domain: spi sdv

text:
Marion Costella
email: marion.costella@usherbrooke.ca

Quentin Avenas

Marie Frénéa-Robin

Julien Marchalot

Pascal Bevilacqua

Paul Charette

Michael Canva

Dielectrophoretic cell trapping for improved surface plasmon resonance imaging sensing

Keywords: Alternating current electro-osmosis EOT: extraordinary optical transmission IDE: Interdigitated electrodes nDEP: negative dielectrophoresis NIR: Near-infrared pDEP: positive dielectrophoresis RIU: Refractive index unit Transverse magnetic SPR: Surface plasmon resonance SPRI: Surface plasmon resonance imaging UV: Ultraviolet biosensing instrumentation, dielectrophoresis, electro-osmosis, surface plasmon resonance, top-bottom electrodes

The performance of conventional surface plasmon resonance (SPR) biosensors can be limited by the diffusion of the target analyte to the sensor surface. This work presents an SPR biosensor that incorporates an active mass-transport mechanism based on dielectrophoresis (DEP) and electroosmotic flow to enhance analyte transport to the sensor surface and reduce the time required for detection. Both these phenomena rely on the generation of AC electric fields that can be tailored by shaping the electrodes that also serve as the SPR sensing areas. Numerical simulations of electric field distribution and microparticle trajectories were performed to choose an optimal electrode design. The proposed design improves on previous work combining SPR with DEP by using face-to-face electrodes, rather than a planar interdigitated design. Two different top-bottom electrode designs were experimentally tested to concentrate firstly latex beads and secondly biological cells onto the SPR sensing area. SPR measurements were then performed by varying the target concentrations. The electrohydrodynamic flow enabled efficient concentration of small objects (3 µm beads, yeasts) onto the SPR sensing area, which resulted in an order of magnitude increased SPR response. Negative dielectrophoresis was also used to concentrate HEK293 cells onto the metal electrodes surrounded by insulating areas, where the SPR response was improved by one order of magnitude.

Color online: See article online to view Figs. 1-5 in color.

Introduction

Surface Plasmon Resonance (SPR) biochips are highly sensitive, real-time and label-free sensors used for surface-based study of biomolecular interactions and detection of biological objects in fluid media [1,2]. They have become standard tools for chemical and biological sensing, and have found many practical applications including medical diagnosis [START_REF] Fu | Handbook of Surface Plasmon Resonance[END_REF]- [6], food safety [7], [8], environmental monitoring [9], [10], and pharmaceutical research [11]. Recent microfabrication advances have enabled SPR devices to become portable [12]- [14]. SPR sensors make use of the evanescent field of a guided electromagnetic mode at a metal/dielectric interface. When using a prism for input/output light coupling (Kretschmann configuration), the mode is excited at a specific wavelength and angle of incidence where transverse magnetic (TM) incident light is resonantly coupled to the surface plasmon mode and the reflected output light intensity is thereby minimized. Local changes in the dielectric close to the metal/dielectric interface (within ~200 nm for visible and near-infrared systems) induced by molecular binding or the presence of biological objects modify the mode properties and the associated coupling conditions. As a result, biomolecular activity close to the sensor surface can be monitored by tracking changes in light output intensity and/or resonance conditions. By using an imaging device (camera), monitoring of biomolecular activity can be spatially resolved on the sensor surface (metal/dielectric interface).

During the last decades, SPR biosensors have been extensively studied and their detection threshold is now close to their theoretical limit [15]. The performance level of current SPR biosensors, estimated as the smallest detectable refractive index change, reaches 10 -7 refractive index units (RIU) [16]. However, the detection of analytes suspended in a medium not only depends on the sensor performance but also on mass transport of analytes to the sensor surface. Indeed, the sensitivity of current SPR biosensors is often limited by diffusion-limited mass transport [17]. This limit can be overcome by increasing the analyte concentration near the sensor surface with active mass transport, for example with dielectrophoresis (DEP) and AC electroosmotic (ACEO) flow [18]- [20]. The biochip proposed here uses a microstructured gold/dielectric film, similar in thickness and optical properties to those used in conventional SPR biochip systems, for both the SPR sensing surface and the electrodes used for control of the active mass transport by DEP and ACEO.

DEP results from the interaction between a polarizable particle and a non-uniform electric field. The dielectrophoretic force applied on a spherical particle of radius r in a fluid medium can be expressed as:

〈 〉 (1)
where ε m is the permittivity of the fluid medium, E rms is the root mean square of the electric field amplitude, and Re(CM) is the real part of the Clausius-Mossotti (CM) factor, given by:

(2)

where and are the complex permittivity of the particle and the fluid medium, respectively.

Depending on the polarization contrast with the fluid medium, the particle can either be attracted to high electric field zones (positive DEP, positive CM factor) or pushed towards weak field zones (negative DEP, negative CM factor). Dielectrophoresis requires an electric field gradient, typically produced by shaping electrodes and distorting field profiles. An alternative is to combine insulating structures with recessed electrodes to produce the electric field gradient and trap objects following the principle of insulator-based dielectrophoresis (iDEP) [21].

Electroosmotic flow occurs when the tangential component of the electric field moves ions in the ionic double layer at the metal/medium interface [22]. While positive dielectrophoresis typically attracts objects to the edge of electrodes, electro-osmosis is able to drag them towards the center of the electrodes [23], which facilitates SPR detection.

Barik et al. have shown [24] that nanohole-enhanced dielectrophoresis and electro-osmosis significantly lower the detection limit of protein like BSA, as measured by exploiting extraordinary optical transmission (EOT). More recently, other groups have demonstrated the combination of plasmonics with active mass transfer by using ACEO to concentrate biomolecules on gold nanoparticles [25], photothermal heating to trap polystyrene beads on a plasmonic nanostructured substrate [26], or dielectrophoresis to concentrate beads or bacteria near a gold-coated optical fiber tip [27]. However, these techniques need nanofabrication steps which require expensive equipment and long manufacturing processes. Dielectrophoresis and ACEO combined with plasmonics have also been used to enhance fluorescently-labeled biological substance detection [28]- [START_REF] Kuroda | IEEE Conference on Electrical Insulation and Dielectric Phenomenon[END_REF]. To the best of our knowledge, Galvan et al. [START_REF] Galvan | [END_REF] were the first to publish work on combining prism-based SPR sensing (the most widely-used SPR configuration, i.e. the Kretschmann configuration) with DEPassisted active mass transport. In their work, the electric field is created using interdigitated electrodes (opposite polarity electrodes are in the same plane).

In this work, we propose an improved configuration for active mass transport with SPR based on face-to-face electrodes that significantly enhances the target collection ability by both DEP and ACEO. Results from both numerical simulations and experimental measurements with latex microbeads and biological cells are presented. Such DEP-SPR biochips can easily be fabricated with standard low-cost photolithography techniques and could therefore be widely distributed and used when needed with minor modifications to existing SPR systems

Materials and methods

SPRI optical set-up

The layout of the SPR-DEP system is depicted in Figures 1a and1b. The major optical components around the biochips are the light source (collimated 740 nm fibered LED, Thorlabs, M740F2), a prism coupler (SF10 prism) and a detector (camera). The SPR biochips are mounted on the prism in the Kretschmann configuration [32]. The optical contact between the prism and the SPR biochip is made using index matching oil. A custom-made device (Figure 1a) clamps together the different parts of the biochip (bottom glass slide with electrode, top-side counter electrode, and fluidic chamber in between) and allows the connection of electrodes to a signal generator (Stanford Research Systems, DS345).

Figure_1

The microfluidic channel is cut out from a 200 µm thick PDMS film obtained by spin coating, which is used as a spacer between the electrode and the counter electrode.

DEP-SPRI biochip fabrication

As shown in Figure 1a and 1b, the chosen electrode configuration for dielectrophoresis is a face-toface (or top-bottom) configuration. The top electrode is an ITO coated glass slide (8-12 Ω/sq, Sigma-Aldrich). The bottom electrode is a microscope glass slide purchased from Fisher Scientific, coated with a 3 nm chromium adhesion layer, and a 48 nm gold layer by evaporation. Two configurations are proposed for the bottom electrode. In the "dielectric structured" configuration (Figure 1c), a 150 nm SiO 2 insulation layer is deposited by plasma-enhanced chemical vapor deposition (PECVD) onto the gold film at 300°C and 1 mTorr. Then, openings are formed in the SiO 2 layer using wet etching.

For this purpose, AZ1512 (MicroChemicals) positive photoresist is first spin-coated on the sample and post-baked at 110°C for 3 min. Then, the photoresist is exposed to UV light (OAI 200, Optical Associated Inc.) through an acetate mask superposed on the sample, before being developed using MF319 developer (Shipley).

Acetate photomasks were used during this step to reduce the cost of the process and allow for the comparison of a wide variety of electrode designs. Finally, the SiO 2 layer is etched with buffered oxide etch (BOE 6:1) prior to removal of the resist mask using acetone.

In the "metal structured" configuration (Figure 1d), the gold film is etched to electrically insulate some zones where cells will be trapped by negative dielectrophoresis. The wet etching process is similar to the one previously described, except that the gold layer and the chromium adhesion layer are etched using Gold Etchant TFA and Chromium Etchant (Transene Company, Inc.), respectively.

Cell and particle preparation

Latex beads solutions (3 µm diameter, Polyscience) were prepared by diluting the stock solution with DI water to obtain a final concentration of 36.5 x 10 6 particles/mL. Human embryonic kidney cells (HEK293) were grown at 37°C under 5% CO 2 in Dulbecco's modified Eaglemedium (DMEM), with 10% fetal bovine serum (FBS), 100 µg/mL streptomycin, and 100 units/mL penicillin. Before each DEP and SPR experiment, cells were detached with a trypsin solution (phosphate-buffered saline containing 0.05% trypsin and 0.02% EDTA) and resuspended in a low conductivity medium (8.5% sucrose (w/v) and 0.3% dextrose (w/v) in DI water).

DEP-SPRI measurement protocol

On the SPR optical bench, cameras and light source are fixed on a rotation stage to control the light incidence and reflection angles. The whole system is controlled using the software developed in the LabVIEW environment. Before each measurement, buffer solution is injected in the microfluidic chamber using a syringe pump. Then, the working angle θ 0 at fixed wavelength is determined from an angular scan. The reflectivity as function of the incidence angle is measured and the working angle θ 0 is chosen as the angle of incidence for which the reflectivity variation is maximal. This angle guarantees the maximal sensitivity of the sensor. After stabilisation of the SPR signal, analytes are To compensate for brightness differences between measurements, all SPR signals are normalized setting their initial value to 1. The reference electrode is an unpatterned, non-polarized gold film.

The SPR signal for this zone corresponds to that detected by a classical SPR biochip.

Optical microscopy setup

Axiocam MRM camera mounted on a Zeiss Axiovert 200 inverted microscope was used for bright field imaging. Similar electrical setup and energy supply were used in both SPR and bright field imaging.

Results and discussion

Numerical simulations for electrode design choice

The SPR signal enhancement of microparticles under DEP forces and ACEO flow generated by coplanar interdigitated electrodes has been previously studied in our group and reported elsewhere [33]. However, with this configuration, particles far away from the electrodes will be less responsive to the DEP forces, due to the rapid electric field decay with the distance from the electrodes.

Figure_2

Face-to-face electrodes can be used as an alternative, since they generate a strong electric field in the whole height of the channel. Dead DEP collection volumes can thus be avoided [34], [35]. The expected consequence would be a greater efficiency of particle trapping. To quantify this effect, simulations of particles trajectories were performed both for coplanar and face-to-face electrodes using a Comsol Multiphysics 5.3a 3D model and the add-on AC/DC, Microfluidics and Particle Tracing modules. Electric field models of channel cross-sections corresponding to the "dielectric structured" and the "metal structured" configuration are depicted in Figure 2a and2b. Figure 2c and2d represent the CM factor for 3 µm latex beads and HEK293 cells calculated with MyDEP software [36].

Electric properties of HEK293 cells present in the MyDEP database were used [37]. Electric properties values of latex beads used in this paper were previously studied by Suzuki et al. [38] in similar conditions (DI water).

The thickness of electrodes and dielectric layer were considered as negligible. First, a frequency study was used to solve the electrical problem in the Electric Current interface of the AC/DC module using Eqs. 3-6:

(

where Q J , σ, ω, D, V, J e , are charge density, conductivity, angular frequency, electric displacement field, applied potential, external generated current density, permittivity of the vacuum, and relative permittivity of the medium, respectively. Q J and J e were set equal to zero in our calculation. Electrodes were considered as equipotential surfaces. The potential of the bottom electrode was set at 5V, and the potential of the top electrode was set at -5V. Electrical insulating boundary conditions were set on the fluidic chamber's walls. Then, the gravity force, the drag force and the dielectrophoretic force were modeled using pre-calculated forces available in the Particle Tracing module. In this module, Newton's second law of movement (Eq. 7) is solved for each particle:

( ) (7)
Where m p is the mass of the particle, v is its velocity, and F is the sum of the forces applied on the particle (DEP force, drag force and gravity force). This model was meshed using a free triangular configuration on the bottom electrodes with a minimum element size of 0.05 µm and a maximum element size of 1 µm. The rest of the fluidic chamber was meshed using a free tetrahedral configuration with a minimum size of 1 µm. The Particle Tracing study was computed in a timedependent mode to predict the particle trajectory inside the fluidic chamber.

Figure_3

Electric field repartition for each configuration is depicted in Figure 3a, 3b and 3c for a 10 V pp applied voltage. For the nDEP model, a floating potential condition is defined on the central square depicted in Figure 1d. A 35 seconds temporal study describes the trajectory of 200 particles randomly distributed in the 200 µm channel height. The particle's position after 25 seconds is represented in Figure 3d, 3e, and 3f. SPR signal grows with the density of analytes trapped at the surface of the sensor. The number of particles trapped on electrodes for the coplanar and face-to-face electrodes versus time is represented in Figure 3g. These simulations reveal a stronger concentration of cells on gold for the face-to-face electrodes than for coplanar electrodes, especially in the pDEP case. In this case, particles are attracted on high electric field zones, at the boundary between gold and SiO 2 layer. This is not ideal for SPR detection. However, this model does not take account ACEO flow, which brings objects on the center of electrodes and allows a better detection. As the surface of electrodes is equivalent for both configurations, the density difference is due to the dielectrophoretic force, and not to a surface effect. The trapping efficiency of the interdigitated electrodes could be enhanced by optimizing some parameters such as the gap between the electrodes and their width, or the voltage. Electroosmotic flow could also be exploited to drag the particles towards the trapping sites. However, our simulations tend to show that the face-to-face configuration may be particularly interesting for the targeted application. For this reason and in the following experimental section, all the SPR-DEP electrodes are in this configuration.

DEP and ACEO experimental trapping

The dielectrophoretic behavior of 3 μm latex particles and HEK293 cells was investigated. In this paper, two approaches are described. In the first one ("dielectric structured"), following the concept of iDEP [39], an insulation layer is patterned to obtain openings on gold, as shown in Figure 1c.

Figure 4a represents the 3 µm latex beads position after few minutes under a 1 V rms and 1 kHz AC voltage in DI water. Under these conditions, the Clausius-Mossotti factor predicts positive dielectrophoresis (Figure 2c) and the beads are attracted to the electric field maxima located at the boundary between insulated zones (SiO 2 ) and conductive zones (gold). As the top and the bottom electrodes are asymmetric, the electric field has a tangential component that sets in motion the mobile ions in the electric double layer. This results in an electro-osmotic (ACEO) flow, which is nonnegligible in the frequency range used [40]. In the "dielectric structured" configuration, the electro-osmotic flow leads to vortexes at the edge of the electrodes [41]. This flow drags the particles from the edge of the electrode to its center, which is an advantage for SPR sensing. Figure 4b shows that the beads accumulate on the electrode surface when the voltage is applied. Particle arrangement shows a crystal structure. When the voltage is switched off, beads are randomly dispersed. We observe that ACEO flow efficiently concentrates 3 µm latex beads and yeasts cells. For bigger objects such as HEK293 cells (R = 7,5 µm), the drag force induced by the EHD flow is too weak compared with the pDEP force to bring objects to the center of the electrodes. As the DEP force grows as R 3 (R being the radius of the particle), the pDEP force is enough to maintain beads on the edge of the electrodes, despite the electroosmotic flow. This configuration is therefore not well adapted for the detection of cells by SPR. In the second approach ("metal structured" configuration), the gold film is directly patterned as displayed in Figure 1d. nDEP trapping of HEK293 is studied in this configuration.

To reach a physiological value of osmolality in a low conductivity medium, cells are suspended in DI water supplemented with sucrose/dextrose. At 5 kHz, cells experienced negative dielectrophoresis.

As predicted by the CM factor (Figure 2d), cells are attracted towards electric field minima located on the electrically isolated gold squares. Due to the floating potential of the isolated gold squares, electric field minima are not located perfectly at the center of these islets. As a result, cells are not perfectly centered on those zones on which SPR sensing is being performed. After a few minutes, all cells are trapped, as shown in Figure 5a.

SPR sensing enhancement

SPR-based sensors are highly sensitive to changes in the refractive index near the metallic film. The application of an external potential difference to the gold film might lead to its oxidation [42], or modify the charges distribution in the double layer at the metal-liquid interface [43]. This could result in an SPR angular shift, which would depend on the voltage and the frequency applied. In this study, the SPR angular shift due to the AC voltage is negligible compared with the angular shift induced by the detection of a biological object.

"Dielectric structured" configuration

Figure 4c represents the TM image corresponding to Figure 4a. To avoid detrimental optical effects, the plasmon propagation direction is aligned along the rectangular electrodes. As shown in Figure 4a and 4b, pDEP attracts the latex beads on 100 µm wide openings on SiO 2 . Therefore, they are concentrated at the center of the electrodes thanks to the ACEO flow.

Figure_4

Figure 4d shows the temporal evolution of the normalized SPR signal on the DEP electrode after injecting the beads, powering on the voltage and washing with DI water. The SPR signal after bead injection is the one obtained with a classical SPR sensor. As soon as the voltage is applied, bead arrival on electrodes induces a strong signal enhancement. Out of the saturation regime, this signal jump is linked to the initial bead concentration in the solution. Then, the voltage is switched off and the SPR signal on electrodes decreases. This is due to the bead density drop which corresponds to the switch between a crystal-like and a random organization of beads. The predominance of electroosmotic flow on the dielectrophoretic force makes this configuration particularly interesting for small objects (such as bacteria) trapping and detection.

"Metal structured" configuration

The image of the "metal structured" gold film is displayed in Figure 5b. Figure 5c represents the temporal evolution of the SPR signal on a patterned gold film and on a planar electrode similar to a classical SPR sensor. After cell injection, a 7 V pp and 5 kHz signal is applied. At this frequency, the Clausius-Mossotti factor predicts negative dielectrophoresis for HEK293 cells in a low conductivity medium (Figure 2d). The arrival of cells on electrodes is monitored by the SPR signal rise, slower than in the precedent configuration because the nDEP force is weaker than the pDEP force.

Figure_5

Indeed, the Clausius-Mossotti factor ranges from -0.5 to 1, which means that at the optimal frequencies conditions, pDEP force is always greater than nDEP force. However, nDEP presents interesting properties for the manipulation of biological objects. As cells are trapped at electric field minima, their membrane is less electrically stressed than by pDEP trapping. The temporal evolution of the SPR signal plotted in Figure 5c shows that nDEP provides an SPR signal significantly stronger than the maximal signal attainable with a classical SPR biochip.

Indeed, the Clausius-Mossotti factor ranges from -0.5 to 1, which means that at the optimal frequency condition, the pDEP force is always greater than the nDEP force. However, the nDEP presents interesting properties for the manipulation of biological objects. As cells are trapped at electric field minima, their membrane is less electrically stressed than by pDEP trapping. The temporal evolution of the SPR signal plotted in Figure 5c shows that nDEP provides an SPR signal significantly stronger than the maximal signal attainable with a classical SPR biochip.

Concluding remarks

Two different designs of a dielectrophoresis-assisted SPRI biochip structure dedicated to the detection of biological objects were considered. Using simulation tools, we numerically demonstrated the greater particle/target collection capabilities of "face to face" electrodes compared with "coplanar" electrodes.

In this "face-to-face" electrodes case, we studied two different types of structures, respectively adapted to negative dielectrophoresis and positive dielectrophoresis. The "dielectric structured" design exploits ACEO and positive dielectrophoresis to center small particles on electrodes, whereas the "metallic structured" design is intended to trap objects on a non-connected area of the metal film by negative dielectrophoresis. Both behaviors were experimentally demonstrated and exhibited significant signal in conditions whereas without the DEP contribution none was obtained.

Furthermore, it is worth pointing out that such structurally modified biochip components can easily be integrated on existing academic or commercial SPR devices and therefore be routinely used to allow a faster and more sensitive target detection for many application whenever needed. Such dielectrophoretic-assisted trapping of analytes is particularly interesting for the detection of ultralow target concentrations, where no detection would be possible within a given allotted time using classical transport-limited SPR biochip reader systems.

As is well known, classical biochips are usually functionalized with a surface chemistry for the selective detection of specific targets. Combined with such surface chemistry, such DEP-SPRI approach will open up new applications making use of rapid and low-detection SPRI sensor instruments. SPR sensors.

Figure captions:

  Another thick PDMS block (0,5 cm) is bounded to the ITO-coated glass slide with O 2 plasma. It distributes the pressure on the channel when the screws are tightened. Contact pins soldered to the circuit board provide electrical contacts to the electrode and the counter electrode. The electric signal is transferred from the bottom board to the top board through the screws. A motorized rotation stage (Thorlabs) controls the incidence angle and the detector position. After reflection at the metal/fluid, the light beam goes through an objective (Mitutoyo, x5 or x10), and a polarizing cube beam splitter to separate TE and TM images. TE and TM images are acquired using two CCD cameras (Allied Vision, Mako, G234B POE). The SPR signal is extracted from the TM image light intensity.

  injected. Then, after a certain time necessary to the signal stabilization, AC voltage is applied for the dielectrophoretic trapping. Throughout the measurement process, transverse magnetic (TM) and transverse electric (TE) images are recorded. Intensity variation in the TM image corresponds to optical index changing near the metallic film, which reveals the presence of beads or biological objects. Several regions of interest (ROI) are defined on the TM image, including DEP electrodes, and reference electrode. The temporal evolution of ROI's average pixel value is monitored by post-processing thanks to the ImageJ software and the Time Series Analyzer V3 plugin. It corresponds to the SPR signal.

Figure 1 :

 1 Figure 1: Scheme of the top-bottom electrode and the fluidic channel in the circuit board

Figure 2 :

 2 Figure 2: Electric field lines for the "dielectric structured" configuration (a) and the "metal

Figure 3 :

 3 Figure 3: Norm of the electric field for the two top-bottom electrodes design studied (a, b)

Figure 4 :

 4 Figure 4: Microscopy image of latex beads trapped by ACEO at 1 kHz and 1Vrms (a). Image

Figure 5 :

 5 Figure 5: Microscopy image of HEK293 cells trapped by nDEP on isolated gold squares

Acknowledgements

This work was supported by doctoral scholarships from MITACS and IDEX Lyon. LN2 is an international laboratory (Unité Mixte Internationale UMI 3463) jointly managed by French CNRS and the Université de Sherbrooke as well as Université de Lyon (ECL, INSA de Lyon, CPE) and the Université Grenoble Alpes (UGA). Authors thank A. Sabac, T. Deschamps, A. Belarouci and the NanoLyon platform for the thin film deposition. The authors also thank U. Froehlich and S. Touchette for cell culture.

The authors have declared no conflict of interest.


Quentin Avenas
email: quentin.avenas@usherbrooke.ca

Julien Moreau

Marion Costella

Arbi Maalaoui

Abdelkader Souifi

Paul Charette

Julien Marchalot

Marie Frénéa-Robin

Michael Canva

<PE-AT>Performance improvement of plasmonic sensors using a combination of AC electrokinetic effects for (bio)target capture

Keywords: Alternating current electroosmosis DEP: Dielectrophoresis Electrophoresis Interdigitated electrodes RIU: Refractive index unit ROI: Region of interest SPR: Surface plasmon resonance SPRI: Surface plasmon resonance imaging TE: Transverse electric TM: Transverse magnetic UV: Ultraviolet Biosensor, Dielectrophoresis, Electroosmosis, Surface plasmon resonance

Analytes concentration techniques are being developed with the appealing expectation to boost the performance of biosensors. One promising method lies in the use of electrokinetic forces. We present hereafter a new design for a microstructured plasmonic sensor which is obtained by conventional microfabrication techniques, and which can easily be adapted on a classical surface plasmon resonance imaging (SPRI) system without further significant modification. Dielectrophoretic trapping and electro-osmotic displacement of the targets in the scanned fluid are performed through interdigitated 200 µm wide gold electrodes that also act as the SPR-sensing substrate. We demonstrate the efficiency of our device's collection capabilities for objects of different sizes (200 nm and 1 µm PS beads, as well as 5-10 µm yeast cells). SPRI is relevant for the spatial analysis of the mass accumulation at the electrode surface. We demonstrate that our device overcomes the diffusion limit encountered in classical SPR sensors thanks to rapid collection capabilities (< 1 minute) and we show a consequent improvement of the detection limit, by a factor greater than 300. This study of an original device combining SPRI and electrokinetic forces paves the way to the development of fully integrated active plasmonic sensors with direct applications in life sciences, electrochemistry, environmental monitoring and agri-food industry.

Introduction 1.1 SPRI

Surface Plasmon Resonance (SPR) is a powerful detection technique for analyzing biomolecular interactions [START_REF] Homola | Surface Plasmon Resonance Based Sensors[END_REF]- [START_REF] Moreau | Handbook of Enhanced Spectroscopy[END_REF] with applications in various domains such as life sciences, electrochemistry or Electrophoresis This article is protected by copyright. All rights reserved. food and environment safety. SPR sensors allow for label-free, real-time, quantitative and sensitive detection and/or analysis [START_REF] Moreau | Biomedical Photonics Handbook, Second Edition: Biomedical Diagnostics[END_REF] of intermolecular events. They are usually used in the Kretschmann configuration, as described on Figure 1.a): the metal film is illuminated through a prism by an incident beam that is then reflected except for a particular angle and wavelength where light is absorbed by the electrons at the metal-dielectric interface. These resonance angle and wavelength depend on the optical properties of the materials near the interface. Biomolecular events at the surface (e.g. target/probe interaction as illustrated on Figure 1.a)) locally change the refractive index and are thus detected by tracking the coupling resonance angle (or wavelength) shifts. In a complementary manner SPR Imaging (SPRI) usually consists in the measurement of reflectivity variations at a fixed angle and wavelength. This technique provides spatial information [START_REF] Rothenhäusler | [END_REF], [6] and led to the development of high-throughput SPR biochips [7]- [10]. The high interest in this technology has led different research groups to reach the maximal theoretical resolution limit in the last decade [11]. However, as a surface-based sensing technique, it can only detect molecules if they are near the surface (typically, less than 200 nm away). Thus, the diffusion limit is the main obstacle to performance enhancement of all surface-based sensors today [12], and particularly SPRI biochips. Figure_1

Electrohydrodynamic (EHD) forces

Microfluidic transport strategies have been studied since the last two decades in order to overcome the diffusion limit [13]. Amongst all the existing techniques, electrokinetic effects are particularly interesting because they are applicable to a wide range of target sizes and types. They also can be induced within devices of various materials and geometries [14], depending on the objective. Thus, they could easily be adapted to the structure of a SPRI sensor using the gold sensing surface as an electrode and thereby bring an answer to the problem of the diffusion limit.

Electrokinetic effects such as electrophoresis, dielectrophoresis (DEP), alternating current electro-osmosis (ACEO) and electro-thermal effect (ETE) have been widely studied [15]- [19] and enable different ways of breaking this limit. Since electrophoresis is conventionally carried out using a direct current field, undesirable effects like alteration of the gold surface may affect the monitored signal. Hence we chose to use AC electrokinetic effects and to implement them on an SPRI sensor.

Pioneering results on sensor enhancement by combined EHD/DEP were reported from 2003 by Hughes' group [20]- [23]. Coupling of electrokinetic actuation and evanescent light sensing on the same device was demonstrated for the first time in 2003 by the same group [24] and AC electric field enhanced nanoplasmonic detection has been reported by two different groups [25], [26] more recently. In this paper, we demonstrate that SPRI can be used in conjunction with AC electrokinetic effects not only to improve the sensor response but also to analyse the respective contributions of DEP and ACEO effects.

Materials and methods

Design and fabrication of the device

Our device consists of coplanar gold interdigitated electrodes (IDE) on a microscope glass slide, as shown on Figure 1.c). Rectangular IDE enable massive parallel manipulation of objects as they can easily be arranged in large arrays [27]. Additionally, their simple fabrication process Electrophoresis This article is protected by copyright. All rights reserved. involves a single photolithography step. Moreover, their symmetrical geometry enables a theoretical study of the device that fits well with the experimental results, as demonstrated later. Lastly, the fact that the electrodes are integrated on the same substrate makes it easily adaptable to a classical SPRI system, in which they can also be used as sensing areas.

Electrodes are 200 µm wide and separated with a 150 µm gap. These dimensions enable easy and rapid fabrication of the biochip. A large gold electrode is also present 1 mm away from the IDE, whose purpose is to provide a comparison with a classical SPRI sensor during experiments. It is not connected to the electrical circuit and it will be referred to as the "control electrode".

The fabrication process is straightforward: the substrate, a classical BK7 glass microscope slide, was first cleaned with acetone, ethanol and water. Then an adhesion layer of Ti (3 nm) and the transducing layer of Au (47 nm) were evaporated onto the substrate. The samples were then spincoated with AZ5214 (MicroChem) and insulated with UV (within an UV-Kub) before the photoresist development using AZ726MIF developer. The principal advantage of the fabrication technique lies in the use of an acetate photomask during this step, which reduces the cost of each new design while suiting our resolution requirements. Finally, the metal layers were etched with Gold etchant and Titanium etchant, the photoresist was stripped with acetone and the samples were cleaned again with acetone, ethanol and DI water.

Experimental protocol

Solution preparation

Aqueous solutions containing different analytes were studied. Polybead® Amino Microspheres of 200 nm and 1 µm diameter were purchased from Polysciences. Each beads solution was prepared by diluting the stock suspension with ultrapure water whose conductivity before the dilutions was measured to be 5.5 x 10 -6 S/m. The initial concentration of the commercial solution of 200 nm beads was 5.68 x 10 12 particles/ml, that of the 1µm beads solution was 1.13 x 10 12 particles/mL. Both types of beads have a positive Clausius-Mossotti (CM) factor in pure water at the considered frequencies (see Figure 4 and section 3.3 about the MyDEP calculations) and are therefore expected to experience positive dielectrophoresis. Solutions of beads were diluted 1000 times for the trapping experiments and spatial study. Several dilutions of the 200 nm beads solution, detailed in Figure 5.b), were made for the study of detection limit enhancement. Baker's yeast cells (saccharomyces cerevisiae, purchased from Vahine TM ) were used as biological model objects. They were rehydrated in water and resuspended at a concentration evaluated to 4.3x10 4 cells/ml with a Malassez counting cell.

For the calculation of the CM factor, a spherical model of concentric layers was adopted. We used a radius of 3.5 µm and considered the cell membrane and the cell wall to be respectively 8 nm and 220 nm thick. Input values for the electrical conductivity of the cytoplasm, the cell membrane and the cell wall were respectively 0.3 S/m, 25 µS/m and 24 mS/m. The dielectric constants of these compartments were respectively set to 50, 6 and 60 (default values extracted from MyDEP database, and originated from [28]). Electrophoresis This article is protected by copyright. All rights reserved.

Experimental workflow

Our device was first mounted on a BK7 glass prism in the Kretschmann configuration. Oil was used to optimize the optical contact between the SPRI chip and the prism. A 90 µm thick Mylar® seal was placed onto the chip before the prism/chip/Mylar® system was clamped against the wall of the experimental bench. This supporting wall has two holes through which medium enters and exits the fluidic cell. A photography of this system is provided in the Supporting Information (Figure S1). Fluid flow was induced through the fluid circuit thanks to a peristaltic pump (Gilson, Minipuls 3).

At the beginning of each experiment, pure water was injected in the fluidic cell and an angular scan was performed to determine the working angle at the chosen wavelength (740 nm). The camera (Hamamatsu, C11440), motors (used to move the camera and the light source) and thermal regulation of the fluidic cell were controlled with a LabVIEW program. Before the beginning of each electrokinetic experiment, a stable baseline was acquired and a calibration step was performed with a glycerol/water solution, equivalent to a variation of 1 x 10 -3 RIU (Refractive Index Units) [7]. Then the function generator (Agilent, 33120A) was operated manually to apply a sinusoidal signal. The application of an electric potential at a low frequency on the gold sensing surface can affect the SPR signal even in pure water, due to oxidation of the metal [29], [30] or changes in the repartition of charges at the metal/dielectric interface [START_REF] Lopatynskyi | Semiconductor Physics Quantum Electronics and Optoelectronics[END_REF]. However, we verified experimentally that with the electrical parameters we used (frequency greater than 500 Hz, voltage lower than 10 Vpp) it had no influence on our SPR measurements, which is consistent with the literature [29].

Two different processes were used for particle collection under AC electrokinetic effects. For the spatial study, the experiments consisted in successive identical sequences: the sample was injected, the pump was switched off and then the function generator was switched on after a short relaxation step. There was therefore no flow during the mass transport step. After particle collection, the function generator was switched off and fresh medium was injected in the fluidic cell before the beginning of the next sequence. The protocol used for determining the limit of detection was different, as the electric field was applied during the injection in order to maximize the quantity of trapped objects.

Imaging methods

The SPRI system was described in a previous article [START_REF] Sereda | [END_REF] and is schematized on Figure 1.c). The fabricated device is mounted on a BK7 glass prism and clamped against the fluidic cell. Electrode contact pads are electrically connected to a function generator thanks to alligator clips.

Images in TE and TM polarizations were collected during the experiment at a framerate of approximately 1 image/s. Intensity measurements on different regions of interest (ROI) were then extracted using ImageJ software, and calculations were made afterwards in order to convert them into RIU variations, based on the calibration step [7]. Intensity measurements were also conducted on the reference electrode, which is not connected to the electrical circuit, for comparison with the signal that would be obtained with a classical SPR biochip. Moreover, diffusive effects induced a second phase of slow signal growth after the rapid trapping phase. In this study we focused on the rapid collection of particles. Thus, for the last part of this study, the signal was measured after a fixed time of 30 s which was the same for each measurement, therefore ensuring their comparability. Electrophoresis This article is protected by copyright. All rights reserved.

Optical microscopy observations (using a 20 × objective) were made with an Axiovert 40 Zeiss microscope (used in bright field mode) and an Eclipse LV150 Nikon microscope (used in dark field mode).

Results and discussion

Collection of different particles

Collection of all the different particles (200 nm beads, 1 µm beads and yeast cells) was accomplished and observed by SPRI. 1µm beads were trapped by applying a sinusoidal signal at 20 Vpp and 5 kHz (Figure 2.b)). Images of the collection of these beads were also acquired by optical microscopy, as shown on Figure 2.a). SPRI shows precise localization of the beads, forming symmetrical bands over the electrodes whereas optical microscopy shows a more homogeneous repartition over the electrode surface. While the same electrical parameters were used during those two experiments, the observable result is different because optical microscopy only allows for seeing volume effects, whereas SPRI allows for sensing what happens directly at the surface.

Figure_2

The reasons for this collection pattern in bands have been explained previously [14]: at this frequency, beads are subjected to positive DEP (the crossover frequency is approximately 2 MHz, see Figure 4) and ACEO simultaneously. Positive DEP exerts a force attracting beads to the electrode edges while ACEO induced vortices that drag them towards the centre of the electrodes. Combined action of these two forces is summarized on Figure 1.b). An equilibrium between both forces is attained at this specific frequency, and the beads form bands at the point where the sum of the forces is null. ETE's influence on the collection pattern is negligible at this conductivity [14].

A similar trapping behavior was observed with the 200 nm beads subjected to identical field conditions, as observed by SPRI. The collection pattern dynamics (formation of bands that progressively shift towards the electrode center) is clearly observable and is shown on Figure 2.c). It is worth noting that switching of the electric field immediately causes the beads to detach from the electrode surface and become unobservable. This could not have been observed by optical microscopy and this highlights one the reason of the relevance of SPRI for biosensing: it enables the detection of sub-micron objects.

SPRI observations of yeast cell collection (Figure 2.d) and 2.e)) show that our system is also efficient for trapping and sensing biological objects. Their different dielectric properties and size distribution induce a collection pattern different from that of the beads as well as different optimal electrical parameters for collection (the frequency was 10 kHz in this case) as observed elsewhere in the literature [21].

SPR as a tool for the study of AC electrokinetic effects: a study of near-surface dynamics

As shown on Figure 2, our SPRI device is capable of providing spatial information about nearsurface dynamics of the particles which is otherwise unavailable. Being able to analyze these phenomena and study the mass transport dynamics at a surface level is important when working on problematics such as active functionalization, for which it is essential to know where the particles are collected. Electrophoresis This article is protected by copyright. All rights reserved.

We performed a series of experiments at three different frequencies (500 Hz, 1 kHz and 2 kHz) and amplitudes in the 2-20 Vpp range with a solution of 200 nm beads diluted 1000 times. Intensity measurements were then extracted from a sequence of identical contiguous ROI across the width of one electrode. Calculations were performed to evaluate the equivalent RIU variations, which are displayed as a function of the amplitude and the position on the electrode in a 3D representation shown on Figure 3.

Figure_3

At 1 kHz and 2 kHz, the equilibrium position of the beads shifts when the amplitude changes. At 2 Vpp the resulting forces are not strong enough to observe the effect of DEP and ACEO. Collection of the beads begins to be observable starting from 6 Vpp. At this amplitude, at t = 30 s, beads are trapped near the edges of the electrodes. Their position at this time shifts progressively towards the center of the electrode when the amplitude is increased. This shift is faster at 1 kHz, and the displacement of the DEP/ACEO equilibrium is not observed at all when the frequency is lowered to 500 Hz.

In order to understand this behaviour, we studied theoretically the influence of both forces. Equation 1 describes the expression of the dielectrophoretic force for a spherical particle with a radius r, where E eff is the RMS value of the electric field, is the complex permittivity of the particle and that of the medium. The DEP force is strongly influenced by the Clausius-Mossotti factor CM, given by Equation 2: if its real part is positive, DEP will be positive (i.e. the force acts in the gradient direction and therefore drives the particle towards areas of maximum field intensity). On the contrary, if Re[CM] is negative, DEP is negative, which means that the force will move the particle against the gradient.

(1)

(2)

We calculated the Clausius-Mossotti factor for each studied type of particle (beads of both sizes and yeast cells) using the MyDEP software [33] and experimental parameters obtained previously (see Supporting Information). Results are displayed as a function of the frequency on Figure 4.c). For the 3 chosen frequencies (500 Hz, 1 kHz and 2 kHz), the Clausius-Mossotti factor is positive and constant, meaning that the particles are attracted to the electrode edges in an identical way in each of the three cases.

(3)

The electroosmotic velocity field in the fluid on the electrodes was calculated according to the theoretical explanations formerly detailed by Morgan and Green [START_REF] Morgan | AC electrokinetics: colloids and nanoparticles, Microtechnologies and microsystems series[END_REF]. Electroosmotic velocity at a distance x from the electrode edge is given by Equation 3, where is the applied potential, η is the dynamic viscosity of the fluid and is a non-dimensional frequency depending on the Debye length 1/κ, the medium conductivity and the angular frequency of the electric field ω. Electrophoresis This article is protected by copyright. All rights reserved.

The electroosmotic velocity of the fluid on the electrode surface, at a distance x = 50 µm from the electrode edge, is displayed on Figure 4.a), clearly showing different behaviours for the 3 different chosen frequencies. The velocity is almost at its maximum at 500 Hz, intermediate at 1 kHz and near to a minimum at 2 kHz. This explains the shape of the 3D graphs on Figure 3: at 500 Hz where the ACEO velocity is maximal, beads are dragged towards the electrode center even at the lowest amplitude whereas for higher frequencies, DEP influence is stronger for lower amplitudes. Additionally, the shift towards the center when increasing the amplitude is faster at 1 kHz than at 2 kHz because the electroosmotic velocity is higher.

Figure_4

Distribution profiles of the beads over the electrode width were extracted from the experimental results for each frequency and a given amplitude of 10 Vpp (see Figure 4.b). They clearly show the shift of the collection site of the beads when changing the frequency. The displacement being towards the electrode center, these findings are consistent with the theoretical results and illustrate the dominance of ACEO over DEP at lower frequencies.

Furthermore, this DEP/ACEO equilibrium is strongly dependent on the nature and size of the analytes. In that respect, SPRI observations of the trapping of 1µm beads (see Error! Reference source not found..b)) show that bigger objects are more attracted to the electrode edges, which is why the bands of 1 µm beads are closer to the electrode edge after 30 s of applying the voltage compared with the bands of 200 nm beads. The size dependence of the collection dynamics is understandable through the equations of both AC electrokinetic effects. Electroosmotic flow induces a drag force on the beads which is proportional to their radius whereas the DEP force, which is still positive as the CM factor on Figure 4.c) shows it, is proportional to the volume (i.e. to r 3 ). Thus, for a bigger object and with every other parameter fixed, DEP grows faster so the collection bands are shifted to the edge (see supplementary information, Figure S2).

Yeast cells (saccharomyces cerevisiae) are different in nature and size. The DEP force that applies on them is still positive for the considered frequency (10 kHz), as indicated by the CM factor (see Figure 4.c)) whereas the electroosmotic velocity is lower at this frequency. If some yeast cells can be seen individually on the electrode surface after applying the voltage, the occurrence of circular irregularities on the electrode edges (Figure 2.e)) indicates a probable predominant attraction of the yeast cells towards the edges, which was later confirmed thanks to optical microscopy observations (Figure 2.f)). Thus, it seems that the DEP force is predominant in this case, which is consistent with our previous explanations about the influence of the target size on the DEP/ACEO equilibrium. The fact that yeast cells are trapped on the edges could be problematic for SPRI observations, but other electrode configurations, such as face-to-face electrodes (paper to be published), solve this easily.

These results prove that the position of the analytes on the electrodes can be electrically controlled and that the collection patterns can be predicted using theoretical tools. Besides, this initial study illustrates the fact that SPRI is particularly suitable for the study of near-surface dynamics when mass transport at a micron scale is involved. Electrophoresis This article is protected by copyright. All rights reserved.

Detection limit enhancement

Knowing that we were able to collect beads on the electrodes, our next objective was to quantify the performances of our device. Being able to predict the exact position of the beads allows for choosing precisely the region over which the signal is quantified, in order to get the maximal sensitivity: in this case, beads are collected at the center of the electrodes and thus, we measured the signal in this region of interest (ROI). We checked that switching on the electric field had no influence on the measured signal when no beads were present in the solution: the signal remained constant while applying the voltage (2 kHz, 20 Vpp) on ultrapure water only. This negative control is plotted on Figure 5.a) for comparison.

Figure_5

In order to show the signal enhancement capabilities of our device and to explain how the signal variations are calculated, an example of the kinetics of the signal during collection of a solution diluted 1000 times is shown on Figure 5.a). The signal for the microstructured sensor was extracted at the electrode center. The signal corresponding to a classical SPR sensor was extracted from an ROI of the same size on the reference electrode. After injection of the beads and a short relaxation period, the function generator was switched on, inducing mass transport of the particles. This generated a huge and rapid rise in the measured signal. The function generator was then switched off, causing the beads to detach from the gold surface and the signal to come back to its baseline. As shown on Figure 5.a), the signal variation of our enhanced device is much bigger than that of a classical SPR sensor. In order to determine the limit of detection of our device, several dilutions of the 200 nm beads solution were made, issuing solutions diluted 1000, 3000, 10000, 30 000, 100 000 and 300 000 times. The different solutions were studied successively on the same sample and with the same electrical parameters (2 kHz, 20 Vpp). We started with the most diluted solution and went gradually towards the most concentrated one, in order to prevent a hysteresis effect in the signal that could be due to bead accumulation on the surface.

During this series of experiments showing the enhancement of the limit of detection, there was no relaxation time: the function generator was switched on before bead injection. We verified experimentally that this process increased the quantity of trapped objects, affecting the signal variations in the same way. As explained earlier, we measured the signal variation at a fixed time of 30 s after the beginning of the particles collection because we were interested in the first-order dynamics of the trapping process.

The white noise was calculated on every ROI separately. The limit of detection is defined as the triple of this quantity. Thus, every signal variation inferior to this quantity is not meaningful. The limit of detection is the concentration which marks the boundary between the range where the sensor is efficient (providing signal variations greater than the detection threshold) and the range where it is not. Figure 5.b) shows the measured signal variations for every dilution, enabling the comparison between our enhanced sensor and a classical SPR sensor. The calculated noise is plotted as a line for convenience. On a classical SPR sensor, every solution diluted more than 3000 times induces a signal variation which is inferior to the noise limit, while the enhanced sensor gives a signal for every Electrophoresis This article is protected by copyright. All rights reserved. solution, including the most diluted one with a 1 000 000 dilution factor). Hence, we can conclude that our device enables the enhancement of the limit of detection by a factor greater than 300 in the given measurement time interval. This experiment was repeated multiple times and similar results were obtained, issuing the same (or greater) enhancement factor.

Conclusion and perspectives

We presented a new design for a SPRI sensor capable of operating AC electrokinetic effects in order to trap the target analytes onto its sensing surface. We demonstrated the efficiency of its collection capabilities for objects of different sizes (200 nm and 1 µm PS beads, yeast of about 7.5 µm). The observed mass transport dynamics were understood and theoretically explained with an excellent consistency with the experimental results. In this regard, SPR appears to be a particularly well-suited tool for the study of AC electrokinetic effects dynamics near the surface of the electrodes. Finally, we demonstrated that our device achieves its goal of overcoming the diffusion limit, by showing that the limit of detection could be enhanced by more than two orders of magnitude.

Aside from highlighting one more achievement in the field of SPRI sensing, this work paves the way to the development of a new generation of active plasmonic biosensors, capable of controlling mass transport to enhance their performance. The fully integrated approach presented here has the advantage of allowing for excellent compatibility of the biochip component with already existing SPR systems and thus for rapid development, commercialization and routine use whenever needed devices. Furthermore, other configurations, such as face-to-face electrodes, or other substrate modifications, such as nanostructuration, also have their own advantages and are currently under further studies. This article is protected by copyright. All rights reserved. Noise and detection threshold were calculated for both electrodes and displayed for convenience (error bars also represent the noise). This experiment has been repeated three times in the same conditions, with a different sample and new dilutions of beads each time. Observed results demonstrated the same enhancement of the limit of detection.

Supporting Information

Figure 1

 1 Figure 1

Figure 1 :

 1 Figure 1 : a) Illustration of a SPR biosensing system in the Kretschmann configuration. b) Side view of the electrodes. Illustration of the combination of AC electrokinetic effects on parallel interdigitated electrodes. Electric field lines are schematized in black. c) Illustration of our experimental device on a SPR system.

Figure 2

 2 Figure 2

Figure 2 :

 2 Figure 2 : Comparison of a) dark field optical microscopy imaging and b) SPRI observations of the collection of 1µm polystyrene beads on the electrodes. c) SPRI observation of the collection dynamics of 200 nm polystyrene beads on one electrode. d) and e) SPRI observation of the collection of yeasts (5-10 µm) on one electrode before (d) and after (e) applying the voltage. f) Optical microscopy image of the yeasts trapped on the electrode. All of these trapping experiments have been repeated at least ten times and the same results have been observed each time.

Figure 3

 3 Figure 3

Figure 3 :

 3 Figure 3 : 3D representation of the trapped 200 nm nanobead position: optical index variations (vertical axis) are displayed over the electrode width (on the 0-200 µm horizontal axis) as a function of the electrical amplitude (on the 0-20 Vpp horizontal axis) for the 3 studied frequencies (2 kHz, 1 kHz, 500 Hz) 30 s after beginning to apply the electric field. This experiment has been repeated twice in the same conditions but with a different chip (of identical geometry) and a new solution of beads each time. The results were qualitatively identical.

Figure 4

 4 Figure 4

Figure 4 :

 4 Figure 4 : a) Electroosmotic velocity at the electrode surface at 50 µm from the electrode edges. Calculations were made according to the theory explained in [25] b) Experimental collection positions of the beads along the electrode width after 30 s, observed for 3 frequencies at 20 Vpp. c) Real part of the Clausius-Mossoti factor for 200 nm polystyrene beads in DI water.

Figure 5 Electrophoresis

 5 Figure 5

Figure S1 :

 S1 Figure S1: Picture of the fluidic cell.

Figure S2 Figure S2 :

 S2S2 Figure S2

Figure 5 :

 5 Figure 5 : a) Example of kinetic monitoring of the signal variations during the injection of a solution of polystyrene beads (200 nm) with a 1000 dilution factor into our biosensor. Both curves were obtained on the same device, during the same experiment, at the same time. A sinusoidal voltage (2 kHz, 20 Vpp) was applied on the electrodes. Steps sequence: (1) Beads are injected. (2) The function generator is switched on. (3) The generator is switched off. Negative control (signal measured while applying the same voltage on ultrapure water only) is plotted for comparison. b) Signal variations for various dilutions of the solution.Noise and detection threshold were calculated for both electrodes and displayed for convenience (error bars also represent the noise). This experiment has been repeated three times in the same conditions, with a different sample and new dilutions of beads each time. Observed results demonstrated the same enhancement of the limit of detection.

Acknowledgements

LN2 is an international laboratory (Unité Mixte Internationale UMI 3463) jointly managed by French CNRS and the Université de Sherbrooke as well as the Université de Lyon (INSA de Lyon, ECL, CPE Lyon) and the Université Grenoble Alpes (UGA). Quentin Avenas acknowledges support from the French doctoral scholarship as well as MITACS and the IDEX Lyon program. He also thanks the Laboratoire Charles Fabry and the Laboratoire Ampère for providing access to their equipment.

The authors have declared no conflict of interest. Electrophoresis

This article is protected by copyright. All rights reserved.

Electrophoresis

This article is protected by copyright. All rights reserved.

(1 µm beads induce much bigger variations than 200 nm beads). As explained in the discussion, the position of the 1 µm beads is closer to the edge because the DEP force grows faster than ACEO with the size of the targeted object. The effective conductivity of a latex particle can be expressed as:

Parameters used in

Where is the particle radius, is the conductivity of latex and and are the Stern layer and the diffusion layer conductance, respectively. is negligible, which is also the case of when the particles are immersed in a low conductivity medium such as DI water. The value can be deduced from the experimental determination of the crossover frequency f 0 by considering that the real part of the Clausius-Mossotti factor Re[CM] cancels at f=f 0 .

As regards 200 nm amino beads, the σ p value was found to be 18.7 × 10 -3 S/m under the experimental conditions, (farads/meter) and m and considering (farads/meter) As regards 1µm amino beads, the σ p value was found to be 3.15 × 10 -3 S/m under similar conditions.