Entropic boundary effects on the elasticity of short DNA molecules

Temperature-dependent elastic properties of DNA

Knowledge of the elastic properties, e.g., the persistence length or interphosphate distance, of single-stranded (ss) and double-stranded (ds) DNA under different experimental conditions is critical to characterizing molecular reactions studied with single-molecule techniques. While previous experiments have addressed the dependence of the elastic parameters upon varying ionic strength and contour length, temperature-dependent effects are less studied. Here, we examine the temperature-dependent elasticity of ssDNA and dsDNA in the range 5°C-50°C using a temperature-jump optical trap. We find a temperature softening for dsDNA and a temperature stiffening for ssDNA. Our results highlight the need for a general theory explaining the phenomenology observed.

Optical Tweezers Approaches for Probing Multiscale Protein Mechanics and Assembly

Multi-step assembly of individual protein building blocks is key to the formation of essential higher-order structures inside and outside of cells. Optical tweezers is a technique well suited to investigate the mechanics and dynamics of these structures at a variety of size scales. In this mini-review, we highlight experiments that have used optical tweezers to investigate protein assembly and mechanics, with a focus on the extracellular matrix protein collagen. These examples demonstrate how optical tweezers can be used to study mechanics across length scales, ranging from the single-molecule level to fibrils to protein networks. We discuss challenges in experimental design and interpretation, opportunities for integration with other experimental modalities, and applications of optical tweezers to current questions in protein mechanics and assembly.

GC-Content Dependence of Elastic and Overstretching Properties of DNA:RNA Hybrid Duplexes

DNA:RNA hybrid duplex plays important roles in various biological processes. Both its structural stability and interactions with proteins are highly sequence dependent. In this study, we utilize homebuilt optical tweezers to investigate how GC contents in the sequence influence the structural and mechanical properties of DNA:RNA hybrid by measuring its contour length, elasticities, and overstretching dynamics. Our results support that the DNA:RNA hybrid adopts a conformation between the A- and B-form helix, and the GC content does not affect its structural and elastic parameters obviously when varying from 40 to 60% before the overstretching transition of DNA:RNA hybrid occurs. In the overstretching transition, however, our study unravels significant heterogeneity and strong sequence dependence, suggesting the presence of a highly dynamic competition between the two processes, namely the S-form duplex formation (nonhysteretic) and the unpeeling (hysteretic). Analyzing the components left in DNA:RNA hybrid after the overstretching transition suggests that the RNA strand is more easily unpeeled than the DNA strand, whereas an increase in the GC content from 40 to 60% can significantly reduce unpeeling. Large hysteresis is observed between the stretching and relaxation processes, which is also quantitatively correlated with the percentage of unpeeling in the DNA:RNA duplex. Increasing in both the salt concentration and GC content can effectively reduce the hysteresis with the latter being more significant. Together, our study reveals that the mechanical properties of DNA:RNA hybrid duplexes are significantly different from double-stranded DNA and double-stranded RNA, and its overstretching behavior is highly sequence dependent. These results should be taken into account in the future studies on DNA:RNA-hybrid-related functional structures and motor proteins.

Submicrometer elasticity of double-stranded DNA revealed by precision force-extension measurements with magnetic tweezers

Submicrometer elasticity of double-stranded DNA (dsDNA) governs nanoscale bending of DNA segments and their interactions with proteins. Single-molecule force spectroscopy, including magnetic tweezers (MTs), is an important tool for studying DNA mechanics. However, its application to short DNAs under 1 μm is limited. We developed an MT-based method for precise force-extension measurements in the 100-nm regime that enables in situ correction of the error in DNA extension measurement, and normalizes the force variability across beads by exploiting DNA hairpins. The method reduces the lower limit of tractable dsDNA length down to 198 base pairs (bp) (67 nm), an order-of-magnitude improvement compared to conventional tweezing experiments. Applying this method and the finite worm-like chain model we observed an essentially constant persistence length across the chain lengths studied (198 bp to 10 kbp), which steeply depended on GC content and methylation. This finding suggests a potential sequence-dependent mechanism for short-DNA elasticity.

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.

Elastic Properties of Nucleic Acids by Single-Molecule Force Spectroscopy

We review the current knowledge on the use of single-molecule force spectroscopy techniques to extrapolate the elastic properties of nucleic acids. We emphasize the lesser-known elastic properties of single-stranded DNA. We discuss the importance of accurately determining the elastic response in pulling experiments, and we review the simplest models used to rationalize the experimental data as well as the experimental approaches used to pull single-stranded DNA. Applications used to investigate DNA conformational transitions and secondary structure formation are also highlighted. Finally, we provide an overview of the effects of salt and temperature and briefly discuss the effects of contour length and sequence dependence.

Simulation Assisted Analysis of the Intrinsic Stiffness for Short DNA Molecules Imaged with Scanning Atomic Force Microscopy

Studying the mechanical properties of short segments of dsDNA can provide insight into various biophysical phenomena, from DNA looping to the organization of nucleosomes. Scanning atomic force microscopy (AFM) is able to acquire images of single DNA molecules with near-basepair resolution. From many images, one may use equilibrium statistical mechanics to quantify the intrinsic stiffness (or persistence length) of the DNA. However, this approach is highly dependent upon both the correct microscopic polymer model and a correct image analysis of DNA contours. These complications have led to significant debate over the flexibility of dsDNA at short length scales. We first show how to extract accurate measures of DNA contour lengths by calibrating to DNA traces of simulated AFM data. After this calibration, we show that DNA adsorbed on an aminopropyl-mica surface behaves as a worm-like chain (WLC) for contour lengths as small as ~20 nm. We also show that a DNA binding protein can modify the mechanics of the DNA from that of a WLC.

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.

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.

Improving signal/noise resolution in single-molecule experiments using molecular constructs with short handles

We investigate unfolding/folding force kinetics in DNA hairpins exhibiting two and three states with newly designed short dsDNA handles (29 bp) using optical tweezers. We show how the higher stiffness of the molecular setup moderately enhances the signal/noise ratio (SNR) in hopping experiments as compared to conventional long-handled constructs (≅700 bp). The shorter construct results in a signal of higher SNR and slower folding/unfolding kinetics, thereby facilitating the detection of otherwise fast structural transitions. A novel analysis, as far as we are aware, of the elastic properties of the molecular setup, based on high-bandwidth measurements of force fluctuations along the folded branch, reveals that the highest SNR that can be achieved with short handles is potentially limited by the marked reduction of the effective persistence length and stretch modulus of the short linker complex.

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.

Bead size effects on protein-mediated DNA looping in tethered-particle motion experiments

Tethered particle motion (TPM) has become an important tool for single-molecule studies of biomolecules; however, concerns remain that the method may alter the dynamics of the biophysical process under study. We investigate the effect of the attached microsphere on an illustrative biological example: the formation and breakdown of protein-mediated DNA loops in the lac repressor system. By comparing data from a conventional TPM experiment with 800 nm polystyrene beads and dark-field TPM using 50 nm Au nanoparticles, we found that the lifetimes of the looped and unlooped states are only weakly modified, less than two-fold, by the presence of the large bead. This is consistent with our expectation of weak excluded-volume effects and hydrodynamic surface interactions from the cover glass and microsphere.

Femtonewton entropic forces can control the formation of protein-mediated DNA loops

We show that minuscule entropic forces, on the order of 100 fN, can prevent the formation of DNA loops-a ubiquitous means of regulating the expression of genes. We observe a tenfold decrease in the rate of LacI-mediated DNA loop formation when a tension of 200 fN is applied to the substrate DNA, biasing the thermal fluctuations that drive loop formation and breakdown events. Conversely, once looped, the DNA-protein complex is insensitive to applied force. Our measurements are in excellent agreement with a simple polymer model of loop formation in DNA, and show that an antiparallel topology is the preferred LacI-DNA loop conformation for a generic loop-forming construct.