliver enzimes, antibodies and dextran, it can be adapted for many kind of molecules and even nanoparticles, although there is a limit in the maximum size of the loaded content.

Briefly, cells grown on coverslips are incubated with a hypertonic medium containing 0.5 M of sucrose crystals, polyethylene glycol PEG 1000 and the macromolecules to be loaded (at high concentration, >100 nM, provided that the medium is not diluted over 70%) for at least 15 min at 37°C. Under this conditions, pinocytic vesicles form, through membrane invagination. Subsequently, the coverslide is plunged for 2 min into an hypotonic medium, consisting of culture medium/deionized water 60:40. Due to osmolitic shock, pinocytic vesicles burst and release their content in the cytoplasm. An example of pinocytic loading of commercial 25 nm fluorescent nanoparticles is shown in figure 3.16. Although the protocol is quite simple and massive, the specific conditions to maximize the amount of loaded material must be optimized for each cell type and for each kind of nanoparticles. Indeed, sometimes the disruption of the vesicle doesn't happen and the nanoparticles remain trapped inside the pinocytic vesicles.

CELL PATTERNING

Cell Patterning

A major goal of our magnetogenetic actuation is to achieve high biological statistics by performing a massive analysis in a parallelized fashion. Our final objective is to investigate the intracellular signaling network by prompting a unified perturbation to cells characterized by identical environmental conditions.

In this context, it is evident that the shapes' heterogeneity of cells seeded onto microscopy slides is the first parameter to be managed. In order to gain control over the cell shape morphology, we took advantage of a micro-pattering techniques, recently developed in Mathieu Piel's lab [START_REF] Azioune | Simple and rapid process for single cell micro-patterning[END_REF]. The protocol involves the seeding of cells on a surface that exhibits areas of different adhesiveness (pattern), obtained by engineering the spatial characteristic of the glass substrate. Indeed, it has been demonstrated that by retraining the adhesion geometry it's possible to induce controlled structural conformation in the plasma membrane, which in turns yields to a controlled orientation of cell polarity [START_REF] Théry | The extracellular matrix guides the orientation of the cell division axis[END_REF]. With this technique is possible to replicate the complex intracellular architecture in a standardized fashion.

The protocol is based on the use of UV light to specifically burn a protein/cellrepellent substrate deposited on glass, through microfeatures defined by a pre-designed photomask. This process creates onto the glass substrate two regions of different protein adhesion, defining areas of preferential seeding for cells. The protein/cellrepellent material chosen is poly-L-lysine-grafted-polyethylene glycol (PLL-g-PEG), a cheap commercially available material that binds strongly on glass.

The protocol develops in three basic steps:

Generation of patterns

Firstly, glass coverslips are cleaned via sonicating bath with acetone and ethanol, 5 min each. Then, dried converslips are exposed to air plasma for 5 min in order to activate the carboxyl groups on the glass surface for further funcionalization. After that, coverslips are incubated with 0.1 mg/ml PLL-g-PEG in 10 mM HEPES at pH 7.4 for 1 h. Finally they are rinsed with water and carefully dried.

Patterns are generated by placing the pegylated coverslips on a quartz photomask, covered on one side by a chromium thin layer reporting the negative of the pattern to be generated. To assure close contact between the glass slides and the mask, a 1.5 µl water droplet is added, which provides a space of few µm. Successively, the substrates are exposed to deep UV light of 5 min and the PEG is burned only in the region not covered by the mask. Substrates are then recovered and can be stored for months.

Seeding of cells

Before seeding, the patterned coverslips are incubated for 30 min with a solution of fibronectin in 100 mM NaHCO 3 (pH 8.5) at a concentration of 25 µg/ml.

CHAPTER 3. MATERIALS AND METHODS

Additionally, fluorescent fibrinogen could be added (10 µg/ml), to identify the patterns' location during the experiment.

After washing the coveslides twice with sterile PBS 1X, the cells are seeded on top of the substrate in few droplets of about 30 µl at a concentration of 300 cells/ml and incubated for 15-20 min at 37°C. Then, 2 ml of warmed medium is gently added and cell are let adhere on the substrate for at least 1 h.

Washing

After checking that most of the cell actually have spread correctly onto the patterned substrates, the unattached cells are removed by extensive washing of the surface.

In figure 3.17 is reported as an example the seeding of HeLa cells on alternating crossbow and disk patterns. The efficiency is of about 30% of patterns with a single cell seeded taking the shape of the micropattern. In general, cells stay attached and confined for at least 24 h. Chapter 4

Characterizations

As mentioned in paragraph 1.3, a great effort has been done in our lab in inducing highly controlled intracellular perturbation by means of functionalized magnetic nanoparticles [START_REF] Etoc | Subcellular control of rac-gtpase signalling by magnetogenetic manipulation inside living cells[END_REF]. In particular, Etoc et al. have shown that 500 nm magnetic nanoparticles, functionalized ex vivo with the GEF Tiam1, can specifically activate the Rho GTPase Rac1 and, moreover, when brought close to the cell membrane, they induce firstly cell protrusion and then the formation of a comet of polymerizing actin (figure 1.16(c)).

However, some limitations arise as a consequence of using nanoparticles with large diameter (500 nm). First of all, inside cells, they are firmly constrained by intracellular obstacles, presumably the cytoskeletal meshwork and the internal membrane network of endoplasmic reticulum. Therefore, magnetic manipulation requires both the application of large forces (in the order of tens of pN) and non physiological condition, such as serum starvation, where the cytoplasmic elasticity is considerably reduced.

Moreover, hindered nanoparticles behave as hot-spot of signaling perturbation, whereas more physiological Rho GTPases' perturbation require the formation of a gradient-like distribution of proteins, with a spatial extension of few microns. Furthermore, the dynamics of nanoparticles displacement (in the order of tens of minutes) is not compatible with the time scale of many cell signaling events.

In addition to that, on the basis of experimental considerations, big nanoparticles are very difficult to inject as they tend to clog micropipettes and only few of them (between 5 and 10) can be delivered without altering cell viability.

All these constraints, has driven us to redesign our perturbation by exploiting smaller nanoparticles, with the aim of generating more physiological, tunable and reversible gradient of protein of interests inside living cells.

Diffusion regimes

First of all, based on the work previously done in the team, we wanted to understand how small magnetic nanoparticles behave in the crowded intracellular environment.

CHAPTER 4. CHARACTERIZATIONS

Previous studies have shown that, when in contact with biological media, nanoparticles get decorated by a "corona" of biological macromolecules, in a dynamic process of continuous adsorption and desorption. The corona can be roughly divided into a hard component, composed by the protein with high affinities towards the nanoparticle, and a soft component of less bounded proteins [START_REF] Monopoli | Physical-Chemical aspects of protein corona: Relevance to in vitro and in vivo biological impacts of nanoparticles[END_REF][START_REF] Lundqvist | Nanoparticle size and surface properties determine the protein corona with possible implications for biological impacts[END_REF][START_REF] Cedervall | Understanding the nanoparticleprotein corona using methods to quantify exchange rates and affinities of proteins for nanoparticles[END_REF].

Protein corona is fundamental in our manipulation, because protein associated to nanoparticles can prompt undesired biological responses on a long term, that can either degrade the nanoparticle, damaging its functional role as signaling platform, or even trigger toxicological reaction, altering cell viability.

In particular, we have identified two keys parameters which play a fundamental role in the ability of manipulating nanoparticles inside living cells: the size of the nanoparticle and its surface functionalization.

Effect of the nanoparticles' size

In order to investigate the effect of the size dependence of the cytoplasmic mechanical parameters, we performed a standard passive microrheology assay [START_REF] Weihs | Bio-Microrheology: A Frontier in Microrheology[END_REF] by measuring the intracellular mobility of fluorescent nanoparticles of different sizes.

We chose commercially available rhodamine-doped latex nanoparticles of 15, 25, 50, 75 and 500 nm, all with streptavidin functionalization. Indeed, by fixing the nanoparticle structure and surface chemistry we homogenize the contribution of nonspecific interactions within the cytoplasm among the experiments, evaluating only the size effect.

After internalization of the particles at low concentration by microinjection, we imaged their motion by fluorescence microscopy. We observed that nanoparticles with diameter of 75 nm and above exhibited a strong confined motion, whereas nanoparticles below 50 nm were diffusing freely inside the cell, as illustrated by the maximum intensity projection of the associated movies in figure 4.1.

To better quantify the diffusion properties of the particles, we tracked their individual motion via MMT Matlab code [START_REF] Sergé | Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes[END_REF]. Then, from each set of individual trajectories, we performed the mean square displacement (MSD) analysis [START_REF] Saxton | Single-particle tracking: the distribution of diffusion coefficients[END_REF] and, from the linear fit of the first four point of the MSD vs time lag τ trend, we derived the instantaneous mean diffusion coefficient D for each family of nanoparticles (figure 4.2).

We observed a dramatic transition in the mobility as the nanoparticle reaches 75 nm: while 15, 25 and 50 nm nanoparticles have median diffusion coefficients around 1 µm 2 /s, 75 nm nanoparticles have a median diffusion coefficient around 0.01 µm 2 /s and 500 nm around 0.001 µm 2 /s. This evidence underlies the heterogeneity of the cytoplasmic micro-environment, and ascertains the simplified conception of the cytoplasm as a poroelastic material [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF].

When considering the individual trajectories, we noticed that, for the particles below 50 nm, the MSD curves showed a standard Brownian motion, reflected by a linear MSD vs τ trend with slopes of 1 (when plotted in semi-logarithmic scale). For this condition, we estimated the intracellular viscosity by the Stokes-Einstein relation1 to be about ten times greater than the viscosity of water. For nanoparticles with a diameter bigger than 75 nm, a sub-diffusive trend was observed (slope less than 1), which implies elastic trapping of the surrounding medium (for more details about sub-diffusive behavior, please refer to [START_REF] Saxton | Single-particle tracking: the distribution of diffusion coefficients[END_REF]).

Effect of the nanoparticles' surface

We explored the effect of the surface charge by investigating the intracellular stability of MNPs exhibiting different ζ-potentials. This was achieved by tuning the excess of succinic anhydride needed to convert the positively charged amino groups on top on the MNPs into the negatively charged carboxyl groups, as reported in the calibration curve in figure 4.3. MNPs with a ζ-potentials of +20 mV at pH of 7.4 (only PEG/amino groups), when microinjected in living cells, immediately localized at the plasma membrane, due to electrostatic interactions with the negatively charged membrane phospholipids (figure 4.4(a)). When the NH 2 groups were only partially converted in COOH, reaching a ζ-potentials of -2 mV, the MNPs after 30 min upon injection, were trapped in subcellular compartments, unable to interact with intracellular components (figure 4.4(b)). A complete colloidal stabilization was achieved by fully converting the surface exposed amines into carboxyl groups (obtaining a ζ-potential of -20 mV). Under this condition, MNPs could freely diffuse in the cell for several hours (figure 4.4(c)).

Subsequently, we investigated the effect of the colloidal stabilization of ferritin accomplished by steric hindrance via PEG2k functionalization. It has been demonstrated that upon injection in living cells, bare iron-loaded ferritin is degraded via autophagy2 [START_REF] Hultcrantz | Intracellular fate of ferritin in HeLa cells following microinjection[END_REF][START_REF] Liße | Monofunctional stealth nanoparticle for unbiased single molecule tracking inside living cells[END_REF]. Moreover, even when directly expressed by human HeLa cells, transfected with the fusion protein plasmid pSEMS-meGFP::LCF::HCF3 , bare ferritin nanoparticles undergo autophagy after few hours (figure 4.5(a)).

These observations entail that, due to its physiological nature, ferritin nanoparticles needs to be protected from the intracellular environment to prevent physiological

Global vision of nanoparticles behavior inside living cells

Summarizing all our findings, we can present a global description of nanoparticles' behavior inside living cells. There exists a size threshold, that we estimate to be around 75 nm, which distinguishes two diffusive regimes. Nanoparticles with a diameter greater than 75 nm explore a rigid elastic environment and they are trapped inside the actin cytoskeleton meshwork. They will need high forces, in the range of tens of pN, to be manipulated. On the contrary, particles above 75 nm in size may diffuse purely Brownianly or with sub-diffusive motion, according to the strength on non-specific intracellular interactions. A schematic of our model is shown in figure 4

Characterization of the magnetic manipulator

As already mentioned in paragraph 3.2.3, to perform magnetic actuation inside living cells, both high magnetic field and high magnetic filed gradient are needed in order to apply an important force onto superparamagnetic nanoparticles.

In this context, the main challenge of our manipulation is to satisfy both requirements with a magnetic manipulator easy to display and sufficiently small for preserving microscope imaging capabilities. For our experiments, we retained the design of a "home-made" magnetic manipulator already employed in previous works [START_REF] Etoc | Subcellular control of rac-gtpase signalling by magnetogenetic manipulation inside living cells[END_REF]. It consists of a parabolic shaped ferromagnetic tip, placed on top of a permanent magnet and supported by a magnetic bar through a plastic pipette tip.

To create the magnetic tip we used a piano string (in particular, the one which corresponds to the most acute key), since it is made of soft iron, a ferromagnetic material characterized by a high value of saturation magnetization (>1.5 T).

The string has a cylindric shape with a diameter of 100 µm, and its edge was shaped into a paraboloid with a radius of curvature of about 50 µm (calculated by fitting the profile of the tip). The shaping procedure was inspired by the one employed for glass micropipettes (par. 3.7.1). The wire, maintained by its two sides, is lowered horizontal onto a flame which softens and narrows the metal. Then a force is applied

CHARACTERIZATION OF THE MAGNETIC MANIPULATOR

to both edges and the wire is broken in the middle, giving two wires with a parabolic end each. The wire is then cut 1 mm below the rounded end and placed on top of a permanent magnet. Alternatively, the wire can be cut longer and hold from one side. In both cases, magnetic interactions keep the tip strongly adherent to the magnet.

The permanent magnet has a rectangular shape (0.5 x 4 x 1.5 mm) and is made of NdFeB N52 with a coercitive force of 796 kA/m (provided by Magnetmonster), and is able to completely saturate the magnetization of the tip. The ensemble of magnet and tip, is inserted into a plastic pipette tip and hold by a metallic bar. This one can be manipulated in x, y and z direction with high precision and stability by a manual micromanupulator Scientifica.

In order to evaluate the force induced in the nanoparticle, we performed the force calibration procedure already developed in the work of Etoc et al. [START_REF] Etoc | Subcellular control of rac-gtpase signalling by magnetogenetic manipulation inside living cells[END_REF].

The magnetic manipulator was placed in a viscous medium (glycerol/water, 70:30 %v/v) of known viscosity, containing a low concentration (in the nM range) of commercial magnetic nanoparticles of 500 nm in diameter. While attracted towards the magnet, the particles trajectories were individually tracked by MTT Matlab software [START_REF] Sergé | Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes[END_REF]. The particles' instantaneous velocity were calculated as the step size divided by the acquisition time. Then, we calculated the local force exerted onto the nanoparticles, thanks to the Stokes law F = 6πηrv, where F is the magnetic drag force, η is the medium viscosity [START_REF] Cheng | Formula for the viscosity of a glycerol-water mixture[END_REF] and r the particle's radius. In figure 4.7(a) the force field map for 500 nm particles in the close region in front of the tip is reported. We extracted the values of the force versus the distance form the pole of the magnetic tip, from two different experiments conducted with different magnification (20X and 60X) and we fitted the results with the theoretical trend, as derived by de Vries et al. [START_REF] Anthony | Micro magnetic tweezers for nanomanipulation inside live cells[END_REF]. Results are shown in figure 4.7(b), where the points indicate experimental data and the red line the theoretical fit. Deviations from the model can be ascribed to the fact that the magnetic manipulator was tilted of about 45°while performing the experiment.

CHAPTER 4. CHARACTERIZATIONS

By estimating the magnetic moment of 500 nm magnetic nanoparticles (details in appendix C), we calculated the corresponding magnetic field gradient (map in fig-

Characterization of the magnetic response

On the basis of our observations, we can infer that in a confined environment, such as a living cell, in the proximity of a magnet, MNPs will be affected both by Brownian diffusion and drag force towards the magnet. Considering the magnitude of the forces involved, it follows that, at cellular scale level, there is a balance between these two phenomena.

From the purely physical point of view, the system can be described by driftdiffusion models equations, for stochastic process with accumulation [START_REF] Leroyer | Drift-diffusion kinetics of a confined colloid[END_REF].

Both transient and steady states are completely determined by the balance between drift and diffusion, but, whereas the determination of the steady state can be straightforward in simplified cases, the kinetics is less obvious.

To describe our model, let's consider a colloidal suspension of magnetic nanoparticles inside a confined mono-dimensional "cell" (schematic in figure 4.9). We suppose the magnetic force, the nanoparticles' diffusion coefficient and the saturation magnetization to be constant. Moreover, we ignore interparticles' colloidal and magnetic interactions.

The profile distribution of the nanoparticles' concentration C(x, t), restricted in the interval 0 ≤ x ≤ h, is completely determined by the Fick's law: where v is the drift velocity and D the nanoparticles' diffusion coefficient. By solving 4.1 for ∂C(x,t) ∂t = 0 the steady state distribution is obtained:

∂C(x, t) ∂t = v ∂C(x, t) ∂x + D ∂ 2 C(x, t) ∂x 2 (4.1)

CHARACTERIZATION OF THE MAGNETIC RESPONSE

C(x, ∞) = C 0 h l e -x/l 1 -e -h/l (4.2)
where the total number of particles per unit of volume C 0 is conserved and l is a length scale l = k B T /F , with F magnetic drag force.

Since, according to our force calibration, the magnetic forces produced by the magnetic tip are in the order of the fN, we found that the l parameter defining the exponential decay of the concentration profile is about few microns.

The description becomes more complicated if we take into account the effects of spatially varying dragging force (a distant-dependent magnetic force field) and discontinuous diffusion coefficient (due to heterogeneities in the intracellular environment). However, our results, illustrated in the following paragraphs, are in good agreement with the previsions of this oversimplified model.

The timescale for establishing the gradient profile can be estimated by the relationship τ e = h v = k B T h F D , which gives for our system a τ e of few seconds. The relaxation time is given by the diffusion time of a Brownian particle over the length h of the cell: τ r = h 2 D and, for a model cell of 40 µm it should be about 20 minutes.

Magnetic response in an in vitro model system of the cell

We validated the possibility to generate graded distribution of MNPs with our magnetic manipulator in an in vitro model system of the cells, mimicking the confined intracellular environment: aqueous droplets inside oil phase.

Droplets have typical diameter between 50 and 100 µm and were created by blowing a solution of MNPs in PBS (concentration >100 nM), inside a mixture of mineral oil and surfactant (L-α-phosphatidylcholine), and letting the droplet adhere on top of a PDMS substrate (figure 4.10).

Approaching the magnetic tip, a sharp gradient of concentration creates (figure 4.11(a)). We fitted the profiles at steady state with a single exponential (equation 4.2), assuming the approximation of constant force, and we found that the decay In aqueous droplets the kinetics of the gradient formation and relaxation are very fast, with an establishment time τ e of about 1 s and a relaxation time τ r of about 12 s. Whereas, by repeating the same experiment in droplets of viscous medium (mixture of water and glycerol), with a viscosity close to the one obtained inside cells (paragraph 4.1.1, ten time greater then water), we sobtained temporal kinetics roughly ten times greater.

The process of gradient formation is completely reversible, as inferred by monitoring

Magnetic response in the living cell

Establishment of a gradient of nanoparticles in living cells

Further, we explored the possibility to generate a tunable and reproducible gradient of nanoparticles also in living cells, without altering cell viability. To this end, we microinjected highly stable carboxyl-coated MNPs into HeLa cells at high concentration (>100 nM) and we brought the magnetic tip close to the cells. Driven by magnetic forces, the nanoparticles were attracted towards the cell edge, creating a sharp and graded distribution profile (figure 4.13). Once reached, the steady state distribution can last for tens of minutes and, after removing the tip, the particles rediffuse back inside the cell. Moreover, we investigated the possibility to tune the nanoparticles' gradient distribution by varying the distance of the magnet. In the example shown in figure 4.14, first we have placed the magnetic tip about 2 µm away from the cell membrane, generating a distribution of 0.58 µm decay length. Then, by distancing the tip at about 10 µm, we increased the decay length up to 4 µm. Remarkably, we found that, on a limited temporal scale, the behavior it completely reversible. Consistently with our in vitro estimations, we found a typical time for magnetic attraction in the order of 2 min and relaxation of about 10 min (figure 4.15(b)). Deviations should be ascribed both to the variability in the cell shape and to the heterogeneity of the intracellular environment. Indeed, cell are not hemispherical droplets, but they resemble more a "sombrero", with a high volumetric center, where there is the nucleus, and a flat surrounding protrusion, in the lamella region. Therefore, the nanoparticles' diffusion is influenced by the peculiar shape of the cell, which also could

CHARACTERIZATION OF THE MAGNETIC RESPONSE

favor the formation of areas of completely different non-specific interactions. To prove the specificity of our actuation we performed a control experiment, where the same transfected cells were microinjected with non functionalized carboxyl-group coated nanoparticles. As shown in figure 4.16(b), we observed a gradient of MNPs but no corresponding changes in the meGFP distribution.

Recruitment of a protein of interest in living cells

Chapter 5

Results

Validation of loading techniques by electron microscopy

Firstly we wanted to verify the ability of both microinjection and bead-loading to deliver nanoparticles correctly in the cytoplasm, without altering cell viability. In particular we wanted to check if these two processes are able to bypass the physiological endocytotic pathways, leaving the nanoparticles' surface viable for further in vivo functionalization.

As a complementary approach to fluorescence microscopy, we decided to preform transmission electron microscopy (TEM) onto fixed cells. In TEM, an electron beam of high voltage (80 kV) is transmitted through a very thin biological sample (less than 100 nm), in order to create a bright-field image of its internal architecture. With a magnification that can reach the nanometer resolution, we were able to identify single nanoparticles and to verify the accessibility of their surface.

In order to relocate loaded cells, we performed the experiment by loading the nanoparticles into HeLa cells grown onto glass bottom dishes, characterized by a grid of 50X50 µm repeat distance.

After the loading, the first stage in preparing the sample for TEM imaging is the chemical fixation, able to halt cellular activity without altering the cellular threedimensional organization. The fixation process was carried out by adding glutaraldehyde 25% in sodium cacodylate 60 mM to the sample, first 1:1 proportion with culture medium (for 10 min) and then pure (for 30 min). After that, the sample was stored at -4 °C overnight.

The following steps are post-fixation, dehydration and embedding, and they were carried out with the help of our collaborators from the UMR 144-Subcellular Structure and Cellular Dynamics at Institut Curie in Paris.

The post-fixation, which was performed with osmium tetraoxide, had the effect of improving the fixation quality and preserving the lipid parts. Afterwards, the sample was dehydrate with several washing steps in ethanol and finally embedded in hydrophobic epoxy resin, supported by a resin tablet.

CHAPTER 5. RESULTS

After embedding, the resin block was sectioned by ultramicrotomy1 in slides of thickness between 60 and 100 nm. Before observation at TEM, the biological samples were stained with 4% uranyl acetate, which reacts strongly with phosphate and aminogroups of proteins and macromolecules. Thanks to its high electron density, uranyl staining increases the contrast of proteins' structure during TEM imaging.

VALIDATION OF INTRACELLULAR TARGETING BY ELECTRON MICROSCOPY

These results demonstrate that bead-loading technique allows effective delivering of functional nanoparticles, with accessible surface into living cells. In fact, we observed that the nanoparticles are freely dispersed in the cytoplasm, without any visible endosomal embedding.

Moreover, we verified the cell viability by looking at the intracellular architecture and we found that, even if bead-loading is a stressfull process, after about 30 min cells completely recover.

Additionally, we performed an equivalent experiment by using microinjection as loading techniques and MNPs as delivered material; the results are summarized in figure 5.2. shows that also upon microinjection, nanoparticles's surface appears accessible in the cytoplasm, and in particular, for MNPs we can also notice the unaltered silica shells, thanks to the higher electron density of silicon dioxide. The intensity profile for a single MNPs, reported in figure 5.2(b), shows an external diameter of about 30 nm with an internal core diameter of about 10 nm, which is consistent with the MNPs sizes measured in vitro (chapter 3). Also for microinjected cells, we observed a complete recovery after about 30 min.

Comparable results were obtained both by microinjecting ferritin nanoparticles and by bead-loading MNPs, demonstrating that both techniques are very efficient in delivering functional nanoparticles inside the cytoplasm of living cells.

Validation of intracellular targeting by electron microscopy

According to what was explained in paragraphs 3.4.2 and 3.5.3, after loading nanoparticles inside living cell, they can get functionalized with proteins of interest, through in vivo recruitment via HaloTag (for MNPs) or GFP/anti-GFP (for ferritin) CHAPTER 5. RESULTS

targeting system.

One way to prove the efficacy of the targeting is by observing, in fluorescence microscopy, the colocalization of two dyes respectively carried by the nanoparticle and the protein (as performed in the experiment presented in chapter 4.3.2).

In addition to fluorescence colocalization, we wanted to further investigate the potentialities of targeting by electron microscopy. To this purpose, we chose as a target, an intracellular distinctive system easy to identify in TEM: mitochondria. With the help of our collaborator in Osnabrück, we cloned a mammalian DNA plasmid encoding for the fusion gene Tom20::mCherry::α-GFP. The protein of interest, Tom20 is a mitochondrial import receptor subunit, which role is to transport mitochondrial proteins from cytosolic ribosomes to the mitocondria [START_REF] Vladimir A Likić | Patterns that define the four domains conserved in known and novel isoforms of the protein import receptor tom20[END_REF][START_REF] Dudek | Mitochondrial protein import: Common principles and physiological networks[END_REF]. HeLa cells tranfected with this fusion gene, show in fluorescence microscopy a clear targeting of the overall motochondrial branched structure as reported in figure 5.3(b). After microinjection, ferritin-GFP nanoparticles are immediately recruited on top of mitochondria via GFP/α-GFP targeting system (figure 5. In TEM images, after relocating the injected cell (figure 5.4(a)) we could identified the magnetic cores of ferritin nanoparticles all around the mitoncondrial membrane, as indicated by whites flashes in figure 5.4(b) and 5.4(c).

Protein manipulation in vivo and probing of protein activity

According to what was explained in chapter 2, the goal of this thesis project is to understand how information is integrated inside cells and, in particular, to define more formally the relationship between molecular components and the flow of information, during cell migration.

We would like to characterize the signaling network architecture by identifying the macromolecular complexes that can be recognize as "signaling modules" and, moreover, we want to understand their peculiar spatio-temporal orchestration and activation kinetics, which lead to the high specificity of cellular response.

To accomplish this task we use a perturbative approach in which the activity of a specific RhoGTPase is manipulated with a highly controlled spatio-temporal resolution and the signaling propagation through the network is analyzed.

To explore the possibility to perturb the small Rho GTPases signaling machinery, we first focused on the activation of Cdc42.

Since the overexpression of a RhoGTPase generate the indiscriminate activation of all the effectors (as already explained in chapter 2), we decided at first to perturb the activity of the endogenous Cdc42 by manipulating its GEF protein Intersectin-I (ITSN-I) [START_REF] N K Hussain | Endocytic protein intersectin-l regulates actin assembly via Cdc42 and N-WASP[END_REF]. Intersectin-I belongs to the Intersectin-s proteins family and it functions through its DH domain as a guanine nucleotide exchange factor (GEF) for Cdc42.

The perturbation occurs by the attraction of the protein and formation of a gradient in different cellular location via magnetogenetic manipulation. The experiments can be distinguished in two categories as a function of the nanoparticles used, but the approach is identical. First of all, we transfected HeLa cells with a DNA construct coding for a fusion gene with three protein: the protein of interest, in our case ITSN-I, the targeting system (HT protein for the experiments with MNPs and aGFP nanobody fot the experiments with ferritin) and a fluorescent protein to follow INTS-I during the experiments. In particular we choose meGFP (green) for MNPs (that have rhodamine fluorescence and therefore are orange-red) and mCherry (red) for ferritin (which is green).

In order to verify the activation of the endogenous Cdc42 we choose, as a read-out, N-WASP protein, that was expressed in HeLa cells fused with IRFP, a fluorescent protein emitting in the far red.

N-WASP (neuronal WASP) belongs to the proteins' family of WASp (Wiskott

PROTEIN MANIPULATION IN VIVO AND PROBING OF PROTEIN ACTIVITY

actin polymerization by creating new nucleation cores [START_REF] Takenawa | WASP and WAVE family proteins: key molecules for rapid rearrangement of cortical actin filaments and cell movement[END_REF].

It has been shown that N-WASP is a downstream effector of Cdc42. In fact, Cdc42 in its active GTP-bound state can bind to the GBD (G-protein binding domain) of N-WASP unmasking the VCA region and therefore releasing its actin nucleator capacity [START_REF] Rohatgi | Mechanism of N-WASP activation by CDC42 and phosphatidylinositol 4,5-bisphosphate[END_REF]. After transfection, the cells were seeded onto glass coverslides and microinjected with functionalized magnetic nanoparticles. Immediately after injection, the fusion CHAPTER 5. RESULTS protein is recruited onto the surface of the particles via its targeting system. By generating a gradient profile of functionalized nanoaparticles at one edge of the cell, we observed the simultaneous formation of an equivalent gradient of INTS-I (figure 5.5(a)), which was not observed in the control experiment (figure 5.5(b)).

We monitored simultaneously nanoparticles, ITSN-I and N-WASP fluorescence and bright field images. For each experiment the cell edge over time was detected, by means of an intensity thresholding algorithm developed in Matlab. As an example, in figure 5.6(a) the evolution of the cell edge during time is reported, with a color code indicating time in minutes. After that, we derived the cell edge displacement as follows: first of all an "average shape" of the cell was extracted by averaging the cell contours over time for the whole experiment. Than, for windows placed along the cell contour, the distance between the We evaluated the spatio-temporal affinity of the three activities by calculating the 2D Pearson correlation coefficient among them, restricting the analysis to the region where the magnetogenetic perturbation is performed. All the results are summarized in the box blots reported in figure 5.8. Remarkably, it can be noticed that the correlation for each couple of signals is higher for the experiment conducted with ferritin nanoparticles. This observation could be explained by the difference in binding affinity between HaloTag and α-GFP targeting systems.

Moreover, it can be pointed out that the cross-correlation between nanoparticles and ITSN-I is overall higher compared to the other couples of signals (ITSN-I/N-WASP and nanoparticles/N-WASP). Following this evidence, we could hypothesize that whereas the binding between nanoparticles and ITSN-I is always present, the recruitment of N-WASP only occurs after the binding and activation of the endogenous Cdc42.

In fact, the ITSN-I expressed by HeLa cells in our experiments only contains the DHPH domain which is know to be GEF domain for Cdc42 [START_REF] N K Hussain | Endocytic protein intersectin-l regulates actin assembly via Cdc42 and N-WASP[END_REF]. This domain is able to bind specifically to Cdc42 in the inactive GDP-bound state and to catalyze the exchange of GDP for GTP (active state). It's only upon activation that Cdc42 can bind the GBD (GTPases binding) domain of N-WASP [START_REF] Ke Prehoda | Integration of multiple signals through cooperative regulation of the N-WASP-Arp2/3 complex[END_REF].

In figure 5.9 is summarized our hypothesis of the recruitment pathway, in the case of MNPs. Therefore, we can conclude that the protein ITSN-I is fully functional even when bound to the nanoparticles. Moreover, according to what stated by Hussain et al. [START_REF] N K Hussain | Endocytic protein intersectin-l regulates actin assembly via Cdc42 and N-WASP[END_REF], our founding could prove the magnetogenetic activation of the endogenous small Rho GT-

PROTEIN MANIPULATION IN VIVO AND PROBING OF PROTEIN ACTIVITY

Pase Cdc42. Thus, our perturbation tool might be conceived as an assembly of "signaling modules" of top of nanoparticles, which recruit N-WASP through the activation of endogenous Cdc42 via ITSN-I-bounded nanoparticles as explained in paragraph 2.4.1 (figure 5.9).

As second goal of our manipulation, we wanted to prompt a highly localized response by displacing the signaling complex in different cellular locations. In particular, we expected to induce actin polymerization by bringing the particles close to the cell periphery. In fact, when N-WASP is bound to Cdc42, in its active GTP-bound state, it is able to interact with Arp2/3, a protein complex which acts as nucleation site for new actin filaments, generating branched actin networks [START_REF] Henry | Activation by cdc42 and pip2 of wiskottaldrich syndrome protein (wasp) stimulates actin nucleation by arp2/3 complex[END_REF].

Indeed in few cases, we observed that, upon localization of the "signaling modules" close to the cell periphery, a cell protrusion was induced, close to the perturbation area. Interestingly, in some experiments we found that around 20 min after the perturbation, N-WASP localizes into endocytic vesicles (figure 5.11)2 . Indeed it has been shown that N-WASP is involved in vesicular trafficking, in particular in endocytosis [START_REF] Miki | N-WASP, a novel actin-depolymerizing protein, regulates the cortical cytoskeletal rearrangement in a PIP2-dependent manner downstream of tyrosine kinases[END_REF]. This behavior could be explained by the hypothesis that the macromolecular com-plex onto the nanoparticle disassembles after prompting the biological response, and N-WASP is recycled in endocytotic pathways. This interpretation is in agreement with the concept of transiently activated "signaling module" explained in chapter 2.

Furthermore, in 50% of the experiments we could observe a pronounced retraction of the cell far from the induced perturbation as shown in the example is figure 5.12. This evidence suggests that the whole signaling machinery might be perturbed and a global response of cell morphology reorganization might be activated. Taking together these results demonstrate that magnetogenetic actuaction is a powerful tool to perturb intracellular signaling machinery in a highly controlled fashion both is space and time.

In order to push forwards the analysis, cell edge dislacement was chosen as "fiduciary" to evaluate the temporal correlation between the localization of the nanoparticles and the formation of cell protrusion. We calculated the temporal cross-covariance3 between nanoparticles' signal and cell edge displacement for each window along the cell edge in the close proximity of the perturbation [START_REF] Machacek | Coordination of Rho GTPase activities during cell protrusion[END_REF]. Then the correlation functions for all windows were averaged and a spline fit was performed for all the curves. Figure 5.13 shows the average correlation function of each experiment (black) and the trend of the spline fit (red).

Although the curves of individual experiments are significantly heterogeneous, we could identify a positive correlation at around 10 s of lag. Therefore, this might indicate the formation of a cell protrusion in within 10 s after the accumulation of nanoparticles.

MAGNETOGENETIC PARALLELIZATION

Cross-covariance

Lag (s) Figure 5.13: Temporal cross-covariance between nanoparticles' signal and cell edge displacement, for all the experiments (in black) and relative spline fit (in red).

Magnetogenetic parallelization

Cell Patterning

Despite the interesting results achieved so far, a limit in our approach is the fact that at present the experiments are single cell restricted and time consuming; moreover they require expertise and long practice.

For these reasons, in our group a great effort was invested in parallelizing the experiments in order to achieve a higher statistics and standardize the perturbation performed.

First of all, the heterogeneity of cells' shapes makes difficult to compare the results obtained in term of cell morphology rearrangement and moreover it become problematic to infer general features regarding single cell behavior.

In particular we found that the peculiar cell shape and architecture in the area of nanoparticles' localization could fundamentally influence the aspect of the intracellular gradient of perturbation and therefore impact on the cellular response. For example, the gradient of nanoparticles that can be generated into a flat lamellipodium is completely different from the one generated in the voluminous region close to the cell's nucleus. Furthermore, the diverse molecular crowing in two different locations could change considerably the cell response.

For all these reasons we decided to move towards cell micropatterning, a popular technology used to control the geometry of cell adhesion which was already described in paragraph 3.8 [START_REF] Azioune | Simple and rapid process for single cell micro-patterning[END_REF][START_REF] Théry | The extracellular matrix guides the orientation of the cell division axis[END_REF]. Micropatterns enable control over both cell shape and functional architecture via pre-defined adhesion pattern. In particular, it has been shown that crossbow pattern induces a polarity axis along the direction of the bow, with the formation of a huge lamellipodium in the front and a sharp end at the rear. of an external magnetic field, each pillar get magnetized up to its saturation limit and became a source of high field gradients close to its periphery. Depending on the orientation of the external field, the gradient maxima will span all the possible orientation in the plane of the substrate. In this direction, encouraging results were recently obtained by Aizel K., post-doc in our lab. He grown paramagnetic pillars of Fe/Ni alloy via controlled electrodeposition onto glass coverslides and covered them with a spin-coated layer of bio-compatible material (PDMS). As shown in figure 5.15(a), when approaching a permanent magnet as source of external magnetic field source, it is possible to observe attraction of MNPs and accumulation in the Nord-South poles of the pillar. Moreover, we observed nanoparticles attraction and manipulation inside living cells grown randomly onto the substrate and injected with MNPs (figure 5.15(b)).

Chapter 6 Conclusion and Perspectives

Magnetogenetic actuation

Cells are able to perform "thoughtful" tasks by interpreting external and internal cues and translating them into the establishment of an axis of polarity. Any polarized state requires a hierarchical organization of the cell machinery that engages many different components and functional diversification on different scales (from µm to nm). The signaling machinery can be conceived as a tangled signaling network in which few molecular components assemble to create "signaling modules" which function through a tight orchestration in space and time (chapter 2). This thesis work presents a novel approach to investigate the network via "perturbative approach": magnetogenetics (chapter 1). It is based on the use of biofunctionalized superparamagnetic nanoparticles, to induce and manipulate protein gradients inside living cells.

We tailored the size and surface properties of both synthetic silica core shell nanoparticles and superparamagnetic GFP-ferritin-based nanoparticles in order to ensure unhindered mobility in the cytosol. These nanoparticles can be rapidly localized in living cells by exploiting biased diffusion at weak magnetic forces in the fN range (chapter 3 and 4). In combination with nanoparticles' surface functionalization for specific in situ capturing of target proteins as well as efficient delivery into the cytosplasm, we can control intracellular protein gradients with a spatial resolution of micrometers and a temporal resolution of a few tens of seconds.

In this work we showed the possibility to precisely control the perturbation of the signaling pathways associated to the small Rho GTPases proteins with relative analysis on signal propagation in terms of effector recruitment and morphological changes (chapter 5).

In conclusion, this thesis work intends to propose a robust and extensive method to investigate and untangle complex intracellular signaling networks. CHAPTER 6. CONCLUSION AND PERSPECTIVES 6.2 Perspectives

Magnetogenetics for cell division

Beside cell motility, our magnetogenetic actuation can be exploit in many others biological contexts, which involve the prompting of intracellular signaling networks to perform complex tasks. One of the most interesting example is oriented cell division (OCD), crucial to correctly organize and shape living organisms' tissues [START_REF] Panbianco | Coordinating cell polarity with cell division in space and time[END_REF]. Indeed, during morphogenesis the correct elongation of tissues requires oriented cell division of epithelial cells with a polarity axis of division aligned along the direction of tissue's growth (figure 6.1). During OCD, the information carried by external cues from the cell micro-environment is encoded to create stable subcellular domains of protein activities, which ultimately leads to the establishment of a correct orientation of the division. Also in the case of OCD, the degree of sensitivity to the external cues reveals an underlying decision making process. Moreover, the orientation of the division axis needs to be highly robust in order to maintain size and shape homeostasis in tissues.

In this context, magnetogenetics actuaction could be exploited by applying a spatially controlled perturbation to mitotic cells at the molecular cell level and, as a global feature read out, the orientation of division could be measured. By doing so, one xan decipher how two fundamental qualities of OCD, sensitivity and robustness, are encoded and balanced at the level of signaling networks.

Additionally to driving morphogenesis, OCD is fundamental in generating cellular diversity by cell fate differentiation [START_REF] Hawkins | Asymmetric cell division: from A to Z[END_REF][START_REF] Morrison | Asymmetric and symmetric stem-cell divisions in development and cancer[END_REF]. In all organisms, from bacteria to mammals, cell diversity is generated by stem cell division producing two daughter cells that adopt distinctive fates. In polarized stem cells, the axis of division determines whether the division will be symmetric (identical daugther, SCD) or asymmetric (different fates, ACD). In ACD, the segregation of cell fate determinants during mitosis orients the polarity axis of division and ensure the faithful differentiation of the two daughter cells, as shown in the cartoon of figure 6.2.

Magnetogenetic perturbation can be useful in this context to perturb the distribution of cell fate determinants and investigate the mechanisms of cell fate differentiation.

"Endo-ferritin"

A further step in the parallelization of magnetogenetic actuation approach will be letting the cell manage the synthesis of the nanoparticles by themselves. Indeed, we have already shown that, via genetic manipulation, HeLa cells can produce and assembly fluorescent ferritin cage ("endo-ferritin"). However a limiting step remains the mineralization of the supermagnetic core in vivo at room temperature. Nonetheless, there are many biological systems, such as magnetotactic bacteria1 , which are able to synthesize monodisperse magnetic nanoparticles called magnetosomes via a redoxcontrolled biomineralization of Fe 3 O 4 crystals in cytoplasmic vesicles [START_REF] Dennis | Magnetosome formation in prokaryotes[END_REF].

Recently it has been shown that it is possible to transfer the ability to biomineralize magnetic nanostructures to a foreign non-magnetic host organism, by the expression of a minimal pool of genes from magnetotactic bacteria [START_REF] Kolinko | Biosynthesis of magnetic nanostructures in a foreign organism by transfer of bacterial magnetosome gene clusters[END_REF]. Although this attempt was successful in prokaryotic organisms, it could be further boosted to genetically endow eukariotic and even multi-cellular organisms with the ability to synthesize tailored magnetic nanostructures.

Time-zero perturbation

One interesting improvement for our magnetogenetic actuation would be the proper definition of a "time-zero" for the application of the perturbation. Indeed, until now, the slow approach of the magnetic tip could lead transient effects that in turns might trigger undesirable cellular responses.

We could envisage as a possible solution, the use of an electromagnetic systems, instead of a permanent magnet, to switch on and off the perturbation. In this scenario, the "time zero" will be defined as the moment at which the nanoparticles start to be attracted.

More attractive would be the use of a combined opto-magnetogenetic system for which the "time zero" point would be the recruitment of active proteins after the formation of a stable gradient of nanoparticles (at the steady state). Upon injection of nanoparticles and iv vivo functionalization with a ligth-sensitive protein, the magnet is approached and the gradient distribution is generated. Afterwards, a light flash is shine on the sample and it triggers the recruitment of a protein of interest via light-induces dimerization.

Local magnetic hyperthermia

One of the most promising therapies in cancer treatment is hyperthermia, which consists in destroying the targeted tissues by heating, reaching temperatures greater than 42°C [START_REF] Jordan | Magnetic fluid hyperthermia (MFH): Cancer treatment with AC magnetic field induced excitation of biocompatible superparamagnetic nanoparticles[END_REF]. Hyperthermia is intrinsically limited by heat diffusivity that prevents localized heating and therefore entails the damage of surrounding non tumor tissues.

Magnetic nanoparticles can generate heat when exposed to high frequency oscillating magnetic field, that excites the magnetic moment fluctuation. Two mechanisms are involved in the transformation of magnetic energy into heat: internal friction of the magnetic moment inside the crystal, originated from anisotropy energy (Néel mechanism) and external friction due to the viscosity of the external fluid, which impedes thermal fluctuation of the particles (Brownian mechanism) [START_REF] Paul Fortin | Intracellular heating of living cells through Néel relaxation of magnetic nanoparticles[END_REF].

Indeed, magnetic nanoparticles have been largely used in cancer therapies as a source of heat thanks to their advantage of keeping the heating region highly localized and therefore limiting the secondary effect on surrounding tissues [START_REF] Gazeau | Optimizing magnetic nanoparticle design for nanothermotherapy[END_REF].

Interestingly, combining hyperthermia with highly specific targeting system such as Halotag or α-GFP nanobody, a discriminative targeting of cancerous cells could be enabled, enhancing the efficacy of therapeutic treatments. Moreover, in the context of single cell biology, we could envisage a localized intracellular hyperthermia, by heating precisely addressed entities in living cells, for example mitochondria or Golgi apparatus (figure 6.3). In this way, the particles can be used as nanosources of heat and the effect of highly localized heating can be tested.

Mechanical perturbation

As shown in chapter 3, by increasing the size of the nanoparticles (hundreds of nm) it is possible to apply forces of few pN. Forces in this order of magnitude are significant for cells, indeed for example, kinesis molecular motors are able to exert forces of few pN 6.2. PERSPECTIVES while walking along micro-tubules [START_REF] Svoboda | Force and velocity measured for single kinesin molecules[END_REF]. Hitherto only in vitro single molecule force spectroscopy techniques (atomic force microscopy, optical tweezers, magnetic tweezers) have been exploited to kinematically characterize molecular motors.

To better understand the mechanism of force generation as a function of the local intracellular chemical environment, magnetogenetic approach can be used. Thanks to the highly specific targeting systems presented in this thesis work, single molecular motors can be targeted with magnetic nanoparticles and pulled via magnetic gradient application (figure 6.4). The opposing generated force can be then measured with a high precision and in an intracellular context-dependent fashion. Additionally, the effect of intracellular membrane pulling can be investigated in the context of actin architecture to understand how forces generated from the interior of the cell could alter the cytoskeleton arrangement.

MAGNEURON FET-OPEN project

It is worthwhile mention that magnetogenetic actuation has been recently introduce as a fundamentally new concept for remote control of cellular function in the MAGNEURON project, one of the 11 projects funded by the European Commission in the framework of Future and Emerging Technologies (FET-OPEN) program.

The long-term goal of MAGNEURON project is to enhance cell replacement treatments in regenerative medicine of the the brain. Cell replacement therapies (CT)2 are considered very promising in the treatment of neurodegenerative disease, such as Parkinson's disease. In particular, the transplantation of embryonic dopaminergic (DA) neurons in the substantia migra of patients' impaired brain has shown encouraging results. However, ethical concerns restrict the use of human embryos in clinical trials. An alternative source of DA precursor neurons was recently found thanks to the advances in stem-cell reprogramming technologies. In fact, pluripotent stem-cell generated from the patient's own cells can generate DA precursor neurons.

However, it remains challenging to control the cell behavior at the site of transplantation, and particularly the differentiation of precursor cells and their oriented growth. In this context, magnetogenetic actuation offers a valid support. In fact, the breakthrought idea is to control the differentiation and oriented growth of transplanted neuron precursors through magnetogenetic stimulation via biofunctionalized nanoparticles. After auto-transplantation, the patient-derived cells will be stimulated at distance by external magnetic field to prompt differentiation and axonal growth guidance as show schematically in figure 6.5.

Appendices A Bead-loading detailed protocol

The following detailed protocol of bead-loading was kindly provided by Tim Stasevich [START_REF] Hayashi-Takanaka | Tracking epigenetic histone modifications in single cells using Fab-based live endogenous modification labeling[END_REF].

What you need to prepare:

-Glass beads (106 µm; Sigma-Aldrich; G-4649) Store glass beads in a safety cabinet or a drawer. When handling, wear gloves and work under a hood if possible to prevent spreading glass beads through the air. To wash and sterilize glass beads, soak them in 2 M NaOH for 2 h and mix gently using a shaker or rotator. For example, pour 10 ml of glass beads into a 50 ml Falcon tube and then add 40 ml 2 M NaOH. Wash glass beads extensively with distilled water until the pH becomes neutral (as beads sediment in water, just wait a few min and then decant the water away). Wash a few times with 100% ethanol. Air-dry overnight at room temperature. (Optional) Make a container for sprinkling glass beads onto samples using a nylon mesh filter (100 µmesh size, figure A.1). Keep glass beads away from moisture; for example, store in a box containing Silica-gel. -Proteins to be loaded Purify protein and, if necessary, label with a fluorescent dye. Dissolve into an isotonic buffer (like PBS) at 0.5-1 mg/ml.

A. BEAD-LOADING DETAILED PROTOCOL

After sprinkling beads:

-For "strong" cells that adhere to the coverslip well (like HeLa), firmly strike the glass-bottom dish against the hood tabletop 6-8 times. Each time raise the dish 5-8 cm above the tabletop before striking down.

-For "weak" cells (like fibroblasts), strike down less forcefully 3-5 times from a height of 3-5 cm to prevent cells from peeling.

-For "very weak" cells (like ES), tap the dish 1-2 times from a height of 1-2 cm.

Immediately add 2 ml of pre-warmed medium to the dish.

-For "strong" cells, wash away glass beads by repeatedly washing with the medium.

-For "weak" and "very weak" cells, it may be better to put the dish back into a CO 2 incubator for 2-4 hr. This will allow cells to recover and firmly re-attach to the dish.

Aspirate the medium and beads. Repeatedly wash with the medium until most beads are removed. Add 2 ml medium to the dish and put it back into a CO 2 incubator or set it on a microscope for imaging.

Note:

The loading efficiency and cell survival rate are a trade-off. If you strike down harder or more, you can load more, but more cells will die or detach from the dish. Therefore, it is very important to determine the condition of loading suitable for your cell type. For 'very weak' or sensitive cells, increasing the concentration of protein may help, because even making a small hole (by gentle hitting) allows the entry of a significant fraction of protein. Fully confluent cells tend to peal in mass, while isolated cells peal more easily than those with neighbors. Thus, a confluency of 80-90% is ideal in our experience.

Note: Be careful not to dry up the cells on the coverslip, as only a small volume of medium/protein solution remains. There is no incubation step throughout the procedure, so perform the whole process quickly (but do not rush).

C. MAGNETIC MOMENT OF 500 NM COMMERCIAL MAGNETIC

NANOPARTICLES.

C Magnetic moment of 500 nm commercial magnetic nanoparticles.

Superparamagnetic nanoparticles of 500 nm were purchased from ademtech, which provides a magnetic susceptibility of approximately 40 emu/g (equivalent to Am 2 /kg), a particle density of 2000 kg/m 3 and iron oxide content of approximately 70%.

With these informations we estimated: -particle's volume = 6.5•10 -20 m 3 ; -particle's mass = 1.3•10 -16 kg; -iron oxide mass = 9.1•10 -17 kg; Therefore, we calculated the "giant" magnetic moment of the nanoparticle by multiplying the magnetic susceptibility and the iron oxide mass per particle: µ= 3.64•10 -15 Am 2 .

According to the equation 3.2:

F = ( µ • ∇) B
after measuring the dragging force toward the tip, we derived the field gradient. Finally, by knowing the magnetic moment of MNPs (1.97•10 -19 Am 2 ) we calculated the relative dragging force (in the order of fN).

  . . . . . . . . 1.5 Magnetic actuation of calcium signaling via nanoparticles-induced oligomerization of IgE-FcεRI receptor complexes [20]. . . . . . . . . . . . . . . . 1.6 Angiogenesis triggered by Tie2 receptor clustering via magnetic filed application. Adapted from [21]. . . . . . . . . . . . . . . . . . . . . . . . 1.7 "Magnetic switch" for the induction of apoptosis, through DR4 receptor clustering. Adapted from [22]. . . . . . . . . . . . . . . . . . . . . . . . . 1.8 "Mechanogenetics" to dissect the role of different mechanotransductive signaling pathways' inputs. Adapted from [23]. . . . . . . . . . . . . . . 1.9 Thermal activation of Ion Channel TRPV1 and consequent cell membrane heating, adapted from [24]. . . . . . . . . . . . . . . . . . . . . . . 1.10 Nanoparticles-induced TRPV1 magneto manipulation and subsequent proinsulin expression in living cells [25]. . . . . . . . . . . . . . . . . . . 1.11 Deep brain stimulation of TVA mice neurons by radio frequency magnetic field heating of TRPV1-Fe 3 O 4 nanoparticles. Adapted from [26]. . 1.12 Magnetic actuation of HEK-293 cells and magnetically-induced behavioral responses in C. Elegans. . . . . . . . . . . . . . . . . . . . . . . . . 1.

2 .

 2 14 Optogenetics' spatial precision. . . . . . . . . . . . . . . . . . . . . . . . 3.1 Atomic dipole configuration for diamagnetic and paramagnetic materials, without and with an applied external magnetic field H. Adapted from [95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Alignment of atomic dipoles in ferromagnets, antiferromagnets and ferrimagnets, which exists even in absence of an external magnetic field. Adapted from [95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Schematic of domains structure and domain walls in ferro(i)magnets, adapted from [95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetization M versus external filed H curve for ferro(i)magnets, adapted from [95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Superparamagnetic behavior: flip of magnetization at room temperature. 3.6 Double layer schematic and curve of net energy in the DLVO theory, adapted from [100]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Core-shell Fe 2 O 3 @SiO 2 superparamagnetic nanoparticles. . . . . . . . . 3.8 Schematic of MNPs synthesis, adapted from [105]. . . . . . . . . . . . . 3.9 Silica shell degradation over time (TEM images). . . . . . . . . . . . . . 3.10 "Click-chemisty" for functionalization of MNPs with HTL. . . . . . . . 3.11 Ferritin-based iron oxide superparamagnetic nanoparticles. . . . . . . . . 3.12 Loaded magneto ferritin: TEM images of shell and core respectively and diameter's measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . x 3.13 SQUID measurements of sample magnetization (Am 2 ) vs applied filed (T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 Microinjection of MNPs into HeLa cells. . . . . . . . . . . . . . . . . . .3.15 Bead-loading of HeLa cells: MNPs and ferritin. . . . . . . . . . . . . . . 3.16 Pinocytic loading of 25 nm fluorescent nanoparticles into HeLa cells. . . 3.17 Crossbow and round shaped cell patterning. . . . . . . . . . . . . . . . . 4.1 Nanoparticles' diffusion in the cytoplasm as a function of their diameter. 4.2 Diffusion coefficients for intracellular latex nanoparticles of different sizes. 4.3 Calibration of MNPs' ζ-potentials versus succinic anhydride excess during functionalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Stability of microinjected MNPs in fuction of their ζ-potentials. . . . . . 4.5 Stability of ferritin without and with PEG2k funtionalization. . . . . . . 4.6 Global vision of nanoparticles' behavior inside living cells . . . . . . . . 4.7 Force calibration of the magnetic manipulator. . . . . . . . . . . . . . . 4.8 Magnetic gradient field map and estimated force vs distance trend for MNPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 1D drift diffusion model of magnetic responce. . . . . . . . . . . . . . . . 4.10 in vitro model system of the cell. . . . . . . . . . . . . . . . . . . . . . . 4.11 Gradient distribution of MNPs inside the droplet can be tuned changing the distance of the magnetic tip. . . . . . . . . . . . . . . . . . . . . . . 4.12 Kymograph of the MNPs' distribution at the center of the droplet. . . . 4.13 Gradient distribution of MNPs in living cells. . . . . . . . . . . . . . . . 4.14 Reversibility of MNPs gradient in living cells. . . . . . . . . . . . . . . . 4.15 Attraction and relaxation kinetics of MNPs. . . . . . . . . . . . . . . . . 4.16 Recruitment of meGFP::HT via MNPs-HTL in vivo HeLa cells. . . . . . 5.1 TEM images of bead-loaded ferritin nanoparticles into HeLa cells. . . . 5.2 TEM images of microinjected MNPs into HeLa cells. . . . . . . . . . . . 5.3 Recruitment of ferritin nanoparticles onto mitocondria via Tom20::mCherry::α-GFP fusion gene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 TEM images of ferritin nanoparticles injected into HeLa and recruited onto mitochondria via Tom20::mCherry::α-GFP fusion gene. . . . . . . 5.5 Selective manipulation of intracellular ITSN-I via magnetogenetic actuation of functionalized HTL-MNPs. . . . . . . . . . . . . . . . . . . . . . 5.6 Cell edge evolution and spatio-temporal map of cell edge displacement. . 5.7 Time courses of nanoparticles', ITSN-I and N-WASP signals in the localized region of attraction. Time along the x axis is in minutes and position along the y axis relates to position markers of figure 5.6(b). Color bar indicate relative intensities. . . . . . . . . . . . . . . . . . . . 5.8 2D Pearson correlation coefficients between nanoparticles, ITSN-I and N-WASP activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 5.9 N-WASP recruitment through the activation of endogenous Cdc42 via ITSN-I-bounded nanoparticles. . . . . . . . . . . . . . . . . . . . . . . . 5.10 Cell protrusion formation upon localization of the "signaling modules" close to the cell periphery. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 N-WASP vesicle formation, about 20 min after the perturbation. . . . . 5.12 Global retraction of the cell far from the induced perturbation. . . . . . 5.13 Temporal cross-covariance between nanoparticles' signal and cell edge displacement, for all the experiments (in black) and relative spline fit (in red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 HeLa cells on crossbow patten, injected with MNPs. Different concentration profiles are generated according to the different cellular locations. 5.15 Parallelization of the magnetic perturbation via array of paramagnetic Fe/Ni pillars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Oriented cell division (OCD) for corrected elongation of cell tissues. . . 6.2 Symmetric and asymmetric cell division of stem cells determine cell fate. Adapted from [146]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Local magnetic hyperthermia. . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Force generation via magnetic actuation. . . . . . . . . . . . . . . . . . . 6.5 Schematics of MAGNEURON project. . . . . . . . . . . . . . . . . . . . A.1 Tube or dish configuration to sprinkle the glass beads. . . . . . . . . . . A.2 Sample washing and solution loading. . . . . . . . . . . . . . . . . . . . A.3 Glass beads sprinkling and sample striking. . . . . . . . . . . . . . . . . B.1 SQUID measured data. . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Tables 3.1 Magnetic characterization of nanoparticles. . . . . . . . . . . . . . . . . 3.2 P-97 Sutter Micropipette puller: retained parameters. . . . . . . . . . . 5.1 Experiment with MNPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Experiment with Ferritin. . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Magnetic moments of nanoparticles. . . . . . . . . . . . . . . . . . . . .

Figure 1 . 1 :

 11 Figure 1.1: Sizes of biological entities compared to magnetic nanoparticles.

Figure 1 . 2 :

 12 Figure 1.2: Schematic representation of the different types of magnetic actuation, adapted from [4].

  (a) Schematic of the stimulation of a single hair bundle with magnetic nanoparticles attached.(b) Pulses of magnetic stimulation with corresponding hair bundle displacement and Ca 2+ influx.

Figure 1 . 3 :

 13 Figure 1.3: Magnetic activation of mechanotransduction channels of inner hair cells. Adapted from [15].

Figure 1 . 4 :

 14 Figure 1.4: β-catenin signaling pathway activation, via magnetic stimulation of UML, injected into mice colon. Adapted from[START_REF] María | Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure[END_REF] and[START_REF] Fernandez-Sanchez | Mechanotransduction's impact on animal development, evolution, and tumorigenesis[END_REF].

  Distance dipendent calcium signaling induction: fluorimetric images and relative quantification.

Figure 1 . 5 :

 15 Figure 1.5: Magnetic actuation of calcium signaling via nanoparticles-induced oligomerization of IgE-FcεRI receptor complexes [20].

  Targeting and magnetic induced clustering of Tie2 receptors. (b) Magnetically induced morphological changes in HUVEC cells.

Figure 1 . 6 :

 16 Figure 1.6: Angiogenesis triggered by Tie2 receptor clustering via magnetic filed application. Adapted from [21].

  A dysfunctional apoptosis leads to the overgrowth of tumor cells; thus the external control of this crucial mechanisms is at the base of many clinical therapies. The membrane docking of biochemical ligans, such as the TNF-related apoptosis inducing ligand (TRAIL), can trigger extrinsic apoptosis signaling by the clustering of membrane death receptors. Cheon et al. designed zinc-doped iron oxide magnetic nanoparticles, decorated with DR4 antibody and thus able to bind specifically to DR4 receptors. The application of 0.2 T magnetic field triggered the receptors' clustering, mimicking the biochemical signaling activation through TRIAL, and switched on the apoptosis (figure 1.7).

Figure 1 . 7 :

 17 Figure 1.7: "Magnetic switch" for the induction of apoptosis, through DR4 receptor clustering. Adapted from [22].

  .8(b)).

  (a) Schematic of the "mechanogenetic" toolkit for selectively activation of mechanoreceptors (Notch or Ecadherin), via different spatial, chemical, temporal and mechanical inputs.

Figure 1 . 8 :

 18 Figure 1.8: "Mechanogenetics" to dissect the role of different mechanotransductive signaling pathways' inputs. Adapted from [23].

  Scheme, drawn to scale, of heatinduced opening of TRPV1 by local heating of superparamagnetic nanoparticles via RF magnetic field stimualtion.

  During application of the RF magnetic field, the local temperature increased at the plasma membrane (red), yet remained constant at the Golgi apparatus (green).

Figure 1 . 9 :

 19 Figure 1.9: Thermal activation of Ion Channel TRPV1 and consequent cell membrane heating, adapted from [24].

CHAPTER 1 .

 1 MAGNETOGENETICS(a) Schema of nanoparticleinduced cell activation and proinsulin gene expression (for a more detailed description please refer to[START_REF] Stanley | Radio-Wave Heating of Iron Oxide[END_REF]).(b) RF magnetic field treatment increase proinsulin gene expression in HEK293T cells transfected with calcium-dependent insulin gene and presenting TRPV1 bound nanoparticles at the cell membrane.

Figure 1 . 10 :

 110 Figure1.10: Nanoparticles-induced TRPV1 magneto manipulation and subsequent proinsulin expression in living cells[START_REF] Stanley | Radio-Wave Heating of Iron Oxide[END_REF].

Figure 1 . 11 :

 111 Figure 1.11: Deep brain stimulation of TVA mice neurons by radio frequency magnetic field heating of TRPV1-Fe 3 O 4 nanoparticles. Adapted from [26].

  Schematic of activation of HEK-293 cells by remote magnetic stimulation (on top). Heat map showing changes of calcium influx-related fluorescence intensity (∆F/F0), before and after magnetic field stimulation (below). (b) Control of behavioral responses in C. Elegans: contraction of body muscle when magnetic field is applied.

Figure 1 . 12 :

 112 Figure 1.12: Magnetic actuation of HEK-293 cells and magnetically-induced behavioral responses in C. Elegans.

Figure 1 . 13 :

 113 Figure1.13: Behavioral responses in zerbafish and mice expressing the cation channel TRPV4 fused to the paramagnetic protein ferritin, after stimulation with static magnetic field. Adapted from[START_REF] Michael | Genetically targeted magnetic control of the nervous system[END_REF].

  Insulin's decrease and glucagon's increase, upon RF magnetic field stimulation.

Figure 1 . 14 :

 114 Figure 1.14: Remote activation of glucose-sensing neurons in mice. Adapted from [30].

  In the upper scheme, Ran/RCC1 bound magnetic nanoparticles are guided throughout the encapsulated cytoplasm. Below, a simplified representation of Ran/RCC1 signaling pathways. accumulation induced by magnetic field Microtubules (b) Upper part, dynamics of Ran-coupled nanoparticles accumulation under magnetic field, within a 60 µm extract droplet.Lower part, microtubule nucleation induced by accumulation of Ran-coupled nanoparticles, under a magnetic field.

Figure 1 . 15 :

 115 Figure 1.15: Intracellular signaling perturbation performed in a functional cytoplasm, reconstituted from Xenopus eggs and encapsulated in spherical droplets. Adapted from [34].

  In situ functionalization scheme: fMNPs functionalized with HTL are microinjected into cells expressing the protein of interest fused to the HT protein. The HT protein binds covalently to its ligand, recruiting the protein of interest to the fMNP. Schematic showing that GEF-MNPs activate GTPases at the membrane, independently of MNP localization, but signal propagation to actin polymerization occurs only close to the cell membrane. TIAM-MNPs magnetically localized into an inactive area create a cell protrusion and subsequently an actin comet.

Figure 1 . 16 :

 116 Figure 1.16: First proof-of-concept of the feasibility of intracellular magnetic manipulation for questioning and control the complex cellular signaling machinery ex vivo, from [35].

Figure 2 . 1 :Figure 2 . 2 :

 2122 Figure 2.1: Drosophila embryo gastrulation. Dorsal, ventral, lateral-left, lateral-right and rotating maximum-intensity projections of a timelapse recording of Drosophila embryo gastrulation. In green cells' nuclei and in pink cell membrane. The video was provided by Keller Lab, HHMI/Janelia Research Campus [42].

  (a) Neuron grown in culture, showing morphological polarity. Dendrites (red), the axon (green) and the nucleus (blue) are shown. The image acquired by H. Misono Doshisha University, Kyoto, Japan was provided by Olympus BioScapes 2012. (b) Gastrula singlelayered cells, showing internacellular polarity. Myosin (red), nuclei (blue), cell-cell junctions (green). The image was provided by [47].

Figure 2 . 3 :

 23 Figure 2.3: Examples of polarized cells: a neuron and epithelial cells.

Figure 2 . 4 :

 24 Figure 2.4: Polarity in a migrating cell. Adapted from [40].

Figure 2 . 5 :

 25 Figure 2.5: Dictyostelium discoideum chemotaxis [50].

Figure 2 . 6 :

 26 Figure 2.6: The RhoGTPases cycle. Adapted from [54].

  (a) Actin filaments (A) and integrin adhesion complexes (B) of wild type fibroblasts. (b) Microinjection of Rac1 induce lamellipodia (E) and focal adhesion formation (F). (c) Microinjection of a GEF of CdC42 leads the formation of filopodia (G) and the associated adhesion complexes (H).

  (d) Rho activation leads to stress fiber (C) and focal adhesion formation (D).

Figure 2 . 7 :

 27 Figure 2.7: Rac1, Cdc42 and RhoA cellular function in the organization of actin cytoskeleton. Adapted from [63].

  (a) On the top left, cell morphology (in DIC) and evolution of cell edge position. On top right, activity maps of cell edge velocity and Rac1 activation, measured by FRET. On the bottom, CCF between edge velocity and Rac1.

  Derived model of Rho GTPases activation during protrusion and retraction. Green indicates Rac1 activation; black, RhoA activation; blue, Cdc42 activation.

Figure 2 . 9 :

 29 Figure 2.9: Machacek's multiplex study of Rho GTPases activity during fibroblast migration. Adapted from [75].

Figure 2 . 11 :

 211 Figure 2.11: Stategies for optogenetic control of protein activity. Adapted from [77].

  Schematic of PA-Rac1 design via LOV light-induced conformational change. (b) Directional cell migration induced by repeated light activation of PA-Rac1 at the cell edge.

Figure 2 . 12 :

 212 Figure 2.12: Genetically encoded photoactivable Rac1 by Wu et al.[83].

  Schematic of PhyB/PIF photodimerization to recruit active proteins at the membrane. Local optogenetic induction of lamellipodia in fibroblasts, obtained by globally irradiating infrared (750nm) light, while focusing a red (650nm) laser on to a small portion of the cell (red circle).

Figure 2 . 13 :

 213 Figure 2.13: Optogenetic control of cell protrusion, adapted from [84].

Figure 2 .

 2 Figure 2.14: Optogenetics' spatial precision.On the top: the diffusion of protein activity (red) from the site of activation destroys the applied spatial pattern. At the bottom: the desired spatial pattern can be maintained by coupling local activation with global inactivation (green).

Figure 3 . 1 :

 31 Figure 3.1: Atomic dipole configuration for diamagnetic and paramagnetic materials, without and with an applied external magnetic field H. Adapted from [95].

Figure 3 . 3 :

 33 Figure 3.3: Schematic of domains structure and domain walls in ferro(i)magnets, adapted from [95].

Figure 3 . 4 :

 34 Figure 3.4: Magnetization M versus external filed H curve for ferro(i)magnets, adapted from [95].

Figure 3 . 5 :

 35 Figure 3.5: Superparamagnetic behavior: flip of magnetization at room temperature.

  The net energy curve obtained by subtracting the van der Waals attraction curve from the electrostatic repulsion curve.

Figure 3 . 6 :

 36 Figure 3.6: Double layer schematic and curve of net energy in the DLVO theory, adapted from [100].

  .7(a) together with TEM images (figure 3.7(b)) and hydrodynamic radius Dynamic Light Scattering measurements (figure 3.7(c)). Schematic of the particles. (b) TEM images of the nanoparticles. (c) Hydrodynamic radius measurements via Dynamic Light Scattering.

Figure 3 . 7 :

 37 Figure 3.7: Core-shell Fe 2 O 3 @SiO 2 superparamagnetic nanoparticles.

Figure 3 . 8 :

 38 Figure 3.8: Schematic of MNPs synthesis, adapted from [105].

Figure 3 . 9 :

 39 Figure 3.9: Silica shell degradation over time (TEM images).

Figure 3 .

 3 Figure 3.10: "Click-chemisty" for functionalization of MNPs with HTL.

  Ferritin mEGFP::HCF meGFP (a) Schematic of mEGF::HCF ferritin. (b) TEM images of the ferritin cage.

Figure 3 .

 3 Figure 3.11: Ferritin-based iron oxide superparamagnetic nanoparticles.

( a )

 a Ferritin cage loaded and PEGylated. (b) Magnetic cores inside the loaded ferritin. (c) Core diameter size distribution.

Figure 3 . 12 :

 312 Figure 3.12: Loaded magneto ferritin: TEM images of shell and core respectively and diameter's measurement.

Figure 3 . 13 :

 313 Figure 3.13: SQUID measurements of sample magnetization (Am 2 ) vs applied filed (T).

  and images during real time microinjection are shown in figure 3.14. micropipette phase contrast illumination fluorescence

Figure 3 . 14 :

 314 Figure 3.14: Microinjection of MNPs into HeLa cells.

  (a) Silica MNPs in red, merged fluorescence channel with phase contrast illumination. (b) Ferritin in green, merged fluorescence channel with phase contrast illumination.

Figure 3 .

 3 Figure 3.15: Bead-loading of HeLa cells: MNPs and ferritin.

Figure 3 . 16 :

 316 Figure 3.16: Pinocytic loading of 25 nm fluorescent nanoparticles into HeLa cells.

Figure 3 . 17 :

 317 Figure 3.17: Crossbow and round shaped cell patterning.

Figure 4 . 1 :

 41 Figure 4.1: Nanoparticles' diffusion in the cytoplasm as a function of their diameter. On the left, HeLa cell injected with latex nanoparticles of 50 nm in diameter. On the top right, single trajectory analysis with examples of intracellular trajectories for 50 nm and 75 nm particles. On the bottom right, maximum intensity projection of 300 frames movie, after injection of 50 nm NPs (left) and 75 nm particles (right).

Figure 4 . 2 :

 42 Figure 4.2: Diffusion coefficients for intracellular latex nanoparticles of different sizes. Median (line) and mean (square) of each distribution are indicated.

Figure 4 . 3 :

 43 Figure 4.3: Calibration of MNPs' ζ-potentials versus succinic anhydride excess during functionalization.

Figure 4 . 4 :

 44 Figure 4.4: Stability of microinjected MNPs in fuction of their ζ-potentials.

Figure 4 . 5 :

 45 Figure 4.5: Stability of ferritin without and with PEG2k funtionalization.

Figure 4 . 6 :

 46 Figure 4.6: Global vision of nanoparticles' behavior inside living cells

  Force vs distance from the pole of the tip for 500 nm particles.

Figure 4 . 7 :

 47 Figure 4.7: Force calibration of the magnetic manipulator.

  ure 4.8(a)). Moreover, by equation 3.2, considering a magnetic moment for MNPs of 1.97•10 -19 Am 2 (as derived in chapter 3.6) we calculated the force vs distance trend for MNPs (figure 4.8(b)).

  Magnetic field gradient map.μ (b) Force vs distance estimated trend for MNPs.

Figure 4 . 8 :

 48 Figure 4.8: Magnetic gradient field map and estimated force vs distance trend for MNPs.

8 Figure 4 . 9 :

 849 Figure 4.9: 1D drift diffusion model of magnetic responce.

Figure 4 . 10 :

 410 Figure 4.10: in vitro model system of the cell.On the left, an aqueous droplet in oil phase filled with MNPs, with the magnet tip below. On the right, MNPs fluorescence, without and with the magnet.

  MNPs' distribution within the droplet for different values of L (b) On the left, MNPs' concentration profiles for different value of distance L. Each curve is corrected for the droplet geometry by dividing by the homogeneous profile inside the droplet in absence of the magnetic tip. On the right, decay length of the MNP concentration profile as a function of L.

Figure 4 . 11 :

 411 Figure 4.11: Gradient distribution of MNPs inside the droplet can be tuned changing the distance of the magnetic tip.

4. 3 .Figure 4 . 12 :

 3412 Figure 4.12: Kymograph of the MNPs' distribution at the center of the droplet.

Figure 4 . 13 :

 413 Figure 4.13: Gradient distribution of MNPs in living cells.

Figure 4 . 14 :

 414 Figure 4.14: Reversibility of MNPs gradient in living cells.

  (a) Normalized fluorescence barycenter diplacement during attraction of MNPs. (b) Attraction (red) and relaxation (blue) times.

Figure 4 . 15 :

 415 Figure 4.15: Attraction and relaxation kinetics of MNPs.

Finally, to

  demonstrate the possibility to recruit in vivo and manipulate targeted proteins of interest, we injected MNPs, functionalized with HTL ligand into living cell, transiently over-expressing the fusion protein meGFP::HT. Few minutes after the injection, we positioned the magnetic tip close to the cell border and we observed the creation of the gradient of nanoparticles. Remarkably, by monitoring the fluorescence in the meGFP channel (green), we observed a corresponding increase, with perfect colocalization of the two signals (figure4.16(a)). The normalized intensity profiles of both MNPs and meGFP distributions, before and after magnetic manipulation, overlap, confirming a net displacement of the protein of interest meGFP via magnetogenetic manipulation. Recruitment in vivo of meGFP::HT via MNPs-HTL. On the right, ratiometric images of the corresponding channels and related intensity profiles. Control experiment with transfected cells and non functionalized MNPs.

Figure 4 . 16 :

 416 Figure 4.16: Recruitment of meGFP::HT via MNPs-HTL in vivo HeLa cells.

Figure 5 .

 5 Figure 5.1(a) shows an example of HeLa cells bead-loaded with magnetic pegylated ferritin, located in a specific region of the glass bottom dish, identified with a letter and a number (an 8 is visible in the bright field image). During TEM imaging, the two cells, pointed by white flash in figure 5.1(a), were relocated and single ferritin nanoparticles were identified by the high dark contrast of their magnetic cores (figure 5.1(b) and 5.1(c)). As shown by the intensity profile for one single ferritin nanoparticles, the core has a physical diameter of about 7 nm (figure 5.1(d)).

  Relocation of the injected cell in in TEM after fixation and ultramicrotomy. The cell corresponds to the one indicated by the white flash in figure 5.1(a). White flashes indicate the nanoparticles.

  Ferritin nanoparticles into the cytoplasm of HeLa cells (white flashes). They are not trapped in vesicles, but free in the cytoplasm.

Figure 5 . 1 :

 51 Figure 5.1: TEM images of bead-loaded ferritin nanoparticles into HeLa cells.

  TEM image of an HeLa cell injected with MNPs. White flashes indicate the nanoparticles. They are not trapped into endocytic vesicle, but free in the cytoplasm.

  Intensity profile of one single MNP found in the injected HeLa cell.

Figure 5 . 2 :

 52 Figure 5.2: TEM images of microinjected MNPs into HeLa cells.

Figure 5 .

 5 Figure 5.2(a) shows that also upon microinjection, nanoparticles's surface appears accessible in the cytoplasm, and in particular, for MNPs we can also notice the unaltered silica shells, thanks to the higher electron density of silicon dioxide. The intensity profile for a single MNPs, reported in figure5.2(b), shows an external diameter of about 30 nm with an internal core diameter of about 10 nm, which is consistent with the MNPs sizes measured in vitro (chapter 3). Also for microinjected cells, we observed a complete recovery after about 30 min.Comparable results were obtained both by microinjecting ferritin nanoparticles and by bead-loading MNPs, demonstrating that both techniques are very efficient in delivering functional nanoparticles inside the cytoplasm of living cells.

  3(c)), giving in fluorescence a perfect colocalization of mCherry and GFP signals (figure 5.3(d)).

  (a) HeLa cells transfected with Tom20::mCherry::α-GFP and injected with ferritin nanoparticles. mitochondria (b) mCherry red fluorescence of mitochondrial branched structure. ferritin (c) GFP green fluorescence of ferritin nanoparticles, localized at Tom20 sites after recruitment via GFP α-GFP targeting system. merged (d) Merged fluorescence shows colocalization of mCherry and GFP.

Figure 5 . 3 :

 53 Figure 5.3: Recruitment of ferritin nanoparticles onto mitocondria via Tom20::mCherry::α-GFP fusion gene.

  HeLa cell transfected with Tom20::mCherry::α-GFP fusion gene (overlay red fluorescence) and injected with GFP ferritin nanoparticles. On the right TEM image of the same cell after relocation in TEM slides.

  TEM image of targeted mitochondria corresponding to the crop region in figure 5.4(a). White flashes highlight the nanoparticles' location.

  TEM image of targeted mitochondria corresponding to the crop region in figure5.4(a).

Figure 5 . 4 :

 54 Figure 5.4: TEM images of ferritin nanoparticles injected into HeLa and recruited onto mitochondria via Tom20::mCherry::α-GFP fusion gene.

  Tables 5.1 and 5.2 summarize the experiments performed with the specifications of the fluorescent channels simultaneously observed during the perturbation.

  HeLa cell, transfected with INTS-I::eGFP::HT and injected with functionalized HTL-MNPs. Upon magnet application a gradient of particles is formed and a corresponding gradient ITSN-I is generated. COOH-MNPs ITSN-I control control (b) Control experiment with HeLa cell, transfected with INTS-I::eGFP::HT and injected with non-functionalized COOH-MNPs.

Figure 5 . 5 :

 55 Figure 5.5: Selective manipulation of intracellular ITSN-I via magnetogenetic actuation of functionalized HTL-MNPs.

  Cell edge evolution over time, derived by intensity thresholding. Color bar indicates the temporal evolution in minutes. (b) Position markers along the cell edge. Cell edge μm (c) Cell edge displacement over time: x-axis represents time and y axis the position along the edge as reported in figure 5.6(b). Color bar indicate the displacement in µm.

Figure 5 . 6 :

 56 Figure 5.6: Cell edge evolution and spatio-temporal map of cell edge displacement.

5. 3 .

 3 PROTEIN MANIPULATION IN VIVO AND PROBING OF PROTEIN ACTIVITYcell edge and the "average shape" was measured. In figure5.6(c) is shown an example of cell edge displacement relative to the cell in figure5.6(a). The x axis is time in minutes and the y axis is the position of the window along the cell contour traveled in the clockwise direction (from 0 to 1, figure5.6(b)). The color code identifies local protrusions and retraction of the cell (in µm), compared to its "average shape" during the whole experiment.Additionally, we measured the fluorescence intensity of nanoparticles, ITSN-I and N-WASP during time, for windows along the cell contour which extend inside the cell over a thickness of about 4 µm. The intensity value per window was obtained by adding the fluorescence intensities of all pixels inside each window.

Figure 5 .

 5 [START_REF] Crick | The physical properties of cytoplasm[END_REF] shows the time courses of nanoparticles, ITSN-I and N-WASP respectively, along the cell contour (x axis) during time (y axis). Signals are normalized over intensity fluctuations of the light source and are reported as relative intensities compared to the average intensity over the whole experiment.

Figure 5 . 7 :

 57 Figure 5.7: Time courses of nanoparticles', ITSN-I and N-WASP signals in the localized region of attraction. Time along the x axis is in minutes and position along the y axis relates to position markers of figure 5.6(b). Color bar indicate relative intensities.

Figure 5 . 8 :

 58 Figure 5.8: 2D Pearson correlation coefficients between nanoparticles, ITSN-I and N-WASP activities.

Figure 5 . 9 :

 59 Figure 5.9: N-WASP recruitment through the activation of endogenous Cdc42 via ITSN-Ibounded nanoparticles.

Figure 5 .

 5 [START_REF] Wang | Mechanotransduction across the cell surface and through the cytoskeleton[END_REF] shows an example of cell protrusion formation due to functionalized particles accumulation.

Figure 5 . 10 :

 510 Figure 5.10: Cell protrusion formation upon localization of the "signaling modules" close to the cell periphery.

Figure 5 .

 5 Figure 5.11: N-WASP vesicle formation, about 20 min after the perturbation.

Figure 5 . 12 :

 512 Figure 5.12: Global retraction of the cell far from the induced perturbation.

  d -s o u t h (a) On the left, Fe/Ni paramagnetic pillars electrodeposited onto glass coverslides (cyan). Black spot correspond to 500 nm magnetic nanoparticles attracted after approaching a permanent magnet. In the middle and right, 40 nm MNPs attracted at the two poles of the magnetized pillar.

  HeLa cell grown close to a pillar and injected with MNPs. Upon magnetization, MNPs are attracted and generate different profile concentration according to the direction of the external magnetizing filed.

Figure 5 . 15 :

 515 Figure 5.15: Parallelization of the magnetic perturbation via array of paramagnetic Fe/Ni pillars.

Figure 6 . 1 :

 61 Figure 6.1: Oriented cell division (OCD) for corrected elongation of cell tissues.

Figure 6 . 2 :

 62 Figure 6.2: Symmetric and asymmetric cell division of stem cells determine cell fate. Adapted from [146].

Figure 6 . 3 :

 63 Figure 6.3: Local magnetic hyperthermia.

Figure 6 . 4 :

 64 Figure 6.4: Force generation via magnetic actuation.

Figure 6 . 5 :

 65 Figure 6.5: Schematics of MAGNEURON project.

Figure A. 1 :

 1 Figure A.1: Tube or dish configuration to sprinkle the glass beads.

  1.1 Sizes of biological entities compared to magnetic nanoparticles. . . . . . 1.2 Schematic representation of the different types of magnetic actuation, adapted from [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Magnetic activation of mechanotransduction channels of inner hair cells.

  First proof-of-concept of the feasibility of intracellular magnetic manipulation for questioning and control the complex cellular signaling machinery ex vivo, from[START_REF] Etoc | Subcellular control of rac-gtpase signalling by magnetogenetic manipulation inside living cells[END_REF]. . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Drosophila embryo gastrulation. . . . . . . . . . . . . . . . . . . . . . . . 2.2 Keratinocytes' migration during wound healing in a scratch assay. . . . 2.3 Examples of polarized cells: a neuron and epithelial cells. . . . . . . . . 2.4 Polarity in a migrating cell. Adapted from [40]. . . . . . . . . . . . . . . 2.5 Dictyostelium discoideum chemotaxis [50]. . . . . . . . . . . . . . . . . . 2.6 The RhoGTPases cycle. Adapted from [54]. . . . . . . . . . . . . . . . . 2.7 Rac1, Cdc42 and RhoA cellular function in the organization of actin cytoskeleton. Adapted from [63]. . . . . . . . . . . . . . . . . . . . . . . 2.8 Schematic of computational multiplexing. Adapted from [74]. . . . . . . 2.9 Machacek's multiplex study of Rho GTPases activity during fibroblast migration. Adapted from [75]. . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Schematic of perturbative approach. Adapted from [77]. . . . . . . . . . 2.11 Stategies for optogenetic control of protein activity. Adapted from

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1.16

  .1). The detailed calculation is reported in appendix B.

	Nanoparticle	Magnetic moment (•10 -20 Am 2 )
	MNP	19.7
	horse spleen ferritin	3.3
	magnetite ferritin	6.6
	Co-loaded ferritin	5.3
	Zn-loaded ferritin	6.1

Table 3 .

 3

1: Magnetic characterization of nanoparticles.

Table 3 .

 3 2: P-97 Sutter Micropipette puller: retained parameters.

Table 5 . 1 :

 51 Experiment with MNPs.

	Ferritin ITSN-I N-WASP
	meGFP mCherry	IRFP
	green	red	far red

Table 5 . 2

 52

: Experiment with Ferritin.

Gastrulation is a regular embryonic process, typical of many multicellular organism, consisting of morphological movements intended to reorganize the single-layered early embryo into a gastrula, i.e. a three-layered embryo. Dorsal and ventral closure are morphological movements, which follow gastrulation.

Fluorescence (or Förster) Resonance Energy Transfer (FRET) is a process by which the radiationless transfer of energy occurs from a donor fluorophore to an acceptor fluorophore, placed in close proximity. The efficiency of the energy transfer is inversely proportional to the sixth power of the distance between donor and acceptor, making FRET extremely sensitive to small changes in distances. By fusioning the donor to a specific Rho GTPase and the acceptor to one of its effector domain (Intermolecular FRET), it is possible to detect the interaction between the two proteins and therefore to reveal the activation of the Rho GTPase. A more reliable activity reporter is the Intramolecular FRET, in which both fluorophores are fused within a single chain and come closer upon a conformational change of the Rho GTPase. For a more detailed description, please refer to the reviews[START_REF] Aoki | Visualization of small GTPase activity with fluorescence resonance energy transfer-based biosensors[END_REF] and[START_REF] Jares-Erijman | FRET imaging[END_REF].

Gene knockdown is a biological technique by which the expression of one or more genes are reduced.

The reduction occurs either through genetic modification or by treatment with a reagent, such as a short DNA or RNA oligonucleotide.

Phototropins are photoreceptor proteins involved in the plant phototropism, i.e. the the growth of the organism in response to a light stimulus.

Paraphrasing the brilliant physician Richard Feynman, it is impossible to give an honest description of magnetisms from the point of view of classical physics, because magnetic effects are completely quanto-mechanical phenomena[START_REF] Richard P Feynman | The Feynman Lectures on Physics, Desktop Edition Volume I[END_REF]. However, for sake of simplicity and for historical reasons (magnetism was described way before the quanto-mechanical physics formulation), we will take advantage of the knowledge of classical magnetisms.

In classical magnetism, the magnetization M is the vector field that expresses the density of magnetic dipole moments per units of volume (Am 2 ).

The magnetic susceptibility χ is a dimensionless proportionality tensor indicating the degree of magnetization M in response to an external magnetic field applied H.

A colloid is a mixture in which one substance of microscopically dispersed insoluble particles is suspended throughout another substance. It can be considered as the intermediate state between a solution and a dispersion.

The ionic strength of a solution is a measure of the concentration of ions in the solution.

A dehalogenase is a type of enzyme that catalyzes the removal of an halogen atom from a substrate.

Native ferritin purified from equine spleen, usually containing a core of ferrihydrite.

The filament is a small rod of glass annealed to the inner wall of the microcapillary. Its presence helps in quick filling the micropipette and prevents air bubbles formation.

The medium used during the experiments was in general Leibovitz's L-15,

10% fetal bovine serum and 1% penicillin-sptreptomycin antibiotics. L-15 is an optimized medium designed for supporting cell growth in environments without CO2 equilibration.

More realistically, the efficiency is around 40% with specific region of the coverslide that can reach 90% of loaded cells.

Pinocytosis is a kind of endocytosis: cells form small vesicles by membrane invagination to absorb extracellular fluids.

Stokes-Einstein equation: D = kBT /6πrη with D diffusion coefficient, r radius of the particle and η dynamic viscosity of the medium.

Autophagy is a natural regulated process by which unnecessary or dysfunctional cellular components are disassembled and destroyed. During autophagy, targeted components are isolated within a vesicle known as an autophagosome, and then it fuses with a lysosome which content is degraded and recycled.

[START_REF] Qa A Pankhurst | Applications of magnetic nanoparticles in biomedicine[END_REF] The fusion plasmid pSEMS-meGFP::LCF::HCF, designed by our collaborators in Osnabrück, codes for the expression in mammalian cells of a ferritin cage composed by 12 LCFs and 12 HCFs, with only 12 meGFP.

Ultramicrotomy is an extremely precise method for cutting biological specimens into nm slides, in order to be observed by the electron beam of TEM microscopes. Slices are ultra-thin cut by the diamond knife of an ultramicrotome and collected on metal mesh grids.

The experiments for which the effect was more evident showed a higher level of N-WASP expression.

Cross-covariance measures the similarity between x and shifted (lagged) copies of y as a function of the lag.

Magnetotactic bacteria are motile prokaryotes able to swim along geomagnetic field lines.

Cell replacement therapies is a therapy in which living cellular material is injected into a patient.

After injecting MNPs in crossbow patterned cells, we found that according to the different location at which the nanoparticles were localized, different profile of concentration were generated. In figure 5.14(a) is shown as an example the extension of the gradient for nanoparticles accumulated close either to the lamellipodium or to the center of the cell. The ratiometric intensity profiles (figure 5.14(b)) indicate that a sharper extension can be obtained if the particles are accumulated in the flat lamellipodium region. This evidence can be justified both considering the volume effect and the different molecular crowding conditions of the two distinctive locations.

Magnetic Array

In combination with cell patterning, the further step will be the creation of an array of magnetic/magnetizable pillars alongside the array of patterned cells, so as to perform the perturbation simultaneously to many cells.

Inspired by the works of di Carlo's [START_REF] Tseng | Rapid and dynamic intracellular patterning of cell-internalized magnetic fluorescent nanoparticles[END_REF][START_REF] Tseng | Magnetic nanoparticle-mediated massively parallel mechanical modulation of single-cell behavior[END_REF] and Dempsey's [START_REF] Zablotskii | Life on Magnets: Stem Cell Networking on Micro-Magnet Arrays[END_REF][START_REF] Kauffmann | Diamagnetically trapped arrays of living cells above micromagnets[END_REF] groups, we are interested in generating glass coverslides provided with arrays of paramagnetic pillars, deposited with µm precision via lithographic techniques. Under the influence

APPENDIX . APPENDICES

The day before:

Plate cells in a glass-bottom dish (e.g., MatTek; P35G-1.5-10-C) so they are 50-90% confluent on the day of loading.

The day of loading:

Warm up media for live imaging (e.g. phenol red-free DMEM) at 37°C. Take a glass-bottom dish out of a CO 2 incubator. Remove the culture medium from the dish using an aspirator. Make sure to also remove residual media around the rim of the glass-bottom part of the dish. Pipette 2-4 µl of protein solution in the center of the glass coverslip part of the dish. To cover the whole coverslip area, use 10 µl of protein solution; this will increase the total number of loaded cells, but it is not usually necessary, as only tens of loaded cells are required for typical live cell imaging (figure A.2).

aspirate medium add loading sol. Sprinkle dried glass beads onto the coverslip to distribute as a single layer or less. Avoid overlay. There are several ways to sprinkle the beads:

-You can make a tube with a nylon mesh cover on the top. Align the tube so the top (i.e., the exit of beads) is just above the glass-bottom dish. Tap the tube to drop the glass beads. As there is air flow in a hood, dropping beads far above the dish will miss the target.

-You can also make a dish with a nylon mesh-bottom. Flip it onto the glassbottom dish and, if necessary, tap once to distribute the beads (figure A. -Alternatively, you can sprinkle beads without a nylon mesh using a spatula or a P-1000 pipette, but care must be taken to sprinkle just a single layer.

B SQUID measurements analysis

The magnetization of an assemble of superparamagnetic nanoparticles is defined by equation B.1:

where n is the number of nanoparticles per unit of volume, µ is the magnetic moment of the nanoparticles, µ 0 H is the applied magnetic field and L(x) is the Langevin equation:

The trends of sample magnetization measured via SQUID (figure B.1) were fitted with the following equation:

where the term e * x accounts for all the diamagnetic contributions eventually present in the sample (holding film, salts, proteins, impurities). Knowing the relationship between w and µ, (w = µ k B T ), we derived the magnetic moment for each nanopaticle (table B.1).

We evaluated also the magnetization normalized over the mass of the nanoparticle and the mass of iron content and results are reported in