Recent Advances in Optical Tweezers

A statistical approach to the estimation of mechanical unfolding parameters from the unfolding patterns of protein heteropolymers

A statistical calculation is described with which the saw-tooth-like unfolding patterns of concatenated heteropolymeric proteins can be used to estimate the forced unfolding parameters of a previously uncharacterized protein. The chance of observing the various sequences of unfolding events, such as ABAABBB or BBAAABB etc, for two proteins of types A and B is calculated using proteins with various ratios of A and B and at different values of effective unfolding rate constants. If the experimental rate constant for forced unfolding, k(0), and distance to the transition state x(u) are known for one protein, then the calculation allows an estimation of values for the other. The predictions are compared with Monte Carlo simulations and experimental data.

Visualizing protein-DNA interactions at the single-molecule level

Recent advancements in single-molecule methods have allowed researchers to directly observe proteins acting on their DNA targets in real-time. Single-molecule imaging of protein-DNA interactions permits detection of the dynamic behavior of individual complexes that otherwise would be obscured in ensemble experiments. The kinetics of these processes can be monitored directly, permitting identification of unique subpopulations or novel reaction intermediates. Innovative techniques have been developed to isolate and manipulate individual DNA or protein molecules, and to visualize their interactions. The actions of proteins that have been visualized include: duplex DNA unwinding, DNA degradation, DNA packaging, translocation on DNA, sliding, superhelical twisting, and DNA bending, extension, and condensation. These single-molecule studies have provided new insights into nearly all aspects of DNA metabolism. Here we focus primarily on recent advances in fluorescence imaging and mechanical detection of individual protein-DNA complexes, with emphasis on selected proteins involved in DNA recombination: DNA helicases, DNA translocases, and DNA strand exchange proteins.

Highly birefringent vaterite microspheres: production, characterization and applications for optical micromanipulation

This paper reports on a simple synthesis and characterization of highly birefringent vaterite microspheres, which are composed of 20-30 nm sized nanocrystalls. Scanning electron microscopy shows a quite disordered assembly of nanocrystals within the microspheres. However, using optical tweezers, the effective birefringence of the microspheres was measured to be Deltan = 0.06, which compares to Deltan = 0.1 of vaterite single crystals. This suggests a very high orientation of the nanocrystals within the microspheres. A hyperbolic model of the direction of the optical axis throughout the vaterite spherulite best fits the experimental data. Results from polarized light microscopy further confirm the hyperbolic model.

Microengineered platforms for cell mechanobiology

Mechanical forces play important roles in the regulation of various biological processes at the molecular and cellular level, such as gene expression, adhesion, migration, and cell fate, which are essential to the maintenance of tissue homeostasis. In this review, we discuss emerging bioengineered tools enabled by microscale technologies for studying the roles of mechanical forces in cell biology. In addition to traditional mechanobiology experimental techniques, we review recent advances of microelectromechanical systems (MEMS)-based approaches for cell mechanobiology and discuss how microengineered platforms can be used to generate in vivo-like micromechanical environment in in vitro settings for investigating cellular processes in normal and pathophysiological contexts. These capabilities also have significant implications for mechanical control of cell and tissue development and cell-based regenerative therapies.

Proposed triaxial atomic force microscope contact-free tweezers for nanoassembly

We propose a triaxial atomic force microscope contact-free tweezer (TACT) for the controlled assembly of nanoparticles suspended in a liquid. The TACT overcomes four major challenges faced in nanoassembly, as follows. (1) The TACT can hold and position a single nanoparticle with spatial accuracy smaller than the nanoparticle size (approximately 5 nm). (2) The nanoparticle is held away from the surface of the TACT by negative dielectrophoresis to prevent van der Waals forces from making it stick to the TACT. (3) The TACT holds nanoparticles in a trap that is size-matched to the particle and surrounded by a repulsive region so that it will only trap a single particle at a time. (4) The trap can hold a semiconductor nanoparticle in water with a trapping energy greater than the thermal energy. For example, a 5 nm radius silicon nanoparticle is held with 10 k(B)T at room temperature. We propose methods for using the TACT as a nanoscale pick-and-place tool to assemble semiconductor quantum dots, biological molecules, semiconductor nanowires, and carbon nanotubes.

Quantitative modeling and optimization of magnetic tweezers

Magnetic tweezers are a powerful tool to manipulate single DNA or RNA molecules and to study nucleic acid-protein interactions in real time. Here, we have modeled the magnetic fields of permanent magnets in magnetic tweezers and computed the forces exerted on superparamagnetic beads from first principles. For simple, symmetric geometries the magnetic fields can be calculated semianalytically using the Biot-Savart law. For complicated geometries and in the presence of an iron yoke, we employ a finite-element three-dimensional PDE solver to numerically solve the magnetostatic problem. The theoretical predictions are in quantitative agreement with direct Hall-probe measurements of the magnetic field and with measurements of the force exerted on DNA-tethered beads. Using these predictive theories, we systematically explore the effects of magnet alignment, magnet spacing, magnet size, and of adding an iron yoke to the magnets on the forces that can be exerted on tethered particles. We find that the optimal configuration for maximal stretching forces is a vertically aligned pair of magnets, with a minimal gap between the magnets and minimal flow cell thickness. Following these principles, we present a configuration that allows one to apply > or = 40 pN stretching forces on approximately 1-microm tethered beads.

The Q motif of a viral packaging motor governs its force generation and communicates ATP recognition to DNA interaction

A key step in the assembly of many viruses is the packaging of DNA into preformed procapsids by an ATP-powered molecular motor. To shed light on the motor mechanism we used single-molecule optical tweezers measurements to study the effect of mutations in the large terminase subunit in bacteriophage lambda on packaging motor dynamics. A mutation, K84A, in the putative ATPase domain driving DNA translocation was found to decrease motor velocity by approximately 40% but did not change the force dependence or decrease processivity substantially. These findings support the hypothesis that a deviant "Walker A-like" phosphate-binding motif lies adjacent to residue 84. Another mutation, Y46F, was also found to decrease motor velocity by approximately 40% but also increase slipping during DNA translocation by >10-fold. These findings support the hypothesis that viral DNA packaging motors contain an adenine-binding motif that regulates ATP hydrolysis and substrate affinity analogous to the "Q motif" recently identified in DEAD-box RNA helicases. We also find impaired force generation for the Y46F mutant, which shows that the Q motif plays an important role in determining the power and efficiency of the packaging motor.

Integrating a high-force optical trap with gold nanoposts and a robust gold-DNA bond

Gold-thiol chemistry is widely used in nanotechnology but has not been exploited in optical-trapping experiments due to laser-induced ablation of gold. We circumvented this problem by using an array of gold nanoposts (r = 50-250 nm, h approximately 20 nm) that allowed for quantitative optical-trapping assays without direct irradiation of the gold. DNA was covalently attached to the gold via dithiol phosphoramidite (DTPA). By using three DTPAs, the gold-DNA bond was not cleaved in the presence of excess thiolated compounds. This chemical robustness allowed us to reduce nonspecific sticking by passivating the unreacted gold with methoxy-(polyethylene glycol)-thiol. We routinely achieved single beads anchored to the nanoposts by single DNA molecules. We measured DNA's elasticity and its overstretching transition, demonstrating moderate- and high-force optical-trapping assays using gold-thiol chemistry. Force spectroscopy measurements were consistent with the rupture of the strepavidin-biotin bond between the bead and the DNA. This implied that the DNA remained anchored to the surface due to the strong gold-thiol bond. Consistent with this conclusion, we repeatedly reattached the trapped bead to the same individual DNA molecule. Thus, surface conjugation of biomolecules onto an array of gold nanostructures by chemically and mechanically robust bonds provides a unique way to carry out spatially controlled, repeatable measurements of single molecules.

Single molecule transcription elongation

Single molecule optical trapping assays have now been applied to a great number of macromolecular systems including DNA, RNA, cargo motors, restriction enzymes, DNA helicases, chromosome remodelers, DNA polymerases and both viral and bacterial RNA polymerases. The advantages of the technique are the ability to observe dynamic, unsynchronized molecular processes, to determine the distributions of experimental quantities and to apply force to the system while monitoring the response over time. Here, we describe the application of these powerful techniques to study the dynamics of transcription elongation by RNA polymerase II from Saccharomyces cerevisiae.

Designing spinning Bloch states in 2D photonic crystals for stirring nanoparticles

Based on an optical analogy of spintronics, the generation of spinning Bloch states is theoretically investigated in two-dimensional photonic crystals without space-inversion symmetry. We address its close relation to the Berry curvature in crystal momentum space, which represents the nontrivial geometric property of a Bloch state. It is shown that the Berry curvature is easily controlled by tuning two types of dielectric rods in a honeycomb photonic crystal. Bloch states with large Berry curvatures appear as optical tornadoes in real space. The radiation force of such a configuration is analyzed, and its possible application for selective optical stirrer is discussed as a complementary proposal in optical tweezers technology.

Precision surface-coupled optical-trapping assay with one-basepair resolution

The most commonly used optical-trapping assays are coupled to surfaces, yet such assays lack atomic-scale ( approximately 0.1 nm) spatial resolution due to drift between the surface and trap. We used active stabilization techniques to minimize surface motion to 0.1 nm in three dimensions and decrease multiple types of trap laser noise (pointing, intensity, mode, and polarization). As a result, we achieved nearly the thermal limit (<0.05 nm) of bead detection over a broad range of trap stiffness (k(T) = 0.05-0.5 pN/nm) and frequency (Deltaf = 0.03-100 Hz). We next demonstrated sensitivity to one-basepair (0.34-nm) steps along DNA in a surface-coupled assay at moderate force (6 pN). Moreover, basepair stability was achieved immediately after substantial (3.4 pN) changes in force. Active intensity stabilization also led to enhanced force precision ( approximately 0.01%) that resolved 0.1-pN force-induced changes in DNA hairpin unfolding dynamics. This work brings the benefit of atomic-scale resolution, currently limited to dual-beam trapping assays, along with enhanced force precision to the widely used, surface-coupled optical-trapping assay.

Mechanoenzymatic cleavage of the ultralarge vascular protein von Willebrand factor

Von Willebrand factor (VWF) is secreted as ultralarge multimers that are cleaved in the A2 domain by the metalloprotease ADAMTS13 to give smaller multimers. Cleaved VWF is activated by hydrodynamic forces found in arteriolar bleeding to promote hemostasis, whereas uncleaved VWF is activated at lower, physiologic shear stresses and causes thrombosis. Single-molecule experiments demonstrate that elongational forces in the range experienced by VWF in the vasculature unfold the A2 domain, and only the unfolded A2 domain is cleaved by ADAMTS13. In shear flow, tensile force on a VWF multimer increases with the square of multimer length and is highest at the middle, providing an efficient mechanism for homeostatic regulation of VWF size distribution by force-induced A2 unfolding and cleavage by ADAMTS13, as well as providing a counterbalance for VWF-mediated platelet aggregation.

FDTD approach to optical forces of tightly focused vector beams on metal particles

We propose an improved FDTD method to calculate the optical forces of tightly focused beams on microscopic metal particles. Comparison study on different kinds of tightly focused beams indicates that trapping efficiency can be altered by adjusting the polarization of the incident field. The results also show the size-dependence of trapping forces exerted on metal particles. Transverse tapping forces produced by different illumination wavelengths are also evaluated. The numeric simulation demonstrates the possibility of trapping moderate-sized metal particles whose radii are comparable to wavelength.

Ensemble inequivalence in single-molecule experiments

In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as statistical systems, where the thermodynamic limit is represented by infinitely long chains. The question of equivalence between different ensembles is not at all obvious and has been addressed in the literature, with sometimes contradicting conclusions. We address this problem by studying the scaling properties of the ensemble difference for two different chain models as a function of the degree of polymerization. By characterizing the scaling behavior of the difference between the isotensional (Gibbs) and isometric (Helmholtz) ensembles in the transition from the low-stretching to the high-stretching regime, we show that ensemble equivalence cannot be reached for macroscopic chains in the low force regime, and we characterize the transition from the inequivalence to the equivalence regime.

Optical force sensor array in a microfluidic device based on holographic optical tweezers

Holographic optical tweezers (HOT) are a versatile technology, with which complex arrays and movements of optical traps can be realized to manipulate multiple microparticles in parallel and to measure the forces affecting them in the piconewton range. We report on the combination of HOT with a fluorescence microscope and a stop-flow, multi-channel microfluidic device. The integration of a high-speed camera into the setup allows for the calibration of all the traps simultaneously both using Boltzmann statistics or the power spectrum density of the particle diffusion within the optical traps. This setup permits complete spatial, chemical and visual control of the microenvironment applicable to probing chemo-mechanical properties of cellular or subcellular structures. As an example we constructed a biomimetic, quasi-two-dimensional actin network on an array of trapped polystyrene microspheres inside the microfluidic chamber. During crosslinking of the actin filaments by Mg(2+) ions, we observe the build up of mechanical tension throughout the actin network. Thus, we demonstrate how our integrated HOT-microfluidics platform can be used as a reconfigurable force sensor array with piconewton resolution to investigate chemo-mechanical processes.

Force mapping of an extended light pattern in an inclined plane: deterministic regime

We present a full quantitative mapping of the non-linear optical trapping force associated to an extended interference pattern of fringes as a function of the position. To map this force, we studied the dynamics of microscopic spherical beads of different sizes (8, 10 and 14.5 microns in diameter) moving through the light pattern. For this range of particle sizes, the system is overdamped due to the viscous drag and the effect of thermal noise is negligible. The novel experimental approach consists in tilting the sample cell a small angle with respect to the horizontal, thus we have a deterministic particle in an inclined plane. The combined action of the optical force and gravity gives rise to a washboard potential. We compared our experimental results with a ray optics model and found a good quantitative agreement. For each size of the microsphere we studied different spatial periods of the interference fringes.

Bacterial translocation motors investigated by single molecule techniques

Translocation of DNA and protein fibers through narrow constrictions is a ubiquitous and crucial activity of bacterial cells. Bacteria use specialized machines to support macromolecular movement. A very important step toward a mechanistic understanding of these translocation machines is the characterization of their physical properties at the single molecule level. Recently, four bacterial transport processes have been characterized by nanomanipulation at the single molecule level, DNA translocation by FtsK and SpoIIIE, DNA import during transformation, and the related process of a type IV pilus retraction. With all four processes, the translocation rates, processivity, and stalling forces were remarkably high as compared with single molecule experiments with other molecular motors. Although substrates of all four processes proceed along a preferential direction of translocation, directionality has been shown to be controlled by distinct mechanisms.

The structural dynamics of macromolecular processes

Dynamic processes involving macromolecular complexes are essential to cell function. These processes take place over a wide variety of length scales from nanometers to micrometers, and over time scales from nanoseconds to minutes. As a result, information from a variety of different experimental and computational approaches is required. We review the relevant sources of information and introduce a framework for integrating the data to produce representations of dynamic processes.

The major architects of chromatin: architectural proteins in bacteria, archaea and eukaryotes

The genomic DNA of all organisms across the three kingdoms of life needs to be compacted and functionally organized. Key players in these processes are DNA supercoiling, macromolecular crowding and architectural proteins that shape DNA by binding to it. The architectural proteins in bacteria, archaea and eukaryotes generally do not exhibit sequence or structural conservation especially across kingdoms. Instead, we propose that they are functionally conserved. Most of these proteins can be classified according to their architectural mode of action: bending, wrapping or bridging DNA. In order for DNA transactions to occur within a compact chromatin context, genome organization cannot be static. Indeed chromosomes are subject to a whole range of remodeling mechanisms. In this review, we discuss the role of (i) DNA supercoiling, (ii) macromolecular crowding and (iii) architectural proteins in genome organization, as well as (iv) mechanisms used to remodel chromosome structure and to modulate genomic activity. We conclude that the underlying mechanisms that shape and remodel genomes are remarkably similar among bacteria, archaea and eukaryotes.

Intersubunit coordination in a homomeric ring ATPase

Homomeric ring ATPases perform many vital and varied tasks in the cell, ranging from chromosome segregation to protein degradation. Here we report the direct observation of the intersubunit coordination and step size of such a ring ATPase, the double-stranded-DNA packaging motor in the bacteriophage phi29. Using high-resolution optical tweezers, we find that packaging occurs in increments of 10 base pairs (bp). Statistical analysis of the preceding dwell times reveals that multiple ATPs bind during each dwell, and application of high force reveals that these 10-bp increments are composed of four 2.5-bp steps. These results indicate that the hydrolysis cycles of the individual subunits are highly coordinated by means of a mechanism novel for ring ATPases. Furthermore, a step size that is a non-integer number of base pairs demands new models for motor-DNA interactions.

Quantifying DNA melting transitions using single-molecule force spectroscopy

We stretched a DNA molecule using atomic force microscope and quantified the mechanical properties associated with B and S forms of double-stranded DNA (dsDNA), molten DNA, and single-stranded DNA (ssDNA). We also fit overdamped diffusion models to the AFM time series and used these models to extract additional kinetic information about the system. Our analysis provides additional evidence supporting the view that S-DNA is a stable intermediate encountered during dsDNA melting by mechanical force. In addition, we demonstrated that the estimated diffusion models can detect dynamical signatures of conformational degrees of freedom not directly observed in experiments.

Constant power optical tweezers with controllable torque

We describe a means for controlling the spin angular-momentum flux of a laser beam at constant power, without introducing any elliptical or linear polarization. This allows a controllable torque, acting to spin the particle uniformly, to be exerted on a birefringent particle in optical tweezers. The constant power means that transverse and axial trapping, and heating due to absorption, are unaffected by changing the torque. The torque can be computer controlled and rapidly changed. In addition, the lateral trapping is kept constant. Very low torques can be obtained such that rotational Brownian motion of birefringent particles can be observed. This has the potential to greatly extend the quantitative applications of the rotation of birefringent objects in optical tweezers.

Quantifying multiscale noise sources in single-molecule time series

When analyzing single-molecule data, a low-dimensional set of system observables typically serves as the observational data. We calibrate stochastic dynamical models from time series that record such observables. Numerical techniques for quantifying noise from multiple time scales in a single trajectory, including experimental instrument and inherent thermal noise, are demonstrated. The techniques are applied to study time series coming from both simulations and experiments associated with the nonequilibrium mechanical unfolding of titin's I27 domain. The estimated models can be used for several purposes, (1) detect dynamical signatures of "rare events" by analyzing the effective diffusion and force as a function of the monitored observable, (2) quantify the influence that conformational degrees of freedom, which are typically difficult to directly monitor experimentally, have on the dynamics of the monitored observable, (3) quantitatively compare the inherent thermal noise to other noise sources, for example, instrument noise, variation induced by conformational heterogeneity, and so forth, (4) simulate random quantities associated with repeated experiments, and (5) apply pathwise, that is, trajectory-wise, hypothesis tests to assess the goodness-of-fit of the models and even detect conformational transitions in noisy signals. These items are all illustrated with several examples.

Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are also used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of Adenylate Kinase.

Calibration of dynamic holographic optical tweezers for force measurements on biomaterials

Holographic optical tweezers (HOTs) enable the manipulation of multiple traps independently in three dimensions in real time. Application of this technique to force measurements requires calibration of trap stiffness and its position dependence. Here, we determine the trap stiffness of HOTs as they are steered in two dimensions. To do this, we trap a single particle in a multiple-trap configuration and analyze the power spectrum of the laser deflection on a position-sensitive photodiode. With this method, the relative trap strengths can be determined independent of exact particle size, and high stiffnesses can be probed because of the high bandwidth of the photodiode. We find a trap stiffness for each of three HOT traps of kappa approximately 26 pN/microm per 100 mW of laser power. Importantly, we find that this stiffness remains constant within +/- 4% over 20 microm displacements of a trap. We also investigate the minimum step size achievable when steering a trap with HOTs, and find that traps can be stepped and detected within approximately 2 nm in our instrument, although there is an underlying position modulation of the traps of comparable scale that arises from SLM addressing. The independence of trap stiffness on steering angle over wide ranges and the nanometer positioning accuracy of HOTs demonstrate the applicability of this technique to quantitative study of force response of extended biomaterials such as cells or elastomeric protein networks.

Single molecule studies of homologous recombination

Single molecule methods offer an unprecedented opportunity to examine complex macromolecular reactions that are obfuscated by ensemble averaging. The application of single molecule techniques to study DNA processing enzymes has revealed new mechanistic details that are unobtainable from bulk biochemical studies. Homologous DNA recombination is a multi-step pathway that is facilitated by numerous enzymes that must precisely and rapidly manipulate diverse DNA substrates to repair potentially lethal breaks in the DNA duplex. In this review, we present an overview of single molecule assays that have been developed to study key aspects of homologous recombination and discuss the unique information gleaned from these experiments.

In singulo biochemistry: when less is more

It has been over one-and-a-half decades since methods of single-molecule detection and manipulation were first introduced in biochemical research. Since then, the application of these methods to an expanding variety of problems has grown at a vertiginous pace. While initially many of these experiments led more to confirmatory results than to new discoveries, today single-molecule methods are often the methods of choice to establish new mechanism-based results in biochemical research. Throughout this process, improvements in the sensitivity, versatility, and both spatial and temporal resolution of these techniques has occurred hand in hand with their applications. We discuss here some of the advantages of single-molecule methods over their bulk counterparts and argue that these advantages should help establish them as essential tools in the technical arsenal of the modern biochemist.

See me, feel me: methods to concurrently visualize and manipulate single DNA molecules and associated proteins

Direct visualization of DNA and proteins allows researchers to investigate DNA–protein interactions with great detail. Much progress has been made in this area as a result of increasingly sensitive single-molecule fluorescence techniques. At the same time, methods that control the conformation of DNA molecules have been improving constantly. The combination of both techniques has appealed to researchers ever since single-molecule measurements have become possible and indeed first implementations of such combined approaches have proven useful in the study of several DNA-binding proteins in real time. Here, we describe the technical state-of-the-art of various integrated manipulation-and-visualization methods. We first discuss methods that allow only little control over the DNA conformation, such as DNA combing. We then describe DNA flow-stretching approaches that allow more control, and end with the full control on position and extension obtained by manipulating DNA with optical tweezers. The advantages and limitations of the various techniques are discussed, as well as several examples of applications to biophysical or biochemical questions. We conclude with an outlook describing potential future technical developments in combining fluorescence microscopy with DNA micromanipulation technology.

Do-it-yourself guide: how to use the modern single-molecule toolkit

Single-molecule microscopy has evolved into the ultimate-sensitivity toolkit to study systems from small molecules to living cells, with the prospect of revolutionizing the modern biosciences. Here we survey the current state of the art in single-molecule tools including fluorescence spectroscopy, tethered particle microscopy, optical and magnetic tweezers, and atomic force microscopy. We also provide guidelines for choosing the right approach from the available single-molecule toolkit for applications as diverse as structural biology, enzymology, nanotechnology and systems biology.