Multiplexed Actuation Using Ultra Dielectrophoresis for Proteomics Applications: A Comprehensive Electrical and Electrothermal Design Methodology

Abstract

In this work, we present a methodological approach to analyze an enhanced dielectrophoresis (DEP) system from both a circuit analysis and an electrothermal view point. In our developed model, we have taken into account various phenomena and constraints such as voltage degradation (due to the presence of the protecting oxide layer), oxide breakdown, instrumentation limitations, and thermal effects. The results from this analysis are applicable generally to a wide variety of geometries and high voltage microsystems. Here, these design guidelines were applied to develop a robust electronic actuation system to perform a multiplexed bead-based protein assay. To carry out the multiplexed functionality, along a single microfluidic channel, an array of proteins is patterned, where each element is targeting a specific secondary protein coated on micron-sized beads in the subsequently introduced sample solution. Below each element of the array, we have a pair of addressable interdigitated electrodes. By selectively applying voltage at the terminals of each interdigitated electrode pair, the enhanced DEP, or equivalently ‘ultra’-DEP (uDEP) force detaches protein-bound beads from each element of the array, one by one, without disturbing the bound beads in the neighboring regions. The detached beads can be quantified optically or electrically downstream. For proof of concept, we illustrated 16-plex actuation capability of our device to elute micron-sized beads that are bound to the surface through anti-IgG and IgG interaction which is on the same order of magnitude in strength as typical antibody-antigen interactions. In addition to its application in multiplexed protein analysis, our platform can be potentially utilized to statistically characterize the strength profile of biological bonds, since the multiplexed format allows for high throughput force spectroscopy using the array of uDEP devices, under the same buffer and assay preparation conditions.

Introduction

Despite the immense progress that has been made in discovery and validation of genomics over the last decade, proteomic biomarkers have lagged behind considerably compared to their genomic counterparts because of the inherent limitations in sensitivity of protein assays and also the ability to perform multiplexed detection of proteins and study of protein-protein interactions. Fluorescence based techniques such as ELISA¹ and also protein microarrays² have served as the gold standard for protein detection. Electronic detection systems are also showing promise for label free detection^3–6. More recently, bead based protein assays have begun emerging as alternatives to fluorescent assays due to several advantages that beads have over fluorophores. The use of beads has been shown to enhance sensitivity in protein assays given the fact that the bead itself serves to amplify the detection signal, whether electrical,^7–10 optical,¹¹ or magnetic.^12–14 Another advantage, given the micron size of beads is that one can better control the force applied to beads and thus measure the affinity of biomolecules’ interactions. This has previously been shown using shear force¹⁵, optical tweezers¹⁶, magnetic tweezers¹⁷, and more recently electrokinetic forces^18–21. Electronic force provides the advantage of scalability and precise addressability when multiplexing. With precise voltage control, one also has better control over the applied force compared to the alternative techniques mentioned. The difficulty with electrokinetic forces lies in the inherent weakness of these forces (1–10 pN) compared to typical biomolecular interactions (~nN). This two order of magnitude gap resulted from a lack of proper modeling of the electrical and thermal behavior of high voltage dielectrophoretic systems. In this manuscript, we demonstrate the ability to study protein-protein interactions in multiplexed format, and more importantly we develop a complete model along with methodological design guidelines for high voltage dielectrophoretic systems coated with thin film insulative layers.

Previously, with the aid of negative dielectrophoresis (nDEP) force in conjunction with shear force and eluting agent, we demonstrated a switch-like functionality to elute specifically bound beads from the surface²¹. The role of the eluting agent, at an optimal concentration, was to sufficiently weaken the bindings such that the nDEP force would be able to push the specifically bound beads off the surface. While the use of the eluting agent assisted with establishing the switching functionality of nDEP as a proof of concept, its use was not desirable in performing multiplexed assay along a single channel. To eliminate the need for the eluting agent, we focused on enhancing the nDEP force significantly, primarily through fabricating high voltage tolerant corrosion proof electrodes that enabled us to apply high ac voltages at the electrodes. This was achieved by depositing a protective pinhole free nanometer-scale thin film layer on electrodes, using Atomic Layer Deposition (ALD).

The ultra thin nature of the film as well as excitation of voltage at high frequency allowed us to capacitvely couple the electrodes to the electrolyte. This minimized the undesired voltage drop across the oxide layer; a phenomenon from which previously proposed solutions suffered due to deposition of thick oxide layers. As a result, we ultimately enhanced the strength of DEP by two orders of magnitude. Development of this localized electrokinetic actuator has expanded the horizon of utilizing DEP in various microfluidic applications. Just recently, the application of ‘ultra’ DEP (uDEP) was demonstrated in a two-component on-chip particle filtering platform that is used for the depletion of cells and highly abundant serum proteins in blood.²² Here, we utilize an array of uDEP electrodes to implement a multiplexed bead-based protein assay, which can be used as a rapid and inexpensive method for screening a panel of proteins in a given sample.

However, prior to implementation of the envisioned platform, a careful circuit and electrothermal analysis is required in order to understand the relevant parameters and constraints in the design space, with the goal of maximizing the DEP force in our system. Therefore, we first present a methodological approach to analyze an enhanced dielectrophoresis (DEP) system accordingly. In our developed model, we have taken into account various phenomena and constraints such as voltage degradation (due to the presence of the protecting oxide layer), oxide breakdown, instrumentation limitations, and thermal effects. The results from this analysis are applicable to a wide variety of geometries and generally high voltage microsystems. Here, they were applied to develop our envisioned electronic actuation system to perform a multiplexed bead-based protein assay.

To implement the multiplexed platform, as illustrated in Figure 1, along a single microfluidic channel, an array of proteins is patterned, where each element is targeting a specific secondary protein coated on micron-sized beads in the subsequently introduced sample solution. Below each element of the array, we have a pair of addressable interdigitated electrodes (IDE). By selectively applying voltage at the terminals of each IDE pair, the enhanced DEP force detaches protein-bound beads from each element of the array, one by one, without disturbing the bound beads in the neighboring regions. The detached beads can be quantified optically or electrically downstream. It is worth mentioning that using IDE as the electrode configuration of choice provided the periodicity and scalability needed to maximize the analyte capture and actuation zone for each element of our array. For proof of concept, we illustrated 16-plex actuation capability of our device to elute micron-sized beads that are bound to the surface through anti-IgG and IgG interaction which is on the same order of magnitude in strength as typical antibody-antigen interactions.

Figure 1.

Bead-based multiplexed assay. Each element of array in the capture region is functionalized with a different protein, each targeting a specific protein that is coated on the micron-sized beads. Specifically bound beads on each element of the array are eluted selectively from the array and are quantified downstream (one element at a time). Here, applying voltage V₁ produces uDEP force, which in turn detaches the specifically bound beads from the surface of the 1^st interdigitated electrode pair (i.e. IDE 1). With no voltage applied at the other IDEs, the protein-bound beads on the respective elements remain attached to the surface.

In addition to its application in multiplexed protein analysis, our platform can potentially enhance the capability of DEP in statistical characterization of the strength profile of biological bonds. The multiplexed format enables performing force spectroscopy of multiple interactions independently in a single channel; minimizing inter-experiment variations that originate from disparities in buffer conditions and assay preparation steps. This approach can be particularly useful when characterizing specific vs. non-specific interactions simultaneously as it facilitates, under the same buffer condition, independent actuation of beads that are specifically bound to the functionalized electrodes (with pre-immobilized antibodies), as well as non-specifically bound beads that are attached to the ‘control’ (non-functionalized) electrodes. This ultimately helps with establishing optimal buffer conditions.

Theoretical Background and Design Methodology

Circuit Model

As mentioned earlier, to prevent the electrode corrosion we deposited a protective pinhole free nanometer-scale thin ALD oxide on our IDEs. From a circuit modeling perspective this insulative thin layer acts as a capacitance in series with the double-layer capacitance at the interface of the electrode-oxide-electrolyte interface, where the oxide capacitance due to its larger thickness and lower effective dielectric constant dominates. As shown in Figure 2(a), the oxide capacitance C_ox at each electrode terminal forms a voltage divider with the conductive solution buffer of resistance R. Formation of this voltage divider effectively causes an unwanted voltage drop V_C across the oxide films at each terminal end, resulting in degradation of electric field and available DEP force inside the solution buffer:

$$V_C=\left|\frac{1}{1+j2\pi f\frac{R{C}_{ox}}{2}}\right|\frac{V_{app}}{2}$$ (1)

Figure 2.

(a) Simplified electrical circuit model of two neighboring electrodes in an IDE pair. Conductive solution is modeled as resistance (R). The capacitance of the deposited oxide layer for each electrode-oxide-electrolyte interface is denoted by C_ox. The electrode coupling is modeled as parasitic capacitance C_par (b,c) Representative design space illustrating V_R,max for (b) t_ox = 10 nm and (c) 1000 nm, while meeting the oxide breakdown criterion (E_BR,ox = 1 V/nm) and instrumentation limitation (V_ac,max = 100 V, I_ac,max = 0.2 A), in the f vs. σ space (assumed 7 µm wide and 7 µm spaced electrodes).

As verified previously¹⁹ for a pair of neighboring electrodes, the oxide capacitance C_ox to the first order can be modeled as a parallel plate capacitance, with permittivity ε_ox, thickness t_ox, and area A_el (bound by the transverse width w_ch of the channel and width w_el of an electrode, equal to w_el×w_ch). Similarly, the buffer solution can be approximated as resistance R with conductivity σ and length s_el equal to that of the conductivity of the buffer and spacing of the electrodes respectively. The effective cross section of R can be estimated as A_el¹⁹. Therefore, V_C can be approximated as:

$$V_C\cong \left|\frac{1}{1+j\pi f\left(\frac{s_{el}}{\sigma A_{el}}\right)\left(\frac{{\epsilon }_0{\epsilon }_{ox}{A}_{el}}{t_{ox}}\right)}\right|\frac{V_{app}}{2}=\left|\frac{1}{1+j\pi f\left(\frac{s_{el}}{\sigma }\right)\left(\frac{{\epsilon }_0{\epsilon }_{ox}}{t_{ox}}\right)}\right|\frac{V_{app}}{2}$$ (2)

To extend the circuit model of the interface of a pair of neighboring electrodes and model the interdigitated configuration with n pair of electrodes, we simply need to consider the parallel combination of n neighboring electrode pairs. Regardless, the derived expression for V_C and our subsequent analysis (for the most part) remain unchanged, since the product RC_ox stays the same, in the parallel configuration. Equation 2 can further be re-organized and simplified to better capture the role of the geometrical (electrode spacing and oxide thickness) and operational (excitation frequency and buffer conductivity) parameters in V_C:

$$V_C\cong \frac{1}{\sqrt{1+{\left[\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\right(\frac{f}{\sigma }\left)\right(\frac{1}{t_{ox}}\left)\right]}^2}}\frac{V_{app}}{2}=\frac{1}{\sqrt{1+{\alpha }^2}}\frac{V_{app}}{2}$$ (3)

where we set $\alpha =\left[\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\right(\frac{f}{\sigma }\left)\right(\frac{1}{t_{ox}}\left)\right]$ to simplify the ensuing derivations. Similarly, for the given voltage divider, we can derive the voltage V_R across the buffer that enables the DEP force:

$$V_R\cong \frac{1}{\sqrt{1+{\left[\right(\frac{1}{\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}}\left)\right(\frac{\sigma }{f}\left)t_{ox}\right]}^2}}{V}_{app}=\frac{1}{\sqrt{1+{\left(\frac{1}{\alpha }\right)}^2}}{V}_{app}$$ (4)

If we are to minimize the undesired voltage drop V_C (or equivalently maximize V_R), and apply the most of V_app directly across the buffer, we need to maximize α. In this expression and for our case, ε_ox is 3.9, corresponding to the dielectric constant of SiO₂ that we used as the ALD oxide layer. We had the more favorable option of using higher dielectric constant ALD oxides Al₂O₃ (ε_ox,Al2O3 ~ 5), and HfO₂ (ε_ox,HfO2 ~ 20), however, from implementation point of view, our efforts in providing a strong PDMS-substrate bond (amenable to microfluidic pressure driven application) was only successful for the case of SiO₂. Furthermore, referring to the derived expression, it can be concluded that s_el can be increased to reduce the undesired voltage drop. However, one should keep in mind that this is achieved at the cost of weakening the electric field strength and subsequently the DEP force; hence its defeats our original purpose.

As a result, the effective design knobs for maximizing V_R are the operational parameters, f, σ, and V_app as well as the fabrication parameter t_ox. The value of f can be simply varied by exciting the electrodes at the desirable frequency, typically in the range of up to 10–100 MHz (for a high voltage excitation system). Moreover, σ can be set, if not restricted by prior implementation requirements, by using a solution buffer with the conductivity of interest (in the wash step), practically ranging from 0.1 mS/m (corresponding to that of the deionized (DI) water) to approximately 10 S/m (NaCl-concentrated-Phosphate Buffered Saline (PBS)²³). With regards to the practical range for t_ox, using techniques such as plasma enhanced chemical vapor deposition we can deposit oxide films of thicknesses down to 50 nm. To deposit thinner oxides, we have to resort to ALD which can typically provide pinhole free oxide layers down to a few nanometers.

In our design space, we need to take into account various constraints. The first constraint is imposed by the electric field oxide breakdown of our ALD thin film (E_BR,ox), which sets an upper bound on the electric field which can be dropped across the thin film (i.e. $E_{ox}=\frac{V_C}{t_{ox}}<E_{BR,ox}$):

$$E_{ox}=\frac{1}{\sqrt{1+{\alpha }^2}}\frac{V_{app}}{2t_{ox}}<E_{BR,ox}$$ (5)

The oxide breakdown criterion effectively limits our ability to simply increase V_app in order to compensate for the degrading effect of the oxide film. We denote V_app,max as the maximum voltage that can be applied at the electrodes, without exceeding the design constraints. To meet the oxide breakdown criterion (formulated by inequality 5) V_app,max can be computed as:

$$V_{\mathit{\text{app,max}}}\cong 2E_{BR,ox}{t}_{ox}\sqrt{1+{\alpha }^2}$$ (6)

Combining equations 4 and 6, yields the expression for maximum voltage V_R,max that can be applied across the buffer without causing oxide breakdown:

$$V_{R,\mathit{\text{max}}}\cong 2E_{BR,ox}{t}_{ox}\sqrt{\frac{1+{\alpha }^2}{1+\frac{1}{{\alpha }^2}}}=2E_{BR,ox}\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\left(\frac{f}{\sigma }\right)$$ (7)

Equation 7 from practical standpoint seems counter-intuitive and also contradictory to our motivation of maximizing the applied voltage across the buffer, as it shows our ability to apply V_R,max is independent of the oxide thickness. Additionally, it implies that we can indefinitely improve V_R,max, by increasing $\left(\frac{f}{\sigma }\right)$. This conundrum can be resolved by taking into account the instrumentation limitation. From instrumentation point of view, our ability to deliver high voltages at the electrodes is constrained by the maximum voltage amplitude at the output of the signal generator V_ac,max, as well as the maximum ac current I_ac,max that the signal generator can deliver to establish the desired voltage across the electrodes. The former translates to $V_{R,\mathit{\text{max}}}=\frac{V_{ac,\mathit{\text{max}}}}{\sqrt{1+{\left(\frac{1}{\alpha }\right)}^2}}$, while the latter sets $V_{R,\mathit{\text{max}}}=I_{ac,\mathit{\text{max}}}\left(\frac{R}{n}\right)\cong I_{ac,\mathit{\text{max}}}\left(\frac{s_{el}}{n\sigma A_{el}}\right)$ (recall n is the number of electrode pairs in our interdigitated configuration). Therefore, to accommodate for this limitations we revise V_app,max and V_R,max expressions accordingly:

$$V_{app,\mathit{\text{max}}}=\text{min}\{2E_{BR,ox}{t}_{ox}\sqrt{1+{\alpha }^2},V_{ac,\mathit{\text{max}}},I_{ac,\mathit{\text{max}}}(\frac{s_{el}}{n\sigma A_{el}}\left)\sqrt{1+{\left(\frac{1}{\alpha }\right)}^2}\right\}$$ (8)

$$V_{R,\mathit{\text{max}}}=\text{min}\left\{2E_{BR,ox}\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\right(\frac{f}{\sigma }),\frac{V_{ac,\mathit{\text{max}}}}{\sqrt{1+{\left[\right(\frac{1}{\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}}\left)\right(\frac{\sigma }{f}\left)t_{ox}\right]}^2}},I_{ac,\mathit{\text{max}}}(\frac{s_{el}}{n\sigma A_{el}}\left)\right\}$$ (9)

To better visualize the design space, in Figures 2(b) and (c) we respectively illustrated V_R,max for t_ox = 10 nm and 1000 nm that can be achieved, while meeting the oxide breakdown criterion (E_BR,ox = E_{BR,ALD SiO2} = 1 V/nm) and instrumentation limitation (here assumed V_ac,max = 100 V, I_ac,max = 0.2 A), in the f vs. σ space. Here we assumed the same IDE geometry as that outlined in ‘Fabrication’ section. As can be seen from these figures, deposition of thin oxide layer (10 nm vs. 1000 nm) provides more flexibility (i.e. wider range of frequency and buffer conductivity conditions) for applying the most of V_app directly across the buffer.

In addition to the electrical modeling aspects that are discussed above, we need to study the thermal behavior of our high ac voltage microsystem. Previously, simplified thermal models for similar electrode-electrolyte configurations have been proposed.^{24, 25} In this work, we build on these efforts and propose a comprehensive model which complements the previous works with more rigorous formulation of temperature increase. This, in turn helps to quantify the thermal constraints in our system more accurately.

Assuming the homogeneous buffer solution in the channel undergoes no phase changes, the general heat equation can be written as:

$$q_g(\mathbf{r},t)+\nabla .k\nabla T=\rho C_p\frac{\partial T}{\partial t}$$ (10)

where q_g is the rate of internal heat density generation, T is the temperature, and ρ, C_p, and k are density, specific heat, and thermal conductivity of the solution buffer respectively. In our case, heat density generation is due to Joule heating caused by the electric field inside the microchannel ($q_g=\sigma E_{RMS}^2$). Assuming steady state and negligible convective effects (low Rayleigh number), the heat equation can be reduced to:

$$k{\nabla }^{2}T+\sigma E_{RMS}^2=0$$ (11)

In our high ac voltage system, Joule heating may increase the temperature considerably in the channel, proportional to the generated power density $\sigma E_{RMS}^2$. Generally, the increase of temperature reduces the solubility of gas in liquid, and in particular, causes bubble formation in microfluidic devices and disrupts the intended operation. This directly limits our ability to apply high voltages in our design space, and more specifically sets an upper-bound on the term $\sigma V_R^2$.

To illustrate the proportionality of the raise in temperature with the generated power density, it helps to analyze a simplified and first-order thermal model of our device. As the channel transverse width is larger than the width and spacing of the electrodes (i.e. w_ch > w_el, s_el) and given the periodicity format of the IDE pair, we may assume a one-dimensional conduction in the direction normal to the plane of the electrodes. Furthermore, we assume that the electrodes are patterned on a substrate with thickness t_sub and thermal conductivity of k_sub, where the bottom of the substrate is kept at constant ambient temperature of T_∞. The side-walls and the ceiling of the channel can be considered as perfect thermal insulators (implying $\frac{dT}{dx}=0$ at the boundary), as in our context, the thermal conductivity of the PDMS housing is substantially smaller than that of the bottom glass substrate. For simplicity, we further suppose uniform internal heat generation of $q_g=\sigma E_{RMS}^2\cong \sigma \left[\right(\frac{1}{2}\left){\left(\frac{V_R}{s_{el}}\right)}^2\right]$ in an effective volume confined by the channel’s sidewalls and surface, and a plane that is at the distance w_el above the surface (corresponding to the volume with relatively strong electric field). Under the above assumptions, and using equation 11, temperature increase ΔT in the channel with respect to T_∞ can be estimated as:

$$\Delta T\cong (\frac{w_{el}}{2k_m}+\frac{t_{\mathit{\text{sub}}}}{k_{\mathit{\text{sub}}}})q_g{w}_{el}\cong (\frac{w_{el}}{2k_m}+\frac{t_{\mathit{\text{sub}}}}{k_{\mathit{\text{sub}}}})\sigma \left[\right(\frac{1}{2}\left){\left(\frac{V_R}{s_{el}}\right)}^2\right]w_{el}\stackrel{t_{\mathit{\text{sub}}}\gg w_{el}}{\overbrace{\cong }}\frac{1}{2}\left(\frac{t_{\mathit{\text{sub}}}{w}_{el}}{{s_{el}}^2}\right)\left(\frac{\sigma }{k_{\mathit{\text{sub}}}}\right){V_R}^2$$ (12)

$$\Delta T=\left(\frac{1}{\beta }\right)\left(\frac{\sigma }{k_{\mathit{\text{sub}}}}\right){V_R}^2$$ (13)

where $\beta =2\left(\frac{{s_{el}}^2}{t_{\mathit{\text{sub}}}{w}_{el}}\right)$ captures the role of geometrical dimensions. Here, we should note that for more accurate results, the exact coplanar IDE pair geometry (where electric-field, and thus, Joule heating are non-uniform) needs to be analyzed. In any case, our first order model correlates well with our COMSOL (COMSOL, Stockholm, Sweden) simulations of coplanar IDE pair (Figure 3(a)), demonstrating the proportionality of the temperature increase with Joule heating and imposing an upper-bound on σV_R² in our design space. To precisely model the thermal behavior of the coplanar configuration, β can be adjusted through calibration with simulation accordingly (in our case increased by ~30%). The discrepancy between simulation and analytical model in determining the value of β is mainly due to the method of approximation used to model the non-uniform electric field. To compare the exact electric field solution computed by the COMSOL simulation with that obtained from our analytical model see the supplementary information.

Figure 3.

(a) Proportionality of the raise in temperature with the generated power density (setting an upper-bound on $\sigma V_R^2$). By adjusting the value of β through calibration with simulation (in our case increased by ~30%) we can precisely model the thermal behavior of the coplanar configuration. Here, we assumed k_sub = 1.1 Wm⁻¹K⁻¹ and t_sub = 100 µm.(b) Representative design space illustrating relative maximum DEP force (proportional to Re{f_CM}V_R,max²) for a 10-nm deposited oxide that can be achieved for 7 µm wide and 7 µm spaced IDE pair geometry while meeting the design constraints. The limitations imposed by the dominant design constraints are annotated on the graph. −/+ values correspond to negative/positive DEP. For our application we prefer the most negative value.

Assuming bubble formation disrupts our operation upon temperature increase of ΔT_max (practically ~ 40–50 °C when operating at room temperature), we can rearrange equation 13, to obtain the expression for thermally limited maximum voltage V_R,max,th that can be applied across the buffer without causing bubble formation:

$$V_{R,\mathit{\text{max}},th}\cong \sqrt{\beta \left(\frac{k_{\mathit{\text{sub}}}}{\sigma }\right)\Delta T_{\mathit{\text{max}}}}$$ (14)

To sum up, based on the developed electrical and thermal models, in our high voltage corrosion-proof microsystem our ability to apply DEP-enabling voltage directly across the solution is constrained by oxide breakdown, instrumentation limitation, and temperature increase.Equation 15 below includes all these limiting phenomena, in a unified expression:

$$V_{R,\mathit{\text{max}}}=\text{min}\left\{2E_{BR,ox}\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\right(\frac{f}{\sigma }),\frac{V_{ac,\mathit{\text{max}}}}{\sqrt{1+{\left(\frac{1}{\alpha }\right)}^2}},I_{ac,\mathit{\text{max}}}(\frac{s_{el}}{n\sigma A_{el}}),\sqrt{\beta \left(\frac{k_{\mathit{\text{sub}}}}{\sigma }\right)\Delta T_{\mathit{\text{max}}}}\}$$ (15)

The above expression can be equivalently referred to input to compute V_app,max:

$$V_{\mathit{\text{app,max}}}=\text{min}\left\{2E_{BR,ox}\pi {\epsilon }_0{\epsilon }_{ox}{s}_{el}\right(\frac{f}{\sigma })\sqrt{1+{\alpha }^2},V_{ac,\mathit{\text{max}}},I_{ac,\mathit{\text{max}}}(\frac{s_{el}}{n\sigma A_{el}})\sqrt{1+{\left(\frac{1}{\alpha }\right)}^2},\sqrt{\beta \left(\frac{k_{\mathit{\text{sub}}}}{\sigma }\right)\Delta T_{\mathit{\text{max}}}[1+{\left(\frac{1}{\alpha }\right)}^2]}\}$$ (16)

As can be seen from all four constraints in equation 15, to maximize V_R, if not restricted by application requirements, it is best to use buffer solution with lowest available conductivity value. Setting the conductivity value would be a reasonable starting point in the design process, followed by deposition of nanometer-scale thin films and operating at highest frequency of excitation deliverable by the instruments. If limited by current delivery capability of instruments, one can consider reducing the number of the electrode fingers in the IDE configuration. Otherwise, in case a slight actuation delay can be tolerated, one can pattern multiple identical IDEs (arranged side-by-side) with proportionally less electrodes and simply switch through the IDEs and activate them consecutively. Furthermore, to reduce the temperature increase and to avoid bubble formation inside the channel, electrodes can be patterned on high thermal conductivity substrates (e.g. using silicon substrate with k_sub = 149 Wm⁻¹K⁻¹ vs. Pyrex with k_sub = 1.1 Wm⁻¹K⁻¹).

To complete our design methodology we should incorporate the above results in the context of our ultimate goal, i.e. maximizing the DEP force. We should note that tuning frequency of operation and conductivity of the buffer to achieve V_R,max does not necessarily allow us to achieve maximum DEP force, F_DEP,max. To illustrate our point, it helps to recall the first order expression for DEP force that is acting on a dielectric sphere:

$$F_{DEP}=2\pi {\epsilon }_0{\epsilon }_m{r}^3\text{Re}\left\{f_{CM}\right\}\nabla {\left|E_{RMS}\right|}^2$$ (17)

where ε_m is the relative permittivity of the surrounding medium, r is the particle radius. The term f_CM in the above equation is the Clausius-Mossotti factor which is related to the effective polarizability of the particle with respect to that of the medium, and can be written as:

$$f_{CM}=\frac{{\epsilon }_p^{*}-{\epsilon }_m^{*}}{{\epsilon }_p^{*}+2{\epsilon }_m^{*}}$$ (18)

where ε_p^* and ε_m^* are the relative complex permittivities of the particle and the medium respectively and both are frequency and conductivity dependent. The sign of the real part of the Clausius-Mossotti factor determines whether the particle is attracted to (positive DEP) or repelled from (nDEP) a region of high electric field strength. As can be seen from equations 17 and 18, F_DEP depends on both excitation frequency and conductivity of the buffer through f_CM and is proportional to the square of the electric field gradient, and equivalently, square of voltage V_R that is applied directly across the buffer. Therefore, in this context to achieve F_DEP,max we should ensure that the conductivity of buffer and frequency of operation are selected such that Re{f_CM}V_R,max² is maximized.Figure 3(b) illustrates the corresponding Re{f_CM}V_R,max² values in the frequency vs. conductivity space which includes all the constraints and considerations that have been discussed so far.

Results and Discussions

Following our developed design guideline, we deposited 20 nm oxide layer, operated at relatively high frequency of 1 MHz, used a low-conductive solution as our wash buffer and excited the electrodes at 50 V_pp to ensure that we are not limited by thermal effects. To illustrate the application of this enhanced and robust DEP device, we demonstrated the multiplexed actuation capability of our device using an array of 16 IDE pairs patterned along a single channel. First, in order to validate the developed circuit model and test the functionality and electrical connectivity of each of the IDE pairs, we measured the impedance spectrum of IDEs and compared them with the spectrum predicted by the model. Figure 4(a) illustrates the overlaid impedance spectrum curves corresponding to the model and four representative IDE pairs. The close agreement between the impedance spectrum curves for all IDEs ensures the same electrical capability and actuation performance across our array of electrodes.

Figure 4.

(a) Modeled vs. measured impedance spectrum of four representative IDEs. (b) Micrographs of five neighboring IDEs 1–5, where initially uDEP was off for all IDEs (row 1), and then uDEP was sequentially turned on by applying voltage at IDEs 1,2, and 3 (corresponding to rows 2,3, and 4).

To illustrate the robust multiplexed actuation capability of our device and 100% detachment of the protein-bound beads from each element of the array, we sequentially turned uDEP on by applying 50 V_pp (1 MHz) at the corresponding IDE pair. After each actuation step, we scanned other IDE pairs (with zero uDEP) to ensure their protein-bound beads have not been disturbed and remained attached to the surface (Figure 4(b)). We repeated the sequential actuation procedure, resulting in 100% bead detachment from each element of the array, with less than one-minute interval between each actuation step, to illustrate multiplex actuation capability in the time-span of a few minutes. This shows that for the envisioned immunoassay application, the amount of time required to sequentially actuate protein-bound beads, is shorter than the incubation time needed to perform such assays, and hence this approach does not significantly prolong the experiment.

In addition to multiplexed protein analysis, our platform enhances the DEP capability in statistical characterization of the force spectrum of biological interactions. The multiplexed format enables performing force spectroscopy on multiple IDEs independently, with high force dynamic range (given two orders of magnitude improvement in force strength offered by uDEP) in a single channel; minimizing inter-experiment variations that originate from disparities in buffer conditions and assay preparation steps. To illustrate this point, we repeated the IgG and anti-IgG assay procedure and ramped up the applied voltage at each of the IDE pairs one-by-one. For a given IDE and at each voltage (and hence F_DEP) increase step, we quantified the number of the detached beads to capture the detachment profile, as shown in Figure 5, which is informative of the distribution of binding forces that are holding the bead down to the surface through protein-protein interactions.

Figure 5.

Detachment percentage of protein-bound beads when ramping up the applied voltage at each of the IDE pairs one-by-one. The results represent the collective detachment profile when actuating anti-IgG-IgG bound beads using our 16-plex platform. The array format allows performing force spectroscopy multiple times while ensuring operation under the same buffer conditions and assay preparation steps (DEP force is proportional to the square of the applied voltage).

Given this force spectroscopy capability, our platform can be used to identify optimal buffer conditions or suitable reference force levels to differentiate between specific vs. non-specific interactions. For this application and using our device, we can study specific and non-specific interactions, by actuating specifically-bound beads (attached to the pre-functionalized IDEs) and non-specifically-bound beads (attached to the ‘control’ non-functionalized IDEs) independently, all while operating in the same microfluidic channel, ensuring the same exact buffer conditions.

Having achieved a robust electrokinetic multiplexed actuating platform, future efforts will be focused on integrating an impedance sensor²⁶ downstream to quantify the detached beads electronically at each actuation step, and fully realize an integrated electronic system. Additionally, we will use this device to quantify and compare various protein-protein interactions, and also validate new protein biomarkers in biological samples. Overall, we envision a plethora of possibilities for performing rapid and inexpensive multiplexed protein analysis, using this electronic device, for applications ranging from biomarker validation and global protein analysis to diagnostics.

Methods

Fabrication

To create the microfluidic channel with 200 µm width, 50 µm height, and 3 cm length, the master mold was patterned onto a silicon substrate using SU-8 photoresist. Next, PDMS (10:1 prepolymer/curing agent) was poured onto the master mold and allowed to cure at 80 °C overnight. Once the PDMS channel was formed, it was peeled off from the mold. Then, to create the channel’s inlet and outlet ports, two holes (2 mm in diameter) were punched, one at each end.

To fabricate the electrodes, we used standard evaporation and lift-off processing techniques. Here, we patterned an array of 16 IDEs, where each element of the array was spaced 700 µm apart from one another. Each IDE was made up of 28 electrode pairs (i.e. n = 28). The Au/Cr electrodes (with width and spacing of 7 µm for both) were fabricated on a glass substrate. Then, to passivate our electrodes, we deposited a 20 nm SiO₂ film using Atomic Layer Deposition (ALD) Fiji F202 system from Cambridge Nanotech. For this purpose, with the wafers transferred to the reaction chamber, high purity Ar was used as a carrier gas. Consecutive pulses of Tris[dimethylamino]Silane and O₂ plasma were generated, for a duration of 0.3 s and 20 s (at 300 W) respectively, achieving an effective deposition rate of 0.7 Å/cycle at 200 °C.

The PDMS microchannel and the oxide-deposited substrate containing the array of IDEs were then aligned and bonded together after standard oxygen plasma treatment, as the last step to create our device. This microfabricated device was then mounted onto a printed circuit board (PCB, Sierra Circuits Inc.) with an array of 16 switches dedicated to drive and control the electrical excitation of the corresponding IDEs patterned on the device. To interface the board with the device, we used a flex-PCB connector in conjunction with 3M z-axis adhesive film for flex-to-glass bonding. This interface solution worked well in our case. However, if we gear the platform for higher multiplexing (larger number of IDEs along the channel) and higher throughput (realized through parallel microfluidic channels, each containing an array of IDEs) applications, the density of electrode-electronics connections could become an issue. In that case, we have to resort to more sophisticated packaging solutions.

Sample Preparation and Surface Chemistry

To demonstrate the multiplexed functionality in eluting specifically-bound beads from the surface we chose anti-IgG and IgG interactions. As was shown previously, anti-IgG-IgG interaction is on the same order of magnitude in strength as typical antibody-antigen interactions^15,21. To perform this assay, 2.8 µm-diameter goat anti-mouse IgG covered beads were used (initially in 0.5% w/v suspension). 500 µL of this solution was washed with PBS (containing 1% Bovine Serum Albumin, BSA and 0.05% Tween) and resuspended in 100 µL of 30x-diluted PBS. To physically adsorb IgG molecules on the channel surface, mouse IgG (originally 2 mg/mL, diluted by ×100) was incubated in the channel for 20 minutes. Then, to eliminate non-specific binding, we introduced BSA (1 mg/ml) in the channel. The channel was flushed and filled with diluted PBS, prior to loading the anti-IgG beads, and performing the experiment. To test for binding specificity, and as a control experiment, the above steps were performed on a separate chip, minus the physical adsorption of mouse IgG, to ensure that non-specific binding is minimized in our assay.

Experiment Setup

The flow rate in the channel was controlled using a syringe pump (Harvard Apparatus, USA). To measure the impedance spectrum and validate the IDEs, we used an impedance spectroscope (Zurich Instruments HF2IS, Switzerland) and a transimpedance amplifier (Zurich Instruments HF2TA, Switzerland). This impedance spectroscope was also used as a signal generator and input to a high voltage 50 V/V amplifier (Trek 2100HF, USA) to excite the electrodes with sine wave at 1 MHz.

Conclusions

In conclusion, we have presented a methodological approach to analyze an enhanced DEP system from both a circuit analysis and an electrothermal view points. In our developed model, we have taken into account various phenomena and constraints such as voltage degradation (due to the presence of oxide layer), oxide breakdown, instrumentation limitations, and temperature. While we performed our analysis and simulations based on the device geometry we fabricated, the principles used in this work can be extended to a wide variety of geometries and buffer conditions in the general context of high ac voltage microsystems.

The results from this analysis were used to develop a robust multiplexed bead-based protein assay platform, which can also be potentially used to perform force spectroscopy on protein-protein interactions. The use of high voltage tolerant corrosion-proof uDEP electrodes in modulating the protein-bound beads was necessary to enhance the DEP force such that to overcome protein-protein interactions that are on the order of a few hundred pico-Newtons.

To perform multiplexed bead-based assay, we patterned an array of 16 uDEP devices along a single microchannel. By selectively applying voltage at each uDEP electrodes, we sequentially detached protein-bound beads from the surface of IDEs. In addition to multiplexed protein analysis, we illustrated the capability of our multiplexed uDEP platform in statistical characterization of the force spectrum of biological interactions. The enhanced DEP force strength allows higher dynamic range of actuation, as compared to the case with the non-uDEP (conventional DEP) IDEs of equivalent dimensions. Furthermore, the multiplexed format (each IDE dedicated to a specific interaction) along a single channel allows independent actuation of various interactions in a single microchannel, ensuring operation under the same buffer conditions; minimizing inter-experiment variations.

Future efforts will be focused on investigating the limits of using buffer properties (given its role in heat generation) to distinguish various interactions between proteins as well as gearing the multiplexed platform to study other antigen-antibody pair interactions. In parallel we will develop an electronic multiplexed protein biosensor, where we integrate the impedance sensor as a counter downstream to quantify the detached beads at each actuation step. This system will be ultimately used to detect a panel of protein biomarkers in human samples and will undoubtedly have a large impact on clinical medicine by equipping clinicians with a point-of-care diagnostic tool to provide personalized healthcare for their patients.