Single-Molecule Projects

Trapping Single Photosynthetic Proteins and Enzymes in Solution: The Anti-Brownian ELectrokinetic (ABEL) Trap

Subgroup Members: Dr. Quan Wang, Dr. Allison Squires, Hsiang-Yu Yang

Support: Department of Energy; Office of Science, Basic Energy Sciences; Chemical Sciences, Geosciences, and Biosciences Division, Physical Biosciences Area


We have developed a new type of trap for nanoscale particles in solution, the ABEL trap. Here's the key ideas:

Nanoscale objects in solution (such as proteins, enzymes, and DNA) are continually bombarded by thermally agitated molecules of solvent. This bombardment makes nanoscale objects jiggle around in solution. The smaller an object is, the faster (and farther) it jiggles. This jiggling, also known as Brownian motion, makes the task of studying nano-objects in solution very difficult: the objects just don't hold still.

The Anti-Brownian Electrokinetic trap (ABEL trap) eliminates the Brownian motion of one object in solution, allowing detailed examination of its properties. The ABEL trap works by carefully measuring the tiny Brownian displacements of the object, and then using a feedback loop to apply electric fields to the solution to exactly cancel these displacements using electrokinetic forces, which may arise from electrophoresis or electroosmosis. This is all done in a microfluidic geometry illustrated in the figure.

To trap very tiny objects, we have to apply the feedback extremely quickly--if there is too much delay, the object escapes before the ABEL trap can bring it back to the target position. Using a variety of approaches, the position update and consequent feedback application time has been made fast enough to trap individual fluorescently labeled protein molecules in solution. When this was first done, these molecules (as small as 10 nm in diameter) were the first proteins trapped in solution and the smallest objects ever trapped in solution. More importantly, we trap the single biomolecules in a region of time-averaged uniform intensity, so that the brightness of the object becomes a useful measurement variable (see figure lower right panel). Compare with fluorescence correlation spectroscopy (FCS), where infomration is obtained from individual ms-long bursts of fluorescence when a biomolecule diffuses through an ellipsoidal-shaped laser focal spot. This achievement opens the possibility of studying the detailed dynamical behavior of individual proteins free-floating in solution where many variables can be measured such as brightness, degree of FRET, lifetime, and emission spectrum.

The ABEL trap gives scientists a new handle on the nano-world. This idea should have applications in diverse areas, including the trapping and study of single biomolecules, nanoscale fabrication, and statistical physics/mechanics. Current projects are addressing conformational changes and enzymatic kinetics in trapped enzymes, photophysics/photodynamics of antenna proteins, measurements of aggregation states of photosynthetic proteins, and the counting of protein subunits.

As a side note, it is interesting to have first demonstrated this trap in 2005, 100 years after Einstein's annus mirabilis, in which one of his key papers of that year addressed the fundamental thermal mechanisms for Brownian motion: Annalen der Physik 17, 549 (1905).


Recent reviews:

Gabriela S. Schlau-Cohen, Samuel Bockenhauer, Quan Wang, and W. E. Moerner, “Single-molecule spectroscopy of photosynthetic proteins in solution: exploration of structure–function relationships,” Minireview, Chem. Sci. 5, 2933-2939 (DOI:10.1039/C4SC00582A, published online 15 April 2014). DOI

Quan Wang, Randall H. Goldsmith, Yan Jiang, Samuel D. Bockenhauer, and W.E. Moerner, “Probing single biomolecules in solution using the Anti-Brownian ELectrokinetic (ABEL) trap,” Acc. Chem. Res. (Paul Barbara Special Issue) 45, 1955-1964 (2012), published online 22 May 2012. DOI

A. E. Cohen and W. E. Moerner, “Anti-Brownian Traps,” in Encyclopedia of Biophysics, G. C. K. Roberts (Ed.) (Springer, Berlin, Heidelberg, 2012), pp. 95-97.

Recent Advances:

Direct single-molecule measurements of phycocyanobilin photophysics for the monomeric C-phycocyanin pigment-protein antenna complex

Phycobilisomes are highly organized pigment–protein antenna complexes found in the photosynthetic apparatus of cyanobacteria and rhodophyta that harvest solar energy and transport it to the reaction center. A detailed bottom-up model of pigment organization and energy transfer in phycobilisomes is essential to understanding photosynthesis in these organisms and informing rational design of artificial light-harvesting systems. In particular, heterogeneous photophysical behaviors of these proteins, which cannot be predicted de novo, may play an essential role in rapid light adaptation and photoprotection. Furthermore, the delicate architecture of these pigment–protein scaffolds sensitizes them to external perturbations, for example, surface attachment, which can be avoided by study in free solution or in vivo. Here, we present single-molecule characterization of C-phycocyanin (C-PC), a threepigment biliprotein that self-assembles to form the midantenna rods of cyanobacterial phycobilisomes. Using the Anti-Brownian Electrokinetic (ABEL) trap to counteract Brownian motion of single particles in real time, we directly monitor the changing photophysical states of individual C-PC monomers from Spirulina platensis in free solution by simultaneous readout of their brightness, fluorescence anisotropy, fluorescence lifetime, and emission spectra. These include single-chromophore emission states for each of the three covalently bound phycocyanobilins, providing direct measurements of the spectra and photophysics of these chemically identical molecules in their native protein environment. We further show that a simple Förster resonant energy transfer (FRET) network model accurately predicts the observed photophysical states of C-PC and suggests highly variable quenching behavior of one of the chromophores, which should inform future studies of higherorder complexes.

Allison H. Squires and W. E. Moerner, “Direct single-molecule measurements of phycocyanobilim photophysics for monomeric C-phycocyanin," Proc. Nat. Acad. Sci. (USA) (2017) (DOI: 10.1073/pnas.1705435114, published online 28 August 2017). DOI [Slide]

Exploring the Pigment Architecture and Photodynamics of the Allophycocyanin Monomer and Trimer Using Multivariate Measurements of Single Molecules in Solution

APC thumbnail overview imageOligomerization plays a critical role in shaping the light-harvesting properties of many photosynthetic pigment-protein complexes, but a detailed understanding of this process at the level of individual pigments is still lacking. To study the effects of oligomerization, we designed a single-molecule approach to probe the photophysical properties of individual pigment sites as a function of protein assembly state. Our method, based on the principles of anti-Brownian electrokinetic trapping of single fluorescent proteins, step-wise photobleaching, and multi-parameter spectroscopy, allows pigment-specific spectroscopic information on single multi-pigment antennae to be recorded in a non-perturbative aqueous environment with unprecedented detail. We focus on the monomer-to-trimer transformation of allophycocyanin (APC), an important antenna protein in cyanobacteria. Our data reveals that the two chemically-identical pigments in APC have different roles. One (α) is the functional pigment that red-shifts its spectral properties upon trimer formation, while the other (β) is a “protective” pigment that persistently quenches the excited state of α in the pre-functional, monomer state of the protein. These results show how subtleties in pigment organization give rise to functionally important aspects of energy transfer and photoprotection in antenna complexes. The method developed here should find immediate application in understanding the emergent properties of other natural and artificial light-harvesting systems.

See Highlight by Robert Blankenship.

Quan Wang and W. E. Moerner, “Dissecting pigment architecture of individual photosynthetic antenna complexes in solution,” Proc. Nat. Acad. Sci. (USA) 112, 13880-13885 (2015) (DOI: 10.1073/pnas.1514027112, published online October 5, 2015).  DOI [Slide]


Single-Molecule Identification of Quenched and Unquenched States of the primary light-harvesting complex in green plants, LHCII

In photosynthetic light harvesting, absorbed sunlight is converted to electron flow with near-unity quantum efficiency. Under high light conditions, plants avoid damage to their molecular machinery by activating a set of photoprotective mechanisms to harmlessly dissipate excess energy as heat. To investigate these mechanisms, we study the primary antenna complex in green plants, light-harvesting complex II (LHCII), at the single-complex level. We use a single-molecule technique, the Anti-Brownian Electrokinetic (ABEL) trap, which enables simultaneous measurements of fluorescence intensity, lifetime, and spectra in solution. With this approach, including the first measurements of fluorescence lifetime on single LHCII complexes, we access the intrinsic conformational dynamics. In addition to an unquenched state, we identify two partially quenched states of LHCII. Our results suggest that there are at least two distinct quenching sites with different molecular compositions, meaning multiple dissipative pathways in LHCII. Furthermore, one of the quenched conformations significantly increasesin relative population under environmental conditions mimicking high light.

Gabriela S. Schlau-Cohen, Hsiang-Yu Yang, Tjaart P. J. Krüger, Pengqi Xu, Michal Gwizdala, Rienk van Grondelle, Roberta Croce, and W. E. Moerner, “Single-Molecule Identification of Quenched and Unquenched States of LHCII,” J. Phys. Chem. Lett6, 860-867 (2015). (DOI: 10.1021/acs.jpclett.5b00034, publ. online February 18, 2015).  DOI [Slide]


Single-molecule motions enable direct visualization of biomolecular interactions in solution

Most single-molecule studies infer the behavior of the system from changes in the emission properties of a fluorescent label, such as brightness, excited state lifetime, or spectrum. At the same time, biomolecular interactions are generally accompanied by modifications in the size and charge of biomolecules at the nanometer scale, but these do not in general lead to changes in the emission of a fluorescent label. Here we describe a new and advanced ABEL trap method to sense these changes in real time based on statistical learning of diffusive and electric field–induced motion parameters of a trapped molecule in solution. Essentially, the analysis system measures the residual motion of the trapped single molecule, which contains information about its diffusion and its response to the trapping fields. In this way, new single-molecule variables are made available, which provide new ways to distinguish different molecules in solution, as well as to observe their dynamical changes. We demonstrate the approach by resolving a monomer-trimer mixture along a protein dissociation pathway and by visualizing the binding-unbinding kinetics of a single DNA molecule.

Quan Wang and W.E. Moerner, "Single-molecule motions enable direct visualization of biomolecular interactions in solution," Nature Methods111, 555-558 (2014), published online 9 March 2014. DOI [Slide]


Single-molecule spectroscopy in the ABEL trap reveals LH2 complexes switch between emissive states

Photosynthetic organisms flourish under low light intensities by converting photoenergy to chemical energy with near unity quantum efficiency and under high light intensities by safely dissipating excess photoenergy and deleterious photoproducts.  The molecular mechanisms balancing these two functions remains incompletely described. One critical barrier to characterizing the mechanisms responsible for these processes is that they occur within proteins whose excited-state properties vary drastically between individual proteins and even within a single protein over time.  In ensemble measurements, these excited-state properties appear only as the average value.  To overcome this averaging, we investigate the purple bacterial antenna protein, light harvesting complex 2 (LH2) from Rhodopsuedomonas acidophila at the single-protein level.  We utilize a novel single-molecule technique, the Anti-Brownian ELectrokinetic trap, to study LH2 in a solution-phase (non-perturbative) environment. By performing the first simultaneous measurements of fluorescence intensity, lifetime and spectra of single LH2 complexes, we identify three distinct states, and observe transitions occurring between them on a timescale of seconds. Our results reveal LH2 complexes undergo photoactivated switching to a quenched state, likely by a conformational change, and thermally revert to the ground state.  This is a previously unknown, reversible quenching pathway, and is one mechanism through which photosynthetic organisms are able to adapt to changes in light intensities.

G.S. Schlau-Cohen, Q. Wang, J. Southall, R.J. Cogdell, W.E. Moerner, "Single-molecule spectroscopy reveals LH2 complexes switch between emissive states," Proc. Nat. Acad. Sci. (USA) 110, 10899-10903 (2013), published online 19 June 2013. DOI [Slide]

Lifetime and spectrally resolved characterization of the photodynamics of SINGLE FLUOROPHORES in solution using the Anti-Brownian Electrokinetic trap

We report simultaneous determination of fluorescence intensity, lifetime and emission spectrum over time scales on the order of seconds for single small organic molecules in solution, using the advanced recent design of the Anti-Brownian Electrokinetic trap. We demonstrate the technique with trapped single fluorophores of Atto647N and Alexa647. Three emission states with distinct intensities, lifetimes and emission peaks are found in the case of Atto647N. Transitions between states happen occasionally. We characterize the three states and quantify the transition probabilities between states using concurrent intensity, lifetime and spectrum data. Alexa647, on the other hand, showed little dynamics.  These results represent a significant advance in the ability to identify and characterize different dynamical states of single molecules in aqueous solution with high precision and ms time resolution.

Quan Wang and W. E. Moerner,  “Lifetime and spectrally resolved characterization of the photodynamics of single fluorophores in solution using the Anti-Brownian Electrokinetic trap,” Special Issue in memory of Paul F. Barbara, J. Phys. Chem. B 117, 4641-4648 (2013), published online 30 November 2012. DOI[Slide]

Spectrally Resolved Anti-Brownian ELectrokinetic (ABEL) Trapping of Single Peridinin-Chlorophyll-Proteins in Solution

We use an Anti-Brownian ELectrokinetic (ABEL) trap to probe spectral emission shifts in solution-phase single Peridinin-Chlorophyll-Proteins (PCPs). The ABEL trap allows localization of single biomolecules in solution in a small volume for extended observation without immobilization. The essential idea combines fluorescence-based position estimation with fast electrokinetic feedback in a microfluidic geometry to counter the Brownian motion of a single nanoscale object, hence maintaining its position in a sub-micron-sized field of view for hundreds of milliseconds to seconds. Peridinin-chlorophyll-protein is a water-soluble antenna protein found in dinoflagellates which uses peridinins (carotenoids) as accessory light harvesting pigments to absorb sunlight in the green region of the spectrum before transferring electronic excitation to chlorophyll. PCP is simpler than many other antenna complexes in that there are only two chlorophyll pigments per monomer which do not form an exciton. We use the ABEL trap to study single PCP monomers in solution for several seconds each. A significant fraction of the molecules show slow spectral shifts between two detection channels, red and blue in the figure (spectral diffusion) which can be characterized with one variable shown in black, relative to the bulk PCP spectrum. This is the first spectral emission measurement conducted in the ABEL trap.

Samuel Bockenhauer, Quan Wang, and W. E. Moerner, “Spectrally Resolved Anti-Brownian ELectrokinetic (ABEL) Trapping of Single Peridinin-Chlorophyll-Proteins in Solution,” Proc. SPIE 8427, 84274C(1-9) (2012). DOI [Slide]

Also see: S. Bockenhauer and W. E. Moerner, “Photo-Induced Conformational Flexibility in Single Solution-Phase Peridinin-Chlorophyll-Proteins,” J. Phys. Chem. A 117, 8399-8406 (2013),, published online 6 August 2013. DOI

Redox Cycling and Kinetic Analysis of Single Molecules of Solution-Phase Nitrite Reductase

Single-molecule measurements are a valuable tool for revealing details of enzyme mechanisms by enabling observation of unsynchronized behavior.  However, this approach often requires immobilizing the enzyme on a substrate, a process which may alter enzyme behavior.  We apply a microfluidic trapping device to allow, for the first time, prolonged solution-phase measurement of single enzymes in solution.  The redox state is sensed by a fluorescent dye attached to the protein near the type I Cu center so that when the Cu site is oxidized, the dye emission is partly quenched, but when the Cu site is reduced, the emission from the dye is unquenched. Individual redox cycling events are observed for single molecules of a blue nitrite reductase and are used to extract the microscopic kinetic parameters of the proposed catalytic cycle.  Changes in parameters as a function of substrate concentration are consistent with a random-sequential substrate binding mechanism.

Randall H. Goldsmith, Leandro C. Tabares, Dorota Kostrz, Christopher Dennison, Thijs J. Aartsma, Gerard W. Canters, and W. E. Moerner, “Redox cycling and kinetic analysis of single molecules of solution-phase nitrite reductase,” Proc. Nat. Acad. Sci. (USA) 108, 17269-17274 (2011), published online 3 October 2011. [Slide] [Journal Link]

Conformational Dynamics of Single G Protein-Coupled Receptors in Solution

G Protein-Coupled Receptors (GPCRs) comprise a large family of seven-helix transmembrane proteins which regulate cellular signaling by sensing light, ligands, and binding proteins. The GPCR activation process, however, is not a simple on-off switch; current models suggest a complex conformational landscape in which the active, signaling state includes multiple conformations with similar downstream activity. The present study probes the conformational dynamics of single β2-Adrenergic Receptors (β2ARs) in the solution phase by Anti-Brownian ELectrokinetic (ABEL) trapping. The ABEL trap uses fast electrokinetic feedback in a microfluidic configuration to allow direct observation of a single fluorescently-labeled β2AR for hundreds of milliseconds to seconds. By choosing a reporter dye and labeling site sensitive to ligand binding, we observe a diversity of discrete fluorescence intensity and lifetime levels in single β2ARs, indicating a varying radiative lifetime and a range of discrete conformational states with dwell times of hundreds of milliseconds. We find that binding of agonist increases the dwell times of these states, and furthermore, we observe millisecond fluctuations within states. The intensity autocorrelations of these faster fluctuations are well-described by stretched exponential functions with stretching exponent β ~ 0.5, suggesting protein dynamics over a range of timescales.

Samuel Bockenhauer*, Alexandre Fürstenberg*, Xiao Jie Yao, Brian K. Kobilka, and W. E. Moerner (*equal contributions), "Conformational Dynamics of Single G Protein-Coupled Receptors in Solution," J. Phys. Chem. B 115, 13328-13338 (2011), published online 19 September 2011. [Slide] [Journal Link]

Sensing Cooperativity in ATP Hydrolysis for Single Multi-Subunit Enzymes in Solution

In order to operate in a synchronized fashion, multi-subunit enzymes use cooperative interactions intrinsic to their enzymatic cycle, but this process remains poorly understood. Accordingly, ATP number distributions in various hydrolyzed states have been obtained for single copies of the mammalian double-ring multi-subunit chaperonin TRiC/CCT in free solution using the emission from chaperonin-bound fluorescent nucleotides and closed-loop feedback trapping provided by an Anti-Brownian ELectrokinetic trap (ABEL trap).  Observations of the 16-subunit complexes as ADP molecules are dissociating shows a peak in the bound ADP number distribution at 8 ADP, whose height falls over time with little shift in the position of the peak, indicating a highly cooperative ADP release process which would be difficult to observe by ensemble-averaged methods. When AlFx is added to produce ATP hydrolysis transition state mimics (ADP∙AlFx) locked to the complex, the peak at 8 nucleotides dominates for all but the lowest incubation concentrations. Although ensemble averages of the single-molecule data show agreement with standard cooperativity models, surprisingly, the observed number distributions depart from standard models, illustrating the value of these single-molecule observations in constraining the mechanism of cooperativity. While a complete alternative microscopic model cannot be defined at present, the addition of subunit-occupancy-dependent cooperativity in hydrolysis yields distributions consistent with the data.

Yan Jiang, Nicholai R. Douglas, Nicholas R. Conley, Erik J. Miller, Judith Frydman, and W. E. Moerner, “Sensing Cooperativity in ATP Hydrolysis for Single Multi-Subunit Enzymes in Solution,” Proc. Nat. Acad. Sci. (USA) 108, 16962-16967 (2011), published online 6 September 2011. [Slide] [Journal Link][Commentary]

An Adaptive Anti-Brownian ELectrokinetic (ABEL) Trap with Real-time Information on Single-Molecule Diffusivity and Mobility

We present the design and implementation of an adaptive Anti-Brownian ELectrokinetic (ABEL) trap capable of extracting estimates of the diffusion coefficient and mobility of single trapped fluorescent nanoscale objects such as biomolecules in solution. This represents an experimental implementation of the optimal trapping strategy published earlier (see below). The system features rapid acousto-optic scanning of a confocal excitation spot on a 2D square lattice in the path of a Knight's tour to encode position information on the arrival time of each detected photon, and a Kalman filter-based signal processing unit for refined position estimation. We demonstrate stable trapping of multi-subunit proteins (D ~ 22 µm2/s ) with a count rate of 6 kHz for as long as 15 seconds and small single-stranded DNA molecules (D ~ 118 µm2/s) at a 15 kHz count rate for seconds. Moreover, we demonstrate real-time measurement of diffusion coefficient and electrokinetic mobility of trapped objects, using adaptive tuning of the Kalman filter parameters.

Quan Wang and W. E. Moerner, "An Adaptive Anti-Brownian ELectrokinetic (ABEL) Trap with Real-time Information on Single-Molecule Diffusivity and Mobility," ACS Nano 5, 5792-5799 (2011) published online May 25, 2011. [Slide] [Journal Link]

Watching conformational- and photodynamics of single fluorescent proteins in solution

APCtocObserving the dynamics of single biomolecules over prolonged time periods is difficult to achieve without significantly altering the molecule through immobilization. It can, however, be accomplished using the Anti-Brownian ELectrokinetic (ABEL) Trap, which allows extended investigation of solution-phase biomolecules - without immobilization - through real-time electrokinetic feedback. Here we apply the ABEL trap to study an important photosynthetic antenna protein, Allophycocyanin (APC). The technique allows the observation of single molecules of solution-phase APC for more than one second. We observe a complex relationship between fluorescence intensity and lifetime that cannot be explained by simple static kinetic models. Light-induced conformational changes are shown to occur and evidence is obtained for fluctuations in the spontaneous emission lifetime, which is typically assumed to be constant. Our methods provide a new window into the dynamics of fluorescent proteins and the observations are relevant for the interpretation of in vivo single-molecule imaging experiments, bacterial photosynthetic regulation, and biomaterials for solar energy harvesting.

Randall H. Goldsmith and W. E. Moerner, "Watching conformational- and photo-dynamics of single fluorescent proteins in solution," Nature Chemistry 2,179-186 (2010) published online January 31, 2010. [pdf iconSlide] [Journal Link] [News and Views]

Optimal Strategy for Trapping Single Fluorescent Molecules in Solution Using the ABEL Trap

Trapping of 10-nm-sized single fluorescent bio-molecules in solution has been achieved using high-speed position sensing and electrokinetic feedback forces in the Anti-Brownian ELectrokinetic (ABEL) trap. The high diffusion coefficient of small objects in solution requires very fast, real-time sensing of position, and this has been previously achieved using a simple rotating beam, but improved strategies are needed for the smallest objects, such as single nanometer-sized fluorescent molecules. At the same time, single molecules are limited in photon emission rate and total number of photons, so each emitted photon must be used as efficiently as possible. We describe a new controller design for the ABEL trap which features fast, knight's tour scanning of an excitation beam on a 2D square lattice and a Kalman filter-based estimator for optimal position sensing. This strategy leads directly to a maximum-likelihood-based method to extract the diffusion coefficient of the object held in the trap. The effectiveness of the algorithms are demonstrated and compared to the simple rotating beam design through Monte Carlo simulations. Our new approach yields tighter trapping and a much improved ability to extract diffusion coefficients.

Quan Wang and W. E. Moerner, "Optimal strategy for trapping single fluorescent molecules in solution using the ABEL trap," Appl. Phys. B 99, 23-30 (2010), published online December 12, 2009. [Slide] [Journal Link]

Dynamics of Single DNA Molecules in Equilibrium

Thermal fluctuations agitate molecules in solution over a broad range of times and distances. By passively watching the shape fluctuations of a thermally driven biomolecule, one can infer properties of the underlying interactions that determine the motion. We applied this concept to single molecules of fluorescently labeled λ-DNA, a key model system for polymer physics. In contrast to most other single-molecule DNA experiments, we examined the unstretched, equilibrium state of DNA by using an anti-Brownian electrokinetic trap to confine the center of mass of the DNA without perturbing its internal dynamics. We analyze the long-wavelength conformational normal modes, calculate their spring constants, and measure linear and nonlinear couplings between modes. The modes show strong signs of nonlinear hydrodynamics, a feature of the underlying equations of polymer dynamics that has not previously been reported and is neglected in the widely used Rouse and Zimm approximations.

A. E. Cohen and W. E. Moerner, "Dynamics of Single DNA Molecules in Equilibrium," Proc. Nat. Acad. Sci. (USA) 104, 12596-12602 (published online May 11, 2007) [PDF] [Movie] [Supporting Information] [Journal Link]

Also see: Conformations of a Single DNA Molecule in Equilibrium


Original ABEL Trap Publications

High speed hardware version of the ABEL trap: Controlling Brownian Motion of Single Proteins and Single Fluorophores in Aqueous Buffer, Optics Express 16, 6941-6956 (2008) [PDF]

Internal Mechanical Response of a Polymer in Solution, Phys. Rev. Lett. 98, 116001-(1-4) (2007)
[PDF] [Supporting Information]

Suppressing Brownian Motion of Individual Biomolecules in Solution (Proc. Nat. Acad. Sci. (USA) v. 103, 4362 (2006)) [PDF] [Journal link] [Supporting Material and Movies].

An All-Glass Microfluidic Cell for the ABEL Trap: Fabrication and Modeling (Proc. SPIE v. 5930, 59300S-1-S-8 (2005)) [PDF]

Control of Nanoparticles with Arbitrary Two-Dimensional Force Fields (AEC, Phys. Rev. Lett. v. 94, 188102 (2005)) [PDF]

The Anti-Brownian ELectrophoretic Trap: Fabrication and Software (Proc. SPIE v. 5699, pp. 296-305 (2005))

Method for trapping and manipulating nanoscale objects in solution (Appl. Phys. Lett. v. 86, 093109 (2005)) [Slide] [PDF]