Femtonewton force spectroscopy of single extended DNA molecules

Approaching the perfect diode limit through a nonlinear interface

We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential for which three different types are considered, namely, harmonic, ϕ^{4}, and Frenkel-Kontorova. The two segments are nonlinearly coupled, between interfacial particles, by means of a power-law potential with exponent μ, which we vary, scanning from subharmonic to superharmonic potentials, up to the infinite-square-well limit (μ→∞). Thermal rectification is investigated by integrating the equations of motion and computing the heat fluxes. As a measure of rectification, we use the difference of the currents, resulting from the interchange of the baths, divided by their average (all quantities taken in absolute value). We find that rectification can be optimized by a given value of μ that depends on the bath temperatures and details of the chains. But, regardless of the type of on-site potential considered, the interfacial potential that produces maximal rectification approaches the infinite square well (μ→∞) when reducing the average temperature of the baths. Our analysis of thermal rectification focuses on this regime, for which we complement numerical results with heuristic considerations.

Electromagnetic Forces and Torques: From Dielectrophoresis to Optical Tweezers

Electromagnetic forces and torques enable many key technologies, including optical tweezers or dielectrophoresis. Interestingly, both techniques rely on the same physical process: the interaction of an oscillating electric field with a particle of matter. This work provides a unified framework to understand this interaction both when considering fields oscillating at low frequencies─dielectrophoresis─and high frequencies─optical tweezers. We draw useful parallels between these two techniques, discuss the different and often unstated assumptions they are based upon, and illustrate key applications in the fields of physical and analytical chemistry, biosensing, and colloidal science.

Elastic property of sickle cell anemia and sickle cell trait red blood cells

SIGNIFICANCE

We introduce a model for better calibration of the trapping force using an equal but oppositely directed drag force acting on a trapped red blood cell (RBC). We demonstrate this approach by studying RBCs' elastic properties from deidentified sickle cell anemia (SCA) and sickle cell trait (SCT) blood samples.

AIM

A laser trapping (LT) force was formulated and analytically calculated in a cylindrical model. Using this trapping force relative percent difference, the maximum (longitudinal) and minimum (transverse) radius rate and stiffness were used to study the elasticity.

APPROACH

The elastic property of SCA and SCT RBCs was analyzed using LT technique with computer controlled piezo-driven stage, in order to trap and stretch the RBCs.

RESULTS

For all parameters, the results show that the SCT RBC samples have higher elastic property than the SCA RBCs. The higher rigidity in the SCA cell may be due to the lipid composition of the membrane, which was affected by the cholesterol concentration.

CONCLUSIONS

By developing a theoretical model for different trapping forces, we have also studied the elasticity of RBCs in SCT (with hemoglobin type HbAS) and in SCA (with hemoglobin type HbSS). The results for the quantities describing the elasticity of the cells consistently showed that the RBCs in the SCT display lower rigidity and higher deformability than the RBCs with SCA.

Multiview microscopy of single cells through microstructure-based indirect optical manipulation

Fluorescent observation of cells generally suffers from the limited axial resolution due to the elongated point spread function of the microscope optics. Consequently, three-dimensional imaging results in axial resolution that is several times worse than the transversal. The optical solutions to this problem usually require complicated optics and extreme spatial stability. A straightforward way to eliminate anisotropic resolution is to fuse images recorded from multiple viewing directions achieved mostly by the mechanical rotation of the entire sample. In the presented approach, multiview imaging of single cells is implemented by rotating them around an axis perpendicular to the optical axis by means of holographic optical tweezers. For this, the cells are indirectly trapped and manipulated with special microtools made with two-photon polymerization. The cell is firmly attached to the microtool and is precisely manipulated with 6 degrees of freedom. The total control over the cells' position allows for its multiview fluorescence imaging from arbitrarily selected directions. The image stacks obtained this way are combined into one 3D image array with a multiview image processing pipeline resulting in isotropic optical resolution that approaches the lateral diffraction limit. The presented tool and manipulation scheme can be readily applied in various microscope platforms.

Roles of entropic and solvent damping forces in the dynamics of polymer tethered nanoparticles and implications for single molecule sensing

Tethering a particle to a surface with a single molecule allows detection of the molecule and analysis of molecular conformations and interactions.

Tethering a particle to a surface with a single molecule allows detection of the molecule and analysis of molecular conformations and interactions. Understanding the dynamics of the system is critical to all applications. Here we present a plasmonic imaging study of two important forces that govern the dynamics. One is entropic force arising from the conformational change of the molecular tether, and the other is solvent damping on the particle and the molecule. We measure the response of the particle by driving it into oscillation with an alternating electric field. By varying the field frequency, we study the dynamics on different time scales. We also vary the type of the tether molecule (DNA and polyethylene glycol), size of the particle, and viscosity of the solvent, and describe the observations with a model. The study allows us to derive a single parameter to predict the relative importance of the entropic and damping forces. The findings provide insights into single molecule studies using not only tethered particles, but also other approaches, including force spectroscopy using atomic force microscopy and nanopores.

Optimization of metallic nanoapertures at short-wave infrared wavelengths for self-induced back-action trapping

This paper presents simulation results for double nanohole and inverted bowtie nanoapertures optimized to resonate in the short-wave infrared regime (1050 nm and 1550 nm). These geometries have shown great promise for trapping nanoparticles with applications in optical engineering, physics, and biology. Using a finite element analysis tool, we found that the outline length for inverted bowtie nanoapertures in a 100 nm thick gold film with a 20 nm gap dimension having an optimized transmission resonance for 1050 nm and 1550 nm optical wavelengths is 106.5 nm and 188.5 nm, respectively. With the same gap size, the radii of the circles for the double nanohole nanoapertures are 72 nm and 128 nm. The near-field enhancements of the two structures are almost the same, while the double nanohole geometries have a 20% larger full width at half-maximum than the inverted bowtie. Next, by studying the effect of changing the inner radii of the inverted bowtie corners, we found that the difference between 2 nm and 6 nm corner radii can blue-shift the optical resonance by up to 45 nm. As a result of not having any inner corners, the double nanohole structure requires less precise fabrication and therefore could potentially have a higher successful yield of nanoapertures during the manufacturing process. Lastly, we will show experimental results that confirm the optical resonance of the nanoapertures at 1550 nm. These results will enable better performance and signal-to-noise ratio in nanoaperture trapping for the short-wave infrared wavelength regime.

Axial electrokinetic trapping of anisotropic particles

Anti-Brownian electrokinetic trapping is a method for trapping single particles in liquid based on particle position measurements and the application of feedback voltages. To achieve trapping in the axial direction, information on the axial particle position is required. However, existing strategies for determining the axial position that are based on measuring the size of the first diffraction ring, theory fitting, advanced optical setups or pre-determined axial image stacks are impractical for anisotropic particles. In this work, axial electrokinetic trapping of anisotropic particles is realized in devices with planar, transparent electrodes. The trapping algorithm uses Fourier-Bessel decomposition of standard microscopy images and is learning from the correlation between applied voltages and changes in the particle appearance. No previous knowledge on the particle appearance, theory fitting or advanced optical setup is required. The particle motion in the trap and the influence of screening of the electric field on this motion are analyzed. The axial trapping method opens new possibilities for measuring properties of anisotropic or isotropic particles and forces acting on such particles.

Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations

Chains of particles coupled through anharmonic interactions and subject to non-Gaussian baths can exhibit paradoxical outcomes such as heat currents flowing from colder to hotter reservoirs. Aiming to explore the role of generic nonharmonicities in mediating the contributions of non-Gaussian fluctuations to the direction of heat propagation, we consider a chain of power-law oscillators, with interaction potential V(x)∝|x|^{α}, subject to Gaussian and Poissonian baths at its ends. Performing numerical simulations and addressing heuristic considerations, we show that a deformable potential has bidirectional control over heat flux.

Automated Dielectrophoretic Tweezers-Based Force Spectroscopy System in a Microfluidic Device

We reported an automated dielectrophoretic (DEP) tweezers-based force spectroscopy system to examine intermolecular weak binding interactions, which consists of three components: (1) interdigitated electrodes and micro-sized polystyrene particles used as DEP tweezers and probes inside a microfluidic device, along with an arbitrary function generator connected to a high voltage amplifier; (2) microscopy hooked up to a high-speed charge coupled device (CCD) camera with an image acquisition device; and (3) a computer aid control system based on the LabVIEW program. Using this automated system, we verified the measurement reliability by measuring intermolecular weak binding interactions, such as hydrogen bonds and Van der Waals interactions. In addition, we also observed the linearity of the force loading rates, which is applied to the probes by the DEP tweezers, by varying the number of voltage increment steps and thus affecting the linearity of the force loading rates. This system provides a simple and low-cost platform to investigate intermolecular weak binding interactions.

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

We performed dynamic force spectroscopy of single dextran and titin I27 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that for such low-frequency dithering experiments, recorded phase information can be unambiguously interpreted within the framework of a transparent theoretical model that starts from a well-known partial differential equation to describe the dithering of an atomic force microscope cantilever and a single molecule attached to its end system, uses an appropriate set of initial and boundary conditions, and does not exploit any implicit suggestions. We conclude that the observed phase (dissipation) signal is due completely to the dissipation related to the dithering of the cantilever itself (i.e., to the change of boundary conditions in the course of stretching). For both cases, only the upper bound of the dissipation of a single molecule has been established as not exceeding 3⋅10(-7)kg/s. We compare our results with previously reported measurements of the viscoelastic properties of single molecules, and we emphasize that extreme caution must be taken in distinguishing between the dissipation related to the stretched molecule and the dissipation that originates from the viscous damping of the dithered cantilever. We also present the results of an amplitude channel data analysis, which reveal that the typical values of the spring constant of a I27 molecule at the moment of module unfolding are equal to 4±1.5mN/m, and the typical values of the spring constant of dextran at the moment of chair-boat transition are equal to 30-50mN/m.

Nanoscopic imaging of thick heterogeneous soft-matter structures in aqueous solution

Precise nanometre-scale imaging of soft structures at room temperature poses a major challenge to any type of microscopy because fast thermal fluctuations lead to significant motion blur if the position of the structure is measured with insufficient bandwidth. Moreover, precise localization is also affected by optical heterogeneities, which lead to deformations in the imaged local geometry, the severity depending on the sample and its thickness. Here we introduce quantitative thermal noise imaging, a three-dimensional scanning probe technique, as a method for imaging soft, optically heterogeneous and porous matter with submicroscopic spatial resolution in aqueous solution. By imaging both individual microtubules and collagen fibrils in a network, we demonstrate that structures can be localized with a precision of ∼10 nm and that their local dynamics can be quantified with 50 kHz bandwidth and subnanometre amplitudes. Furthermore, we show how image distortions caused by optically dense structures can be corrected for.

Integration time limits the capacity of super-resolution microscopy to study dynamics. Here, Bartsch et al. use the 3D scanning of a nanoparticle held in an optical trap, and its thermal noise motion within the trap, to image the local dynamics of soft-matter structures with a 50 kHz bandwidth.

Dynamics of single-stranded DNA tethered to a solid

Tethering is used to deliver specific biological and industrial functions. For example, single-stranded DNA (ssDNA) is tethered to polymerases and long sequences of double-stranded DNA (dsDNA) during replication, and to solids in DNA microarrays. However, tethering ssDNA to a large object limits not only the available ssDNA conformations, but also the range of time-scales over which the mechanical responses of ssDNA are important. In this work we examine the effect of tethering by measurement of the mechanical response of ssDNA that is tethered at each end to two separate atomic force microscope cantilevers in aqueous solution. Thermal motion of the cantilevers drives the ends of the ssDNA chain at frequencies near 2 kHz. The presence of a tethered molecule makes a large difference to the asymmetric cross-correlation of two cantilevers, which enables resolution of the mechanical properties in our experiments. By analysis of the correlated motion of the cantilevers we extract the friction and stiffness of the ssDNA. We find that the measured friction is much larger than the friction that is usually associated with the unencumbered motion of ssDNA. We also find that the measured relaxation time, ∼30 μs, is much greater than prior measurements of the free-molecule relaxation time. We attribute the difference to the loss of conformational possibilities as a result of constraining the ends of the ssDNA.

Subfemtonewton Force Spectroscopy at the Thermal Limit in Liquids

We demonstrate thermally limited force spectroscopy using a probe formed by a dielectric microsphere optically trapped in water near a dielectric surface. We achieve force resolution below 1 fN in 100 s, corresponding to a 2 Å rms displacement of the probe. Our measurement combines a calibrated evanescent wave particle tracking technique and a lock-in detection method. We demonstrate the accuracy of our method by measurement of the height-dependent force exerted on the probe by an evanescent wave, the results of which are in agreement with Mie theory calculations.

Slowing DNA Translocation in a Nanofluidic Field-Effect Transistor

Here, we present an experimental demonstration of slowing DNA translocation across a nanochannel by modulating the channel surface charge through an externally applied gate bias. The experiments were performed on a nanofluidic field-effect transistor, which is a monolithic integrated platform featuring a 50 nm-diameter in-plane alumina nanocapillary whose entire length is surrounded by a gate electrode. The field-effect transistor behavior was validated on the gating of ionic conductance and protein transport. The gating of DNA translocation was subsequently studied by measuring discrete current dips associated with single λ-DNA translocation events under a source-to-drain bias of 1 V. The translocation speeds under various gate bias conditions were extracted by fitting event histograms of the measured translocation time to the first passage time distributions obtained from a simple 1D biased diffusion model. A positive gate bias was observed to slow the translocation of single λ-DNA chains markedly; the translocation speed was reduced by an order of magnitude from 18.4 mm/s obtained under a floating gate down to 1.33 mm/s under a positive gate bias of 9 V. Therefore, a dynamic and flexible regulation of the DNA translocation speed, which is vital for single-molecule sequencing, can be achieved on this device by simply tuning the gate bias. The device is realized in a conventional semiconductor microfabrication process without the requirement of advanced lithography, and can be potentially further developed into a compact electronic single-molecule sequencer.

Axial Optical Traps: A New Direction for Optical Tweezers

Optical tweezers have revolutionized our understanding of the microscopic world. Axial optical tweezers, which apply force to a surface-tethered molecule by directly moving either the trap or the stage along the laser beam axis, offer several potential benefits when studying a range of novel biophysical phenomena. This geometry, although it is conceptually straightforward, suffers from aberrations that result in variation of the trap stiffness when the distance between the microscope coverslip and the trap focus is being changed. Many standard techniques, such as back-focal-plane interferometry, are difficult to employ in this geometry due to back-scattered light between the bead and the coverslip, whereas the noise inherent in a surface-tethered assay can severely limit the resolution of an experiment. Because of these complications, precision force spectroscopy measurements have adapted alternative geometries such as the highly successful dumbbell traps. In recent years, however, most of the difficulties inherent in constructing a precision axial optical tweezers have been solved. This review article aims to inform the reader about recent progress in axial optical trapping, as well as the potential for these devices to perform innovative biophysical measurements.

DNA motion capture reveals the mechanical properties of DNA at the mesoscale

Single-molecule studies probing the end-to-end extension of long DNAs have established that the mechanical properties of DNA are well described by a wormlike chain force law, a polymer model where persistence length is the only adjustable parameter. We present a DNA motion-capture technique in which DNA molecules are labeled with fluorescent quantum dots at specific sites along the DNA contour and their positions are imaged. Tracking these positions in time allows us to characterize how segments within a long DNA are extended by flow and how fluctuations within the molecule are correlated. Utilizing a linear response theory of small fluctuations, we extract elastic forces for the different, ∼2-μm-long segments along the DNA backbone. We find that the average force-extension behavior of the segments can be well described by a wormlike chain force law with an anomalously small persistence length.

Surface-modified complex SU-8 microstructures for indirect optical manipulation of single cells

We introduce a method that combines two-photon polymerization (TPP) and surface functionalization to enable the indirect optical manipulation of live cells. TPP-made 3D microstructures were coated specifically with a multilayer of the protein streptavidin and non-specifically with IgG antibody using polyethylene glycol diamine as a linker molecule. Protein density on their surfaces was quantified for various coating methods. The streptavidin-coated structures were shown to attach to biotinated cells reproducibly. We performed basic indirect optical micromanipulation tasks with attached structure-cell couples using complex structures and a multi-focus optical trap. The use of such extended manipulators for indirect optical trapping ensures to keep a safe distance between the trapping beams and the sensitive cell and enables their 6 degrees of freedom actuation.

Improved axial trapping with holographic optical tweezers

Conventional optical tweezers suffer from several complications when applying axial forces to surface-tethered molecules. Aberrations from the refractive-index mismatch between an oil-immersion objective's medium and the aqueous trapping environment both shift the trap centre and degrade the trapping strength with focal depth. Furthermore, interference effects from back-scattered light make it difficult to use back-focal-plane interferometry for high-bandwidth position detection. Holographic optical tweezers were employed to correct for aberrations to achieve a constant axial stiffness and modulate artifacts from backscattered light. Once the aberrations are corrected for, the trap height can be precisely determined from either the back-scattered light or Brenner's formula.

Force generation by the growth of amyloid aggregates

The generation of mechanical forces are central to a wide range of vital biological processes, including the function of the cytoskeleton. Although the forces emerging from the polymerization of native proteins have been studied in detail, the potential for force generation by aberrant protein polymerization has not yet been explored. Here, we show that the growth of amyloid fibrils, archetypical aberrant protein polymers, is capable of unleashing mechanical forces on the piconewton scale for individual filaments. We apply microfluidic techniques to measure the forces released by amyloid growth for two systems: insulin and lysozyme. The level of force measured for amyloid growth in both systems is comparable to that observed for actin and tubulin, systems that have evolved to generate force during their native functions and, unlike amyloid growth, rely on the input of external energy in the form of nucleotide hydrolysis for maximum force generation. Furthermore, we find that the power density released from growing amyloid fibrils is comparable to that of high-performance synthetic polymer actuators. These findings highlight the potential of amyloid structures as active materials and shed light on the criteria for regulation and reversibility that guide molecular evolution of functional polymers.

Label-free DNA sequencing using Millikan detection

A label-free method for DNA sequencing based on the principle of the Millikan oil drop experiment was developed. This sequencing-by-synthesis approach sensed increases in bead charge as nucleotides were added by a polymerase to DNA templates attached to beads. The balance between an electrical force, which was dependent on the number of nucleotide charges on a bead, and opposing hydrodynamic drag and restoring tether forces resulted in a bead velocity that was a function of the number of nucleotides attached to the bead. The velocity of beads tethered via a polymer to a microfluidic channel and subjected to an oscillating electric field was measured using dark-field microscopy and used to determine how many nucleotides were incorporated during each sequencing-by-synthesis cycle. Increases in bead velocity of approximately 1% were reliably detected during DNA polymerization, allowing for sequencing of short DNA templates. The method could lead to a low-cost, high-throughput sequencing platform that could enable routine sequencing in medical applications.

Universal axial fluctuations in optical tweezers

Optical tweezers (OTs) allow the measurement of fluctuations at the nanoscale, in particular fluctuations in the end-to-end distance in single molecules. Fluctuation spectra can yield valuable information, but they can easily be contaminated by instrumental effects. We identify axial fluctuations, i.e., fluctuations of the trapped beads in the direction of light propagation, as one of these instrumental effects. Remarkably, axial fluctuations occur on a characteristic timescale similar to that of conformational (folding) transitions, which may lead to misinterpretation of the experimental results. We show that a precise measurement of the effect of force on both axial and conformational fluctuations is crucial to disentangle them. Our results on axial fluctuations are captured by a simple and general formula valid for all OT setups and provide experimentalists with a general strategy to distinguish axial fluctuations from conformational transitions.

Extracting physical chemistry from mechanics: a new approach to investigate DNA interactions with drugs and proteins in single molecule experiments

In this review we focus on the idea of establishing connections between the mechanical properties of DNA–ligand complexes and the physical chemistry of DNA–ligand interactions.

Multiscale dynamics of semiflexible polymers from a universal coarse-graining procedure

Simulating the dynamics of a semiflexible polymer across time and length scales that bridge the rigid and flexible regimes requires a physically sound method for generating coarse-grained representations of the polymer. Here, we study the dynamic behavior of the discrete stretchable, shearable wormlike chain model, which can be used to coarse-grain a continuous semi-elastic chain at an arbitrary discretization. We show that the dynamics of this universal model match those of the wormlike chain at length scales above the discretization length. The evolution of the stress correlation, as probed through Brownian dynamics simulations, is found to reproduce the predicted behavior in both the rigid and flexible regimes, spanning over six orders of magnitude in time scales. The coarse-graining approach employed here thus enables dynamic simulation of semiflexible polymers at lengths and times that were previously inaccessible with conventional methods.

Force and conductance molecular break junctions with time series crosscorrelation

Force and conductance, measured across 4,4'-bipyridine simultaneously, are crosscorrelated using a two dimensional (2D) histogram method. The result is a 2D multivariate statistical analysis superior to current one dimensional histogram techniques for exploring significant conductance and force modulations within SMBJs. This method is sensitive enough to crosscorrelate signal modulations between force and conductance traces associated with contact geometry perturbations predicted in literature such as Au-molecule contact twisting and slipping during junction elongation.

DNA topology and transcription

Chromatin is a complex assembly that compacts DNA inside the nucleus while providing the necessary level of accessibility to regulatory factors conscripted by cellular signaling systems. In this superstructure, DNA is the subject of mechanical forces applied by variety of molecular motors. Rather than being a rigid stick, DNA possesses dynamic structural variability that could be harnessed during critical steps of genome functioning. The strong relationship between DNA structure and key genomic processes necessitates the study of physical constrains acting on the double helix. Here we provide insight into the source, dynamics, and biology of DNA topological domains in the eukaryotic cells and summarize their possible involvement in gene transcription. We emphasize recent studies that might inspire and impact future experiments on the involvement of DNA topology in cellular functions.

Quantitative influence of macromolecular crowding on gene regulation kinetics

We introduce macromolecular crowding quantitatively into the model for kinetics of gene regulation in Escherichia coli. We analyse and compute the specific-site searching time for 180 known transcription factors (TFs) regulating 1300 operons. The time is between 160 s (e.g. for SoxS M_w = 12.91 kDa) and 1550 s (e.g. for PepA₆ of M_w = 329.28 kDa). Diffusion coefficients for one-dimensional sliding are between for large proteins up to for small monomers or dimers. Three-dimensional diffusion coefficients in the cytoplasm are 2 orders of magnitude larger than 1D sliding coefficients, nevertheless the sliding enhances the binding rates of TF to specific sites by 1–2 orders of magnitude. The latter effect is due to ubiquitous non-specific binding. We compare the model to experimental data for LacI repressor and find that non-specific binding of the protein to DNA is activation- and not diffusion-limited. We show that the target location rate by LacI repressor is optimized with respect to microscopic rate constant for association to non-specific sites on DNA. We analyse the effect of oligomerization of TFs and DNA looping effects on searching kinetics. We show that optimal searching strategy depends on TF abundance.

Coupled motion of microscale and nanoscale elastic objects in a viscous fluid

We study the coupled dynamics of two closely spaced micron or nanoscale elastic objects immersed in a viscous fluid. The dynamics of the elastic objects are coupled through the motion of the surrounding viscous fluid. We consider two cases: (i) one object is driven externally by an imposed harmonic actuation force and the second object is passive and (ii) both objects are driven by a Brownian force to yield stochastic dynamics. Using a harmonic oscillator approximation for the elastic objects and the unsteady Stokes equations to describe the fluid dynamics, we develop analytical expressions for the amplitude and phase of the displacement of the oscillating objects. For the case of an imposed actuation we use an impulse in force to determine the resulting dynamics over all frequencies. For the Brownian-driven objects the stochastic dynamics are found using the fluctuation-dissipation theorem. We validate our theoretical expressions by comparison with results from finite-element numerical simulations of the complete fluid-solid interaction problem. Our results yield interesting features in the amplitude and phase of the displacement of the elastic objects due to the fluid motion. We find that the dynamics depend on the separation of the objects, a measure of the mass loading due to the fluid, and the frequency parameter which acts as a frequency-based Reynolds number. Our results are valid over the range of parameters typical of micron and nanoscale elastic objects in fluid. The range of dynamics found can be understood in terms of the interplay between the viscous and potential components of the fluid flow field described by the unsteady Stokes equation for an oscillating cylinder. For small values of the frequency parameter, typical of nanoscale elastic objects, the dynamics are overdamped due to the dominance of viscous forces over inertial forces. For moderate and large values of the frequency parameter, typical of micron-scale elastic objects, we find that the dynamics of the fluid-coupled objects exhibits an interesting mode splitting to yield a bimodal signature in the amplitude-frequency plots. We find that the mode splitting can be described using a normal mode analysis containing only potential fluid interactions between the cylinders.

Nonequilibrium distributions and hydrodynamic coupling distort the measurement of nanoscale forces near interfaces

We calculate the displacement of a single spherical particle from the minimum of a harmonic well positioned near a plane wall and immersed in a uniform flow. A failure to account for the fluctuations in particle position orthogonal to the plane (leading to fluctuations in hydrodynamic drag) results in large discrepancies, with the naive displacement calculated by assuming no fluctuations in the balance of forces. The chief criterion for neglecting such fluctuations is that the stiffness of the harmonic potential exceeds the thermal stresses on the particle by at least two orders of magnitude. For micrometer-diameter particles typically employed in force spectroscopy of DNA, macromolecules, and molecular motors, this can lead to errors of up to 100% in the measured properties. The Supporting Material to the article provides an implementation of this model intended to fit experimental measurements for the stiffness of the harmonic potential constraining the particle.

Force spectroscopy with dual-trap optical tweezers: molecular stiffness measurements and coupled fluctuations analysis

Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies.

Counter-propagating dual-trap optical tweezers based on linear momentum conservation

We present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces.

Rapid internal contraction boosts DNA friction

Macroscopic objects are usually manipulated by force and observed with light. On the nanoscale, however, this is often done oppositely: individual macromolecules are manipulated by light and monitored with force. This procedure, which is the basis of single-molecule force spectroscopy, has led to much of our quantitative understanding of how DNA works, and is now routinely applied to explore molecular structure and interactions, DNA-protein reactions and protein folding. Here we develop the technique further by introducing a dynamic force spectroscopy set-up for a non-invasive inspection of the tension dynamics in a taut strand of DNA. The internal contraction after a sudden release of the molecule is shown to give rise to a drastically enhanced viscous friction, as revealed by the slow relaxation of an attached colloidal tracer. Our systematic theory explains the data quantitatively and provides a powerful tool for the rational design of new dynamic force spectroscopy assays.

Remote control of DNA-acting enzymes by varying the Brownian dynamics of a distant DNA end

Enzyme rates are usually considered to be dependent on local properties of the molecules involved in reactions. However, for large molecules, distant constraints might affect reaction rates by affecting dynamics leading to transition states. In single-molecule experiments we have found that enzymes that relax DNA torsional stress display rates that depend strongly on how the distant ends of the molecule are constrained; experiments with different-sized particles tethered to the end of 10-kb DNAs reveal enzyme rates inversely correlated with particle drag coefficients. This effect can be understood in terms of the coupling between molecule extension and local molecular stresses: The rate of bead thermal motion controls the rate at which transition states are visited in the middle of a long DNA. Importantly, we have also observed this effect for reactions on unsupercoiled DNA; other enzymes show rates unaffected by bead size. Our results reveal a unique mechanism through which enzyme rates can be controlled by constraints on macromolecular or supramolecular substrates.

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.

Rheology of fluids measured by correlation force spectroscopy

We describe a method, correlation force spectrometry (CFS), which characterizes fluids through measurement of the correlations between the thermally stimulated vibrations of two closely spaced micrometer-scale cantilevers in fluid. We discuss a major application: measurement of the rheological properties of fluids at high frequency and high spatial resolution. Use of CFS as a rheometer is validated by comparison between experimental data and finite element modeling of the deterministic ring-down of cantilevers using the known viscosity of fluids. The data can also be accurately fitted using a harmonic oscillator model, which can be used for rapid rheometric measurements after calibration. The method is non-invasive, uses a very small amount of fluid, and has no actively moving parts. It can also be used to analyze the rheology of complex fluids. We use CFS to show that (non-Newtonian) aqueous polyethylene oxide solution can be modeled approximately by incorporating an elastic spring between the cantilevers.

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.

On the role of DNA biomechanics in the regulation of gene expression

DNA is traditionally seen as a linear sequence of instructions for cellular functions that are expressed through biochemical processes. Cellular DNA, however, is also organized as a complex hierarchical structure with a mosaic of mechanical features, and a growing body of evidence is now emerging to imply that these mechanical features are connected to genetic function. Mechanical tension, for instance, which must be felt by DNA within the heavily constrained and continually fluctuating cellular environment, can affect a number of regulatory processes implicating a role for biomechanics in gene expression complementary to that of biochemical regulation. In this article, we review evidence for such mechanical pathways of genetic regulation.

Dual-trap optical tweezers with real-time force clamp control

Single molecule force clamp experiments are widely used to investigate how enzymes, molecular motors, and other molecular mechanisms work. We developed a dual-trap optical tweezers instrument with real-time (200 kHz update rate) force clamp control that can exert 0-100 pN forces on trapped beads. A model for force clamp experiments in the dumbbell-geometry is presented. We observe good agreement between predicted and observed power spectra of bead position and force fluctuations. The model can be used to predict and optimize the dynamics of real-time force clamp optical tweezers instruments. The results from a proof-of-principle experiment in which lambda exonuclease converts a double-stranded DNA tether, held at constant tension, into its single-stranded form, show that the developed instrument is suitable for experiments in single molecule biology.

Probability distribution of a trapped brownian particle in plane shear flows

We investigate the statistical properties of an overdamped brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and are substantiated by numerical results. There is good agreement between the two approaches for a wide range of parameters.

Effect of hydrodynamic interaction on polymeric tethers

Weak bonds are ubiquitous in biological structures. They often act as adhesive contacts within an extended structure, for example, the internal bonds in a folded protein or a DNA/RNA loop. They also act as linkers between two structures, for example, a protein grafted in a cell membrane or a protein linking the cell membranes of two neighboring cells. Typically, the breakage of a bond depends on the strength of the binding potential and viscosity of the medium. But when extended structures couple to the bond, as in the above examples, the dynamics of the structure also has to be considered in order to understand the bond breakage phenomenon. Here we consider a generic model, a stretched polymer (an extended structure) tethered to a soft bond and study how the dynamics of the polymer, in addition to thermal noise, influences bond breakage. We also explore how the hydrodynamic interaction due to the fluid medium, which couples the distant parts of the polymer, change the bond breakage rate. We find that hydrodynamic interaction enhances the breakage rate and also makes the motion of the unstable collective mode of the polymer more coherent.

Influence of noise on force measurements

We demonstrate how the ineluctable presence of thermal noise alters the measurement of forces acting on microscopic and nanoscopic objects. We quantify this effect exemplarily for a Brownian particle near a wall subjected to gravitational and electrostatic forces. Our results demonstrate that the force-measurement process is prone to artifacts if the noise is not correctly taken into account.

Optical trapping of colloidal particles and cells by focused evanescent fields using conical lenses

We demonstrate advantages in terms of trapping force distribution and laser efficiency that come from using a telescopic pair of conical lenses ('axicon') to generate a ring-like beam, that in conjunction with a high NA objective is used for direct optical trapping with a focused evanescent field near a surface. Various field geometries are considered and compared. First, a Gaussian beam and a laser beam focused on the back focal plane of the objective are compared with each other, and they are scanned across the inlet aperture of the objective. This allows to detect the point of total internal refraction, and to study the trapping power near the surface. We confirm that the hollow beam generated by the conical lenses can generate an evanescent field after a high NA objective lens, and that micron-sized particles can be trapped stably. Finally, we apply the focused evanescent field to erythrocytes under flow, showing that cells are trapped against the flow and are held horizontally against the surface. This is a different equilibrium condition compared to conventional single beam traps, and it is particularly favorable for monitoring the cell membrane. We foresee the integration of this type of trapping with the imaging techniques based on total internal refraction fluorescence (TIRF).

Stretching submicron biomolecules with constant-force axial optical tweezers

Optical tweezers have become powerful tools to manipulate biomolecular systems, but are increasingly difficult to use when the size of the molecules is <1 microm. Many important biological structures and processes, however, occur on the submicron length scale. Therefore, we developed and characterized an optical manipulation protocol that makes this length scale accessible by stretching the molecule in the axial direction of the laser beam, thus avoiding limiting artifacts from steric hindrances from the microscope coverslip and other surface effects. The molecule is held under constant mechanical tension by a combination of optical gradient forces and backscattering forces, eliminating the need for electronic feedback. We demonstrate the utility of this method through a measurement of the force-extension relationship of a 1298 bp ds-DNA molecule.

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.

Determining protein-induced DNA bending in force-extension experiments: theoretical analysis

Computer simulations were used to investigate the possibility of determining protein-induced DNA bend angles by measuring the extension of a single DNA molecule. Analysis of the equilibrium sets of DNA conformations showed that shortening of DNA extension by a single protein-induced DNA bend can be as large as 35 nm. The shortening has a maximum value at the extending force of approximately 0.1 pN. At this force, the DNA extension experiences very large fluctuations that dramatically complicate the measurement. Using Brownian dynamics simulation of a DNA molecule extended by force, we were able to estimate the observation time needed to obtain the desired accuracy of the extension measurement. Also, the simulation revealed large fluctuations of the force, acting on the attached magnetic bead from the stretched DNA molecule.

Confinement spectroscopy: probing single DNA molecules with tapered nanochannels

We demonstrate a confinement spectroscopy technique capable of probing small conformational changes of unanchored single DNA molecules in a manner analogous to force spectroscopy, in the regime corresponding to femtonewton forces. In contrast to force spectroscopy, various structural forms of DNA can easily be probed, as indicated by experiments on linear and circular DNA. The extension of circular DNA is found to scale according to the de Gennes exponent, unlike for linear DNA.

Atomic hydrodynamics of DNA: coil-uncoil-coil transitions in a wall-bounded shear flow

Extensive experimental work on the response of DNA molecules to externally applied forces and on the dynamics of DNA molecules flowing in microchannels and nanochannels has been carried out over the past two decades, however, there has not been available, until now, any atomic-scale means of analyzing nonequilibrium DNA response dynamics. There has not therefore been any way to investigate how the backbone and side-chain atoms along the length of a DNA molecule interact with the molecules and ions of the flowing solvent and with the atoms of passing boundary surfaces. We report here on the application of the nonequilibrium biomolecular dynamics simulation method that we developed [G. M. Wang and W. C. Sandberg, Nanotechnology 18, 4819 (2007)] to analyze, at the atomic interaction force level, the conformational dynamics of short-chain single-stranded DNA molecules in a shear flow near a surface. This is a direct atomic computational analysis of the hydrodynamic interaction between a biomolecule and a flowing solvent. The DNA molecules are observed to exhibit conformational behaviors including coils, hairpin loops, and figure-eight shapes that have neither been previously measured experimentally nor observed computationally, as far as we know. We relate the conformational dynamics to the atomic interaction forces experienced throughout the length of a molecule as it moves in the flowing solvent past the surface boundary. We show that the DNA conformational dynamics is related to the asymmetry in the molecular environment induced by the motion of the surrounding molecules and the atoms of the passing surface. We also show that while the asymmetry in the environment is necessary, it is not sufficient to produce the observed conformational dynamics. A time variation in the asymmetry, due in our case to a shear flow, must also exist. In order to contrast these results with the usual experimental situation of purely diffusive motion in thermal equilibrium we have also carried out computations with a zero shear rate. We show that in thermal equilibrium there is asymmetry and an atomic hydrodynamic coupling between DNA molecules and the solvent molecules but there is no coil-uncoil transition.