DC corral trapping of single nanoparticles and macromolecules in solution

Methods for manipulating single molecules in aqueous solution are key for the controlled assembly of molecular-scale devices and are expected to lead to new analytical tools, sensors, and devices for biomedical diagnosis with single molecule sensitivity.^1,2 They are also valuable for studying biophysical processes that are limited by diffusion over extended periods of time. Over the years, some new and promising techniques have been developed for confining nanoscale material in aqueous solution. For example, nanoparticles have been trapped in an aqueous Paul trap,³ near structured glass surfaces such as pockets^4,5 and apertures,⁶ in size-tunable magnetic traps,⁷ and by highly localized thermal gradients.⁸ 

Only few techniques, however, have been successfully employed to trap molecular-size particles (either individually or in larger numbers). Dielectrophoretic and optical forces were used to attract DNA,^9–11 nucleotides,¹⁰ proteins,^12–15 and nanoscale particles^16,17 to regions of high-field gradients near surfaces. The proximity of solid–liquid interfaces and high-field strengths, however, is known to be a source for structural changes such as stretching¹⁰ and unfolding¹⁴ that can alter the biological function of the trapped molecule. Similar effects have been observed when single DNA molecules were trapped at the stagnation point in a hydrodynamic trap;¹⁸ a micropipette-based version has been used to accumulate membrane proteins under the aperture.¹⁹ 

More gentle, quasi-electrostatic forces are employed in the anti-Brownian electrokinetic trap,^20–23 allowing manipulation of single molecules in their native solution environment. It uses a feedback-driven electric field to counteract the Brownian motion of a selected molecule in solution but requires complex hardware and continuous real-time monitoring of particle position and can only trap a single object at a time. The question thus arises whether a trap for nanoparticles and single molecules can be devised that shares many of these advantages but does not require any feedback loop or location information for continuous particle confinement.

This question has motivated our conception of the corral trap,²⁴ which uses intrinsic electrokinetic forces to confine charged micro- and nanoscale objects and even single molecules to nanoscale dimensions in solution and without any external feedback control. Trapping occurs in low-field regions, which is especially favorable for the gentle manipulation of biomolecules. Recently, we have shown that AC voltages applied to corral traps can be used for size-selective, dielectrophoretic trapping of microscale particles.^25–27 Here, we present experimental results on using DC voltages with corral traps for the controlled, reversible trapping of a single DNA molecule and other charged micro- and nanoparticles in dilute aqueous electrolyte and demonstrate that stable confinement can be achieved over extended periods of time. We further show that trap stiffness is controlled by the applied voltage and that both exclusive trapping of a single particle or simultaneous trapping of multiple particles can be achieved.

Corral trapping occurs due to a void in a conductive layer (such as a metal film) that is electrically charged and exposed to sample solution. Such patterned metal films can be created using photolithography techniques but can also be obtained through simple shadow evaporation,²⁴ as is the case for the experiments presented here.

Corral traps consisted of circular, uncoated areas 10.0 µm in diameter in a thin metal film on a glass substrate [Fig. 1(a)]. Sample solution was sandwiched between the corral trap electrode and a top coverslip [Fig. 1(b)] so that a solution layer with a height of less than 1 µm was formed (correspondingly higher solution layers were used in the microsphere experiments). A stabilized DC power supply connected to a building ground delivered charges to the corral trap. The resulting distribution of charges on the metal surface and especially around the rim of the trap generates an electric field that is responsible for trapping. While a grounded, metalized top coverslip would increase the charge density on the trapping electrode, it would also lead to electrolysis and solution squeezing between the oppositely charged electrodes. Instead, we made use of the small (but unknown) self-capacitance of the thin metal film, which was sufficient for trapping in the cases reported here; other experimental setups are currently under investigation to improve consistency. The assembly was mounted onto an inverted wide-field microscope for observation in brightfield or epifluorescence mode [Fig. 1(c)].

A first set of experiments was carried out with negatively charged, 2.0 μm diameter microspheres in solution flow. As soon as a microsphere moved into the trapping region, the corral trap was negatively charged by applying a potential of −10 V. As shown in Fig. 2(a), the microsphere remained trapped while the potential was applied and was released when the charges were removed from the trapping electrode. The clear correlation between the particle confinement and applied potential as well as the reversibility of the event demonstrates that nonspecific binding to the exposed glass substrate is not responsible for the observed behavior. The movement of the trapped particle drops immediately after trap activation, as evidenced by the frame-to-frame displacements shown in Fig. 2(b), while free microspheres far away from the active trap are largely unaffected.

Microspheres heading toward an active trap are deviated, however, as can be seen from particle trajectories shown in Fig. 2(a). Thus, in contrast to the dielectrophoretic traps mentioned above, the corral trap is non-aggregating (exclusive), i.e., it confines a single particle over an extended period of time without admitting other particles into the trapping region.

A more negative applied potential (−20 V) leads to higher charge density on the corral trap, resulting in tighter particle confinement and reduced motion as evidenced by the almost stationary position of the trapped particle in the top row of Fig. 2(c), the speed histogram in Fig. 2(d), and the first half of the time trace in Fig. 2(e).

If desired, multiple particles can be trapped simultaneously as shown in the bottom row of Fig. 2(c). The microsphere indicated by an arrow in frame 70 was admitted into the corral trap by temporarily pulling its potential to 0 V, which resulted in the successful trapping of both microspheres; they performed a circular motion around a common center until they were released through trap deactivation. It is interesting to note that these “dancing microspheres” kept a constant distance from each other, as dictated by their charges and the charge density on the surrounding charge corral. Moreover, both microspheres have similar average distances from the trap center (supplementary material, Fig. 1) and show the same drop in particle speed [Fig. 2(e)], which is expected as both carry a comparable charge.

Corral trapping was also successful with the smallest commercially available carboxylate-modified polystyrene beads (mean diameter 21 nm). They typically carry ∼900 carboxyl groups each although the effective number of charges at higher pH is probably smaller due to charge shielding by strongly bound cations and incomplete deprotonation in proximity to high local charge concentrations. The fluorescence images in Fig. 3(a) show the trapping of a nanobead, which remained stably trapped until the trap was turned off about 2 min later. In other experiments, nanobeads were trapped for more than an hour and successfully released by trap deactivation.

Trajectories of nanobeads at different applied potentials [Fig. 3(b)] were reconstructed by tracking the bead positions across 100 video frames recorded at each trapping potential using super-resolution localization methods.^28–31 Again, the results show that tighter confinement is achieved at higher applied potentials. Note that there is a small but noticeable offset between the geometric trap center and the mean of bead positions, which cannot be explained by Stokes drag (the solution flows from top to bottom) but may be due to small defects or non-uniformities in the metal layer.

The bead positions at each trapping potential can be fit to a two-dimensional Gaussian distribution function [Fig. 3(c)]. If the potential is harmonic, $Ux,y=12k(x−x0)2+(y−y0)2$⁠, the Boltzmann probability P of finding the particle at coordinates (x, y) becomes

where (x₀, y₀) defines the trap center, k is the trap stiffness (which is the same along x and y due to symmetry), k_B is the Boltzmann constant, and T is the absolute temperature. This means that the trap stiffness k can be estimated from the variance σ² = k_BT/k of the Gaussian fit to the recorded x and y positions, which evaluates to 3 × 10⁻⁴ pN/nm at −30 V. This compares favorably with a trap stiffness of 10⁻³ pN/nm³² for comparably sized gold nanoparticles in single-beam optical tweezers at high laser power; under the same conditions, dielectric particles of the same size experience an ∼6–7 lower optical trap stiffness³³ due to their reduced polarizabilities.

If the force acting on the particle derives from a harmonic potential and is directly proportional to the electric field, then the trap stiffness k should scale linearly with the charge density and therefore with the applied potential ϕ. A plot of the variance σ² as a function of the 1/ϕ should then be linear; however, the data show that σ² increases more rapidly than 1/ϕ. This can, in part, be attributed to a continued axial repulsion of the negatively charged nanoparticle as the applied potential is sequentially changed from −30 to −20, −15, and −10 V; at larger axial distances, the trap stiffness decreases, resulting in greater-than-expected values of σ². It is more likely, however, that the main reason lies in the anharmonicity of the trapping potential and the phenomena underlying the trapping mechanism.

Several electrokinetic phenomena could be at the origin of the observed behavior with the most important ones being the direct electrostatic and dielectrophoretic interactions of the charged particles with the non-uniform electric field generated by the corral trap. To model these interactions, we calculated the electric field by numerically solving Gauss’s law using a finite element method (FEM) simulation software. Due to the cylindrical symmetry of the problem, only the field distribution in a cross-sectional plane normal to the substrate and containing the center of the trap needs to be simulated (2D axisymmetric model).

While it is straightforward to carry out electric field simulations using FEM in systems containing two electrodes held at different potentials, modeling the electric field in proximity to a non-uniform surface charge distribution on a single electrode is more involved. To do this, we introduced an imaginary, plane-parallel counter electrode and carried out a geometry sweep where the distance of separation between the corral trap electrode and the counter electrode was increased from 1 µm to 1 mm. To maintain the surface charge density on the corral trap electrode during the sweep, the potential difference was also increased from 1 to 1000 V. The corral trap electrode was assigned the higher potential, which was arbitrarily set to 0 V.

In the region of interest for corral trapping, i.e., at axial distances up to a few μm, the electric potential values converge rapidly as the electrode separation increases, which is exemplified by the line plot in Fig. 4(a). Starting at an electrode separation of 30 µm, the plots become essentially indistinguishable from the plot for the 1 mm case (which represents the best model for a charged corral trap electrode). The same trends were observed at 40501 grid points in the region of interest, which were evenly spaced in the lateral and axial direction (every 50 nm from the trap center out to 20 µm and every 50 nm from 0 to 5 µm, respectively). As shown in Fig. 4(b), the magnitudes of the errors relative to a 1 mm electrode separation drop quickly as the electrode separation increases. At 50 µm electrode separation, both the maximum and mean relative errors are below 0.25%—a great improvement over the 70% maximum relative error (mean: 19%) for an electrode separation of 1 µm.

For all further calculations, we therefore used an electrode separation of 50 µm as an accurate model for the charged corral trap electrode; any additional gains due to larger electrode separation are insignificant and come at a higher computational cost. It was further verified that the calculated electric potentials scale linearly with the potential difference at constant electrode separation, which means that the qualitative features of the model do not depend on the actual potential difference chosen for the simulations.

The electric field $E⃗$ surrounding the charged corral trap electrode is indicated by the arrows in Fig. 5(a). The colored background represents the electric potential Φ from which the electric field derives (⁠$E⃗=−∇⃗ϕ$⁠) with equipotential lines at regular intervals drawn in black. The electric field is proportional to the force $F⃗$ that a positively charged particle experiences (⁠$F⃗=qE⃗$⁠, where q is the particle charge); the same force acts on a negatively charged particle if the corral trap electrode is negatively charged, as is the case for the experiments described above. It can be seen that the electric forces generated by the charged corral trap electrode repel a like-charged particle upward and—if the particle is in the trapping region—toward the corral trap axis, which is consistent with the observed trapping behavior.

Dielectrophoresis (DEP) is the motion of a polarizable particle in a spatially non-uniform electric field and can be directed toward high-field (positive DEP) or low-field regions (negative DEP) depending on the electrical properties of the particle and surrounding medium. The DEP force acting on a spherical particle³⁴ is given by

where ɛ_m is the (absolute) permittivity of the suspending medium, R is the radius of the suspended particle, $∇⃗E2$ is the gradient of the square of the electric field, and Re[CM] is the real part of the (frequency-dependent) Clausius–Mossotti factor. Positive values of Re[CM] lead to positive DEP (the dielectrophoretic force points in the direction of the steepest increase in E²), while negative values lead to negative DEP.

Under DC conditions, the Clausius–Mossotti factor reduces to, Ref. 35,

where σ_p and σ_m are the conductivities of the particle and suspending medium, respectively. If σ_m > σ_p, which is the case for particles of low conductivity suspended in a strong electrolyte, the Clausius–Mossotti factor is negative and negative DEP is observed. This is consistent with the measured conductivity of the medium (NaOH at pH 10), σ_m = 11.2 µS/cm, and typical literature values for carboxylate-modified polystyrene beads that are in the range of σ_p = 1–5 µS/cm.³⁶ 

Like the electrostatic force acting on a charged particle, we can separate the dielectrophoretic force acting on a spherical particle into a part that depends on particle and medium properties (namely, the factor up to and including the Clausius–Mossotti factor) and a part that depends on field properties (the gradient term). In analogy to the definition of the electric field, we will therefore refer to $−∇⃗E2$ as the dielectrophoretic field $E⃗DEP$ for the purpose of this discussion.

The dielectrophoretic field created by the charged corral trap is pictured in Fig. 5(b). It is strongly concentrated around the trap rim and at locations inside the corral trap and points downward and toward the trap center, while it points outward anywhere outside of the trap. Because $E⃗DEP$ and $F⃗DEP$ are colinear for our negative-DEP particles, a particle that is in the trapping region is therefore pushed toward the trap center, which is again in agreement with the observed trapping behavior. Contrary to the electrostatic force, however, the dielectrophoretic force pushes a trapped particle toward the bottom of the trap. In addition, unlike the electrostatic force, the dielectrophoretic force pushes particles away from the corral trap as they are approaching the (charged) trap, which explains the particle deviations observed in the experiments.

Other electrokinetic effects that may have an influence on trapping include electro-osmosis and electrohydrodynamic flow. Lateral potential gradients within the fluid polarization layer above differently charged surfaces lead to tangential electric fields that can induce convective currents of counterions, resulting in particle aggregation in the high-field region. This electrohydrodynamic flow (EHD) has been observed at the interface between dielectric and conductive regions³⁷ and between regions of different faradaic or photoinduced current densities.^38,39 While it is expected that EHD flow is present during corral trapping, it cannot fully explain the observed behavior; for example, particle confinement in the corral trap occurs in the low-field region and is exclusive, i.e., averts particle aggregation.

The same is true for a related electrokinetic effect, namely, electroosmotic flow (EOF), which is bulk fluid flow due to the migration of counterions in the mobile polarization layer next to a charged surface when a tangential electric field is externally applied. EOF is also known to exist above certain dielectric substrates when brought in contact with aqueous solutions; silica surfaces, for example, spontaneously acquire a negative surface charge due to the deprotonation of silanol groups in neutral and alkaline media. However, EOF is known to promote aggregation^40,41 or, in some cases, separation,⁴² which is not observed in our single- and dual-trapping experiments.

While the qualitative features of DC corral trapping are accounted for by our model, we acknowledge that complications occur due to the establishment of an electric double layer near the corral trap electrode surface under DC conditions. At first sight, it may appear that the predicted Debye length of only 30 nm for a 10⁻⁴ M 1:1 electrolyte would make electrostatic trapping impossible a few Debye lengths into the solution, but this view is overly simplistic for several reasons. First, it is well known that predictions from Gouy–Chapman–Stern-type electrolyte theories⁴³ result in unrealistically high ion concentrations near electrodes due to the point charge and mean field approximations, especially at higher applied potentials. Mean field theories that explicitly account for the ion size³⁸ predict more far-reaching screening lengths, but they are still considered problematic for applied potentials beyond a few 100 mV,^44,45 a regime for which a complete electrolyte theory is still lacking.⁴⁶ In addition, most importantly, all current theories implicitly assume an equilibrium with an infinitely large reservoir of ionic charges, an assumption that no longer holds for the finite, microliter volumes of dilute electrolyte solution used here. As a result, the double layer is much more diffuse, and the electrostatic field penetrates much deeper into the ion-depleted solution than predicted by electrolyte theories. Experiments and theoretical work to address these questions in greater detail are currently underway.

Based on the successful nanobead confinement, we proceeded with the trapping of a single biomolecule with comparable charge load, namely, 800-nucleotide long, single-stranded deoxyribonucleic acid (800-nt ssDNA) in standard buffer solution. To counteract the increase in electrolyte concentration, the sample was spin-coated onto the corral trap and covered by a top coverslip as described earlier. Each ssDNA molecule was covalently linked to a single Cy3 fluorophore and imaged by fluorescence excitation using an electron-multiplying CCD camera.

The successful corral trapping of a single ssDNA molecule is shown in Fig. 6(a). Intermittency in fluorescence emission (blinking) was observed several times during the experiment [Fig. 6(b)], confirming that the observed fluorescence spots are due to single molecule emitters. Dark periods lasting 300–400 ms on average are attributed to photoinduced, triplet state mediated charge transfer to the DNA backbone.⁴⁷ It is worth noting that during dark periods, the molecule remained stably trapped even though its exact position was unknown: corral trap confinement only depends on the presence of charges and does not require position information.

Once a single ssDNA molecule was trapped, the applied potential was cycled from −30 to −10 V and back to −30 V in steps of 10 V, and trajectories were reconstructed from 2D Gaussian fits as before [Fig. 6(c)]. The excursions from the trap center increase with decreasing applied potential, and the plot of σ² as a function of 1/ϕ now exhibits a more linear relationship, as expected from a harmonic potential well (supplementary material, Fig. 2). This indicates that the ssDNA remained at the same axial distance from the trap throughout the experiments, as further evidenced by the −30 V histograms of particle excursions, which are almost identical at the start and end of the experiment. The ssDNA molecule remained trapped for 70.9 s until the charges were removed from the corral trap, even during times when the particle location was not monitored. It was again observed that the corral trap acted locally and exclusively (supplementary material, Fig. 3). The trap stiffness varied from about 2 × 10⁻⁶ pN/nm at −10 V to more than 1.6 × 10⁻⁴ pN/nm at −30 V, similar to the 20 nm nanobead experiments.

Corral traps were fabricated as previously described²⁴ by thermal evaporation of ∼5 nm 60:40 Au–Pd or Ni–Cr onto a cleaned, 25 × 25 mm² glass coverslip masked with 10.0 μm diameter polystyrene spheres followed by removal of the spheres with toluene. The cleaning of coverslips was found to be more effective using the following series of 15 min sonication steps: acetone at 35 °C (VWR BJ010-4, HPLC grade), methanol at 35 °C (Sigma-Aldrich 650609, HPLC grade), dichloromethane at room temperature (VWR DX0831-6, HPLC grade), and isopropyl alcohol at 35 °C (Sigma-Aldrich 650447, HPLC grade). Higher quality corral traps were obtained by cleaning the solution of polystyrene beads that served as masks for the shadow evaporation step. The original polystyrene bead stock solution was first centrifuged to separate the beads from most of the solvent, and the beads were resuspended in an equal volume of ultrapure water (Sartorius Arium 611V). This procedure was repeated four times, resulting in little or no impurities at the base of the beads after solvent evaporation as confirmed by scanning electron microscopy.

After visual and electrical characterization, a single copper wire was attached to one corner of the corral trap using silver paste or carbon tape and connected to a stabilized DC power supply (BK Precision 9123A). We note that the formation of gas bubbles has never been observed during any of the trapping experiments although potentials much higher than the room temperature electrolysis threshold of water were applied over extended periods of time. The absence of faradaic activities is consistent with the fact that no direct conductance pathway exists across the solution to the building ground.

1 µl of sample solution (bead solutions titrated to pH 10, ssDNA in TBE buffer consisting of 44 mmol/l Tris, 44 mmol/l boric acid, and 1 mmol/l EDTA) was applied, covered with an 18 × 18 mm² top coverslip and mounted onto an inverted microscope (Zeiss Axiovert 200M). Directional flow was induced either by applying gentle pressure to one side of the sample chamber or by tilting it slightly. Brightfield and fluorescence imaging was performed using an electron-multiplying CCD camera (Photometrics Cascade II:512) with a ×100 oil immersion objective (Zeiss α-Plan-FLUAR 100X/1.45) using either the microscope’s halogen lamp or the 514.5 nm line of an argon ion laser (Spectra-Physics Stabilite 2017-AR), respectively. Laser light was coupled into the back port of the inverted microscope and focused near the back focal point of the microscope objective (epifluorescence mode). A set of optical filters adapted to the laser line and the fluorescence emission characteristics of the investigated samples were used to suppress excitation light in the fluorescence images (excitation filter z514/10, dichroic filter z514rdc, emission filter hhq519lp, Chroma).

To ensure that the observed particle motion was not influenced by drift of the sample stage, control experiments were conducted on immobilized fluorophores. A dilute solution of protoporphyrin IX (PPIX) in dimethyl sulfoxide was added to a solution of PMMA in toluene (8.2 g l⁻¹), and a thin film was produced by spin coating 100 µl of the solution (final PPIX concentration: 64 pmol l⁻¹) onto a clean coverslip at 5000 rpm for 15 s. 500 fluorescence images were acquired over a period of about 150 s with a 100 ms exposure time. The fluorescence peak of a selected single molecule was isolated in a 20 × 20 pixel sub-image and localized by 2D Gaussian fitting using the single fluorophore localization routines developed in Samuel T. Hess' group.⁴⁸ The fitting was accomplished using a point spread function (PSF) radius of 205 nm (estimated from the optical parameters of the setup), rolling ball background subtraction,⁴⁹ and an expansion factor of 12 for creating 91.8 nm² sub-pixels. The average single frame localization precision was 22.2 ± 6.8 nm. In comparison, the x and y coordinates of the centers from the Gaussian fits yielded standard deviations of x and y positions of 34 ± 5 nm and 23 ± 5 nm, respectively, in good agreement with the average single frame localization precision, indicating that stage drift was indeed small within the timeframe of the experiment. For a typical experiment lasting 100 s, we estimate a stage drift (from the slopes of linear fits to the data) of 0.24 pixel (26.7 nm) in the x and 0.04 pixel (4.7 nm) in the y direction.

The sample consisted of a 2 × 10⁻⁶ mg/ml stock solution of 2.0 ± 0.13 µm carboxylate-modified microspheres (Invitrogen F-8827) in a 1:1 v/v mixture of water and glycerol (Aldrich No. 191612, spectrometric grade), which was added to slow down particle movement. The solution was titrated to pH 10 with 1 mol l⁻¹ sodium hydroxide solution to fully deprotonate the carboxylic acids on the bead’s surface. According to manufacturer data, full deprotonation results in ∼10⁸ charge groups per bead.

Axial confinement was provided by a Vaseline wet mount of the sample solution, which resulted in a thin, disc-shaped fluid volume in the z direction. 1 µl of the solution was deposited in the region of a previously located corral trap. A second, non-metalized coverslip with a thin layer of Vaseline applied along its edges was then placed over the sample, and slight pressure was applied to spread the solution as much as possible while maintaining its continuity. The thickness of the solution layer, determined from the volume and covered area, was about 2–3 µm. The use of Vaseline also helped reduce solvent evaporation, allowing for longer observation and trapping times. The application of some pressure near the edge of the sample chamber induced directional flow of the beads in the solution.

Brightfield images of the sample were acquired at 1 s intervals with an exposure time of 100 ms. After data acquisition, the multi-dimensional tiff-file containing the entire video sequence captured by the CCD camera was imported into MATLAB (MathWorks) and separated into individual frames. For each frame, the locations of the trapped bead(s) were determined using the following procedure. First, a sub-image framing the trapping region was selected, and a Canny filter was applied for edge localization at the subpixel level. Once a bead was identified, an ellipse was overlaid onto the filtered image, and the bead center was determined from the center coordinates of the ellipse.

The sample consisted of a 10⁴-fold dilution of an aqueous suspension (2% solids) of 21 ± 3 nm carboxylate-modified, fluorescent polystyrene beads (Invitrogen F-8787, λ_max = 505 nm) in a 5% v/v glycerol–water solution (Aldrich No. 191612, spectrometric grade). The solution was titrated to pH 10 with 1 mol l⁻¹ sodium hydroxide solution to fully deprotonate the carboxylic acids on the bead’s surface. According to manufacturer data, 21 nm beads carry about 940 charge groups (between 590 and 1400 charge groups in the size range of 21 ± 3 nm).

1 µl of the solution was deposited onto a previously located corral trap and then spin-coated for 30 s at 8000 rpm (Laurell Technologies WS-400B-6NPP/LITE/10 K). This process resulted in a thin sample with a thickness of ∼1 µm (as determined from the deposited volume and the covered area). To reduce solvent evaporation, a closed chamber was produced by sealing a second coverslip to the corral trap coverslip using Vaseline, as in the experiments with 2.0 µm beads. The sample chamber was mounted onto the microscope, and flow was induced by tilting the sample slightly during mounting.⁵⁰ This was accomplished by shimming two corners of the corral trap with slivers of a coverslip, which resulted in a tilt angle of about 1.5°.

Fluorescence imaging of the sample was performed using the multiplication gain amplifier at a 5 MHz readout rate with an exposure time of 100 ms and a custom frame-to-frame delay, which resulted in a frame rate of 3.3 fps. Since the fluorescence signal of a single bead is relatively strong, high contrast images were obtained with an on-chip electron-multiplication gain of unity and a preamplifier gain of three electrons per count unit.

After data acquisition, the multi-dimensional tiff-file containing the entire video sequence captured by the CCD camera was analyzed in MATLAB (MathWorks). Fluorescence spots of user-selected particles were tracked across the sequence of frames by fitting a 7 × 7 pixel area around the brightest pixel in the search area to a symmetric, two-dimensional Gaussian with background using a nonlinear least-squares routine. A starting value of 0.25 pixel for the Gaussian RMS width (standard deviation σ) was used, which allowed the rejection of single, high-intensity noise pixels from fluorescent particles. The search area of initially 11 × 11 pixel was centered on the last identified particle position and successively increased until the new position was identified; the search was abandoned once a search area of 31 × 31 pixel was reached.

To determine the exact location of the corral trap center, a brightfield image of the trap was converted into a binary image using a threshold value set to a 36% between the minimum (0%) and maximum values (100%). The trap center was identified as the mean of the pixels inside the trap. Histograms were obtained using 12 bins symmetrically distributed across the sample data and fit to a binned Gaussian function (calculated from the values of the Gauss error function at the bin edges) by a nonlinear least-squares solver.

The ssDNA solution consisted of an 8 nmol l⁻¹ solution of 800-nt ssDNA sizing standard labeled with a single Cy3 indocarbocyanine dye molecule (Bioventures, Inc) in a TBE buffer. The solution was titrated to pH 8.5 with 1 mol l⁻¹ sodium hydroxide to ensure deprotonation of the phosphodiester backbone. The sample was applied to the corral trap, and flow was induced in the same manner as in the 20 nm bead experiments.

Fluorescence imaging of the sample was performed in non-overlap mode using the multiplication gain amplifier at a 5 MHz readout rate with an exposure time of 100 ms, which resulted in a frame rate of 7.0 fps. Since the fluorescence signal of a single molecule is very weak, the on-chip electron-multiplication gain was set to its maximum value, resulting in an ∼1000-fold signal amplification.⁵¹ The preamplifier gain was set to three electrons per count unit.

Individual fluorescence spots were tracked as described for the 20 nm nanobead experiments. The location of the corral trap center was identified with the center of motion of the trapped ssDNA molecule using position data from all trapping voltages; the trap outline was inferred from images of size calibration standards using a (nominal) trap size diameter of 10.0 µm. Histograms were constructed as before using 12 symmetrically distributed bins, except for the −10 V datasets where seven symmetrically distributed bins were used due to a lower number of frames during which the trap was active.

The fluorescence time trace [Fig. 6(b)] shows the integrated intensity of a 3 × 3 pixel area around the Gaussian center; if the particle cannot be located, its last known position is used instead. Background intensity is the summed intensity of a column of nine pixels located well outside (six columns to the left of) the fluorescence spot.

Electric field calculations were performed in COMSOL Multiphysics 5.5 (COMSOL, Inc.) using a 2D axisymmetric model with the actual corral trap geometry; a counter electrode was added for the reasons described in the text. The Electrostatics (es) interface was used to compute the electric field at 20 °C by solving Gauss’s law using water (relative permittivity ε_r = 80.1) in the solution space and copper as the electrode material. The thickness of the electrode layer was set to 10 nm, and the top corner was rounded with a radius of 1 nm to avoid singularities in the simulation.

The simulations were carried out with a user-controlled, triangular mesh with element size in the range of 0.1–1 nm for the 10 nm thick metal layer, which imposed a very fine mesh for the remainder of the geometry (general mesh size between 12.5 nm and 0.5 µm with a maximum element growth rate of 1.1). The complete mesh for the 20 × 50 µm² 2D cross section consisted of about 750 000 mesh elements narrowly distributed around an average mesh quality of 0.9 or better for all quality measures (minimum: 0.5).

Our results demonstrate that corral traps can be used under DC conditions to capture and release charged particles of micro- and nanoscale dimensions, including single molecules, in solution, on demand, and without any apparent limitation to the achievable trapping time. The trap stiffness can be fine-tuned by adjusting the applied potential so that true nanoscale confinement is obtained by simply increasing the amount of charge delivered onto the trap. Furthermore, it has been observed that trapping is stable and exclusive (non-trapped particles are deviated when they approach the trapping region) but that multiple particles can be trapped simultaneously by temporarily lowering the applied potential. Numerical simulations of the electric field generated by a charged corral trap electrode were carried out and confirmed that both electrostatic and dielectrophoretic interactions are consistent with the observed trapping behavior. However, only the existence of dielectrophoretic forces, which are particularly strong near the trap rim, explains the deviations of particles as they approach an active trap.

Our data show that negatively charged, 20 nm polystyrene beads and 800-nt ssDNA molecules in TBE buffer can be confined to nanoscale dimensions with standard deviations of 120 nm and 140–160 nm, respectively, obtained at the maximum voltage (−30 V) that our power supply is capable of producing. It appears that the confinement is only limited by the applicable voltage, however, and that a tighter confinement should be feasible at higher DC voltages. Further experiments are needed to establish whether a fundamental limit due to electrical breakdown or other technical issues exists.

Because the applied potential and particle charge contribute in the same way to the trapped particle’s potential energy, it appears feasible to use 3D localization microscopy to determine the charge state of the trapped molecule from the observed trajectories in the corral trap or to quantify forces involved in molecular motion, which opens up new avenues for fundamental chemical and biophysical research. In addition, two-dimensional arrays containing hundreds or thousands of corral traps can easily be fabricated using photolithography techniques, which means that DC corral trapping should be scalable for use in lab-on-a-chip systems where multiple particles or macromolecules are trapped and interrogated in parallel at different locations of the array.

The supplementary material contains three supplementary figures (position histogram of the two simultaneously trapped, 2.0 µm diameter microspheres, dependence of Gaussian fit variance on the absolute value of the inverse trapping potential, and trajectories of non-trapped 800-nt ssDNA molecules) and the descriptions of the two supplementary movies mentioned in the text.

This work was funded, in part, by grants from the National Science Foundation (Grant Nos. CHE0820832 and CHE0723002) and through Research Growth Initiative and Discovery and Innovation Grant awards by the UWM Research Growth Initiative. We acknowledge the Office of Undergraduate Research at the University of Wisconsin-Milwaukee (UWM) for supporting undergraduate students in our lab (Thomas Bate, Huy Ju Mun, Erika Johansen, and Razia Hafeez) through Support for Undergraduate Research Fellows (SURF) awards. We are indebted to Michael J. Nasse for help with the initial imaging setup and Yi Hu for the measurement of sample stage drift.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.