1. Introduction

For dynamical or spectroscopic measurements of a single molecule in solution, a confocal fluorescence microscope with a high numerical aperture (NA) objective provides efficient light collection and a limited volume from which background is collected [1,2]. However, a freely diffusing molecule in solution will randomly walk out of the confocal volume, typically within about a millisecond [1], thereby limiting the observation time and number of photons available for measurements. Tethering the molecule to a surface can prolong the observation time but also alters the local environment, restricts rotational diffusion, and may hinder conformational dynamics or perturb spectroscopic properties [3]. Trapping of a single molecule in solution would also extend the observation time, but for most methods, such as optical, magnetic, or acoustic tweezers, the trapping force scales with the volume of the particle and becomes too small to hold a single molecule without tethering it to a larger particle [4]. Near-field optical trapping, which utilizes the enhanced optical field near a nanostructure, can directly hold a single nanoparticle or biomolecule [5], but only very close to a surface. In practice, change in optical transmission through the nanostructure rather than fluorescence is used for detection and significant heating of the molecule by the enhanced optical trapping field can occur [6], although there can be an orders-of-magnitude reduction in the required local intensity if the trapped object itself alters the local field to enhance the trapping force [7].

Real-time control of electrokinetic motion of the solution and/or molecule (via electroosmosis and/or electrophoresis), as envisioned in the early single-molecule detection literature [1], offers favorable size scaling for trapping a single molecule or nanoparticle with <100 nm diameter [4]. It does not cause aggregation, as diffusional trajectories are uncorrelated, and the feedback can be correct for only one molecule. Also, it is less perturbative than other trapping methods, as the electrokinetic motion is uniform over an extended volume and does not create a potential well or force gradient [3]. The effective trapping force depends mostly on the frequency of corrections, the latency or time delay between sensing the displacement and initiating each correction, and the speed and accuracy of the corrections.

The Anti-Brownian ELectrokinetic (ABEL) trap has been thoroughly developed for feedback-driven-trapping in two dimensions (2D) (see [8] for a recent review) and applied in numerous biomolecular studies with increasing sophistication of methods (see [3] for just one recent example). However, for trapping in 2D, the molecule is confined between closely spaced surfaces and is subject to collisions with the surfaces at kilohertz rates due to the Brownian diffusion in the direction normal to the surfaces [15]. Frequent collisions have the possibility to perturb delicate molecular complexes and/or alter the local environment of the molecule under study [18], the avoidance of which is usually a key motivation for using trapping rather than immobilization to achieve prolonged observation. Also, additives are often needed to reduce non-specific adsorption of the trapped molecule to the surfaces [9], but progress has been made on this front and in many cases only a surface pretreatment (such as the deposition of polyelectrolyte multilayers, which prevent sticking while increasing electroosmotic flow), is needed to prevent significant surface interactions, as seen by the apparent lack of sticking and comparison of the trapped molecule properties to those in bulk. Feedback-driven electrokinetic trapping of a single molecule in one dimension, while confining the solution within a nanochannel, has also been developed, although surface interactions and non-specific binding can become even more problematic [10], but have also been addressed by surface treatments [11].

Feedback-driven tracking of a molecule by adjusting the position of the sample in three dimensions (3D) with a piezo stage to re-center the molecule in the confocal volume extends the observation time while avoiding surface interactions but is limited by the response time, speed, and travel range of the piezo stage [12,13]. ABEL trapping in 2D combined with feedback-driven tracking in the axial dimension has been demonstrated for nanoparticles in a high viscosity solution with $D$ = 5.5 × 10⁻³ µm²/s [14]. Feedback-driven electrokinetic trapping in 3D also avoids surface collisions, possible sticking, and background from surfaces, whereas the corrective motion can be faster and effectively unlimited in range of travel. Despite these advantages, only a few experimental demonstrations of 3D electrokinetic trapping have been reported in the literature so far.

In the first, a device with four platinum electrode tips spaced by ∼100 µm in a tetrahedral arrangement was used to trap a 40 nm nanoparticle in a glycerol/water solution with slowed diffusivity of 5.2 µm²/s [15]. Wide-field illumination and astigmatic imaging and processing were used for 3D nanoparticle position determination, which limited corrections to 30 Hz with a delay of ∼7.7 ms. The four-electrode setup was proposed in an earlier paper [16], which also modelled 3D position determination by use of four laser beams focused to offset points with pulse-interleaved excitation and time-gated photon counting, as used in [13] and in our present work. In the second demonstration, a microfluidic device with five 250 µm thick layers and eight electrodes was used to manipulate and trap a 5 µm diameter microparticle using feedback via camera imaging and analysis of defocusing [17]. In the third [18,19], 3D electrokinetic trapping of a 25 nm diameter fluorescent nano-diamond was achieved using a microfluidic device with five electrodes at the ends of five intersecting channels, four in a planar layer intersecting in a cross and the fifth in a layer above connected to the center of the intersection point. The axial position was found by defocused imaging on a camera with 10 ms exposure and 4 ms image-processing time, which limited the feedback rate and latency for axial corrections. The paper that proposed the four-electrode setup also proposed a simpler microfluidic configuration with only four electrodes and two crossed channels intersecting at the faces of the channels [16], which is the basis of the trapping device presented below.

2. Microfluidic device design and fabrication

Figure 1 shows photographs and a schematic of the device, which consists of two glass coverslips (#1.5, 22 mm × 22 mm × 180 µm), each with a 25 ± 2 µm thick spin-coated layer of polydimethylsiloxane (PDMS), sandwiched together by plasma bonding of the PDMS layers, and also a schematic of the steps involved in fabrication. Before bonding, a channel is formed in each PDMS layer by completely removing the PDMS down to the glass employing a laser machining facility with a 250 kHz, 4 µJ, 130 fs, Ti:Sapphire laser [20], using underwater ablation at 1.0 NA in 5 passes with 0.7 µJ pulses at 10 mm/s XY translation speed, under LabVIEW control. This allows diffraction-limited imaging through the coverslip with the microscope used in the trapping experiments, which uses a 1.2 NA water immersion objective with correction collar adjusted for the #1.5 coverslip.

 

Fig. 1. (a) Photograph of the center of the device, showing two 25 µm thick PDMS layers with crossed channels. (b) Photograph of assembled device, with 70 mm square aluminum baseplate screwed to the microscope’s 3D piezo stage. (c) Schematic giving channel dimensions: a = 100–110 µm, b = 500 µm, c = 1 mm, d = 5 mm. (d) Fabrication steps: 1. PDMS is spin coated 25 µm thick onto two 180 µm thick glass coverslips; 2. On each, a single channel is formed by removing the PDMS by dithered fs laser ablation under water; 3. In one, four fluid access through-holes are laser-machined using an annular path; 4. For both, uneven PDMS around edges is scraped off using a razor; 5. The PDMS is activated though oxygen-air plasma treatment, then the two coverslips are aligned and bonded together to form the cross channel device. The ‘*’ symbols in the side views indicate an expanded-scale detail of the channel region.

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For 1.2 NA, the collection angle in water is sin⁻¹(1.2/1.33) = 64.5°, so for unobstructed imaging of the center of the crossing region of the channels where the nanoparticle is to be trapped, the width of the channels should be 2 × tan(64.5°) × 25 µm = 105 µm. The Ti:Sapphire laser ablates the PDMS to leave trapezoidal cross-section channels 100 µm wide at the glass surface and 110 µm at the top, so the edges of the channel only slightly obstruct the NA for light collection. The laser machining is also used to cut four 1 mm diameter access holes through one of the coverslips, (using 4 µJ pulses, 5 mm/s XY translation speed, and 10 µm Z-steps, with 1.0 NA ablation under water). Four 100 µm diameter platinum wire electrodes are set to make contact with the solution in the holes once the two coverslips are bonded together and mounted with silicone O-ring seals to a hood machined from poly(methyl methacrylate), as shown in Fig. 1(b).

As shown in Fig. 1(c), the widths of the channels are tapered to funnel the flow and decrease the distance b across which most of the potential is applied and thereby increase the electroosmotic flow speed at the face of intersection of the channels. Electroosmotic flows were modeled using COMSOL Multiphysics software to assess different taper designs and dimensions. For the given design and dimensions (chosen in part to facilitate fabrication and bonding) and with approximated rectangular channel cross sections and estimated zeta potential of 70 mV [21], the theoretical flow speed in the X-direction for V₁ = 10 V, V₂ = −10 V, V₃ = V₄ = 0 V was 0.44 mm/s, whereas in the Z-direction for V₁ = V₂ = −10 V, V₃ = V₄ = 10 V it was 0.22 times smaller (approximately the same factor as the 1:4 depth-to-width of the channels needed for the 1.2 NA). The corresponding experimentally measured flow speed in the X-direction was 0.3 mm/s, obtained by imaging the motion of nanoparticles over a 25 µm wide field using wide-field illumination with the voltages pulsing on and off at ∼20 kHz. The speed in Z was not measured but is estimated to be 0.22 × 0.3 mm/s.

3. Optical configuration and microscope

The microfluidic assembly (shown in Fig. 1(b)) is positioned using a 3D piezo stage so that the confocal volume of the fluorescence microscope is at the center of the intersection of the crossed channels. The microscope is custom-built as described in [13], except that the interference filter is replaced by Omega 3RD 660LP as the excitation wavelength is now 640 nm, the pinhole diameter is increased to 400 µm (to collect light from an extended depth), the mirror before the pinhole is replaced by a 50% beam-splitter, and an electron-multiplying charge-coupled device (EM-CCD) camera (Andor iXon 897) is placed after the beam-splitter parfocal to the pinhole to allow simultaneous imaging of the trapping region.

Trapping experiments used 100 pM solutions of 40 nm and 20 nm diameter nanoparticles (Invitrogen Dark Red (660/680) FluoSpheres) and streptavidin conjugated Alexa 647 (from the same batch as in [13]) in distilled water at 20 °C, with calculated diffusivities of 12.1 µm²/s, 24.1 µm²/s, and 96.5 µm²/s. Fluorescence excitation of the sample is provided by a 76 MHz, 1 ps synchronously pumped dye laser (Coherent 702 with DCM Special dye) tuned to wavelength $\lambda $ = 640 nm and an angle-tuned 10 nm notch filter to reject broadband luminescence from the laser. As shown schematically in Fig. 2, six beam splitters, five variable neutral density filters, mirrors, and two pairs of lenses used as a beam expander and an adjustable collimator, are used to split, optically delay, and recombine the beams into four almost-collinear beams with equal power and interleaved pulses at 4 × 76 = 304 MHz (separated by 3.3 ns).

 

Fig. 2. Optical configuration.

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The components are adjusted so that the size, divergence, and pointing angle of the four beams at the pupil of the microscope objective are such that the waists are offset from the center of the confocal volume in a tetrahedral pattern. The beams slightly underfill the objective pupil and produce waists ${\omega _0}$ of ∼0.5 µm ($1/{e^2}$ intensity radius), hence the $1/{e^2}$ axial extents are ∼4.1 µm ($\sqrt {{e^2} -1} \pi \omega _0^2n/\lambda $, with refractive index of water $n = 1.33$). The four waist positions in µm are (−0.38, 0.38, 1.6), (0.38, −0.38, 1.6), (−0.38, −0.38, −1.6), and (0.38, 0.38, −1.6), for beams 1, 2, 3, and 4, as determined by Gaussian fitting of images of the beams reflected from a coverslip-water interface, which is scanned in axial position with the piezo stage in a LabVIEW program; see Fig. 3. The upper channel is along the X-axis and the lower channel is along the Y-axis, so the coordinate system is as shown in Fig. 1(c), with the origin at the center of the intersection face. The four beams together give an excitation region with ∼2.1 µm lateral diameter at Z = 0 and an axial diameter of ∼11.4 µm (2 × (4.1 + 1.6)), whereas the pinhole and objective define a region of collection with ∼4.8 µm lateral diameter and ∼6.3 µm axial diameter (from geometrical optics calculations obtained by using lens equations to find object positions that give image disks with $1/{e^2}$ of their areas overlapping the pinhole [22]) and the depth of the crossing microfluidic channels is 50 µm. To help visualize the trapping region, Fig. 4 presents scaled sketches of the microfluidic device and the trapping region defined by the four laser foci and the pinhole.

 

Fig. 3. Images of 2, 2, and 4 reflected beams with coverslip positioned to Z = 1.6, −1.6, and 0 µm. The clearly visible camera pixels in the images are 16 µm square in size. The 3-pixel long scale bar is for image space. Object space is smaller by the optical magnification (83.3).

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Fig. 4. Scaled sketches of the microfluidic device, laser beams, and fluorescence collection region.

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4. Electronics and algorithm for flow control

As the nanoparticle moves within the confocal volume, a custom-built circuit performs time-gated sorting of photon signals into four channels synchronous with pulses in the four beams, counts the numbers of photons from the four channels each 13.5 µs, and uses the counts in a simple algorithm to update voltages applied between the four fluidic inlets of the crossed channels to turn on and off the electroosmotic flows in attempt to equalize the counts and thereby trap the nanoparticle.

The circuit contains a field programmable gate array (FPGA) (Intel Altera Cyclone II programmed using Intel’s Quartus II software) and an integrated circuit (Analog Devices LTC2704) with four ± 10 V digital-to-analog converters (DACs), which provide the trapping potentials. The microscope, as previously described [13], has two single-photon avalanche diodes (SPADs) for polarization-resolved photon detection, which output fast negative NIM (nuclear instrumentation module) timing pulses (−1 V into 50 Ω with ∼1 ns width). These pass through adjusted cable delays to adjustable leading-edge discriminators (which provide sub-nanosecond timing adjustment due to time-walk) and trigger internal TTL (transistor-transistor-logic) pulses within the FPGA. For time-gated sorting of photons into channels corresponding to the four laser beams, 76 MHz pulses from a photodiode monitoring the pump laser are used to phase-lock a TTL clock signal at 304 MHz (76 MHz × 4) within the FPGA, and logic gates are used to generate a pulse in one of four channels whenever the leading edge of either internal SPAD pulse occurs within the matching cycle of the clock. The timing jitter from the SPADs and electronics (∼0.4 ns FWHM, compared to the 3.3 ns width of the time-gate) and the finite fluorescence lifetimes (2.2 ns for the nanoparticles and 1.0 ns for streptavidin-Alexa 647) lead to cross-talk, whereby a photon generated by one laser beam gives a TTL pulse in a different channel [16]. Experimental counts using low laser power excitation of a micromolar solution of streptavidin-Alexa 647 indicate that channels have equal probabilities with all beams on, and if all but one beam is blocked, once the cable delays and leading edge discriminators are correctly adjusted, about 90% of photons fall in the correct channel and almost 10% in the next. In theory [16], the percentages are 96%, 3.6%, 0.13% and 0.005% for 1.0 ns lifetime and 78%, 17%, 3.9% and 0.86% for 2.2 ns.

The FPGA also generates a clock at 74.2 kHz (76 MHz /1024) with a period of ∼13.5 µs, and with each cycle it reads out the counts of photons in the four channels N₁, N₂, N₃, N₄, and uses them in a simple algorithm to determine four output potentials to be applied across the electrodes of the microfluidic device. If the sum of the counts is < 3, it is assumed that the particle has escaped and the voltage values will be set to (V₁, V₂, V₃, V₄) = (10, 10, −10, −10) in an attempt to bring a new particle to the trap with flow in the −Z-direction. Otherwise, the algorithm estimates into which octant (or boundary) of the Cartesian coordinate system the particle has diffused and chooses voltages to move it towards the origin. For example, if N₁ + N₃ > N₂ + N₄, N₂ + N₃ > N₁ + N₄, and N₃ + N₄ > N₁ + N₂, the particle is estimated to be in the octant with X < 0, Y < 0, and Z < 0, so it needs V₂ < V₁ to move in the positive X-direction, V₄ < V₃ to move in the positive Y-direction, and V₁ + V₂ < V₃ + V₄ to move in the positive Z-direction, which is achieved with (0, −10, 10, 0). Table 1 lists all 27 possibilities.

Table 1. A. Comparison of counts to determine octant or boundary location of particle. B. Voltage settings for each octant or boundary.

View Table

The FPGA determines the four voltage values within ∼0.1 µs using the 304 MHz clock, then sends them to the DAC chip serially together with other commands and ending with a command to switch all voltages together. In all, 255 bits are sent at a clock rate of 76 MHz × 2/3 so there is a delay of ∼5.0 µs before the DAC chip begins to slew the four voltages. The FPGA then waits for 3.4 µs while the potentials reach their designated values with a slew rate of 10 V/3.4 µs. After this, it sends commands to switch the voltages back to zero, so there is a further delay of ∼5.0 µs before the DAC chip begins to slew the potentials back to zero. The FPGA then waits ∼0.1 µs for the counts from the next cycle.

5. Demonstration of 3D trapping and analysis

With the motion control as described above, trapping of single 40 nm nanoparticles was demonstrated in many different experiments. As expected, a trapped nanoparticle immediately escapes if any or all laser beams are momentarily blocked. Very good trapping of the same nanoparticle for over 240 s was achieved with 1 µW power in each beam (see Figs. 5(a)–5(c) and Visualization 1). During this time, the total average count rate was ∼6 × 10⁶ photons/s with a background of ∼1 × 10⁵ photons/s, corresponding to a signal-to-background of 59:1 and about 20 ± 5 photons in each channel for each 13.5 µs cycle.

Within the ∼8.4 µs interval for which the voltages are applied each cycle, the particle would be displaced only 2.5 × 10⁻³ µm for electroosmotic motion in the X-direction at 0.3 mm/s (or a 0.22 times smaller distance in Z), whereas the root-mean-square (rms) diffusional distance for a 40 nm nanoparticle in the cycle time $t$ = 13.5 µs is $\sqrt {2Dt} $ = 1.8 × 10⁻² µm, which is a factor of 7 larger. Hence, trapping is achieved as a result of accumulated corrective motions over many cycles.

From analysis of video frames in Visualization 1, the estimated rms X-displacement of the nanoparticle from the center of the trap is $\sigma $ = 0.2 µm, so by the equipartition theorem, the effective spring constant in X is ${k_B}T/{\sigma ^2}$ = 0.1 µN/m. However, for feedback-driven trapping, there is always a possibility of escape from the trap, so the effective potential is not truly harmonic but is finite in depth. One expects that the effective spring constant in Z will be weaker due to the 0.22 times slower electroosmotic flow-speed, but that trapping can be sustained with greater axial excursions as the confocal volume is elongated in Z. With the camera displaced to defocus the image (but with the image at the pinhole still well focused), fluctuations in the Z-position of the nanoparticle are apparent from the fluctuations in the diameter of the image. From analysis of the video frames in Visualization 1, the $1/{e^2}$ radius of the defocused image has a mean of 130 µm and standard deviation of 15 µm, which corresponds to a fluctuation in the Z-displacement of the nanoparticle from the center of the trap with standard deviation of 0.6 µm (from a geometrical optics calculation obtained by using the lens equation to find object positions that give image disks of 130 ± 15 µm [22]).

In trapping 20 nm nanoparticles (with the same setup), the power per laser beam had to be increased to provide enough photons-per-cycle for the trapping algorithm and in most experiments was ∼12 µW. In one session, trapping for over 25 s was observed (see Fig. 5(d) and Visualization 2) and there were several instances with almost the same trapping duration. The total count rate was 8.4 × 10⁶ photons/s and the signal-to-background was about 20:1. A shorter trapping time compared to that for 40 nm nanoparticles is to be expected due to the larger diffusion coefficient and greater ratio of background.

 

Fig. 5. Frames from: (a) Visualization 1 (40 nm nanoparticle) with camera defocused; (b) Visualization 1 at t = 253.125 s; (c) Visualization 1, as the particle escapes, at t = 253.561 s; (d) Visualization 2 (20 nm nanoparticle); (e) Visualization 3 (streptavidin-Alexa 647). (The scale bar is for image space and applies to all images and the magnification is 83.3.)

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Fig. 6. Photon counts summed over 20 cycles of 13.5 µs for each channel and in total during trapping of a single molecule of streptavidin-Alexa 647.

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The system was also tested for trapping single molecules of streptavidin-Alexa 647. Each streptavidin protein molecule is labeled with three Alexa 647 fluorophores, as specified on the certificate of analysis for the batch, so the brightness is much less than that of the nanoparticles, which typically have about 180 (350) fluorophores per 20 (40) nm nanoparticle. The simple feedback algorithm used in this work switches the flow to bring in a new molecule if there are less than 3 photons detected in any 13.5 µs interval, so to trap for many such intervals in succession the count rate must exceed ∼10⁶ /s. Hence to obtain a sufficient count rate for the algorithm, the power per beam was increased to 30 µW, which gives close to the saturation intensity at the center of each beam focus. With this increase in laser power, the background increases and the signal to background is at times only about 1:1, but trapping is still possible (Fig. 5(e)). Visualization 3 shows several instances of trapping (with long blank periods between molecule occurrences removed to keep the video short) and Fig. 6 shows the photon counts (summed over 20 cycles to smooth the graph) for one instance lasting about 1.25 s. Data from which to form a histogram of trapping times was not collected as improvements in the trapping should be possible, as discussed in the following section.

In Fig. 6, the fluctuations in the ratios of counts and in the total counts are because the molecule moves within the detection volume rather than being tightly trapped at the center. The correlation between the motion of the molecule within the trapping region as seen on the camera and the fluctuations in the counts is clear when observing experiments in real time with the counts plotted as they are collected. When the concentration is increased, one can see on the camera when a second molecule enters the trap and displaces the first, but in Fig. 6, the concentration is low enough that this is unlikely, and it is not observed on the camera. Although the count rate is not steady enough to observe photophysical brightness changes due to blinking or sequential bleaching, the trap extends the observation time and total number of photons. During the time the molecule is in the confocal volume, >2.2 × 10⁶ photons are detected (including ∼10⁶ background). By comparison, the diffusional residence time within a 2.1 µm diameter cylindrical confocal volume would be 2.9 ms and ∼5×10³ photons in total would be detected.

6. Conclusions and discussion

As demonstrated above, control of flows in the crossed channels enables trapping of single 40 nm fluorescently labelled nanoparticles with diffusivity $D$ = 12 µm²/s for times up to 240 s, single 20 nm nanoparticles with $D$ = 24 µm²/s for up to 25 s, and single molecules of streptavidin-Alexa 647 with $D$ = 96 µm²/s for up to 1.2 s, which is an improvement over previous 3D traps. The trap enables significant increases in the observation times and numbers of collected photons compared to those from a molecule freely diffusing in 3D through the probe region of a confocal fluorescence microscope, which would be immediately advantageous for certain single-molecule studies, such as observations of dynamical changes or measurements that require large numbers of photons for statistical precision. For investigations of protein-folding dynamics, molecular heterogeneities, or conformational changes in biomolecules, the microscope could be modified for two-color detection for single-molecule Förster resonance energy transfer measurements (as reported in 1D [11] and 2D [23] experiments) by replacing the polarization splitter with a dichroic beam-splitter. Background could be reduced by adding a short-pass or band-pass filter to reduce Raman scatter from water and Rayleigh scatter of long wavelength fluorescence from the dye laser and making the flow cell from fused silica rather than glass to minimize scattered autofluorescence.

Moreover, several improvements in the 3D trapping performance should be possible. To increase the electrokinetic flow speeds with the same driving potentials, the center part of the microfluidic device (dimensions a and b in Fig. 1(c) and the thickness of the PDMS layers) could be scaled down in size by a factor of 2 or more, as the 50 µm depth of the crossed channels is still ∼8 times larger than the present ∼6.3 µm axial diameter of the confocal volume. Also, the duty cycle for which voltages are applied could be increased by reprogramming the FPGA to directly switch voltages to the new values without resetting them to zero within each cycle. While the Cyclone II FPGA can be synchronized to the external 76 MHz frequency, as needed for time-gating with the dye laser used in this work, it does not allow algorithm parameters to be adjusted during an experiment, and the compilation and downloading of program revisions is slow and prone to internal timing changes that require SPAD cable lengths to be readjusted for optimum time-gating. On the other hand, more flexible FPGA circuits are commercially available that could achieve time-gating of photons by synchronized triggering of modern picosecond-pulsed laser diodes at a clock frequency determined by the FPGA, which could be set to reduce crosstalk to an acceptable level for the fluorescence lifetime of the particular molecule under study. More sophisticated feedback algorithms could be deployed, not only for trapping (e.g., Kalman filter), but to execute more rapid reloading of the trap by searching for a nearby molecule, and only after many intervals with low counts, so that sustained high count rates are not necessary. Although such changes should enable considerable technical improvements in the 3D trapping performance (ultimately limited by fundamental tradeoffs, see e.g., [12]), the results presented demonstrate that a microfluidic device based on two crossed channels has a simple, easy-to-fabricate geometry and provides an effective platform for 3D feedback-driven trapping of single molecules or nanoparticles with clear aperture for 1.2 NA confocal fluorescence detection.