Jeffrey Teillet

Quentin Martinez

Inga Tijunelyte

Bayan Chami

Aurélien Bancaud

Affiliation

Characterization and minimization of band broadening in DNA electrohydrodynamic migration for enhanced size separation

INTRODUCTION

The technologies to perform DNA separation by size can be coarsely cast intro three main classes, namely electrophoresis through polymer matrices, transport through artificial micro/nanofabricated matrices, and matrix-free DNA separation. The mechanism of DNA migration in the first two classes has been the subject of intense research [START_REF] Duke | Electrophoretic Mobility of DNA in Gels. I. New Biased Reptation Theory Including Fluctuations[END_REF][START_REF] Slater | Joule Heating, and Band Broadening in Capillary Gel Electrophoresis of DNA[END_REF][START_REF] Slater | Theory of Band Broadening for DNA Gel Electrophoresis and Sequencing[END_REF][START_REF] Slater | New Biased-Reptation Model for Charged Polymers[END_REF][START_REF] Lumpkin | Mobility of DNA in Gel Electrophoresis[END_REF][START_REF] Lerman | Why Does the Electrophoretic Mobility of DNA in Gels Vary with the Length of the Molecule? Biopolym[END_REF] , which aimed at elucidating the size dependence of the migration and the sources of band broadening, as reviewed in refs. [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Machanisms[END_REF][START_REF] Dorfman | DNA Electrophoresis in Microfabricated Devices[END_REF] . These mechanistic studies were coupled to tremendous experimental efforts to optimize separation matrices [START_REF] Guttman | Gel and Polymer-Solution Mediated Separation of Biopolymers by Capillary Electrophoresis[END_REF][START_REF] Albarghouthi | Polymeric Matrices for DNA Sequencing by Capillary Electrophoresis[END_REF] , which have synergistically contributed to enhance DNA separations. The base resolution is now routinely achieved for sequencing applications [START_REF] Dovichi | DNA Sequencing by Capillary Array Electrophoresis[END_REF] .

Interest for matrix-free separation technologies is more recent [START_REF] Wang | Resolving DNA in Free Solution[END_REF] with fewer studies on the separation mechanism despite key advantages in terms of reusability and simplicity of implementation. Matrix-free separation has been achieved with one force field, either hydrodynamic [START_REF] Liu | Single-Molecule Analysis Enables Free Solution Hydrodynamic Separation Using Yoctomole Levels of DNA[END_REF][START_REF] Duan | On-Chip Hydrodynamic Chromatography of DNA through Centimeters-Long Glass Nanocapillaries[END_REF] or electrophoretic [START_REF] Pennathur | Free-Solution Oligonucleotide Separation in Nanoscale Channels[END_REF] . In both cases the degree of confinement appeared to be critical given that experiments were carried out in microchannels of ~1 µm in thickness. The combination of electric and hydrodynamic actuation acting in opposite directions has been exploited to perform size separation in larger channels of 2 to 50 µm using Newtonian [START_REF] Zheng | Anomalous Radial Migration of Single DNA Molecules in Capillary Electrophoresis[END_REF][START_REF] Zheng | Mechanism for the Separation of Large Molecules Based on Radial Migration in Capillary Electrophoresis[END_REF][START_REF] Milon | ΜLAS Technology for DNA Isolation Coupled to Cas9-Assisted Targeting for Sequencing and Assembly of a 30 Kb Region in Plant Genome[END_REF] or viscoelastic [START_REF] Ranchon | DNA Separation and Enrichment Using Electro-Hydrodynamic Bidirectional Flows in Viscoelastic Liquids[END_REF][START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF] fluids. The separation mechanism relies on transverse size-dependent forces oriented toward the channel walls, which have been studied analytically or numerically in Newtonian for DNA [START_REF] Butler | Kinetic Theory of a Confined Polymer Driven by an External Force and Pressure-Driven Flow[END_REF] and viscoelastic fluids for DNA and particles [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF][START_REF] Lee | Cross-Stream Forces and Velocities of Fixed and Freely Suspended Particles in Viscoelastic Poiseuille Flow: Perturbation and Numerical Analyses[END_REF] . Some predictions of models have been tested experimentally and validated [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF][START_REF] Socol | Contraction and Tumbling Dynamics of DNA in Shear Flows under Confinement Induced by Transverse Viscoelastic Forces[END_REF][START_REF] Montes | Transverse Migration and Microfluidic Concentration of DNA Using Newtonian Buffers[END_REF] .

Furthermore, dual actuation aroused attention because it enabled the concentration of DNA in microchannels with a funnel geometry [START_REF] Milon | ΜLAS Technology for DNA Isolation Coupled to Cas9-Assisted Targeting for Sequencing and Assembly of a 30 Kb Region in Plant Genome[END_REF][START_REF] Ranchon | DNA Separation and Enrichment Using Electro-Hydrodynamic Bidirectional Flows in Viscoelastic Liquids[END_REF][START_REF] Arca | Electro-Hydrodynamic Concentration of Genomic Length DNA[END_REF][START_REF] Montes | Trapping DNA with a High Throughput Microfluidic Device[END_REF][START_REF] Milon | A Tunable Filter for High Molecular Weight DNA Selection and Linked-Read Sequencing[END_REF] . The operations of DNA concentration and separation could be performed on-line with the so-called µLAS (µ-Laboratory for DNA Analysis and Separation) technology to produce high sensitivity DNA profiles with a limit of detection of 10 fg/µL [START_REF] Andriamanampisoa | BIABooster: Online DNA Concentration and Size Profiling with a Limit of Detection of 10 Fg/ΜL and Application to High-Sensitivity Characterization of Circulating Cell-Free DNA[END_REF][START_REF] Malbec | Sizing of Expanded Trinucleotide Repeats with Femtomolar Sensitivity in Less than 5 Minutes[END_REF] .

Whereas the physics of DNA separation in viscoelastic electrohydrodynamic migration has been studied experimentally [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF][START_REF] Socol | Contraction and Tumbling Dynamics of DNA in Shear Flows under Confinement Induced by Transverse Viscoelastic Forces[END_REF] , the mechanism of band broadening remains more elusive. In this report, we designed a microfluidic chip together with an experimental workbench to perform a systematic investigation of DNA dispersion in the pressure-electric field parameter space. Our study starts with the derivation of a model of band broadening based on Taylor-type arguments. We then motivate our research based on the evidence that the optimal separation of two bands corresponds to a minimum for band broadening. We thus focus on the diffusion coefficient of one single DNA band of 600 bp in three actuation schemes, namely electrohydrodynamic, hydrodynamic and electrophoretic. Our results show that the electrohydrodynamic diffusion coefficient is bonded by the electrophoretic and hydrodynamic responses and can be modulated finely in this parameter space. Furthermore, the diffusion coefficient appears to be mainly controlled by the electric field and marginally by the flow velocity, in excellent agreement with our model. Given that the voltage is a versatile actuation parameter, we finally investigate whether the temporal modulation of the electric field enables the minimization of band broadening, and clarify how to optimize separation experiments by the temporal control over the electric field. Altogether, our study represents a step forward towards the development of high performance analytical technologies for matrix-free DNA separation.

MATERIALS AND METHODS

Chemicals and Biological material

The viscoelastic polymer solutions contained polyvinylpyrrolidone 5% (PVP) of molecular weight (MW) 360 KDa purchased from Sigma Aldrich. The viscosity of the solution was 25 mPa.s and the fluid viscoelastic relaxation time was 0.6 ms, according to the method developed in ref. [START_REF] Naillon | Dynamics of Particle Migration in Confined Viscoelastic Poiseuille Flows[END_REF] . Dissolution of the polymer powders in 1X-TAE buffer (Tris-Acetate-EDTA [START_REF] Sambrook | Molecular Cloning: A Laboratory Manual[END_REF] ) was performed during 1 day before filtration at 0.2 µm pore size. One or two bands of dsDNA of 600 or 1000 bp (Thermo-Scientific) were then added at a concentration of 0.3 µM together with the intercalating dye YOYO-1 (Thermo-Scientific) at a dye to base pair ratio of 1:8. The channels were initially filled with 70% ethanol to prevent the formation of bubbles, briefly rinsed with deionized water (18.2 MΩcm), and then flushed with the buffer solution containing DNA.

Chip fabrication

The glass-silicon microfluidic chips were processed in clean room using photolithography and plasma etching, as described in ref. [START_REF] Ranchon | Metrology of Confined Flows Using Wide Field Nanoparticle Velocimetry[END_REF] . Briefly, two steps of silicon etching were carried out on a silicon 4-inch wafer, first engraving a shallow channel of 2 μm in depth with a constriction shape (see layout in Fig. 1A) and then a thicker channel of 16 μm away from the constriction to limit the hydraulic resistance of the microfluidic channel. Note that etch depth are defined with 10% reproducibility. The maximal and minimal channel widths were 800 and 5 μm, respectively. Inlets and outlets were then drilled by sand blasting, and the silicon was insulated with a layer of 300 nm of thermally-grown oxide. The devices were eventually sealed by anodic bonding with an AF32 glass wafer for microscopy observation.

Experimental settings for the study of band broadening

We designed an experimental bench to monitor the dynamics of a DNA band throughout its migration in the microchannel. The microfluidic channel consisted of a DNA concentration module based on funnel-shape geometry followed by a linear separation channel of 1.6 mm in length. The length of the separation channel typically matched the field of view of a microscopy platform comprising a 10X objective (Numerical Aperture=0.5, Olympus) and an sCMOS camera (Hamamatsu, ORCA Flash 4.0 lt+) with 2048 pixels of 6.5 µm (yellow dashed rectangle in Fig. 1A). Videos were mostly recorded at inter-frame intervals of 10 ms, but larger intervals were also chosen in the case of slow dynamics. Experiments were run in batch by synchronizing video acquisition and electrohydrodynamic actuation through a home-made software developed in LabVIEW. The pressure controller (MFCS, Fluigent) operated in the range of 1 to 5 bar, and the voltage generator consisted of a 0-10 V supply (USB acquisition card from National Instruments), which is used with a 100X multiplier to obtain an output in the range of 0 to 200 V.

Data post-treatment consisted in extracting the band profile with a Gaussian fit (Igor Pro) to measure its full width at half maximum (FWHM) and position at time t. The diffusion coefficient was finally estimated between the times and and using the expression:

(1)

We also used two metrics to assess the quality of separation experiments. Knowing the passage time and of band 1 and 2 in front of the detector and their respective widths and , we expressed the resolution as:

(

The theoretical plate number per meter [START_REF] Ettre | Nomenclature for Chromatography (IUPAC Recommendations[END_REF] was evaluated to assess the sharpness of DNA bands after 1.3 mm of migration:

(3)

MODEL OF TRANSPORT AND DISPERSION

Equation of transport:

We model the evolution of the concentration (x,t) with the Fick diffusion-advection equation, defining the migration velocity and the diffusion coefficient .

(

) 4
The solution of equation ( 4) is a Gaussian function in the form:

(5)

In the following paragraphs, we express and in the context of electrophoretic, hydrodynamic, and electrohydrodynamic migration. In electrophoresis, the DNA velocity is proportional to the electric field with and is the electrophoretic mobility. In the limit of vanishing electric field, band broadening is dictated by Brownian fluctuations [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Machanisms[END_REF] , so that the electrophoretic diffusion coefficient is equal to the bulk diffusion coefficient . The situation is more complex for oriented molecules [START_REF] Slater | Joule Heating, and Band Broadening in Capillary Gel Electrophoresis of DNA[END_REF][START_REF] Tinland | Broadening in Gel Electrophoresis: Scaling Laws for the Dispersion Coefficient Measured by FRAP[END_REF] with a linear dependence of the normalized diffusion coefficient with the electrophoretic mobility (see ref. [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Machanisms[END_REF] , for review).

Hydrodynamic migration is described by the Taylor-Aris model [START_REF] Taylor | Dispersion of Solute Matter in Solvant Flowing Slowly through a Tube[END_REF][START_REF] Aris | On the Dispersion of a Solute in a Fluid Flowing through a Tube[END_REF] . For molecules smaller than the channel cross-dimension, the migration velocity is equal to the average speed of the flow and the diffusion coefficient is enhanced due to the coupling of longitudinal advection with diffusion transverse to the flow direction. The diffusion process reaches a steady-state once the time scale of flow advection (with the position of the detector along the channel) is greater than the diffusion time across the channel height . For a slit-like channel, the normalized diffusion coefficient is:

Physics of µLAS and prediction for the diffusion coefficient

In electrohydrodynamic migration, DNA transport in a hydrodynamic flow with an opposing electrophoretic force characterized by the velocity is associated to a transverse force oriented toward the channel upper and lower walls [START_REF] Ranchon | DNA Separation and Enrichment Using Electro-Hydrodynamic Bidirectional Flows in Viscoelastic Liquids[END_REF] . Close to the wall, can be modeled by an elastic spring, which stiffness increases linearly with and 4,5 :

with the size of the chain, the height of the channel, and the distance from the walls. The use of Boltzmann statistics allows one to deduce DNA average position from the wall [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF][START_REF] Socol | Contraction and Tumbling Dynamics of DNA in Shear Flows under Confinement Induced by Transverse Viscoelastic Forces[END_REF] :

Close to the wall and neglecting hydrodynamic interactions, the Poiseuille flow can be linearized and the DNA velocity therefore reads: (9) Boltzmann statistics also enables us to compute the variance of the DNA vertical position, which is on the order of [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF][START_REF] Socol | Contraction and Tumbling Dynamics of DNA in Shear Flows under Confinement Induced by Transverse Viscoelastic Forces[END_REF] . We then assume that DNA migration occurs in a space domain delimited by vertical boundaries comprised between =0 and . The diffusion coefficient can then be estimated using Taylor-type arguments 37 : (10) Note that without confinement, i.e. for , this expression is equal to Eq. ( 6). In the presence of the transverse viscoelastic force, the leading order term is that on the right, allowing one to estimate the diffusion coefficient by plugging Eq. ( 8) in Eq. ( 10): (11) In electrohydrodynamic actuation, the diffusion coefficient therefore depends on but not on . This counter-intuitive prediction comes from the fact that the hydrodynamic mixing takes place in a volume set by and .

RESULTS AND DISCUSSION

Optimal DNA separation is associated to minimal dispersion

In order to evaluate the impact of band broadening on the separations with electrohydrodynamic actuation, we performed series of experiments with on-line concentration and separation in a microfluidic chip with a funnel shape geometry (Fig. 1A, see Methods for fabrication details). The µLAS operation [START_REF] Andriamanampisoa | BIABooster: Online DNA Concentration and Size Profiling with a Limit of Detection of 10 Fg/ΜL and Application to High-Sensitivity Characterization of Circulating Cell-Free DNA[END_REF][START_REF] Malbec | Sizing of Expanded Trinucleotide Repeats with Femtomolar Sensitivity in Less than 5 Minutes[END_REF] consisted of a first phase of concentration during 10 s using a high electric field (red curve in Fig. 1B), which allowed us to stop and accumulate molecules in the funnel, i.e. ahead of the separation channel. At time t 0 , the electric field was decreased either linearly over time or abruptly to a second plateau (Fig. 1B), and the DNA band started to migrate in the separation channel, as shown in the time lapse of Fig. 1C. After the full passage of the DNA band, the electric field was turned off to flush the chip and start another experiment. The bands could be characterized either in temporal or in spatial mode. The temporal mode consisted in recording the variation of the intensity signal with a ROI of 20x20 µm 2 at 1.3 mm from the funnel. The spatial mode used the entire width of the camera sensor to determine the profile of the band in the course of its migration (Fig. 1D). In a first round of 36 DNA separation experiments, we used two bands of 600 and 1000 bp, and modulated the hydrodynamic pressure in the range of 2 to 5 bar, corresponding to average hydrodynamic velocities spanning 2.4 to 6 mm/s, while applying linear ramps in electric field starting from a maximum tension of 80 V, equivalently , down to 0 V (green curve of Fig. 2A). Fluorescence intensity was recorded in the temporal mode (blue dataset in Fig. 2A), and the peaks were automatically fitted with a Gaussian function (black curves in Fig. 2A). We used the resolution [START_REF] Heller | Principles of DNA Separation with Capillary Electrophoresis[END_REF] , which is the ratio of the distance between two consecutive peaks divided by their breadth (see Eq. ( 2)), to gauge the quality of the separations. The maximum resolution of 4.1 was obtained for a pressure of 3 bar and a slope of -7 V/s (Fig. 2B). The complete analytical process, which is reported in the plot of Fig. 2A, took 23 s including 10 s of pre-concentration in the funnel.

Interestingly, the maximum resolution also corresponded to a sharp peak of the theoretical plate number for the 1000 bp band of 1.5 10 6 plates/m (Eq. ( 3) and Fig. 2C). This result therefore showed that band broadening should be minimized for optimal DNA separation, and in turn motivated our study on dispersion in electrohydrodynamic migration.

Diffusion in the electrophoretic and hydrodynamic regimes

As a starting point, we assayed the diffusion coefficient in the reference regime of free diffusion using the 600 bp DNA as probe. These experiments started with a phase of concentration using a pressure of 2 bar and a tension of 150 V during 10 s, which enabled us to form a band of FWHM ~55 µm in the funnel region (Supplementary Fig. S1). Electrohydrodynamic actuation was then turned off, and the dispersion of the band was monitored during 60 s. The band profile was fitted with a Gaussian function in order to extract its width and then determine the diffusion coefficient of µm 2 /s using Eq. ( 1). This estimate appeared to be slightly larger, yet comparable to the prediction of Stokes-Einstein's law of 0.04 µm 2 /s taking 200 nm for DNA hydrodynamic diameter (i.e., two Kuhn segments).

We then focused on diffusion with hydrodynamic actuation in the Taylor dispersion regime (Fig. 3A). We measured the breadth of the band for three different pressure drops of 2, 3, and 4 bar, which corresponded to average migration velocities of 1.7, 2.7, and 3.4 mm/s (not shown).

increased with the flow velocity, and its amplitude of ~10 6 indicated that mixing was enhanced by hydrodynamics. The increase of the diffusion coefficient in the course of the migration showed that the steady state for the Taylor dispersion regime was not reached. This observation was in fact expected because the diffusion time in the vertical direction of tens of seconds was greater than the migration time of ~1 s. Conversely, the Taylor dispersion would require an even distribution of molecules across the channel section, as obtained for a transverse diffusion time much shorter than the advection time. Nevertheless, we noted that the amplitude of the normalized dispersion coefficient predicted by the Taylor model (Eq. ( 6)) of ~10 7 for a flow velocity of 2 mm/s was consistent and slightly larger than our measurements. We then performed the same experiment using electrophoretic actuation setting the tension to 25, 50 and 100 V, which corresponded to migration velocities of 0.12, 0.25 and 0.60 mm/s (not shown). We noted that (i) the normalized electrophoretic dispersion coefficient was much greater than 1 and in the range of 3,000 to 40,000, and (ii) increased with DNA electrophoretic velocity (Fig. 3B). This onset in dispersion was qualitatively consistent with the process of band broadening in gel electrophoresis, which is characterized by a power-law variation of the diffusion coefficient with the electric field associated to an exponent of 1.5 at high electric field [START_REF] Slater | Joule Heating, and Band Broadening in Capillary Gel Electrophoresis of DNA[END_REF][START_REF] Tinland | Broadening in Gel Electrophoresis: Scaling Laws for the Dispersion Coefficient Measured by FRAP[END_REF] . Indeed, using the plateau value of the normalized diffusion coefficient in Fig. 3, we measured a power-law scaling exponent of 1.47 for the diffusion vs. electric field response (Supplementary Fig. S2).

Additional mechanisms, including e.g. Joule heating, may be invoked to account for electrophoretic band broadening, but they are not the scope of the current study. Rather, our comparison of band broadening in electrophoresis, hydrodynamics, and free-diffusion showed a diffusion coefficient that spanned more than six decades, suggesting the existence of a broad parameter space domain for diffusion in electrohydrodynamic migration. We then focused on electro-hydrodynamic migration and monitored the breadth of the 600 bp band after ~600 µm of migration in the separation channel. We first performed a set of experiments at a constant electric field associated to a voltage of 20 V (equivalently ) after a concentration phase of 10 s at 150 V. The pressure was modulated in the range of 1, 2 and 3 bar, equivalently the average migration velocity was 0.8, 1.7, and 2.7 mm/s (Fig. 4A). We first measured that the speed of the DNA band of 0.36, 0.66 to 1.04 mm/s for the three pressure settings, and noticed that the ratio decreased from 0.45 to 0.38 as the flow rate increased. This result was explained by the onset of the viscoelastic transverse force with (Eq. ( 7)), which enhanced the degree of confinement of the molecules near the walls. On the contrary, the normalized diffusion coefficient appeared to be roughly constant and equal to 10 5 for the three pressure settings.

Diffusion with constant electro-hydrodynamic actuation

This value was bounded between our electrophoretic and hydrodynamic measurements of 10 3 and 10 6 , respectively. Furthermore, the constant value of the diffusion coefficient was in excellent agreement with the prediction of our model of electrohydrodynamic migration (Eq. ( 11)), in which band spreading is predominantly piloted by the electric field. Notably, in contrast to our measurements with hydrodynamic actuation (Fig. 3A), we measured a constant diffusion coefficient in space. This result implied that despite the use of hydrodynamic flow, the diffusive process was at steady-state. This result could be explained by the confinement of the molecules near the walls, which set valid conditions for the Taylor dispersion regime. Indeed, the migration time was on the order of 1 s for =1 mm and . The time scale of transverse diffusion is much shorter than with hydrodynamic actuation, because molecules are confined in a spatial region delimited between z=0 and (see definition in Eq. ( 8)). Taking the values of , , and at 2 bar and 20 V of 1.7, 0.7 and 0.1 mm/s, respectively, we deduced that was ~0.2 µm from Eq. ( 9), and that the transverse diffusion time was on the order of tens of ms. We thus concluded the time scale of transverse fluctuation was much shorter than the migration time, and confirmed that Taylor dispersion regime was relevant to this study.

We finally measured the normalized diffusion coefficient at a constant pressure of 1 bar and using three different settings for the electric field associated to voltages of 10, 20, and 50 V (Fig. 4B).

We again noted that the band velocity of 0.55, 0.36, and 0.15 mm/s decreased more than the mere subtraction of of 0.65, 0.6, and 0.45 mm/s, respectively, due to the build-up in transverse viscoelastic force with the electrophoretic actuation (see Eq. ( 7)). Furthermore, as in the previous experiment, the diffusion coefficient was roughly stationary in space, but contrariwise it appeared to change dramatically with the electric field. It was indeed divided by a factor of 18 from 3.3 10 5 down to 1.8 10 4 as we set the voltage to 10 and 50 V, confirming the strong dependence of the diffusion coefficient with the electrophoretic force predicted by Eq. ( 11). More quantitatively, we measured the power law scaling exponent of the diffusion coefficient vs. electrophoretic velocity of ~-1.6, and confirmed its qualitative agreement with the exponent -2 derived from our model. Consequently, our data corroborated our analytical model of diffusion during electrohydrodynamic migration, and also showed that the band dispersion was tunable and controlled by the electric field.

Minimization of band broadening with the temporal modulation of the electric field

Because separation experiments were carried out with an electric field that decreased linearly with time (Fig. 2), we finally assayed band broadening by applying different ramps of electric field spanning -10 to -5 V/s. In these settings, the diffusion coefficient varied in the time course of the migration, so we chose to report the breadth of the band after 1.3 mm of migration (Fig. 5). The band width was 3 times narrower for a slope of -10 V/s as compared to -5 V/s with a constant hydrodynamic velocity of (Fig. 5A). Conversely, changing the hydrodynamic velocities by three-fold for a given slope of -6.5 V/s marginally changed the band breadth (Fig. 5B).

This data generally confirmed that diffusion was primarily controlled by the electric field and marginally by the flow velocity, as studied in the previous section (Fig. 4). This statement was strengthened by solving numerically the breadth of the band. Indeed, the migration velocity (Eq. ( 9))

and diffusion coefficient (Eq. ( 11)) could be extracted from the model, and then integrated to obtain the solution of Fick equation (Eq. ( 5); see details in Supplementary Material). The resulting data was consistent with our data, as shown by the dashed line in Fig. 5A and 5B, thereby comforting our comprehension of dispersion during viscoelastic electrohydrodynamic migration. From an analytical perspective, this study also showed that a rapid decrease of the electric field was more suitable to reduce band broadening.

Comparison of the electric actuation strategies

We finally wished to compare band broadening using constant or temporally-variable electric fields. Our thrust was to (i) identify optimal actuation strategies for the reduction of dispersion during separation experiments, and (ii) recapitulate the DNA separation data shown in Fig. 2. We characterized the profile of the 600 bp band after 1 mm of migration with four actuation settings based on electrohydrodynamics or hydrodynamics (Fig. 6). Migration at 2 bar was associated to a velocity of in the separation channel (green dataset in Fig. 6). Spreading in this situation was expectedly maximal, as inferred from the width of the band of ~500 µm after 1 s. We then used a constant electric field associated to a voltage of 20 V (equivalently , dark blue dataset in Fig. 6). The use of a constant electric field slowed down the migration that was characterized by a velocity of , as well as narrowed down the band width to ~110 µm. Notably, the asymmetry of the band profile with these actuation settings was due to the inhomogeneous boundary conditions near the lateral walls of the rectangular separation channels (Supplementary Fig. S3).

We subsequently assayed band broadening with an electric field variable over time using a sharp slope of -15 V/s starting from a voltage of 150 V (cyan dataset in Fig. 6). The convection over a distance of 1 mm took 11 s. Yet, given the slope of 15 V/s, the electric field was null during the last second of the migration, accounting for the rapid hydrodynamic-driven migration of the band during the last 1.5 s (the band travelled over ~600 µm travelled in 1.5 s vs. 200 µm using a constant electric field). Interestingly, whereas the band profile was peaked after 9.5 s with a FWHM of 95 µm, the prevalence of hydrodynamics rapidly broadened up its width to ~300 µm after 11 s. This observation clarified our separation data shown in Fig. 2, and more specifically the sharp dependence of the theoretical plate number with the slope of the electric field. Indeed, as shown in Fig. 2A, optimal separations were obtained for the concomitant passage of the band in front of the detector and vanishing of the electric field. Given that band broadening decreased as the slope of the electric field increased (Fig. 5A), separation optimization appeared to be a trade-off between the sharpest slope and a non-vanishing electric field as the band reached the detector.

Finally, we aimed to show that electrohydrodynamic actuation enabled to finely control band broadening. We chose to use the same linear slope of 15 V/s and stopped it at 20 V in order to maintain transverse viscoelastic forces throughout the migration (purple dataset in Fig. 6). Note that this strategy was already tested successfully for high MW DNA separation in capillary format [START_REF] Milon | ΜLAS Technology for DNA Isolation Coupled to Cas9-Assisted Targeting for Sequencing and Assembly of a 30 Kb Region in Plant Genome[END_REF] . The passage time was significantly expanded to 16 s, corresponding to a lag of ~8 s with a sharp decrease of the electric field and slow migration, followed by 8 s of migration under constant electrohydrodynamic settings (as in the dark blue dataset). The migration velocity in front of the detector was expectedly similar to that measured with a constant electric field (compare purple and dark blue datasets). Interestingly, this actuation strategy yielded the sharpest band after 1 mm of migration with a FWHM of 79 µm, i.e. an increase of 24 µm compared to the initial breadth of 55 µm during the concentration phase (see calibration of ). The comparison of the dark blue and purple datasets also showed that the broadening of the band during the last 1.5 s was comparable with or without slope, in agreement with the fact that electrohydrodynamic actuation is identical during this time period. Altogether, this experiment demonstrated that the temporal control over the electric field provided an efficient solution to tune and reduce band broadening during electrohydrodynamic migration.

CONCLUSION

In this study, we characterized band broadening in electrohydrodynamic DNA migration and confronted our data to a model of diffusion based on Taylor-type arguments. Our key findings are that dispersion is mainly controlled by the electric field and in consequence that fine tuning of the electric field over time enables the reduction of band broadening. This data also provides hints to a rational explanation of optimal conditions for DNA separation experiments. Taken collectively, these results therefore contribute to enhancing the performances of DNA separation platforms based on electrohydrodynamic actuation. Future lines of research include the integration of a DNA migration model with that of band dispersion so as to obtain a complete in silico toolbox that can be tested and validated for additional optimizations. Accordingly, whether or not a linear variation of the electric field over time is an optimal strategy for band broadening minimization remains to be elucidated. It should also be clarified whether this model can be adapted to other types of targets in the form of single stranded nucleic acids, e.g. RNA, or particles. In the latter case, many studies have addressed the physics of particle focusing in Poiseuille flows [START_REF] D'avino | Particle Migration Due to Viscoelasticity of the Suspending Liquid and Its Relevance in Microfluidic Devices[END_REF][START_REF] Yuan | Recent Progress of Particle Migration in Viscoelastic Fluids[END_REF] , and recent interest has emerged for microorganism separation [START_REF] Nam | Sheathless Shape-Based Separation of Candida Albicans Using a Viscoelastic Non-Newtonian Fluid[END_REF] , but dispersion remains to be studied and modelled, potentially with the same types of arguments based on the Taylor model.

BIBLIOGRAPHY

m ; Lp = 1.3 mm ; U h = 1.7 10 -3 m/s ; =0.05 mm. The value of U 0 is computed from the conditions of arrest at t=0 (Eq. S2), yielding U 0 =800 µm/s. The time interval between the two images is 5 s. The band appears to "leak" near the side walls. This result is due to the boundary conditions for a rectangular channel of 10 µm in width and 2 µm in height. The flow velocity field is slowed down near the walls over a distance of ~1 µm. The electric field is thus comparatively higher in this region, and the band migration is further slowed down.

Figure 1 :

 1 Figure 1: Experimental workbench for band broadening characterization. (A) Micrograph of the microfluidic chip with green and red arrows to depict the hydrodynamic and electrophoretic velocities, respectively. The yellow rectangle is the field of view of the camera. (B) The graph sketches the temporal sequence of our experiments with a first phase of concentration at high pressure and high voltage. At time t 0 , video recording starts and the electric field is modulated to start the separation phase. (C) The three fluorescence micrographs represent the dynamics of a single band as it migrates through the separation channel. (D) The graph represents the spatial intensity profile of one DNA band for eight consecutive time points separated by 500 ms. The solid lines correspond to Gaussian fits.

Figure 2 :

 2 Figure 2: µLAS separation of 600 and 1000 bp bands. (A) The plot reports DNA electrohydrodynamic separation using a constant pressure drop of 3 bar and an electric field that decreases linearly over time starting from 80 V (green line). The blue dataset represents fluorescence intensity, as measured after 1.3 mm of migration in the separation channel. The two bands are fitted with Gaussian functions (solid black line). (B) The contour plot shows the resolution of the separation as a function of pressure drop and absolute value of the voltage slope. (C) The theoretical plate number for the 1000 bp band is reported as a function of pressure drop and absolute value of the voltage slope.

Figure 3 :

 3 Figure 3: Diffusion in hydrodynamics and electrophoresis. The normalized diffusion coefficient of a 600 bp DNA band is plotted as a function its position along the separation channel for three different pressure settings (A) or voltage settings (B).

Figure 4 :

 4 Figure 4: Electrohydrodynamic diffusion with constant actuation settings. (A) The plot in the left shows the diffusion coefficient normalized to as a function of the position of the band along the channel. The three graphs in the right correspond to raw datasets of the spatial intensity distribution of one DNA band imaged at two consecutive time points separated by 200 ms. Note that peak intensity increases with the pressure because the mass of DNA accumulated during the concentration phase builds up with the flow rate . (B) Same dataset as in (A) with a constant pressure and different settings for the voltage, as indicated in the legend. For the raw intensity distribution plots in the right, we use the same time interval of 200 ms for the two graphs at the top, but change it to 1 s for the lower one.

Figure 5 :

 5 Figure 5: Electrohydrodynamic diffusion with a linear ramp in electric field. (A) The plot shows the FWHM of the 600 bp band after 1.3 mm of migration using four slopes for the electric field and setting the flow velocity set to 1.5 mm/s. The dashed line corresponds to the numerical solution of our model, which is described in Supplementary Material. (B) The plot represents the FWHM of the 600 bp band for a given slope of -6.5 V/s and three pressure settings, together with the prediction of the model.

Figure 6 :

 6 Figure 6: Control of band broadening in electrohydrodynamic migration. The four plots represent the spatial distribution of a 600 bp DNA band in the course of its migration with hydrodynamic actuation associated to (green dataset) or electrohydrodynamic actuation with a constant electric field of 20 V ( , blue dataset) or linear slope of -15 V/s starting from 150 to 0 V (cyan dataset) and a linear slope of -15 V/s from 150 to 20 V (purple dataset). In each graph, two consecutive profiles are reported with their respective times noted in inset. The number in bold corresponds to the FWHM of the band after ~1 mm of migration.

Figure S1 :

 S1 Figure S1:The plot presents the half-spatial intensity distribution of a 600 bp DNA band. Spreads is due to Brownian dispersion. Each dataset is fitted with a Gaussian function (solid lines).

Figure S2 :

 S2 Figure S2:The plot presents the steady value of the normalized electrophoretic diffusion coefficient, inferred from Fig.3, as a function of the electric field. The solid line is a fit of the data associated to a power-law scaling response of 1.47, given that the normalized diffusion coefficient is set to 1 at zero electric field.

Figure S3 :

 S3 Figure S3:The two fluorescence micrographs present the migration of a DNA band with a constant electric field of 20 V and a pressure of 2 bar. The time interval between the two images is 5 s. The band appears to "leak" near the side walls. This result is due to the boundary conditions for a rectangular channel of 10 µm in width and 2 µm in height. The flow velocity field is slowed down near the walls over a distance of ~1 µm. The electric field is thus comparatively higher in this region, and the band migration is further slowed down.

Study of DNA band broadening in electrohydrodynamic migration for separation optimization

Jeffrey Teilet 1 , Quentin Martinez 1 , (who else) [START_REF] Duke | Electrophoretic Mobility of DNA in Gels. I. New Biased Reptation Theory Including Fluctuations[END_REF] , Aurélien Bancaud 1

Supplementary Material

Width of the DNA band with an electric field linearly decreasing over time Let us first evaluate the passage time in front of the detector. For this, we invert the migration velocity knowing the distance to the detector :

The electrohydrodynamic velocity is given by (Eq. ( 9)) and we define the slope of the decrease of the electric field as :

(S2)

Integration of Eq. (S2) leads to the following polynomial equation, that can be solved numerically to determine :

The width of the band is finally determined using Eq. ( 11) according to:

(S4)

These equations are solved numerically with the following set of parameters: k B = 6 10 - 23 J/K; T = 300 K ; a = (N_bp/300)*lk = 200 nm ; = 0.5 10 -3 s ; = 30 10 -3 Pa.s ; H = 2 10 -6


Bayan Chami

Nicolas Milon

Juan-Luis Fuentes Rojas

Samuel Charlot

Jean-Christophe Marot

Aurélien Bancaud

Affiliation

Signle-step electrohydrodynamic separation of 1-150 kbp in less than 5 min using homogeneous Glass/Adhesive/Glass microchips

Electrohydrodynamic migration, which is based on hydrodynamic actuation with an opposing electrophoretic force, enables the separation of DNA molecules of 3 to 100 kbp in capillary systems within one hour. Here, we wish to enhance these performances using microchip technologies. This study starts with the development of a fabrication process to obtain microchips with uniform surfaces, which is motivated by our observation that band splitting occurs in microchannels made out of heterogeneous materials such as glass and silicon. The resulting glass-adhesive-glass microchips feature the highest reported bonding strength of 11 MPa for such materials (115 kgf/cm 2 ), a high lateral resolution of critical dimension 5 µm, and minimal auto-fluorescence. These devices enable us to report the separation of 13 DNA bands in the size range of 1-150 kbp in one experiment of 5 minutes, i.e. 13 times faster than with capillary electrophoresis. In turn, we provide evidence that band splitting in heterogeneous glasssilicon microchips arises from differential Electro-Osmotic Flow (EOF) in between the upper and lower walls of the channel. We further indicate that differential EOF occurs in microchip electrophoresis and constitutes an underappreciated source of band broadening. We finally prove that our separation data compare favorably to state-of-the-art microchip technologies in terms of resolution length and theoretical plate numbers.

INTRODUCTION

The gold standard in genetic analysis is capillary electrophoresis, which is based on the migration of DNA molecules through a separation matrix that slows them down proportionally to their molecular weight (MW) [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Mechanisms[END_REF]. Using a continuous and mono-directional electric field, separation performances reach a limit above a threshold size on the order of ~10 kbp [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Mechanisms[END_REF][START_REF] Dorfman | DNA Electrophoresis in Microfabricated Devices[END_REF]). The use of pulsed-field increases this size threshold by up to two orders of magnitude, however at the expense of overly long separation times of 10 hours [START_REF] Dorfman | DNA Electrophoresis in Microfabricated Devices[END_REF]. Alternatively, free solution DNA separation based on hydrodynamic actuation in narrow capillaries of ~2 µm enabled the fractionation of molecules of up to 100 kbp in one hour [START_REF] Wang | Pressure-Induced Transport of DNA Confined in Narrow Capillary Channels[END_REF]. The combination of electrophoresis and hydrodynamics acting in opposite directions, hereafter called electrohydrodynamic migration, also appeared as a free solution separation technology efficient for long molecules, as initially reported with 5 and 50 kbp DNA [START_REF] Zheng | Anomalous Radial Migration of Single DNA Molecules in Capillary Electrophoresis[END_REF] and recently improved in the range of 3 to 200 kbp with a separation time of one hour [START_REF] Milon | ΜLAS Technology for DNA Isolation Coupled to Cas9-Assisted Targeting for Sequencing and Assembly of a 30 Kb Region in Plant Genome[END_REF]. In order to consolidate the promising performances of electrohydrodynamic migration, which relies on the existence of size-dependent transverse forces that set molecules close to the walls [START_REF] Ranchon | DNA Separation and Enrichment Using Electro-Hydrodynamic Bidirectional Flows in Viscoelastic Liquids[END_REF]) (ADD here 2 papers from Butler), we wished to test whether microchips would allow us to gain time and extend the separation range.

DNA separation techniques have indeed benefited from microchip technologies in reducing sample consumption and analysis time and increasing the sensitivity and efficiency [START_REF] Pfohl | Trends in Microfluidics with Complex Fluids[END_REF]. Gains in performance have been achieved through the control of sample injection using sophisticated channel geometries (Nathan A. [START_REF] Lacher | Microchip Capillary Electrophoresis/ Electrochemistry[END_REF], as well as the engineering of artificial matrices tailored for low or high MW molecules [START_REF] Doyle | Self-Assembled Magnetic Matrices for DNA Separation Chips[END_REF][START_REF] Kaji | Separation of Long DNA Molecules by Quartz Nanopillar Chips under a Direct Current Electric Field[END_REF][START_REF] Rahong | Ultrafast and Wide Range Analysis of DNA Molecules Using Rigid Network Structure of Solid Nanowires[END_REF][START_REF] Cao | Fast DNA Sieving through Submicrometer Cylindrical Glass Capillary Matrix[END_REF]. The fabrication of microchips relies on the assembly of a patterned substrate with a transparent one using a variety of micromachining and bonding technologies. The transparent substrate is most often made out of glass, which remains the most relevant material for analytical microfluidics due to its chemical, mechanical and electric resistance in addition to its transparency and low background fluorescence, which make it ideal for optical detection [START_REF] Giri | 2 -Fabrication of a Glass Microfluidic Device[END_REF]. In contrast to capillaries, which present homogeneous surfaces, microchip devices are in general heterogeneous in composition, for instance with polymer/glass or silicon/glass walls. Yet, some reports have shown the degradation of separation performances in microchips made out of hybrid materials (M.-S. Kim et al. 2005). We therefore set out to perform our experiments in conventional silicon-glass microchips as well as in specifically developed microfluidic devices with homogeneous surfaces.

The first section of this paper presents the fabrication process of selectively bonded glassglass microchips with an epoxy-based negative resist (PermiNex). The characterization of these microchips notably shows the highest bonding strength of ~11 MPa (115 kg/cm 2 ), enabling the application of pressures up to 7 bar during separation experiments. We then probe the migration of high MW molecules using electrohydrodynamics in homogeneous PermiNex-bonded vs. heterogeneous microchips obtained by silicon-glass anodic bonding. DNA bands tend to split in heterogeneous chips, but remain stable in Perminex-bonded devices. We propose that this effect stems from the difference in electroosmotic flow (EOF) in between the upper and lower walls of slit-like microchannels. By investigating DNA electrophoretic transport, we further suggest that differential EOF accounts for the build-up in band broadening in heterogeneous chips. Finally, we perform a long-range separation of 13 DNA bands from 1 to 150 kbp in PerminNex bonded glass-glass microchips, which is achieved in less than five minutes with a resolution length (minimum resolvable size) and theoretical plate number that compare well to the state of the art microchip techniques. Altogether, we conclude that DNA electrohydrodynamic separation performances can be enhanced using microchips fabricated with the Perminex bonding technology.

MATERIALS AND METHODS

We used four-inch wafers of 500 µm thick alkali-free glass AF 32® (Schott) and p-doped silicon wafers. silicon/glass chips were fabricated following the process described in ref. [START_REF] Ranchon | DNA Separation and Enrichment Using Electro-Hydrodynamic Bidirectional Flows in Viscoelastic Liquids[END_REF]. Photoresists were purchased from Microchem Corp. Cleaning steps were carried out with oxygen plasma (TEPLA) at a power of 400 W and a flow rate of 1000 ml/min for 5 min. We performed tests of adhesion using XYZTEC Condor Sigma bond tester with chips of 0.25 cm 2 .

Experimental setup:

Polymer solution PVP (polyvinylpyrrolidone) 10 KDa 2.5% (w/v) (Sigma Aldrich) is prepared in TBE 1X (Tris-Borate-EDTA) (Sigma Aldrich) and supplemented with 2% (w/v) DTT (Dithiothréitol, Sigma Aldrich). The solution is then filtered with 0.2 µm pore syringe filter. 150 kbp BAC-clone DNA band (gift from CNRGV) or phiX174 DNA (5,386 bp, Sigma Aldrich) are diluted in a volume of the PVP solution at a concentration of 0.3 µM. Intercalating dye YOYO-1 (Thermo Fischer) is used to label the DNA at a ratio of 1:8 (1 intercalating molecule per 8 base pairs).

Microfluidic channels in Si/glass and glass/glass are filled with 70% ethanol to eliminate bubbles. The channels are then filled with PVP buffer followed by an injection, at the inlet, of PVP containing the labeled DNA molecules. A pressure and voltage are applied across the Tshaped channels to create opposing hydrodynamic and electrophoretic flows. Lateral flows are applied from the side channels to concentrate the DNA in a plug that is then pushed into the main separation channel where the DNA bands are detected by an sCMOS camera (Andor Zyla) at 35 mm from the T-junction (see Fig. 2 in Results). Fluorescence intensity as a function of time is recorded and peaks are fitted using Igor Pro (WaveMetrics).

Metrics of the separations:

We compared the separation of 1-150 kbp DNA ladder to those of state of the art microchip technologies using two parameters; the resolution length (RSL) and the theoretical plate number. The RSL in bp defines the smallest size that can be resolved and is given by: [START_REF] Han | Separation of Long DNA Molecules in a Microfabricated Entropic Trap Array[END_REF] where is the difference in base pair between consecutive bands, and the resolution obtained at baseline by fitting the peaks with a Gaussian distribution. For temporal separations, the resolution is calculated as follows:

(2) where is the migration time of the DNA band and the width of the band at the baseline. For spatial separations, we similarly define , where is the spatial position of the band.

The theoretical plate number (N) is a measure of the separation efficiency, which is calculated for separations in time, using the following formula:

(3) where is the migration time of the band and is its baseline width. To perform the comparison between different separation techniques, theoretical plate number per meter is used instead. It is defined as:

(3)

Where L is the separation length in cm.

RESULTS

Fabrication of homogeneous glass microchips with high-resolution:

Two approaches can be considered to fabricate homogeneous glass microfluidic devices, namely (i) the formation of channels by photolithography and etching followed by glass-to-glass bonding, or (ii) selective bonding using photo-patternable adhesives or glass frit. The former approach is mostly carried out with fusion bonding [START_REF] Stjernström | Method for Fabrication of Microfluidic Systems in Glass[END_REF], which amounts to fusing glass substrates together under pressure and temperature of up to 600° C [START_REF] Deng | Development of Glass-Glass Fusion Bonding Recipes for All-Glass Nanofluidic Devices[END_REF]. Similar techniques include plasma activated bonding [START_REF] Howlader | Room Temperature Wafer Level Glass/Glass Bonding[END_REF]Y. Xu et al. 2012) and UV bonding [START_REF] Schlautmann | Fabrication of a Microfluidic Chip by UV Bonding at Room Temperature for Integration of Temperature-Sensitive Layers[END_REF]), yet they require immense care for the cleanliness of the glass substrates [START_REF] Mayer | Comparing Fusion Bonding Methods for Glass Substrates[END_REF]. On the other hand, glass frit bonding, which involves the use of an intermediate glass frit layer heated until molten enabling the hermitic sealing of wafers (Knechtel 2015), suffers from its low lateral resolution, which makes it difficult to define straight channel borders [START_REF] Knechtel | Glass Frit Wafer Bonding[END_REF].

We chose to perform selective bonding with a photo-patternable adhesive to circumvent most of these limitations.

The fabrication of PermiNex microchips starts with the spin coating of a positive resist AZ ECI 3027 and exposure to UV through a negative polarity mask of a glass wafer (Fig. 1a-b). Two layers of amorphous silicon (a-Si) of 120 nm and SiO 2 of 200 nm are deposited by inductively coupled plasma enhanced chemical vapor deposition (PECVD) (Fig. 1c). The wafer is cleaned and 3.5 mL of the adhesive photoresist PermiNex® 2005 is spin-coated to form a 2.5 µm film (Fig. 1d-e). The soft bake is performed at 95 °C during 9 min followed by UV exposure for 45 sec at 870 mJ/cm 2 using the same negative polarity mask, in hard contact and with alignment with the a-Si/SiO 2 patterned layer (Fig. 1f). The post-exposure bake time is set to 6 min at a temperature of 72 °C. Note that this step is critical for the conservation of the patterns during the development with the organic SU8-developer during one min. The final step is a hard bake at 180 °C for 5 min. The wafer is then cleaned using O 2 Plasma for 2 min at low power and flow rate of (200 W and 400 mL/min), enough to remove organic contaminants but at the same time preserve the adhesive resist. A decrease in the adhesive thickness of 300 +/-100 nm is noticed after the Plasma treatment. The wafer is eventually clamped with another glass wafer, where via holes are drilled by sand blasting, using the fixture of Bond Aligner (Suss MicroTec) to perform the alignment (Fig. 1g). The temperature and pressure program consists of heating the wafers to 150-200 °C and applying a pressure of 4-5 bar for 30 sec establishing a force of 10-16 kN under vacuum (5×10 -2 mbar). The whole bonding process takes less than 15 min. An SEM image of the formed 2-µm channel is shown in supplementary Figure S1. Using a microchip design with a funnel-shape geometry, as reported in [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF], we demonstrate the ability to fabricate channels with critical size of 5 µm using a layer of PermiNex of 2.2 +/-0.1 µm by comparing the mask feature to that imprinted in the final microchip (Fig. 2a). Since the process comprises a low temperature bonding step, gold electrodes of 200 nm in thickness can be fabricated on the glass substrate and glued with the PermiNex layer (Fig. 2c-d). The PermiNex layer adheres very well to the gold and no leakage is observed at the level of the electrodes or any other area in the device (data not shown). This integration scheme can serve to perform electrical operation, such as electrochemical and/or amperometric detection.

Tests of adhesion with pull-off tensile machine (see Methods) show that the bond fracture failed each time because of either die fracture or breaking of the glue attaching the dolly to the chips. Using shear tests, we evaluate the bonding strength of ~11 MPa (115 kgf/cm 2 ) before the glass breaks. It is the highest bonding strength, to our knowledge, obtained for glass/adhesive/glass microchannels in comparison to SU-8 (S G Serra et al. 2007), BCB [START_REF] Niklaus | Adhesive Wafer Bonding for Microelectronic and Microelectromechanical Systems[END_REF], and silicone-based resins (J. [START_REF] Kim | Studies on the Polymer Adhesive Wafer Bonding Method Using Photo-Patternable Materials for MEMS Motion Sensors Applications[END_REF]. The PermiNex bonding breaks with a maximum pull force of 2.93 kgf bonding (~1.15 MPa bond strength) only when the microchips is heated at 50°C. At this stage, the bonding is irreversible unlike in processes that use wax as bonding adhesive [START_REF] Gong | Wax-Bonding 3D Microfluidic Chips[END_REF].

The final microchips offer several advantages for electrohydrodynamic separation. First, the bonding strength enables the application of pressures of up to 7 bar for separation experiments. Second, the PermiNex microchips withstand very high electric fields, whereas breakdown of the oxide layer occurs for a maximum applied voltage of 450 V using an oxide layer of 400 nm in anodically bonded silicon/glass chips (Supplementary Fig. S2). Specifically, we did not detect any problems as we used electrophoretic actuation with up to 800 V, i.e. with electric fields of more than 200 V/cm (not shown). Minimization of PermiNex auto-fluorescence:

One disadvantage of PermiNex comes from its high auto-fluorescence in the entire visible spectrum [START_REF] Kubicki | Optical Properties and Real Application of New Photoimageable Bonding Adhesives[END_REF]. A patterned a-Si layer, which is strongly adsorbing light in the visible spectrum, is deposited underneath the PermiNex layer (Fig. 1) in order to block the excitation and emission light and hence reduce auto-fluorescence. Figure 3 shows a glass/glass chip bonded directly with PermiNex without the deposition of a-Si (panels a & c) versus a chip where an a-Si layer of 120 nm and an oxide layer of 200 nm are deposited before the spin-coating of PermiNex (panels b & d). A slight miss-alignment between the PermiNex layer and the a-Si layer allows seeing the channel borders in Fig. 3b. As an example of the adverse effects of PermiNex auto-fluorescence, we report fluorescence micrographs of 150 kbp DNA molecules in the course of their electrophoretic migration in a separation microchip (Fig. 3 c &d, design of the chip in Fig. 3e). Even with the use of a field diaphragm to mask the autofluorescence signal from the PermiNex layer, the signal to noise ratio of individual molecules increases by a factor of 1.35 with the absorbing layer (dark blue curve in Fig. 3f). Consequently, our microchip fabrication process is readily suited to bioanalytical operations with a minimal signal to noise ratio and a strong resistance to pressure and electric fields. Peak splitting in silicon/glass microchips is suppressed in glass/PermiNex/glass microchips:

We then focus on DNA electrohydrodynamic migration in Glass-glass vs. heterogeneous microchips. We perform experiments with a single DNA band of 150 kbp and electrohydrodynamic actuation associated to maximum flow and electrophoretic velocities of and , respectively. In glass/Si microchips, we notice that the DNA band splits into two populations of equal intensity in front of the detector placed 35 mm downstream of the injection plug (see chip design in Fig. 3e, Cyan curve in Fig. 4c). The analysis of the fluorescence micrographs recorded by the camera indicates that the two DNA bands migrate at different vertical positions across the channel height. A first DNA "band" appears to be out of focus (close to the Si wall) at t=30.6 s (Fig. 4a) and the second one in focus (close to the glass wall) at t=39 s (Fig. 4b). Small white arrows pointing contaminations stuck to the glass wall help indicate the difference in focus between the two DNA populations.

Splitting can readily be eliminated in PermiNex-bonded microchips using the same actuation settings (dark blue curve in Fig. 4c). It can also be recovered in "asymmetric" PermiNex microchips (intermediate blue curve in Fig. 4c) obtained with the same fabrication protocol except that PermiNex is developed with its standard developer that contains the quaternary ammonium salt Tetramethylammonium hydroxide (TMAH). Because TMAH is known to etch SiO 2 surfaces [START_REF] Chen | The Characteristic Behavior of TMAH Water Solution for Anisotropic Etching on Both Silicon Substrate and SiO2 Layer[END_REF][START_REF] Biswas | Etch Characteristics of KOH, TMAH and Dual Doped TMAH for Bulk Micromachining of Silicon[END_REF][START_REF] Suttijalern | Study of UMSM Photodetectors Fabrication Technique by Silicic Acid Added in TMAH Solution[END_REF], the development step likely creates differential roughness in between the two glass surfaces, i.e. heterogeneities in surface properties despite the same composition. Consequently, differences in surface molecular composition or in roughness appear to trigger splitting in electrohydrodynamic separation. We suggest that peak splitting stems from the difference in EOF between the upper and lower surfaces of the microchip. Differential EOF indeed induces a shear Couette-like flow across the channel height (purple arrows in Fig. 4d) (Andreev, Dubrovsky, and Stepanov 1997a). Because transverse migration to the walls is dictated by the fluid viscoelastic properties [START_REF] Chami | Modeling of DNA Transport in Viscoelastic Electro-Hydrodynamic Flows for Enhanced Size Separation[END_REF], we suggest that molecules travel at the same distance from the upper and lower wall, i.e. at equal hydrodynamic velocities, and that the peak splitting is dictated by the difference of EOF.

Notably, the consequences of differential EOF readily appear in electrohydrodynamic transport, because DNA spatial distribution is uneven across the channel height. Should this effect occur in electrophoresis, we expect the shear flow induced by differential EOF to create mixing by some type of Taylor dispersion mechanism arising from the coupling of longitudinal speed gradients with transverse diffusion. Accordingly, previous electrophoresis studies have shown that even a 10% difference in the zeta-potential between upper and lower walls of a microchip leads to band broadening (Andreev, Dubrovsky, and Stepanov 1997b;[START_REF] Bianchi | Electroosmotic Flow in Composite Microchannels and Implications in Microcapillary Electrophoresis Systems[END_REF][START_REF] Herr | Electroosmotic Capillary Flow with Nonuniform Zeta Potential[END_REF]. We set out to check our proposition further by performing another set of experiments with electrophoresis only.

Evidence for differential electro-osmosis in Si/glass microchips:

Using silicon-glass chips, we probe the response of single phiX-174 DNA with three values of the electric field. Note that phiX-174 only contains 5 kbp MW, but its spherical shape under the microscope simplifies its tracking. The trajectories of 40 molecules, each containing 100 points at least, have been recorded in 2D in order to extract the velocity distribution along and across the electric field direction as was performed by our team to characterize confined flows [START_REF] Ranchon | Metrology of Confined Flows Using Wide Field Nanoparticle Velocimetry[END_REF]. The lateral velocity distribution (perpendicular to electrophoresis direction), centered at zero, represents Gaussian noise due to thermal diffusion (green histogram in Fig. 5a). The longitudinal velocity distribution (along the electrophoresis direction) is instead shifted due to electrophoretic advection (blue histogram in Fig. 5a). Assuming the electrophoretic force to be homogeneous across the channel height, we expect the longitudinal dispersion to equate that in the transverse direction. However, we notice that the breadth in the longitudinal vs. lateral direction is increased by a factor of 1.2, consistent with the observation that the diffusion coefficient characterizing DNA bands in electrophoresis is larger than that expected from Brownian fluctuations [START_REF] Ross | Imaging of Electroosmotic Flow in Plastic Microchannels[END_REF]. Furthermore, this onset appears to increase with the amplitude of the electric field by a factor of 1.1 to 1.7 for an electrophoretic velocity of 9.8 and 21 µm/s, respectively (not shown).

We then test whether the increase of the breadth stems from a difference in EOF between the upper and lower channel walls. Considering that a molecule travels at by electrophoresis, the effect of the electroosmotic mobility , assumed to be homogeneous at the upper and lower wall, sets the DNA net velocity to [START_REF] Viovy | Electrophoresis of DNA and Other Polyelectrolytes: Physical Mechanisms[END_REF]. In hybrid microchips, then takes the form of an affine function (Andreev, Dubrovsky, and Stepanov 1997b):

(4) Because molecules can be assumed to be evenly dispersed in , the longitudinal velocity distribution is the deconvolution of a Heavyside function centered at of breadth with the Brownian noise measured by the transverse velocity distribution (Fig. 5b). According to this model, the fit of the velocity distribution informs us on the difference in EOF between the glass and Si walls. By setting the electric field to three different values, we observe that the difference in EOF increases linearly as DNA velocity increase, passing through zero without electrophoresis and with a proportionality factor of 0.43 (Fig. 5c). We then compare inferred from electrophoresis measurements to the difference of velocity between the two DNA peaks in electrohydrodynamic migration, shown in Fig. 4c. The time difference between the split DNA bands allows us to estimate that . Furthermore, given that the electrophoretic velocity opposed to the hydrodynamic flow is equal to 460 µm/s, we deduce that the ratio between the DNA split band velocity difference and the electrophoretic speed is 0.41. Hence, the broadening of the longitudinal velocity distribution observed with electrophoresis together with the splitting of DNA bands in electrohydrodynamic migration can be explained by the same difference in EOF in between the upper and lower walls of heterogeneous Si/glass chips.

Separation 1-150 kbp using a glass/PermiNex/glass T-shaped channel:

Finally, the newly fabricated glass/PermiNex/glass microchip is used for the separation of a kbp DNA ladder supplemented with a 150 kbp band, allowing us to cover more than two decades in MW from 0.5 kbp to 150 kbp. Optimal result is obtained by setting the pressure and voltage to 500 mbar and 170 V, respectively, corresponding to a flow speed of 0.6 mm/s and an electrophoretic velocity of 85 µm/s. The separation of the 14 bands is achieved in less than 5 min (Fig. 6) with baseline separation for the bands from 2 kbp. The separation can be reproduced more than 10 times in the same chip without band splitting, demonstrating the relevance of our technology with homogeneous upper and lower surfaces. Consequently, the microchip format enhances the performances of electrohydrodynamic separations not only in terms separation time, which is decreased from 30 to 5 minutes, but also with a broader separation range starting from 1 instead of 3 kbp. Comparison to microchip technologies for high MW DNA separation:

We now compare our separation performance to other microchip devices for fractionating high MW DNA (1-200 kbp). We use the resolution length (RSL) and theoretical plates per meter as readouts of the different techniques (see expression in the Method section) and report this data in plots (Fig. 7) as well as in Table 1.

Micro-capillary electrophoresis (MCE) devices with polymer matrices like linear polyacrylamide can be used for DNA separation in the size range of 1-10 kbp [START_REF] Bousse | High-Performance DNA Separations in Microchip Electrophoresis Systems[END_REF][START_REF] Mueller | A Microfluidic System for High-Speed Reproducible DNA Sizing and Quantitation[END_REF][START_REF] Lu | A Robust Cross-Linked Polyacrylamide Coating for Microchip Electrophoresis of DsDNA Fragments[END_REF] with high resolution and theoretical plate numbers. An extension of the separation size range to 15 or 20 kbp can be obtained using low viscosity polymers (F. [START_REF] Xu | Reduced Viscosity Polymer Matrices for Microchip Electrophoresis of Double-Stranded DNA[END_REF] and with the addition bacterial cellulose fibrils to the low viscosity sieving medium [START_REF] Tabuchi | Design for DNA Separation Medium Using Bacterial Cellulose Fibrils[END_REF]. (Sun, Lin, and Barron 2011) could further extend the separation range to 40 kbp using polymer blends. They separated 13 bands in the size range of 1-40 kbp within 2 min.

Microchip gel electrophoresis (MGE) systems, where cross-linked gels like agarose are incorporated inside the microchannels, can also separate 1-20 kbp DNA. [START_REF] Ghanim | Low Electric Field DNA Separation and In-Channel Amperometric Detection by Microchip Capillary Electrophoresis[END_REF]) used amperometric detection coupled with MGE in agarose to separate 1-20 kbp with a minimal RSL of 50 bp, however the separation took 37.5 min. (J.-H. [START_REF] Kim | Development of a Microfabricated Disposable Microchip with a Capillary Electrophoresis and Integrated Three-Electrode Electrochemical Detection[END_REF]) used electrochemical detection with MGE to separate 1-10 kbp in 2.5 min. Most recently, [START_REF] Gumuscu | Exploiting Biased Reptation for Continuous Flow Preparative DNA Fractionation in a Versatile Microfluidic Platform[END_REF]) demonstrated that continuous separation can be performed using MGE. They fractionated 4 DNA bands of 1-10 kbp continuously within 2 min.

To overcome common limitations of MGE including Joule heating and limited reusability, artificial gels constructed using micro/nanofabrication techniques were developed. Nano-colloidal arrays (NCA), which are self-assembled closely-packed nanospheres were used to size 1-15 kbp bands using electro-hydrodynamic actuation 1.7 min with high efficiency [START_REF] Tabuchi | Nanospheres for DNA Separation Chips[END_REF]). Using electrophoresis [START_REF] Zeng | Self-Assembled Colloidal Arrays as Three-Dimensional Nanofluidic Sieves for Separation of Biomolecules on Microchips[END_REF] used NCA formed of 330-900 nm silica beads to continuously separate 2-27 kbp [START_REF] Zeng | Microfluidic Self-Patterning of Large-Scale Crystalline Nanoarrays for High-Throughput Continuous DNA Fractionation*[END_REF] as well as to fractionate two bands of 13 kbp and λ DNA (48.5 kbp) in 7 min. [START_REF] Kuo | Monolithic Integration of Well-Ordered Nanoporous Structures in the Microfluidic Channels for Bioseparation[END_REF]) used NCA to form ordered nanoporous structure that resembles cross-linked gels to fractionate 1-10 kbp DNA in XX min.

Higher MW DNA up to 209 kbp could be separated using micro and nanopillar arrays (MPA/NPA). First, MPA enabled the separation of λ and T4 DNA (168.9 kbp) within 10 s using pulsed fields [START_REF] Bakajin | Separation of 100-Kilobase DNA Molecules in 10 Seconds[END_REF]). (Lotien Richard Huang, Tegenfeldt, et al. 2002) also used alternating electric fields to continuously fractionate 4 bands in the range of 61-209 kbp in 15 s in a hexagonal array of 2 µm diameter pillars called DNA prism. To facilitate the fabrication of pillar arrays, [START_REF] Doyle | Self-Assembled Magnetic Matrices for DNA Separation Chips[END_REF]) used self-assembled superparamagnetic nanoparticles that form 3D post arrays under a magnetic field form a coil. This technology could separate 3 bands of DNA in the ranges of 15-48.5 kbp and 48-145.5 kbp yet with low efficiency. Later, [START_REF] Regtmeier | Dielectrophoretic Manipulation of DNA: Separation and Polarizability[END_REF] showed that MPA can be used for trapping long DNA using electrodeless dielectrophoresis. With the combination of electrophoresis and dielectrophoretic trapping, the separation of 7 and 14 kbp in addition to λ and T2 (164 kbp) was performed in 6 min.

NPA were widely used for the fast separation of few bands of DNA in the range of 1-166 kbp [START_REF] Baba | DNA Size Separation Using Artificially Nanostructured Matrix[END_REF][START_REF] Kaji | Separation of Long DNA Molecules by Quartz Nanopillar Chips under a Direct Current Electric Field[END_REF][START_REF] Chan | High-Throughput Design and Fabrication of an Integrated Microsystem with High Aspect-Ratio Sub-Micron Pillar Arrays for Free-Solution Micro Capillary Electrophoresis[END_REF][START_REF] Shi | Highly Parallel Mix-and-Match Fabrication of Nanopillar Arrays Integrated in Microfluidic Channels for Long DNA Molecule Separation[END_REF]. [START_REF] Yasui | Arrangement of a Nanostructure Array To Control Equilibrium and Nonequilibrium Transports of Macromolecules[END_REF] showed that a non-equilibrium transport phenomenon inside NPA can yield fast separation of 3 bands of DNA of 1-48 kbp with very high efficiency (20×10 6 plates/m). [START_REF] Rahong | Ultrafast and Wide Range Analysis of DNA Molecules Using Rigid Network Structure of Solid Nanowires[END_REF] fabricated a new structure of rigid 3D nanowire arrays to separate DNA of 1-166 kbp under DC electric field. The separation of 4 bands in this size range proved to be ultrafast in 13 sec [START_REF] Kaji | Separation of Long DNA Molecules by Quartz Nanopillar Chips under a Direct Current Electric Field[END_REF][START_REF] Rahong | Ultrafast and Wide Range Analysis of DNA Molecules Using Rigid Network Structure of Solid Nanowires[END_REF]. Most recently, high resolution separation of λ and T4 DNA was obtained in a nanorod sieving matrix fabricated using localized oblique angle deposition under constant electric field within 12 s [START_REF] Cao | High-Resolution Separation of DNA/Proteins through Nanorod Sieving Matrix[END_REF]. In general, MPA and NPA showed very fast separations of long DNA molecules, however only few bands could be fractionated with high RSL.

High MW DNA can also be separated using entropic trapping in slit-well motifs (SWM), which are alternating shallow slits and deep wells fabricated by photolithography. Long molecules stretch through the narrow slits and escape the traps faster than shorter molecules into the deep wells (J [START_REF] Han | Entropic Trapping and Escape of Long DNA Molecules at Submicron Size Constriction[END_REF]. SWM were used to separate 8 bands of a 5kbp DNA ladder with T2 and T7 DNA (37.9 kbp) and 4 bands of 24.5-97 kbp DNA in 15 to 40 min (J. [START_REF] Han | Separation of Long DNA Molecules in a Microfabricated Entropic Trap Array[END_REF][START_REF] Han | Characterization and Optimization of an Entropic Trap for DNA Separation[END_REF]. A faster separation in 4 min of 6 bands in the range 3-21 kbp was obtained using a capillary well motif (CWM) with nano-capillaries of 750 nm diameters [START_REF] Cao | Fast DNA Sieving through Submicrometer Cylindrical Glass Capillary Matrix[END_REF]. Another entropic trapping device of anisotropic nanofilter array (ANA) was developed to continuously separate 5 bands of 2-23 kbp in 1 min using orthogonal electric fields [START_REF] Fu | A Patterned Anisotropic Nanofluidic Sieving Structure for Continuous-Flow Separation of DNA and Proteins[END_REF]. Globally, entropic trapping in SWM feature even performances when compared to the other technologies (Table 1).

Obstacle arrays (OA) of different shapes and organization can be fabricated in microchannels to separate long DNA through several physical mechanisms. A Brownian Ratchet (BR) mechanism, where the DNA is separated based on differences in Brownian diffusion of different sizes in an array of obstacles, was used to separate λ and T2 DNA in 70-140 min (Lotien Richard [START_REF] Huang | Role of Molecular Size in Ratchet Fractionation[END_REF][START_REF] Huang | Tilted Brownian Ratchet for DNA Analysis[END_REF]. Using this mechanism, the separation takes a long time since only low flow rates (or electric fields) can be used to allow for Brownian diffusion to separate the different species [START_REF] Xuan | Size Separation of Biomolecules and Bioparticles Using Micro/Nanofabricated Structures[END_REF]. Another mechanism that also relies on diffusion is size exclusion chromatography (SEC). In SEC, the array of obstacles forms narrow and wide gaps where smaller DNA molecules can pass through the narrow gaps while larger molecules continue their path in the wide gaps. SEC was used for the separation of 2, 5 and 10 kbp DNA in around 6 min [START_REF] Baba | DNA Size Separation Using Artificially Nanostructured Matrix[END_REF]). High flow rates can be used in OA with rows equally shifted with respect to one another. The separation mechanism in such an array was dubbed deterministic lateral displacement (DLD), since defined laminar flows that go through the OA control the path of molecules depending on their size. This technique was able to separate 61 and 158 kbp in 10 min (L. R. [START_REF] Huang | Continuous Particle Separation Through Deterministic Lateral Displacement[END_REF]. Separations in OA tend to be lengthy because they rely on molecular diffusion to achieve good performances.

Finally, through the adsorption of DNA on nano-patterned surfaces, 6 bands of 1-10 kbp could be separated with high resolution. This technique does not require the use of separation media and yields high theoretical plates, however, the fractionation of 1-8 kbp can take more than 30 min [START_REF] Seo | DNA Electrophoresis on Nanopatterned Surfaces[END_REF].

Compared to all the aforementioned methods, electro-hydrodynamic separation carried out in PermiNex chips compared favorably in terms of theoretical plates in the high MW limit, and featured the broadest analytical range, where 13 bands of 1-150 kbp were separated with a single round within less than 5 min (thick burgundy lines in Fig. 7). Very noticeably, despite the use of hydrodynamics and the large breadth of the injection plug (~ 20 µm, not shown), which tends to further increase band broadening due to Taylor dispersion, we achieved high theoretical plate numbers per m and low RSL of XX m -1 and XX bp, respectively, for molecules longer than 10 4 bp. This result is due to the confinement of molecules near the walls (as shown in Fig. 4), that restricts transverse fluctuations in a region where flow velocity variations are small.

CONCLUSION

The primary motivation of our work was the improvement of electro-hydrodynamic separation of high MW molecules using microchips. This objective is fulfilled as we show the separation of 14 DNA bands in the range of 0.5 to 150 kbp in less than 5 minutes with state-ofthe-art RSL and theoretical plate number. This achievement has been reached through the implementation of a novel process for glass/adhesive/glass microchip fabrication, which offers several key advantages, namely (i) a very strong bonding strength, (ii) a low auto-fluorescence, and (iii) most importantly, homogeneous surface properties. A source of band broadening associated to differential EOF is indeed detected in heterogeneous microchip devices. Given that the inner surface of capillaries is homogeneous by virtue of design, it is tentative to suggest that the state-of-the-art format for high performance DNA separation remains the capillary despite years of research in Lab-on-Chip due to the hybrid format of most microchip devices [START_REF] Ross | Imaging of Electroosmotic Flow in Plastic Microchannels[END_REF].

Although surface coating is a well-worked out solution to reduce the EOF [START_REF] Milanova | Effect of PVP on the Electroosmotic Mobility of Wet-Etched Glass Microchannels: Microfluidics and Miniaturization[END_REF][START_REF] Kaneta | Suppression of Electroosmotic Flow and Its Application to Determination of Electrophoretic Mobilities in a Poly(Vinylpyrrolidone)-Coated Capillary[END_REF][START_REF] Ghosal | Fluid Mechanics of Electroosmotic Flow and Its Effect on Band Broadening in Capillary Electrophoresis[END_REF], it remains unclear whether its efficiency will be even on the surfaces of heterogeneous microchips. This remark is validated by the fact that the separation buffer of our experiments contains poly-vinylpirrolidone, which is known to reduce the EOF [START_REF] Milanova | Effect of PVP on the Electroosmotic Mobility of Wet-Etched Glass Microchannels: Microfluidics and Miniaturization[END_REF][START_REF] Kaneta | Suppression of Electroosmotic Flow and Its Application to Determination of Electrophoretic Mobilities in a Poly(Vinylpyrrolidone)-Coated Capillary[END_REF], and differential EOF is nevertheless detected in electrophoresis actuation. We therefore propose that our process for glass-adhesive-glass microchip fabrication could be useful to enhance the separation performances of virtually every separation technology based on electrophoretic, electro-hydrodynamic or hydrodynamic actuation.

ASSOCIATED CONTENT

Supporting Information

The supplementary material contains two figures. Supplementary Fig. S1 shows an electron micrograph of the section of PermiNex chips, and Supplementary Fig. S2 is a plot of the oxide breakdown voltage of Si-glass chips for different thicknesses of oxide.

Figure 1 :

 1 Figure 1: Glass/PermiNex/Glass process flow. (a) Spin coating of the positive photoresist AZ ECI 3027 on a glass wafer. (b) UV exposure with the use of a negative mask following the standard protocol. (c) a-Si and oxide deposition using PECVD. (d) ECI development using acetone. (e) Spin coating of PermiNex at a speed of 8000 rpm and acceleration of 2500 rpm/s for 60 sec. (f) UV exposure with a negative mask and development of PermiNex with SU-8 developer. (g) Adhesive bonding of the two glass wafers with PermiNex as intermediate layer.

Figure 2 :

 2 Figure 2: High-resolution microfluidic funnel geometries and electrode integration. (a) Comparison between the chromium mask feature of 5 µm critical size and the microfluidic funnel geometry patterned using PermiNex (shown in inset). (b) and (c) present bright field images of the microchip with integrated 200 nm gold electrodes.

Figure 3 :

 3 Figure 3: Blocking the auto-fluorescence of PermiNex. . (a) Glass/glass chip bonded using PermiNex without the deposition of an a-Si layer. (b) Glass/glass bonded chip with an a-Si and oxide layers deposited below the PermiNex layer. The auto-fluorescence is totally blocked. A slight misalignment between the PermiNex and a-Si layer allows distinguishing the channel borders. (c) and (d) A plug of DNA migrates in channels without and with a-Si layer, respectively. (e) The design of a 4 cm microchip where a plug of DNA is formed at the junction with side channels and the fluorescence detector placed 35 mm away. (f)The S/N ratio is calculated for molecules in (c) and (d), it increases by a factor of 1.35 with the blocking layer.

Figure 4 :

 4 Figure 4: Evidence of band splitting in Silicon/Glass chips. (a) Time sequence of a 150 kbp DNA band in a Si/glass channel at the detecting region showing unfocused DNA molecules migrating close to the Si surface after migration time of 30.6 sec and (b) focused DNA molecules migrating close to the glass surface and passing in front of the detector 8.4 sec later. The small white arrows point small contaminations stuck to the glass surface, which demonstrate the difference in focus between the two DNA populations. (c) Fluorescence intensity profiles showing a

Figure 5 :

 5 Figure 5: Analysis of DNA electrophoretic velocity distribution. (a) Velocity distributions of 2D tracked phiX174 DNA molecules in a 2-µm Si/glass channel for a time interval of 100 ms. Lateral velocity distribution (green) representing thermal diffusion across the flow direction is centered at zero. Longitudinal velocity distribution (blue) is the convolution of Gaussian noise and diffusion-free velocity along the flow direction. (b) Analysis of the velocity distribution with a

Figure 6 :

 6 Figure 6: Separation of 1-150 kbp DNA in a glass/PermiNex/glass channel. Fluorescence micrograph of a kbp DNA ladder separated in a glass/PermiNex/glass microfluidic chip using opposing electrohydrodynamic flows in viscoelastic polymer solution PVP 10 KDa 2.5%. The separation parameters are 500 mbar and 170 V, corresponding to a hydrodynamic speed of 0.6 mm/s and electric field of 42 V/cm, respectively.

Figure 7 :

 7 Figure 7: Comparison with state of the art microchip separation of long DNA. (a) Resolution length (RSL) for DNA molecules of 1-200 kbp obtained using different microchip separation techniques. The RSL defines the minimum size that can be resolved. (b) Theoretical plate numbers obtained using different microchip separation techniques. Our technology of electrohydrodynamic separation in viscoelastic polymers in glass/PermiNex/glass chips is comparable to the state of the art for long DNA separation.

Table 1 :

 1 Comparison of microchip separation techniques for long DNA (1-200 kbp) in terms of size range, separation time, minimal RSL and theoretical plates/m.

This work was partly supported by the LAAS-CNRS micro and nano-technologies platform, member of the French RENATECH network. B.C. PhD fellowship is supported by the "Ligue contre le cancer". This project was partly supported by the project "Gene Extractor" from Région Midi-Pyrénées and by the ANR µLAS (ANR-16-CE18-0028-01) and the ANR Biopulse (ANR-16-ASTR-0020).

AUTHOR INFORMATION

Corresponding Author

Correspondence should be sent to Aurélien BANCAUD (abancaud@laas.fr, +33 5 61 33 62 46)

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT


M.D Jebrane Bouaoud
email: jebrane.bouaoud@gmail.com

Jean-François Honart

Yasmine Bennis

Nicolas Leymarie

Keywords: Microsurgery, reconstruction, free flap, calcification, atherosclerosis, radiotherapy

Head and neck reconstructive microsurgery in patients with calcified vessels (atherosclerosis 2 or radiotherapy) is challenging. Preoperative reconstruction planning should meticulously 3 evaluate the pedicle length and caliber aiming to select the most adapted free flap type and 4 to plan the need for harvesting two free flaps or a venous graft. During surgery, end-to-end 5 microanastomosis should be preferred, without artery clamps on calcified vessels and using 6 open-loop sutures, a limited number of microsutures and a round needle with inside-outside 7 directed bites (no atherosclerotic plaque removal). Before declamping, fibrin sealants are 8 used to prevent minor leakage around the anastomosis as well as before wound closure to fix 9 the optimal position of the pedicle avoiding pressure on the vessels or pedicle kinking. 10 Calcified vessels are not a barrier to microsurgery and do not constitute a contraindication. 11

Several options are useful to safely perform microsurgical head and neck reconstruction. 12

16

Demographic changes and medical progresses led to increasing diagnoses and managements 17 of head and neck (HN) cancers in elderly patients with more comorbidities [START_REF] Reiter | Head and neck reconstruction in the elderly patient: a safe procedure? Eur Arch Oto-Rhino[END_REF][START_REF] Wu | Study of surgical treatment for elderly patients with head and neck cancer[END_REF] . Surgeons 18 therefore face to technical challenges such poor vascular capitals with calcified vessels which 19 may affect the success of microsurgery [START_REF] Chen | Guidelines for the optimization of microsurgery in atherosclerotic patients[END_REF] . Calcified arteries lose their elasticity and are more 20 prone to thrombosis. 21 22 HN reconstructive microsurgery is characterized by anatomical and technical specificities. 23

Inferior limb free flaps are useful, but their vessels are often affected by atherosclerosis. 24 Furthermore, recipient vessels can be calcified due to atherosclerosis or radiotherapy. 25

26

We provide specific advice for safe HN microsurgical reconstruction based on our experience 27 with calcified vessels.

Technical description 29 30

Patients should be evaluated thoroughly before, during and after the surgery. The 31 microsurgical technique should be meticulous. 32 33

Pre-operative 34

A thorough vascular assessment is crucial, especially for patients with cardiovascular history [START_REF] Scaglioni | Microsurgical head and neck reconstruction in patients with coronary artery disease: A perioperative assessment algorithm[END_REF] . 35 Physical examination (palpable pulses) and evaluation of the vascular flows (echography 36 doppler) are mandatory. We recommend CT-Scans for angiographic study of free flap and 37 recipient vessels to specify the presence/size of atheroma plaque and the stenosis degree, 38 especially for the external carotid arteries. Some authors privileged the Magnetic resonance 39 angiography (MRA) because it is effective and less invasive [START_REF] Gryseleyn | Influence of preoperative imaging on fibula free flap harvesting[END_REF] . Anyway, in case of common 40 carotid artery stenosis > 80%, an endarterectomy is realized prior to reconstruction. If three 41 of the four carotid/vertebral axes are stenosed, the procedure is contraindicated. 42

For lower limb free-flaps essels of leg tripod anterior tibial posterior tibial and fibular 43 arteries) are investigated. 44 45 Perioperative 46

Free flap harvesting and recipient vessels preparation 47

To limit ischemia of the limb operated, flap harvesting is realized quickly (< 1 hour) or if 48 possible, without pneumatic tourniquet. 49

Careful dissection of vessels is crucial to avoid traumatisms and to allow a safe anastomosis. 50

To choose the best location for the anastomosis, surgeon inspect and palpate the recipient 51 vessel checking for the presence of calcifications, thrombus or atherosclerotic plaques 3 . As far 52 as possible, get away from the major vascular axes to preserve them and avoid excessive 53 atheromatous infiltrations. The arterial anastomosis is generally performed on one of the 54 terminal branches of the external carotid artery, away from all side branches (avoiding flow 55 modifications) that should be ligated. In all cases, vessels diameter should be as equal as 56 possible since the rigidity of the walls does not allow correction of diameter incongruences. 57 58 Anastomosis 59

We privilege end-to-end anastomoses [START_REF] Chen | Guidelines for the optimization of microsurgery in atherosclerotic patients[END_REF][START_REF] Lee | An Open-Loop Technique to Facilitate Microtubal Anastomoses in the Rat[END_REF][START_REF] Cigna | Microsurgical anastomosis with the PCA technique[END_REF] . To avoid traumatisms of vessels, we recommend to 60 not flush the flap, not use artery clamps for flap vessels, not strip the adventitia and not dilate 61 vessels. To visualize the vessels lumen, we limit irrigation with heparinized saline and prefer 62 careful drying with gauzes. Surgeons should not put instruments into the lumen blindly and 63 should use a round needle while limiting the number and the tension of microsutures. The 64 bites are directed from the inside to the outside for the atherosclerotic arteries (avoiding 65 removal of atherosclerotic plaque). 66 67

We privilege the open-loop suture technique [START_REF] Lee | An Open-Loop Technique to Facilitate Microtubal Anastomoses in the Rat[END_REF][START_REF] Cigna | Microsurgical anastomosis with the PCA technique[END_REF] for more secure anastomosis with clear 68 visualization of the vessels lumen during every pass of the needle (better eversion and 69 elevation of the edges using the tips of the forceps). We vary the size of loops to easily identify 70 loops that should successively be cut and tied. To improve the microvascular anastomosis 71 efficiency, experienced surgeons combine Open-Loop and Airborne Suture Techniques [START_REF] Sakarya | Improving Microvascular Anastomosis Efficiency by Combining Open-Loop and Airborne Suture Techniques[END_REF] . The 72 anterior and the back sides of the anastomosis are successively sutured. 73

Once the microsuture is completed, apply fibrin sealant around the anastomosis (tubulization 74 of the anastomosis) and wait until it dries before declamping. The objective is to prevent any 75 minimal leakage. 76

The use of an anastomotic coupler device is not recommended for atherosclerotic 78 microanastomoses (vessels rigidity, traumatism risk). 79 80

Wound closure 81

After declamping, we avoid manipulation of the pedicle (no permeability tests) to not create 82 turbulence and/or damage the vessel walls. 83

Before wound closure, we replace the patient head in physiological position (no neck 84 extension/rotation) and fix the pedicle optimal position using fibrin sealant ensuring that 85 there is no pressure or kinking of the pedicle. Kinking of the pedicle with calcified vessels is 86 more frequent than usual due to its length or difference in vessels walls rigidity. 87 88

Specific situations 89

To avoid anastomosis with both recipient and donor calcified vessels, surgeon can choose 90 vessels more prone to microanastomosis by dissecting more proximally the recipient vessel, 91 including sometimes the ''mother vessels'' [START_REF] Cigna | Management of microanastomosis in patients affected by vessel diseases[END_REF] (external carotid) or by using alternative recipient 92 vessels such Transverse cervical vessels which are rarely in the radiation fields of HN cancers 93 and offer good vascular flow. However, this last option requires longer pedicle and sometimes 94 the use of venous graft bypass or Chain-link sequential flaps. In this case, forearm free flaps 95 are suitable (longer, tension-free pedicle, far from the affected zone) and should be harvested 96 during the same surgery (one-stage reconstruction). The proximal part of its pedicle is 97 branched with the alternative recipient vessels while the distal part is sequentially branched 98 with the main free flap. Another option is the interposition venous grafting between the two 99 calcified vessels [START_REF] Hosein | A Novel Technique for Microsurgery on Calcified Arteries: Venous Interposition Grafting[END_REF] (Figure 1). The main disadvantages are the need to perform two anastomoses, increasing the operating time and the risk of thrombosis (venous graft 101 blockages due to different pressure regimes with calcified arteries) [START_REF] Lin | Intraoperative factors associated with free flap failure in the head and neck region: a four-year retrospective study of 216 patients and review of the literature[END_REF] . In all situations, double 102 needle sutures are useful.

Figure 1

 1 Figure1Illustration of a venous grafting between two vessels (not calcified in this case). A.

Figure 1 C

 1 Figure 1

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Discussion 104 105 Calcified vessels are not a barrier to microsurgery and do not constitute a contraindication. 106

Preoperative surgical planning meticulously evaluates the pedicle length and caliber to choose 107 the best free flap type and anticipate the need for harvesting two flaps or venous graft [START_REF] Zhang | Microsurgical free flap reconstructions of the head and neck region: Shanghai experience of 34 years and 4640 flaps[END_REF] . 108

During surgery, thrombosis can be avoided by respecting integrity of the vessels, choosing the 109 best location for an end-to-end anastomosis. End-to-side anastomosis increase the thrombus 110 formation risk because of more direct exposure of the atherosclerotic plaque. Vascular 111 clamps, stripping of adventitia and dilatation of vessels should be avoided given the risk of 112 traumatism and thrombus. Arterial dilatations with lidocaine, papaverine or amlodipine are 113 not performed because vasospasm is uncommon in calcified vessels. Tapered needles with a 114 cutting tip can be used to easily puncture the plaque while avoiding a laceration [START_REF] Hosein | A Novel Technique for Microsurgery on Calcified Arteries: Venous Interposition Grafting[END_REF] . Fibrin 115 sealants are useful to ensure that the optimal pedicle position is respected during healing. 116 Several options are useful when encountering both flap and recipient calcified vessels.