Force-free measurements of the conformations of DNA molecules tethered to a wall

Optimizing Binding among Bimolecular Tethered Complexes

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.

Sensing force and charge at the nanoscale with a single-molecule tether

Measuring the electrophoretic mobility of molecules is a powerful experimental approach for investigating biomolecular processes. A frequent challenge in the context of single-particle measurements is throughput, limiting the obtainable statistics. Here, we present a molecular force sensor and charge detector based on parallelised imaging and tracking of tethered double-stranded DNA functionalised with charged nanoparticles interacting with an externally applied electric field. Tracking the position of the tethered particle with simultaneous nanometre precision and microsecond temporal resolution allows us to detect and quantify the electrophoretic force down to the sub-piconewton scale. Furthermore, we demonstrate that this approach is suitable for detecting changes to the particle charge state, as induced by the addition of charged biomolecules or changes to pH. Our approach provides an alternative route to studying structural and charge dynamics at the single molecule level.

Slow chromatin dynamics enhances promoter accessibility to transcriptional condensates

Enhancers are DNA sequences at a long genomic distance from target genes. Recent experiments suggest that enhancers are anchored to the surfaces of condensates of transcription machinery and that the loop extrusion process enhances the transcription level of their target genes. Here, we theoretically study the polymer dynamics driven by the loop extrusion of the linker DNA between an enhancer and the promoter of its target gene to calculate the contact probability of the promoter to the transcription machinery in the condensate. Our theory predicts that when the loop extrusion process is active, the contact probability increases with increasing linker DNA length. This finding reflects the fact that the relaxation time, with which the promoter stays in proximity to the surface of the transcriptional condensate, increases as the length of the linker DNA increases. This contrasts the equilibrium case for which the contact probability between the promoter and the transcription machineries is smaller for longer linker DNA lengths.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Measuring the Conformation and Persistence Length of Single-Stranded DNA Using a DNA Origami Structure

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a challenge that has been addressed by different methods lately. The short persistence length, fragile structure, and the appearance of stem loops complicate the measurement, and this leads to a large variability in the measured values. Here we describe an innovative method based on DNA origami for studying the biophysical properties of ssDNA. By synthesizing a DNA origami structure that consists of two rigid rods with an ssDNA segment between them, we developed a method to characterize the effective persistence length of a random-sequence ssDNA while allowing the formation of stem loops. We imaged the structure with an atomic force microscope (AFM); the rigid rods provide a means for the exact identification of the ssDNA ends. This leads to an accurate determination of the end-to-end distance of each ssDNA segment, and by fitting the measured distribution to the ideal chain polymer model we measured an effective persistence length of 1.98 ± 0.72 nm. This method enables one to measure short or long strands of ssDNA, and it can cope with the formation of stem loops that are often formed along ssDNA. We envision that this method can be used for measuring stem loops for determining the effect of repetitive nucleotide sequences and environmental conditions on the mechanical properties of ssDNA and the effect of interacting proteins with ssDNA. We further noted that the method can be extended to nanoprobes for measuring the interactions of specific DNA sequences, because the DNA origami rods (or similar structures) can hold multiple fluorescent probes that can be easily detected.

Inequivalence of fixed-force and fixed-extension statistical ensembles for a flexible polymer tethered to a planar substrate

Recent advances in single macromolecule experiments have sparked interest in the ensemble dependence of force-extension relations. The thermodynamic limit may not be attainable for such systems, which leads to inequivalence of the fixed-force and the fixed-extension ensembles. We consider an ideal Gaussian chain described by the Edwards Hamiltonian with one end tethered to a rigid planar substrate. We analytically calculate the force-extension relation in the two ensembles and we show their inequivalence, which is caused by the confinement of the polymer to half space. The inequivalence is quite remarkable for strong compressional forces. We also perform Monte-Carlo simulations of a tethered wormlike chain with contour length 20 times its persistence length, which corresponds to experiments measuring the conformations of DNA tethered to a wall. The simulations confirm the ensemble inequivalence and qualitatively agree with the analytical predictions of the Gaussian model. Our analysis shows that confinement due to tethering causes ensemble inequivalence, irrespective of the polymer model.

Correlation anisotropy and stiffness of DNA molecules confined in nanochannels

The anisotropy of orientational correlations in DNA molecules confined in cylindrical channels is explored by Monte Carlo simulations using a coarse-grained model of double-stranded (ds) DNA. We find that the correlation function ⟨C(s)⟩_⊥ in the transverse (confined) dimension exhibits a region of negative values in the whole range of channel sizes. Such a clear-cut sign of the opposite orientation of chain segments represents a microscopic validation of the Odijk deflection mechanism in narrow channels. At moderate-to-weak confinement, the negative ⟨C(s)⟩_⊥ correlations imply a preference of DNA segments for transverse looping. The inclination for looping can explain a reduction of stiffness as well as the enhanced knotting of confined DNA relative to that detected earlier in bulk at some channel sizes. Furthermore, it is shown that the orientational persistence length P_or fails to convey the apparent stiffness of DNA molecules in channels. Instead, correlation lengths P_∥ and P_⊥ in the axial and transverse directions, respectively, encompass the channel-induced modifications of DNA stiffness.

The role of near-wall drag effects in the dynamics of tethered DNA under shear flow

We utilized single-molecule tethered particle motion (TPM) tracking, optimized for studying the behavior of short (0.922 μm) dsDNA molecules under shear flow conditions, in the proximity of a wall (surface). These experiments track the individual trajectories through a gold nanobead (40 nm in radius), attached to the loose end of the DNA molecules. Under such circumstances, local interactions with the wall become more pronounced, manifested through hydrodynamic interactions. To elucidate the mechanical mechanism that affects the statistics of the molecular trajectories of the tethered molecules, we estimate the resting diffusion coefficient of our system. Using this value and our measured data, we calculate the orthogonal distance of the extended DNA molecules from the surface. This calculation considers the hydrodynamic drag effect that emerges from the proximity of the molecule to the surface, using the Faxén correction factors. Our finding enables the construction of a scenario according to which the tension along the chain builds up with the applied shear force, driving the loose end of the DNA molecule away from the wall. With the extension from the wall, the characteristic times of the system decrease by three orders of magnitude, while the drag coefficients decay to a plateau value that indicates that the molecule still experiences hydrodynamic effects due to its proximity to the wall.

Transcription dynamics stabilizes nucleus-like layer structure in chromatin brush

We use a brush of DNA in a solution of transcriptional machinery and histone proteins to theoretically predict that this brush shows phase separation due to the instability arising from the disassembly of nucleosomes during transcription. In the two-phase coexistent state, collapsed chains (with relatively large nucleosome occupancy) lie at the grafting surface and swollen chains (with relatively small nucleosome occupancy) are distributed at the space above the collapsed chains, analogous to the structure of chromatin in differentiated cells. This layer structure is stabilized by the lateral osmotic pressure of swollen chains. For a relatively small grafting density, DNA brushes show tricritical points because the entropic elasticity with respect to the lateral excursion of swollen chains balances with the lateral osmotic pressure of these chains. At the tricritical points, DNA brushes show large fluctuations of local nucleosome concentration, which may be reminiscent of the fluctuations observed in embryonic stem cells.

Interference based localization of single emitters

The ability to localize precisely a single optical emitter is important for particle tracking applications and super resolution microscopy. It is known that for a traditional microscope the ability to localize such an emitter is limited by the photon count. Here we analyze the ability to improve such localization by imposing interference fringes. We show here that a simple grating interferometer can introduce such improvement in certain circumstances and analyze what is required to increase the localization precision further.

Multiplexed, Tethered Particle Microscopy for Studies of DNA-Enzyme Dynamics

DNA is the carrier of genetic information and, as such, is at the center of most essential cellular processes. To regulate its physiological function, specific proteins and motor enzymes constantly change conformational states with well-controlled dynamics. Twenty-five years ago, Schafer, Gelles, Sheetz, and Landick employed the tethered particle motion (TPM) technique for the first time to study transcription by RNA polymerase at the single-molecule level. TPM has since then remained one of the simplest, most affordable, and yet incisive single-molecule techniques available. It is an in vitro technique which allows investigation of DNA-protein interactions that change the effective length of a DNA tether. In this chapter, we will describe a recent strategy to multiplex TPM which substantially increases the throughput of TPM experiments, as well as a simulation to estimate the time resolution of experiments, such as transcriptional elongation assays, in which lengthy time averaging of the signal is impossible due to continual change of the DNA tether length. These improvements allow efficient study of several DNA-protein systems, including transcriptionally active DNA-RNA polymerase I complexes and DNA-gyrase complexes.

Increased localization precision by interference fringe analysis

We report a novel optical single-emitter-localization methodology that uses the phase induced by path length differences in a Mach-Zehnder interferometer to improve localization precision. Using information theory, we demonstrate that the localization capability of a modified Fourier domain signal generated by photon interference enables a more precise localization compared to a standard Gaussian intensity distribution of the corresponding point-spread function. The calculations were verified by numerical simulations and an exemplary experiment, where the centers of metal nanoparticles were localized to a precision of 3 nm.

Transcription rates in DNA brushes

We theoretically predict the rate of transcription (TX) in DNA brushes by introducing the concept of TX dipoles that takes into account the unidirectional motion of enzymes (RNAP) along DNA during transcription as correlated pairs of sources and sinks in the relevant diffusion equation. Our theory predicts that the TX rates dramatically change upon the inversion of the orientation of the TX dipoles relative to the substrate because TX dipoles modulate the concentrations of RNAP in the solution. Comparing our theory with experiments suggests that, in some cases, DNA chain segments are relatively uniformly distributed in the brush, in contrast to the parabolic profile expected for flexible polymer brushes.

Skewed brownian fluctuations in single-molecule magnetic tweezers

Measurements in magnetic tweezers rely upon precise determination of the position of a magnetic microsphere. Fluctuations in the position due to Brownian motion allows calculation of the applied force, enabling deduction of the force-extension response function for a single DNA molecule that is attached to the microsphere. The standard approach relies upon using the mean of position fluctuations, which is valid when the microsphere axial position fluctuations obey a normal distribution. However, here we demonstrate that nearby surfaces and the non-linear elasticity of DNA can skew the distribution. Through experiment and simulations, we show that such a skewing leads to inaccurate position measurements which significantly affect the extracted DNA extension and mechanical properties, leading to up to two-fold errors in measured DNA persistence length. We develop a simple, robust and easily implemented method to correct for such mismeasurements.

Enhanced tethered-particle motion analysis reveals viscous effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl2 or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA–protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein–nucleic acid interactions.

Crosslink-induced shrinkage of grafted Gaussian chains

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single crosslink on two ideal (Gaussian) chains grafted onto a rigid planar surface. Both the crosslink and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the crosslink is a reduction in the effective Kuhn length of a tethered chain. The crosslink-induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension

Simultaneous measurements of DNA twist and extension have been used to measure physical properties of the double helix and to characterize structural dynamics and mechanochemistry in nucleoprotein complexes. However, the spatiotemporal resolution of twist measurements has been limited by the use of angular probes with large rotational drags, preventing the detection of short-lived intermediates or small angular steps. Here we introduce AuRBT, demonstrating a >100X improvement in time resolution over previous techniques. AuRBT employs gold nanoparticles as bright low-drag rotational and extensional probes, relying on instrumentation that combines magnetic tweezers with objective-side evanescent darkfield microscopy. In an initial application to molecular motor mechanism, we have examined the high-speed structural dynamics of DNA gyrase, revealing an unanticipated transient intermediate. AuRBT also enables direct measurements of DNA torque with >50X shorter integration times than previous techniques; here we demonstrate high-resolution torque spectroscopy by mapping the conformational landscape of a Z-forming DNA sequence.

Silica encapsulation of fluorescent nanodiamonds for colloidal stability and facile surface functionalization

Fluorescent nanodiamonds (FNDs) emit in the near-IR and do not photobleach or photoblink. These properties make FNDs better suited for numerous imaging applications compared with commonly used fluorescence agents such as organic dyes and quantum dots. However, nanodiamonds do not form stable suspensions in aqueous buffer, are prone to aggregation, and are difficult to functionalize. Here we present a method for encapsulating nanodiamonds with silica using an innovative liposome-based encapsulation process that renders the particle surface biocompatible, stable, and readily functionalized through routine linking chemistries. Furthermore, the method selects for a desired particle size and produces a monodisperse agent. We attached biotin to the silica-coated FNDs and tracked the three-dimensional motion of a biotinylated FND tethered by a single DNA molecule with high spatial and temporal resolution.

Dynamic analysis of a diffusing particle in a trapping potential

The dynamics of a diffusing particle in a potential field is ubiquitous in physics, and it plays a pivotal role in single-molecule studies. We present a formalism for analyzing the dynamics of diffusing particles in harmonic potentials at low Reynolds numbers using the time evolution of the particle probability distribution function. We demonstrate the power of the formalism by simulation and by measuring and analyzing a nanobead tethered to a single DNA molecule. It allows one to simultaneously extract all the parameters that describe the system, namely, the diffusion coefficient and the restoring-force constant.

High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion

Tethered particle motion (TPM) monitors the variations in the effective length of a single DNA molecule by tracking the Brownian motion of a bead tethered to a support by the DNA molecule. Providing information about DNA conformations in real time, this technique enables a refined characterization of DNA-protein interactions. To increase the output of this powerful but time-consuming single-molecule assay, we have developed a biochip for the simultaneous acquisition of data from more than 500 single DNA molecules. The controlled positioning of individual DNA molecules is achieved by self-assembly on nanoscale arrays fabricated through a standard microcontact printing method. We demonstrate the capacity of our biochip to study biological processes by applying our method to explore the enzymatic activity of the T7 bacteriophage exonuclease. Our single molecule observations shed new light on its behaviour that had only been examined in bulk assays previously and, more specifically, on its processivity.