Recent Advances in Optical Tweezers

Molecular plasmonics for biology and nanomedicine

The optical excitation of surface plasmons in metal nanoparticles leads to nanoscale spatial confinement of electromagnetic fields. The confined electromagnetic fields can generate intense, localized thermal energy and large near-field optical forces. The interaction between these effects and nearby molecules has led to the emerging field known as molecular plasmonics. Recent advances in molecular plasmonics have enabled novel optical materials and devices with applications in biology and nanomedicine. In this article, we categorize three main types of interactions between molecules and surface plasmons: optical, thermal and mechanical. Within the scope of each type of interaction, we will review applications of molecular plasmonics in biology and nanomedicine. We include a wide range of applications that involve sensing, spectral analysis, imaging, delivery, manipulation and heating of molecules, biomolecules or cells using plasmonic effects. We also briefly describe the physical principles of molecular plasmonics and progress in the nanofabrication, surface functionalization and bioconjugation of metal nanoparticles.

Acoustic trapping with a high frequency linear phased array

A high frequency ultrasonic phased array is shown to be capable of trapping and translating microparticles precisely and efficiently, made possible due to the fact that the acoustic beam produced by a phased array can be both focused and steered. Acoustic manipulation of microparticles by a phased array is advantageous over a single element transducer since there is no mechanical movement required for the array. Experimental results show that 45 μm diameter polystyrene microspheres can be easily and accurately trapped and moved to desired positions by a 64-element 26 MHz phased array.

Optical trapping, driving, and arrangement of particles using a tapered fibre probe

The ability of manipulating mesoscopic objects with high precision and flexibility is extremely important for a wide variety of fields from physics, biochemistry, to biomedicine. Particularly, the ability of arranging particles/cells into desired patterns precisely is a challenge for numerous physical and biological applications. Here, we report a strategy of realizing highly flexible trapping, driving, and precise arrangement of particles using a tapered fibre probe. Using randomly distributed 3-µm-diameter silica particles as an example, we demonstrate that the strategy is able to stably trap the particles and drive them to targeted regions, subsequently arrange the particles into desired patterns. To further demonstrate the ability of this strategy, experiments were done using sub-micron sized particles and biological samples (bacteria and cells). This strategy provides a new approach to manipulate mesoscopic objects precisely and flexibly, and hopefully can be used in future fundamental and applied researches of interdiscipline.

Optically-actuated translational and rotational motion at the microscale for microfluidic manipulation and characterization

The single beam optical trap (optical tweezers), a highly focused beam, is on its way to revolutionizing not only the fields of colloidal physics and biology, but also materials science and engineering. Recently, spatially-extended three-dimensional light patterns have gained considerable usage for exerting force to alter, manipulate, organize and characterize materials. To advance the degree of manipulation, such as rotation of materials in microfluidic environments along with spatial structuring, other beam parameters such as phase and polarization have to be configured. These advances in optical tweezers' technology have enabled complex microfluidic actuation and sorting. In addition to remotely (in a non-contact way) applying force and torques in three-dimensions, which can be continuously varied unlike mechanical manipulators, optical tweezers-based methods can be used for sensing the force of interaction between microscopic objects in a microfluidic environment and for the characterization of micro-rheological properties. In this review, we place emphasis on applications of optical actuation based on novel beams in performing special functions such as rotation, transportation, sorting and characterization of the microscopic objects. Further, we have an extended discussion on optical actuation (transport and rotation) with fiber optic microbeams and spectroscopic characterization in the microfluidic environment. All these advancements in optical manipulation would further facilitate the growing use of optical tools for complex microfluidic manipulations.

Video-based and interference-free axial force detection and analysis for optical tweezers

For measuring the minute forces exerted on single molecules during controlled translocation through nanopores with sub-piconewton precision, we have developed a video-based axial force detection and analysis system for optical tweezers. Since our detection system is equipped with a standard and versatile CCD video camera with a limited bandwidth offering operation at moderate light illumination with minimal sample heating, we integrated Allan variance analysis for trap stiffness calibration. Upon manipulating a microbead in the vicinity of a weakly reflecting surface with simultaneous axial force detection, interference effects have to be considered and minimized. We measured and analyzed the backscattering light properties of polystyrene and silica microbeads with different diameters and propose distinct and optimized experimental configurations (microbead material and diameter) for minimal light backscattering and virtually interference-free microbead position detection. As a proof of principle, we investigated the nanopore threading forces of a single dsDNA strand attached to a microbead with an overall force resolution of ±0.5 pN at a sample rate of 123 Hz.

Auto- and cross-power spectral analysis of dual trap optical tweezer experiments using Bayesian inference

The thermal fluctuations of micron-sized beads in dual trap optical tweezer experiments contain complete dynamic information about the viscoelastic properties of the embedding medium and-if present-macromolecular constructs connecting the two beads. To quantitatively interpret the spectral properties of the measured signals, a detailed understanding of the instrumental characteristics is required. To this end, we present a theoretical description of the signal processing in a typical dual trap optical tweezer experiment accounting for polarization crosstalk and instrumental noise and discuss the effect of finite statistics. To infer the unknown parameters from experimental data, a maximum likelihood method based on the statistical properties of the stochastic signals is derived. In a first step, the method can be used for calibration purposes: We propose a scheme involving three consecutive measurements (both traps empty, first one occupied and second empty, and vice versa), by which all instrumental and physical parameters of the setup are determined. We test our approach for a simple model system, namely a pair of unconnected, but hydrodynamically interacting spheres. The comparison to theoretical predictions based on instantaneous as well as retarded hydrodynamics emphasizes the importance of hydrodynamic retardation effects due to vorticity diffusion in the fluid. For more complex experimental scenarios, where macromolecular constructs are tethered between the two beads, the same maximum likelihood method in conjunction with dynamic deconvolution theory will in a second step allow one to determine the viscoelastic properties of the tethered element connecting the two beads.

Combined versatile high-resolution optical tweezers and single-molecule fluorescence microscopy

Optical trapping and single-molecule fluorescence are two major single-molecule approaches. Their combination has begun to show greater capability to study more complex systems than either method alone, but met many fundamental and technical challenges. We built an instrument that combines base-pair resolution dual-trap optical tweezers with single-molecule fluorescence microscopy. The instrument has complementary design and functionalities compared with similar microscopes previously described. The optical tweezers can be operated in constant force mode for easy data interpretation or in variable force mode for maximum spatiotemporal resolution. The single-molecule fluorescence detection can be implemented in either wide-field or confocal imaging configuration. To demonstrate the capabilities of the new instrument, we imaged a single stretched λ DNA molecule and investigated the dynamics of a DNA hairpin molecule in the presence of fluorophore-labeled complementary oligonucleotide. We simultaneously observed changes in the fluorescence signal and pauses in fast extension hopping of the hairpin due to association and dissociation of individual oligonucleotides. The combined versatile microscopy allows for greater flexibility to study molecular machines or assemblies at a single-molecule level.

The interrelation between mechanical characteristics of contracting muscle, cross-bridge internal structure, and the mechanism of chemomechanical energy transduction

The cross-bridge working stroke is regarded as a continuous (without jumps) change of myosin head internal state under the action of a force exerted within the nucleotide-binding site. Involvement of a concept of continuous cross-bridge conformation enables discussion of the nature of the force propelling muscle, and the Coulomb repulsion of like-charged adenosine triphosphate (ATP) fragments ADP(2-) and P (i) (2-) can quite naturally be considered as the source of this force. Two entirely different types of working stroke termination are considered. Along with the fluctuation mechanism, which controls the working stroke duration t (w) at isometric contraction, another interrupt mechanism is initially taken into account. It is triggered when the lever arm shift amounts to the maximal value S ≈ 11 nm, the back door opens, and P(i) crashes out. As a result, t (w) becomes inversely proportional to the velocity v of sliding filaments t (w) ≈ S/v for a wide range of values of v. Principal features of the experimentally observed dependences of force, efficiency, and rate of heat production on velocity and ATP concentration can then be reproduced by fitting a single parameter: the velocity-independent time span t (r) between the termination of the last and beginning of the next working stroke. v becomes the principal variable of the model, and the muscle force changes under external load are determined by variations in v rather than in the tension of filaments. The Boltzmann equation for an ensemble of cross-bridges is obtained, and some collective effects are discussed.

An efficient computational method for calculating ligand binding affinities

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, the docking scores are not sufficiently precise to represent the protein-ligand binding affinity. Here, we developed an efficient computational method for calculating protein-ligand binding affinity, which is based on molecular mechanics generalized Born/surface area (MM-GBSA) calculations and Jarzynski identity. Jarzynski identity is an exact relation between free energy differences and the work done through non-equilibrium process, and MM-GBSA is a semimacroscopic approach to calculate the potential energy. To calculate the work distribution when a ligand is pulled out of its binding site, multiple protein-ligand conformations are randomly generated as an alternative to performing an explicit single-molecule pulling simulation. We assessed the new method, multiple random conformation/MM-GBSA (MRC-MMGBSA), by evaluating ligand-binding affinities (scores) for four target proteins, and comparing these scores with experimental data. The calculated scores were qualitatively in good agreement with the experimental binding affinities, and the optimal docking structure could be determined by ranking the scores of the multiple docking poses obtained by the molecular docking process. Furthermore, the scores showed a strong linear response to experimental binding free energies, so that the free energy difference of the ligand binding (ΔΔG) could be calculated by linear scaling of the scores. The error of calculated ΔΔG was within ≈ ± 1.5 kcal.mol(-1) of the experimental values. Particularly, in the case of flexible target proteins, the MRC-MMGBSA scores were more effective in ranking ligands than those generated by the MM-GBSA method using a single protein-ligand conformation. The results suggest that, owing to its lower computational costs and greater accuracy, the MRC-MMGBSA offers efficient means to rank the ligands, in the post-docking process, according to their binding affinities, and to compare these directly with the experimental values.

Light activated cell migration in synthetic extracellular matrices

Synthetic extracellular matrices provide a framework in which cells can be exposed to defined physical and biological cues. However no method exists to manipulate single cells within these matrices. It is desirable to develop such methods in order to understand fundamental principles of cell migration and define conditions that support or inhibit cell movement within these matrices. Here, we present a strategy for manipulating individual mammalian stem cells in defined synthetic hydrogels through selective optical activation of Rac, which is an intracellular signaling protein that plays a key role in cell migration. Photoactivated cell migration in synthetic hydrogels depended on mechanical and biological cues in the biomaterial. Real-time hydrogel photodegradation was employed to create geometrically defined channels and spaces in which cells could be photoactivated to migrate. Cell migration speed was significantly higher in the photo-etched channels and cells could easily change direction of movement compared to the bulk hydrogels.

High-resolution detection of Brownian motion for quantitative optical tweezers experiments

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

Trapping and rotating microparticles and bacteria with moiré-based optical propelling beams

We propose and demonstrate trapping and rotation of microparticles and biological samples with a moiré-based rotating optical tweezers. We show that polystyrene beads, as well as Escherichia coli cells, can be rotated with ease, while the speed and direction of rotation are fully controllable by a computer, obviating mechanical movement or phase-sensitive interference. Furthermore, we demonstrate experimentally the generation of white-light propelling beams and arrays, and discuss the possibility of optical tweezing and particle micro-manipulation based on incoherent white-light rotating patterns.

Site-specific attachment of a protein to a carbon nanotube end without loss of protein function

Establishing a nanobiohybrid device largely relies on the availability of various bioconjugation procedures which allow coupling of biomolecules and inorganic materials. Especially, site-specific coupling of a protein to nanomaterials is highly useful and significant, since it can avoid adversely affecting the protein's function. In this study, we demonstrated a covalent coupling of a protein of interest to the end of carbon nanotubes without affecting protein's function. A modified Staudinger-Bertozzi ligation was utilized to couple a carbon nanotube end with an azide group which is site-specifically incorporated into a protein of interest. We demonstrated that Ca(2+)-sensor protein, calmodulin, can be attached to the end of the nanotubes without affecting the ability to bind to the substrate in a calcium-dependent manner. This procedure can be applied not only to nanotubes, but also to other nanomaterials, and therefore provides a fundamental technique for well-controlled protein conjugation.

Optimization of plasmonic nanostructure for nanoparticle trapping

We present a detailed analysis of nanoparticle trapping using plasmonic nanostructures, which predicts an improvement of two orders of magnitude in trapping force obtained by optimizing the plasmon resonance of the nanostructures. As the result, a total of four orders of magnitude enhancement in trapping force can be achieved comparing to the case without the nanostructures. In addition, it is illustrated that tuning the resonance wavelength is achievable by varying the diameter and/or the height of the nanorods.

Optical alignment and confinement of an ellipsoidal nanorod in optical tweezers: a theoretical study

Within the Rayleigh approximation, we investigate the behavior of an individual ellipsoidal metal nanorod that is optically confined in three dimensions using a single focused laser beam. We focus on the description of the optical torque and optical force acting upon the nanorod placed into a linearly polarized Gaussian beam (scalar description of the electric field) or a strongly focused beam (vector field description). The study comprises the influence of the trapping laser wavelength, the angular aperture of focusing optics, the orientation of the ellipsoidal nanorod, and the aspect ratio of its principal axes. The results reveal a significantly different behavior of the nanorod if the trapping wavelength is longer or shorter than the wavelength corresponding to the longitudinal plasmon resonance mode. Published experimental observations are compared with our theoretical predictions with satisfactory results.

Dynamic trapping and high-throughput patterning of cells using pneumatic microstructures in an integrated microfluidic device

Microfluidic trapping methods create significant opportunities to establish highly controlled cell positioning and arrangement for the microscale study of numerous cellular physiological and pathological activities. However, a simple, straightforward, dynamic, and high-throughput method for cell trapping is not yet well established. In the present paper, we report a direct active trapping method using an integrated microfluidic device with pneumatic microstructures (PμSs) for both operationally and quantitatively dynamic localization of cells, as well as for high-throughput cell patterning. We designed and fabricated U-shape PμS arrays to replace the conventional fixed microstructures for reversible trapping. Multidimensional dynamics and spatial consistency of the PμSs were optically characterized and quantitatively demonstrated. Furthermore, we performed a systematic trapping investigation of the PμSs actuated at a pressure range of 0 psi to 20 psi using three types of popularly applied mammalian cells, namely, human lung adenocarcinoma A549 cells, human hepatocellular liver carcinoma HepG2 cells, and human breast adenocarcinoma MCF-7 cells. The cells were quantitatively trapped and controlled by the U-shape PμSs in a programmatic and parallel manner, and could be opportunely released. The trapped cells with high viability were hydrodynamically protected by the real-time actuation of specifically designed umbrella-like PμSs. We demonstrate that PμSs can be applied as an active microfluidic component for large-scale cell patterning and manipulation, which could be useful in many cell-based tissue organization, immunosensor, and high-throughput imaging and screening.

Physics of bacterial morphogenesis

Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.

Tunable optical tweezers for wavelength-dependent measurements

Optical trapping forces depend on the difference between the trap wavelength and the extinction resonances of trapped particles. This leads to a wavelength-dependent trapping force, which should allow for the optimization of optical tweezers systems, simply by choosing the best trapping wavelength for a given application. Here we present an optical tweezer system with wavelength tunability, for the study of resonance effects. With this system, the optical trap stiffness is measured for single trapped particles that exhibit either single or multiple extinction resonances. We include discussions of wavelength-dependent effects, such as changes in temperature, and how to measure them.

Controlled photonic manipulation of proteins and other nanomaterials

The ability to controllably handle the smallest materials is a fundamental enabling technology for nanoscience. Conventional optical tweezers have proven useful for manipulating microscale objects but cannot exert enough force to manipulate dielectric materials smaller than about 100 nm. Recently, several near-field optical trapping techniques have been developed that can provide higher trapping stiffness, but they tend to be limited in their ability to reversibly trap and release smaller materials due to a combination of the extremely high electromagnetic fields and the resulting local temperature rise. Here, we have developed a new form of photonic crystal "nanotweezer" that can trap and release on-command Wilson disease proteins, quantum dots, and 22 nm polymer particles with a temperature rise less than ~0.3 K, which is below the point where unwanted fluid mechanical effects will prevent trapping or damage biological targets.

DNA looping by FokI: the impact of twisting and bending rigidity on protein-induced looping dynamics

Protein-induced DNA looping is crucial for many genetic processes such as transcription, gene regulation and DNA replication. Here, we use tethered-particle motion to examine the impact of DNA bending and twisting rigidity on loop capture and release, using the restriction endonuclease FokI as a test system. To cleave DNA efficiently, FokI bridges two copies of an asymmetric sequence, invariably aligning the sites in parallel. On account of the fixed alignment, the topology of the DNA loop is set by the orientation of the sites along the DNA. We show that both the separation of the FokI sites and their orientation, altering, respectively, the twisting and the bending of the DNA needed to juxtapose the sites, have profound effects on the dynamics of the looping interaction. Surprisingly, the presence of a nick within the loop does not affect the observed rigidity of the DNA. In contrast, the introduction of a 4-nt gap fully relaxes all of the torque present in the system but does not necessarily enhance loop stability. FokI therefore employs torque to stabilise its DNA-looping interaction by acting as a ‘torsional’ catch bond.

DNA translocation of ATP-dependent chromatin remodeling factors revealed by high-resolution optical tweezers

ATP-dependent chromatin remodeling complexes (remodelers) use the energy of ATP hydrolysis to regulate chromatin structures by repositioning and reconfiguring nucleosomes. Ensemble experiments have suggested that remodeler ATPases are DNA translocases, molecular motors capable of processively moving along DNA. This concept of DNA translocation has become a foundation for understanding the molecular mechanisms of ATP-dependent chromatin remodeling and its biological functions. However, quantitative characterizations of DNA translocation by representative remodelers are rare. Furthermore, it is unclear how a unified theory of chromatin remodeling is built upon this foundation. To address these problems, high-resolution optical tweezers have been applied to investigate remodeler translocation on bare DNA and nucleosomal DNA substrates at a single-molecule level. Our strategy is to hold two ends of a single DNA molecule and measure remodeler translocation by detecting the end-to-end extension and tension changes of the DNA molecule in response to chromatin remodeling. These single-molecule assays can reveal detailed kinetics of remodeler translocation, including velocity, processivity, stall force, pauses, direction changes, and even step size. Here we describe instruments, reagents, sample preparations, and detailed protocols for the single-molecule experiments. We show that optical tweezer force microscopy is a powerful and friendly tool for studies of chromatin structures and remodeling.

Unzipping single DNA molecules to study nucleosome structure and dynamics

DNA unzipping is a powerful tool to study protein-DNA interactions at the single-molecule level. In this chapter, we provide a detailed and practical guide to performing this technique with an optical trap, using nucleosome studies as an example. We detail protocols for preparing an unzipping template, constructing and calibrating the instrument, and acquiring, processing, and analyzing unzipping data. We also summarize major results from utilization of this technique for the studies of nucleosome structure, dynamics, positioning, and remodeling.

Single-molecule studies of viral DNA packaging

Many double-stranded DNA bacteriophages and viruses use specialized ATP-driven molecular machines to package their genomes into tightly confined procapsid shells. Over the last decade, single-molecule approaches - and in particular, optical tweezers - have made key contributions to our understanding of this remarkable process. In this chapter, we review these advances and the insights they have provided on the packaging mechanisms of three bacteriophages: φ 29, λ, and T4.

Single-molecule optical-trapping measurements with DNA anchored to an array of gold nanoposts

Gold-thiol chemistry is one of the most successful chemistries for conjugating biomolecules to surfaces, but such chemistry has not been exploited in optical-trapping experiments because of laser-induced ablation of gold. In this work, we describe a method to combine these two separate technologies without undue heating using DNA anchored to gold nanostructures (r = 50-250 nm; h ≈ 20 nm). Moreover, we demonstrate a quantitative and mechanically robust (>100 pN) optical-trapping assay. By using three dithiol phosphoramidites (DTPAs) incorporated into a polymerase chain reaction (PCR) primer, the gold-DNA bond remained stable 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 (mPEG-SH). Overall, this surface conjugation of biomolecules onto an ordered array of gold nanostructures by chemically and mechanically robust bonds provides a unique way to carry out spatially controlled, repeatable measurements of single molecules.

The ribosome modulates nascent protein folding

Proteins are synthesized by the ribosome and generally must fold to become functionally active. Although it is commonly assumed that the ribosome affects the folding process, this idea has been extremely difficult to demonstrate. We have developed an experimental system to investigate the folding of single ribosome-bound stalled nascent polypeptides with optical tweezers. In T4 lysozyme, synthesized in a reconstituted in vitro translation system, the ribosome slows the formation of stable tertiary interactions and the attainment of the native state relative to the free protein. Incomplete T4 lysozyme polypeptides misfold and aggregate when free in solution, but they remain folding-competent near the ribosomal surface. Altogether, our results suggest that the ribosome not only decodes the genetic information and synthesizes polypeptides, but also promotes efficient de novo attainment of the native state.

Plasmonic nanoparticle chain in a light field: a resonant optical sail

Optical trapping and driving of small objects has become a topic of increasing interest in multidisciplinary sciences. We propose to use a chain made of metallic nanoparticles as a resonant light sail, attached by one end point to a transparent object and propelling it by the use of electromagnetic radiation. Driving forces exerted on the chain are theoretically studied as a function of radiation's wavelength and chain's alignments with respect to the direction of radiation. Interestingly, there is a window in the frequency spectrum in which null-torque equilibrium configuration, with minimum geometric cross section, corresponds to a maximum in the driving force.

Single-molecule analysis of telomerase structure and function

The telomerase ribonucleoprotein is a specialized reverse transcriptase required to maintain protective chromosome end-capping structures called telomeres. In most cells, telomerase is not active and the natural shortening of telomeres with each round of DNA replication ultimately triggers cell growth arrest. In contrast, the presence of telomerase confers a high level of renewal capacity upon rapidly dividing cells. Telomerase is aberrantly activated in 90% of human cancers and thus represents an important target for anticancer therapeutics. However, the naturally low abundance of telomerase has hampered efforts to obtain high-resolution models for telomerase structure and function. To circumvent these challenges, single-molecule techniques have recently been employed to investigate telomerase assembly, structure, and catalysis.

Colored noise in the fluctuations of an extended DNA molecule detected by optical trapping

We studied fluctuations of an optically trapped bead connected to a single DNA molecule anchored between the bead and a cover glass or between two optically trapped beads. Power spectral densities of the bead position for different extensions of the molecule were compared with the power spectral density of the position fluctuations of the same bead without the molecule attached. Experiments showed that the fluctuations of the DNA molecule extended up to 80% by a force of 3 pN include the colored noise contribution with spectral dependence 1/f (α) with α ~ 0.75.

Robust control approach to force estimation in a constant position optical tweezers

Feedback enhanced optical tweezers with position regulation capability enable detection and estimation of forces in the pico-Newton regime. In this article we delineate the fundamental limitations and challenges of existing approaches for regulating position and force estimation in an optical tweezer. A modern control systems approach is shown to improve the bandwidth of force estimation by three to four times which is corroborated experimentally.

Positional stability of holographic optical traps

The potential of digital holography for complex manipulation of micron-sized particles with optical tweezers has been clearly demonstrated. By contrast, its use in quantitative experiments has been rather limited, partly due to fluctuations introduced by the spatial light modulator (SLM) that displays the kinoforms. This is an important issue when high temporal or spatial stability is a concern. We have investigated the performance of both an analog-addressed and a digitally-addressed SLM, measuring the phase fluctuations of the modulated beam and evaluating the resulting positional stability of a holographic trap. We show that, despite imparting a more unstable modulation to the wavefront, our digitally-addressed SLM generates optical traps in the sample plane stable enough for most applications. We further show that traps produced by the analog-addressed SLM exhibit a superior pointing stability, better than 1 nm, which is comparable to that of non-holographic tweezers. These results suggest a means to implement precision force measurement experiments with holographic optical tweezers (HOTs).

Stretching short sequences of DNA with constant force axial optical tweezers

Single-molecule techniques for stretching DNA of contour lengths less than a kilobase are fraught with experimental difficulties. However, many interesting biological events such as histone binding and protein-mediated looping of DNA, occur on this length scale. In recent years, the mechanical properties of DNA have been shown to play a significant role in fundamental cellular processes like the packaging of DNA into compact nucleosomes and chromatin fibers. Clearly, it is then important to understand the mechanical properties of short stretches of DNA. In this paper, we provide a practical guide to a single-molecule optical tweezing technique that we have developed to study the mechanical behavior of DNA with contour lengths as short as a few hundred basepairs. The major hurdle in stretching short segments of DNA is that conventional optical tweezers are generally designed to apply force in a direction lateral to the stage (see Fig. 1). In this geometry, the angle between the bead and the coverslip, to which the DNA is tethered, becomes very steep for submicron length DNA. The axial position must now be accounted for, which can be a challenge, and, since the extension drags the microsphere closer to the coverslip, steric effects are enhanced. Furthermore, as a result of the asymmetry of the microspheres, lateral extensions will generate varying levels of torque due to rotation of the microsphere within the optical trap since the direction of the reactive force changes during the extension. Alternate methods for stretching submicron DNA run up against their own unique hurdles. For instance, a dual-beam optical trap is limited to stretching DNA of around a wavelength, at which point interference effects between the two traps and from light scattering between the microspheres begin to pose a significant problem. Replacing one of the traps with a micropipette would most likely suffer from similar challenges. While one could directly use the axial potential to stretch the DNA, an active feedback scheme would be needed to apply a constant force and the bandwidth of this will be quite limited, especially at low forces. We circumvent these fundamental problems by directly pulling the DNA away from the coverslip by using a constant force axial optical tweezers. This is achieved by trapping the bead in a linear region of the optical potential, where the optical force is constant-the strength of which can be tuned by adjusting the laser power. Trapping within the linear region also serves as an all optical force-clamp on the DNA that extends for nearly 350 nm in the axial direction. We simultaneously compensate for thermal and mechanical drift by finely adjusting the position of the stage so that a reference microsphere stuck to the coverslip remains at the same position and focus, allowing for a virtually limitless observation period.

Shear-flow-enhanced barrier crossing

We consider a single Brownian particle confined in a double well potential (DWP) and investigate its response to a linear shear flow by means of the probability density and current determined via numerical solution of the Fokker-Planck equation. Besides a shear-dependent distortion of the probability distribution, we find that the associated current crossing the potential barrier exhibits a convex dependency on the shear rate when the DWP's minima are far apart. With decreasing distance this functional dependency changes from a convex to concave characteristics accompanied with an increase of the probability current crossing the DWP's barrier. Through the difference map of the particle density distribution it is possible to extract the shear-flow-induced contribution to the particle density driving the barrier-crossing current. This may open the possibility to design specific flow profiles to optimize flow-induced activated transport of nanoparticles.

Quantitative analysis of shape and volume changes in activated thrombocytes in real time by single-shot spatial light modulator-based differential interference contrast imaging

We suggest to use a combination of optical tweezers and single-image quantitative differential interference contrast (DIC) emulated by a spatial light modulator (SLM) to study physiological shape changes in thrombocytes after activation and demonstrate the effectiveness of this system for the given task. A specially designed phase mask displayed at the SLM enables quantitative phase calculation from only a single recording. The optical tweezers stabilize trapped thrombocytes for long-time monitoring of changes in the optical thickness profile of thrombocytes during activation by adenosine diphosphate (ADP).

Self-assembled enzymatic monolayer directly bound to a gold surface: activity and molecular recognition force spectroscopy studies

Escherichia coli dihydrofolate reductase (ecDHFR) has one surface cysteine, C152, located opposite and distal to the active site. Here, we show that the enzyme spontaneously assembles on an ultraflat gold surface as a homogeneous, covalently bound monolayer. Surprisingly, the activity of the gold-immobilized ecDHFR as measured by radiographic analysis was found to be similar to that of the free enzyme in solution. Molecular recognition force spectroscopy was used to study the dissociation forces involved in the rupture of AFM probe-tethered methotrexate (MTX, a tight-binding inhibitor of DHFR) from the gold-immobilized enzyme. Treatment of the ecDHFR monolayer with free MTX diminished the interaction of the functionalized tip with the surface, suggesting that the interaction was indeed active-site specific. These findings demonstrate the viability of a simple and direct enzymatic surface-functionalization without the use of spacers, thus, opening the door to further applications in the area of biomacromolecular force spectroscopy.

Triaxial AFM probes for noncontact trapping and manipulation

We show that a triaxial atomic force microscopy probe creates a noncontact trap for a single particle in a fluid via negative dielectrophoresis. A zero in the electric field profile traps the particle above the probe surface, avoiding adhesion, and the repulsive region surrounding the zero pushes other particles away, preventing clustering. Triaxial probes are promising for three-dimensional assembly and for selective imaging of a particular property of a sample using interchangeable functionalized particles.

Detection of Steps in Single Molecule Data

Over the past few decades, single molecule investigations employing optical tweezers, AFM and TIRF microscopy have revealed that molecular behaviors are typically characterized by discrete steps or events that follow changes in protein conformation. These events, that manifest as steps or jumps, are short-lived transitions between otherwise more stable molecular states. A major limiting factor in determining the size and timing of the steps is the noise introduced by the measurement system. To address this impediment to the analysis of single molecule behaviors, step detection algorithms incorporate large records of data and provide objective analysis. However, existing algorithms are mostly based on heuristics that are not reliable and lack objectivity. Most of these step detection methods require the user to supply parameters that inform the search for steps. They work well, only when the signal to noise ratio (SNR) is high and stepping speed is low. In this report, we have developed a novel step detection method that performs an objective analysis on the data without input parameters, and based only on the noise statistics. The noise levels and characteristics can be estimated from the data providing reliable results for much smaller SNR and higher stepping speeds. An iterative learning process drives the optimization of step-size distributions for data that has unimodal step-size distribution, and produces extremely low false positive outcomes and high accuracy in finding true steps. Our novel methodology, also uniquely incorporates compensation for the smoothing affects of probe dynamics. A mechanical measurement probe typically takes a finite time to respond to step changes, and when steps occur faster than the probe response time, the sharp step transitions are smoothed out and can obscure the step events. To address probe dynamics we accept a model for the dynamic behavior of the probe and invert it to reveal the steps. No other existing method addresses the impact of probe dynamics on step detection. Importantly, we have also developed a comprehensive set of tools to evaluate various existing step detection techniques. We quantify the performance and limitations of various step detection methods using novel evaluation scales. We show that under these scales, our method provides much better overall performance. The method is validated on different simulated test cases, as well as experimental data.

Transverse superresolution technique involving rectified Laguerre-Gaussian LG(p)⁰ beams

A promising technique has been proposed recently [Opt. Commun. 284, 1331 (2011), Opt. Commun. 284, 4107 (2011)] for breaking the diffraction limit of light. This technique consists of transforming a symmetrical Laguerre-Gaussian LG(p)⁰ beam into a near-Gaussian beam at the focal plane of a thin converging lens thanks to a binary diffractive optical element (DOE) having a transmittance alternatively equal to -1 or +1, transversely. The effect of the DOE is to convert the alternately out-of-phase rings of the LG(p)⁰ beam into a unified phase front. The benefits of the rectified beam at the lens focal plane are a short Rayleigh range, which is very useful for many laser applications, and a focal volume much smaller than that obtained with a Gaussian beam. In this paper, we demonstrate numerically that the central lobe's radius of the rectified beam at the lens focal plane depends exclusively on the dimensionless radial intensity vanishing factor of the incident beam. Consequently, this value can be easily predicted.

Single-molecule studies of viral DNA packaging

Assembly of many dsDNA viruses involves packaging of DNA molecules into pre-assembled procapsids by portal molecular motor complexes. Techniques have recently been developed using optical tweezers to directly measure the packaging of single DNA molecules into single procapsids in real time and the forces generated by the molecular motor. Three different viruses, phages phi29, lambda, and T4, have been studied, revealing interesting similarities and differences in packaging dynamics. Single-molecule fluorescence methods have also been used to measure packaging kinetics and motor conformations. Here we review recent discoveries made using these new techniques.

Biological mechanisms, one molecule at a time

The last 15 years have witnessed the development of tools that allow the observation and manipulation of single molecules. The rapidly expanding application of these technologies for investigating biological systems of ever-increasing complexity is revolutionizing our ability to probe the mechanisms of biological reactions. Here, we compare the mechanistic information available from single-molecule experiments with the information typically obtained from ensemble studies and show how these two experimental approaches interface with each other. We next present a basic overview of the toolkit for observing and manipulating biology one molecule at a time. We close by presenting a case study demonstrating the impact that single-molecule approaches have had on our understanding of one of life's most fundamental biochemical reactions: the translation of a messenger RNA into its encoded protein by the ribosome.

Laser-induced thermophoresis of individual particles in a viscous liquid

This paper presents a detailed investigation of the motion of individual micro-particles in a moderately-viscous liquid in direct response to a local, laser-induced temperature gradient. By measuring particle trajectories in 3D, and comparing them to a simulated temperature profile, it is confirmed that the thermally-induced particle motion is the direct result of thermophoresis. The elevated viscosity of the liquid provides for substantial differences in the behavior predicted by various models of thermophoresis, which in turn allows measured data to be most appropriately matched to a model proposed by Brenner. This model is then used to predict the effective force resulting from thermophoresis in an optical trap. Based on these results, we predict when thermophoresis will strongly inhibit the ability of radiation pressure to trap nano-scale particles. The model also predicts that the thermophoretic force scales linearly with the viscosity of the liquid, such that choice of liquid plays a key role in the relative strength of the thermophoretic and radiation forces.