Operation of the concentration module

In a 2D microfluidic funnel of maximal and minimal width W and w, respectively [Fig. 1(a)], the hydrodynamic flow velocity at the centerline of the channel typically ranges from v0max×w/W to v0max, according to mass conservation laws, and similarly, the electric field spans Emax×w/W to Emax. Given that v0max is typically 50 mm/s (Table I), the Reynolds number is ∼0.01 and the flow is laminar. The use of electric fields neither induces detectable temperature change in the silicon chip nor does it alter DNA hybridization reactions, as we showed in Ref. 2727. I. Tijunelyte, R. Malbec, B. Chami, J. Cacheux, C. Dez, T. Leichlé, P. Cordelier, and A. Bancaud, Biosens. Bioelectron. 178, 112992 (2021). https://doi.org/10.1016/j.bios.2021.112992.

TABLE I. Electrohydrodynamic parameters for the microfluidic chip geometries used in this study as deduced from finite element simulations (see the Materials and Methods section).

Chip geometry2 μm4 μm6 μmGSLHydraulic resistance (1016 kg/m4 s)27.43.61.119.5Electric resistance (MΩ)13.87.95.912.0v0max (mm/s)37 (@ 5 bar)57 (@ 2 bar)61 (@1 bar)51 (@5 bar)Emax (kV/cm)23 (@ 290 V)20 (@ 290 V)12 (@290 V)17 (@190 V)The funnel shape is reminiscent of the geometry of dielectrophoretic trapping modules.35–3735. C.-F. Chou, J. O. Tegenfeldt, O. Bakajin, S. S. Chan, E. C. Cox, N. Darnton, T. Duke, and R. H. Austin, Biophys. J. 83, 2170 (2002). https://doi.org/10.1016/S0006-3495(02)73977-536. I.-F. Cheng, S. Senapati, X. Cheng, S. Basuray, H.-C. Chang, and H.-C. Chang, Lab Chip 10, 828 (2010). https://doi.org/10.1039/b925854j37. B. J. Sanghavi, W. Varhue, J. L. Chávez, C.-F. Chou, and N. S. Swami, Anal. Chem. 86, 4120 (2014). https://doi.org/10.1021/ac500155g Our actuation strategy is, however, very different because we apply continuous electric fields and dielectrophoretic trapping is most frequently based on high-frequency electric fields. Notably, a few contributions described DNA concentration by direct current insulator-based gradient dielectrophoresis,38–4038. S. Li, Z. Ye, Y. S. Hui, Y. Gao, Y. Jiang, and W. Wen, Biomicrofluidics 9, 054115 (2015). https://doi.org/10.1063/1.493217739. F. Camacho-Alanis, L. Gan, and A. Ros, Sens. Actuators B 173, 668 (2012). https://doi.org/10.1016/j.snb.2012.07.08040. R. C. Gallo-Villanueva, C. E. Rodríguez-López, R. I. Díaz-de-la-Garza, C. Reyes-Betanzo, and B. H. Lapizco-Encinas, Electrophoresis 30, 4195 (2009). https://doi.org/10.1002/elps.200900355 but the size of funnels of less than 100 nm and the elimination of hydrodynamic forces to achieve concentration cannot be compared to our experimental settings. Thus, we claim that DNA trapping in our module is enabled by a transverse force FVE perpendicular to the flow direction and oriented toward the upper and lower walls [shown in the xz plane of Fig. 1(a)]. We use a salty and viscoelastic solution (see the Materials and Methods section), implying that FVE arises from the variation of the normal stress in the gradient direction,4141. M. Socol, H. Ranchon, B. Chami, A. Lesage, J.-M. Victor, M. Manghi, and A. Bancaud, Macromolecules 52, 1843 (2019). https://doi.org/10.1021/acs.macromol.8b02184 rather than from hydrodynamic interactions around DNA created by the electric field.4242. R. J. Montes, A. J. Ladd, and J. E. Butler, Biomicrofluidics 13, 044104 (2019). https://doi.org/10.1063/1.5110718 As we showed in Ref. 4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C, this force FVE can be expressed analytically with a linear dependence on the hydrodynamic and electric field v0 and E, FVE→(z)∼−Nh×v0×E×(1−2zh)×uz→,(1)with z being the distance from the lower wall in Fig. 1(a), N is the size of the molecule, h is the channel height, and uz→ is the unit vector. Note that this transverse force depends on the equilibrium end-to-end distance of the chain N because hydrodynamic interactions are screened out in viscoelastic solutions and the Rouse model applies, as shown in Ref. 4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C. Fluctuations of the length of the molecules during their migration are discussed in Ref. 4141. M. Socol, H. Ranchon, B. Chami, A. Lesage, J.-M. Victor, M. Manghi, and A. Bancaud, Macromolecules 52, 1843 (2019). https://doi.org/10.1021/acs.macromol.8b02184.Equation (1) is valid for molecules far from the wall because it is derived by the reflection method.4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C In Ref. 4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C, we suggested an extrapolation for the force profile, considering that additional repulsive forces, including electrostatic and/or shear-induced electroviscous forces4444. O. Schnitzer and E. Yariv, J. Fluid Mech. 786, 84 (2016). https://doi.org/10.1017/jfm.2015.647 and/or lubrication4545. J. Klein, Annu. Rev. Mater. Sci. 26, 581 (1996). https://doi.org/10.1146/annurev.ms.26.080196.003053 forces, balance the viscoelastic transverse force. The resulting effective force vanishes toward the wall and may be approximated by a linear drop, following the expression Fwall→(z)∼−N×v0×E×zh2×uz→.(2)Note that expression (2) is valid for the lower wall in Fig. 1(a). Predictions based on this model have been successfully confronted to an extensive set of more than 300 data in Ref. 4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C.Let us now define the regime of operation of the concentration module. Far upstream from the constriction, hydrodynamic and electrophoretic velocities are low, and the transverse force can be neglected. Molecules reach the concentration module if the average flow velocity is greater than the electrophoretic velocity, equivalently v0max>2μ0Emax with μ0 the electrophoretic mobility. The sector represented in green in Fig. 1(b) corresponds to v0max<2μ0Emax. As molecules migrate toward the funnel, electrophoretic and hydrodynamic velocities increase, and so does Fwall. The concentration module operates if the regime of migration is dominated by electrophoresis at the apex of the funnel. Applying Boltzmann statistics to the transverse force in Eq. (2), we infer the average distance of the molecules to the wall zDNA that scales as (Nv0E/h2)−0.5. Linearizing the expression of the flow velocity near the bottom wall 4v0maxzDNA/h, the condition of dominant electrophoretic migration at the apex readsIf this condition is unfulfilled, the migration is dominated by hydrodynamics everywhere in the concentration module, and the corresponding sector is depicted in red in Fig. 1(b). In the light blue sector, hydrodynamic forces prevail over electrophoresis at the entry of the funnel, whereas electrophoresis is predominant at the tip of the apex. Hence, one position of balanced electrophoretic and hydrodynamic forces exists along the funnel, and hybridized DNA molecules, continuously conveyed toward, accumulate at this stagnation position. Moreover, unbound probes, which have a smaller molecular weight than the target:probe complex, undergo transverse forces of lower amplitude. They can thus be flushed out, and selective target detection is achieved, as was demonstrated in Ref. 2727. I. Tijunelyte, R. Malbec, B. Chami, J. Cacheux, C. Dez, T. Leichlé, P. Cordelier, and A. Bancaud, Biosens. Bioelectron. 178, 112992 (2021). https://doi.org/10.1016/j.bios.2021.112992. Notably, the resulting theoretical diagram is in qualitative agreement with that reported in Ref. 4646. M. Arca, A. J. Ladd, and J. E. Butler, Soft Matter 12, 6975 (2016). https://doi.org/10.1039/C6SM01022A based on experimental measurements of high MW genomic DNA.

Optimization of the concentration module

The phase diagram in Fig. 1(b) can be investigated experimentally by applying a constant electric field and gradually increasing hydrodynamic forces, or using a constant pressure and increasing the electric field [orange and purple arrows in Fig. 1(b), respectively]. We first report an experiment performed in a chip of 2 μm in height [Fig. 2(a)], in which v0max is set to 30 mm/s and Emax is increased stepwise. For each step indicated by the green dashed lines in Fig. 2(a), the position of stagnation shifts away from the constriction (see the selected snapshots recorded at times t1, t2, and t3). Below 21.5 kV/cm, each electric field step is associated with an increase in the maximum intensity [Fig. 2(b)]. At 22 kV/cm and above, the maximum intensity signal decreases, but the total fluorescence signal still rises (Fig. S4 in the supplementary material). This experiment shows that the concentration module is optimal for a set of electrohydrodynamic actuation parameters, which correspond to Emax of ∼21 kV/cm with this microchip geometry. The result is confirmed by the mirror experiment that consists in increasing the pressure at constant electric field while recording fluorescence intensity in the funnel [Fig. 2(c); this corresponds to the orange arrow in the diagram of Fig. 1(b)]. The signal is initially null in the concentration module because the migration is dominated by electrophoresis. Fluorescence intensity then increases to reach an optimum for v0max of ∼2.3, 2.9, and 3.1 cm/s depending on the salt concentration in the solution and decreases due to the leaks associated with a regime of concentration dictated by prevalent hydrodynamic forces.The kinetics of molecular accumulation can be used as a readout to optimize the performance of the concentration module. The inset of Fig. 2(b) shows that the typical time scale of concentration increases from 1 to 10 s as Emax increases from 16 to 21 kV/cm, respectively. The saturation of the signal after the concentration phase is explained by the occurrence of velocity fluctuations around the stagnation position, as described in Refs. 4141. M. Socol, H. Ranchon, B. Chami, A. Lesage, J.-M. Victor, M. Manghi, and A. Bancaud, Macromolecules 52, 1843 (2019). https://doi.org/10.1021/acs.macromol.8b02184 and 4343. B. Chami, M. Socol, M. Manghi, and A. Bancaud, Soft Matter 14, 5069 (2018). https://doi.org/10.1039/C8SM00611C. For a low electric field, the stagnation position is close to the apex, and fluctuations are likely to disengage T:P from the concentration module. The onset of the electric field forces T:P complexes to shift away from the constriction, reducing their chances to escape and, in turn, increasing their residence time in the module. Hence, the electric field allows us to increase the time of concentration and enhance the detection signal, making a connection between kinetics and performance.

Long targets and short probes enable high sensitivity detection

The technology is expected to concentrate high MW targets more rapidly because they undergo larger transverse forces and can thus be captured with a higher hydrodynamic flow for a given electric field [see Eq. (2)]. This hypothesis has been tested by measuring the concentration of four different targets of increasing MW of 44, 98, 114, and 120 nt (see the definition of genomic sequences in the Materials and Methods section). Using the same electrohydrodynamic actuation associated to v0max and Emax of 30 mm/s and 23 kV/cm in a microfluidic chip of 2 μm in height, the maximum intensity after 60 s of actuation increases with the size of the target [Fig. 3(a)]. Moreover, the spatial distribution of concentrated targets becomes more distant from the apex with the size of the target, as indicated by the orange arrow in the snapshots of Fig. 3(b). Moreover, the concentration kinetics become slower [Fig. 3(c)], in agreement with our discussion on the relationship between the time of concentration and the accumulation position (see above). Interestingly, the peak fluorescence signal is enhanced by 27-fold between the 120 and 44 nt target [black and purple curves in Fig. 3(a), respectively], and the difference in signal is consistently observed for a broad range of electric fields, as reported in Fig. S5 in the supplementary material.These experiments also show that the difference of size between the target and the probe is critical to achieve high sensitivity and selective signals. Indeed, the signal of a single strand of 98 nt is 37% lower than that of a complex formed by pairing 22 nt SP with 92 nt LT, the so-called target of 114 nt (blue and green curves in Fig. 3). Conversely, we do not detect any signal for the 22 nt probe under these actuation conditions (not shown) and collect the maximum signal with the 120 nt complex. Consequently, the concentration module works optimally with a long target of more than ∼100 nt and a short hybridization probe of less than ∼30 nt.

Grayscale microfluidic chips to enhance the LOD by 100-fold

In our recent study on short targets of 25 nt, we reported an LOD of 2 pM in microchips with a channel height of 2 μm.2727. I. Tijunelyte, R. Malbec, B. Chami, J. Cacheux, C. Dez, T. Leichlé, P. Cordelier, and A. Bancaud, Biosens. Bioelectron. 178, 112992 (2021). https://doi.org/10.1016/j.bios.2021.112992 Here, using the same microfluidic chip, we reach a tenfold enhanced limit of detection of 0.2 pM with the long target and short probe [blue dataset inFig. 4(a), see details of calculation in the Materials and Methods section]. In order to enhance these performances, we aimed to increase the flow rate to accumulate more DNA complexes during the concentration process. For this, we fabricated microfluidic chips of 4 and 6 μm in height. The hydraulic resistance of the chips indeed scales as h−3, implying that the flow rate sharply increases by 26-fold for a threefold increase of the channel vertical dimension (Table I). The electric field is, on the other hand, less confined at the apex when the height increases, i.e., the gradient of voltage is more evenly distributed throughout the chip. Emax decreases by twofold as h increases from 2 to 6 μm (Table I). Notably, the scaling of the electrical resistance of h−1 is not observed because the contribution of the thick lateral channel cannot be neglected (see size specifications and calculations in the supplementary material).Using the maximum electric field of 290 V that the oxide layer could withstand, detection is achieved at relatively low pressures of 2 and 1 bar for h of 4 and 6 μm, respectively. Despite the possible application of more pressure (our system can deliver 5 bar), the low value of the electric field in these 2D chips (gray lines in Table I) prevents us from taking advantage of the reduced hydraulic resistance. The resulting electrohydrodynamic actuation parameters v0max and Emax are comparable to that used in the 2 μm chip (Table I). The kinetics of concentration is rapid with a plateau after ∼4 s [Figs. 4(b) and 4(c)], indicating a leaky regime due to the insufficient strength of the electrophoretic force. The LODs of 4 and 5 pM are determined for chips of 4 and 6 μm, respectively, i.e., an order of magnitude higher than the one obtained with 2 μm chips [Fig. 4(a)]. Albeit the enhanced flow rate in thick microfluidic chips, the electric field becomes limiting to reach a regime of efficient concentration.In order to deliver high flow rates and high electric fields, we used GSL to produce a channel with a height gradually decreasing from 5.2 to 1.9 μm [Fig. 5(a)]. This geometry indeed enables us to increase v0max by 40% in comparison to the 2 μm chip (Table I). Furthermore, the spatial extent of the concentration region, as measured by the intensity profile along the symmetry axis of the channel [red arrow in Fig. 5(a)], can be significantly reduced in GSL chips. Setting v0max to 15, 56, and 51 mm/s, the full width at half maximum decreases from 67 to 49 to 24 μm, respectively [light green, dark green, and black curves in Fig. 5(b)]. Moreover, the width of the target band in the 4 and 2 μm chips [blue and orange datasets in Fig. 5(b), respectively] of 135 μm compare unfavorably to that in the GSL chip. T:P concentration occurs in a region typically reduced by (135/24)2–30-fold, allowing us to reach enhanced detection performances with an LOD of 4 fM [Fig. 5(c)], i.e., threefold lower compared to our previous report.2727. I. Tijunelyte, R. Malbec, B. Chami, J. Cacheux, C. Dez, T. Leichlé, P. Cordelier, and A. Bancaud, Biosens. Bioelectron. 178, 112992 (2021). https://doi.org/10.1016/j.bios.2021.112992 This performance is explained by the use of long targets and the design of GSL chips, which feature equal gains in sensitivity of 27- and 30-fold, respectively. Furthermore, the dynamic range using the same electrohydrodynamic actuation settings is five decades [Fig. 5(c)], and the concentration kinetics are insensitive to the target concentration [Fig. 5(d)] with a time scale of 16 s, as inferred from exponential fitting. Notably, the global turnaround time of our assay, including target:probe incubation, sample loading in the chip, and image analysis is on the order of 1 h. Nevertheless, our technology appears as a good trade-off between sensitivity and time to result. While a sub-fM level of detection can be achieved by nanosensors,77. M. I. H. Ansari, S. Hassan, A. Qurashi, and F. A. Khanday, Biosens. Bioelectron. 85, 247 (2016). https://doi.org/10.1016/j.bios.2016.05.009,8 the response time is on the order of 20 min for nanopore, nanowire, cantilever, or surface acoustic wave sensors. Record performances, which feature an LOD of 10−17 M in 4 min with quartz microbalance,4747. Z. Mo, H. Wang, Y. Liang, F. Liu, and Y. Xue, Analyst 130, 1589 (2005). https://doi.org/10.1039/b500949a 10−15 M in 30 s using nanowires,4848. A. Gao, N. Lu, Y. Wang, P. Dai, T. Li, X. Gao, Y. Wang, and C. Fan, Nano Lett. 12, 5262 (2012). https://doi.org/10.1021/nl302476h or 10−15 M in 4 min with nanopores,4949. M. Wanunu, T. Dadosh, V. Ray, J. Jin, L. McReynolds, and M. Drndić, Nat. Nanotechnol. 5, 807 (2010). https://doi.org/10.1038/nnano.2010.202 compare relatively favorably with our technology.Let us determine the number of complexes trapped in the concentration module. Given that the flow rate is 0.2 μl/min (Table I), we expect to process a volume of ∼0.1 μl after 30 s of concentration. Therefore, for a target concentration of 20 fM, ∼1200 molecules are accumulated in the concentration volume. The background signal is produced by probes at a concentration of 20 nM, which amounts for 1800 molecules in the concentration volume of 23 × 3.5 × 1.9 μm3 (see the characterization of the detection volume Fig. S6 in the supplementary material). The readout signal is indeed equal to 1.8 times the background in our experiment (Fig. S7 in the supplementary material). Taken together, we conclude that GSL chips enable us to enhance detection by nearly 100-fold with no compromise on the concentration kinetics and on the dynamic range, as well as with electric field settings of 190 V that are less prone to induce oxide breakdown.DNA detection in biological samples (e.g., body fluids)5050. R. Malbec, J. Cacheux, P. Cordelier, T. Leichlé, P. Joseph, and A. Bancaud, Micro Nano Eng. 1, 25 (2018). https://doi.org/10.1016/j.mne.2018.10.003 raises complications due to the large amounts of background molecules, which lead to non-specific interactions, as well as to ionic conditions. We already studied whether and to what extent background species in purified and unsalted solutions impaired the detection of our technology.2727. I. Tijunelyte, R. Malbec, B. Chami, J. Cacheux, C. Dez, T. Leichlé, P. Cordelier, and A. Bancaud, Biosens. Bioelectron. 178, 112992 (2021). https://doi.org/10.1016/j.bios.2021.112992 Here, we further investigate that detection using GSL chips operates in unpurified plasma, i.e., with a salty solution as well as background protein and nucleic acids. Using equimolar concentrations of target and probes of 20 nM, we spike the running buffer with gradual amounts of plasma of 17%, 50%, and 100% (Fig. S8 in the supplementary material). Detection is obtained in 17% and 50% plasma-containing solutions with a moderate to an important decrease of the signal by 30% and 60%, respectively. Detection was not achieved in 100% plasma samples due to oxide layer breakdown and irreversible damage of the chip. The salinity of biofluids is a harsh environment for silicon based microfluidic devices due to oxide insulating layer breakdown and to a lesser extent Joule heating. Nevertheless, our results suggest that DNA detection can be operated in plasma provided that the sample is diluted typically fivefold before analysis.