Probing the conformational distributions of subpersistence length DNA.
ABSTRACT: We have measured the bending elasticity of short double-stranded DNA (dsDNA) chains through small-angle x-ray scattering from solutions of dsDNA-linked dimers of gold nanoparticles. This method, which does not require exertion of external forces or binding to a substrate, reports on the equilibrium distribution of bending fluctuations, not just an average value (as in ensemble fluorescence resonance energy transfer) or an extreme value (as in cyclization), and in principle provides a more robust data set for assessing the suitability of theoretical models. Our experimental results for dsDNA comprising 42-94 basepairs are consistent with a simple wormlike chain model of dsDNA elasticity, whose behavior we have determined from Monte Carlo simulations that explicitly represent nanoparticles and their alkane tethers. A persistence length of 50 nm (150 basepairs) gave a favorable comparison, consistent with the results of single-molecule force-extension experiments on much longer dsDNA chains, but in contrast to recent suggestions of enhanced flexibility at these length scales.
Project description:We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the 'looping J factor' (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k(B)T, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical 'open' conformation of the LacI tetramer.
Project description:The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.
Project description:Recently, several studies have shown that short doubled-stranded DNA (dsDNA) loops more readily than the wormlike chain model predicts. In most of these experiments, the intrinsic bendedness of dsDNA, which in theory can dramatically influence looping dynamics, was either avoided or unaccounted for. To investigate the effect of the shape of dsDNA on looping dynamics, we characterized the shapes of several synthetic dsDNA molecules of equal length but different sequences using gel electrophoresis. We then measured their looping rates using a FRET (Förster resonance energy transfer)-based assay and extracted the looping probability density known as the J factor (jM). We also used, for comparison, several dinucleotide angular parameter sets derived from the observed electrophoretic mobility to compute the jM predicted by the wormlike chain model. Although we found a strong correlation between curvature and jM, the measured jM was higher than most dinucleotide model predictions. This result suggests that it is difficult to reconcile the looping probability with the observed gel mobility within the wormlike chain model and underscores the importance of determining the intrinsic shape of dsDNA for proper theoretical analysis.
Project description:The bending stiffness of double-stranded DNA (dsDNA) at high curvatures is fundamental to its biological activity, yet this regime has been difficult to probe experimentally, and literature results have not been consistent. We created a 'molecular vise' in which base-pairing interactions generated a compressive force on sub-persistence length segments of dsDNA. Short dsDNA strands (<41 base pairs) resisted this force and remained straight; longer strands became bent, a phenomenon called 'Euler buckling'. We monitored the buckling transition via Förster Resonance Energy Transfer (FRET) between appended fluorophores. For low-to-moderate concentrations of monovalent salt (up to ?150 mM), our results are in quantitative agreement with the worm-like chain (WLC) model of DNA elasticity, without the need to invoke any 'kinked' states. Greater concentrations of monovalent salts or 1 mM Mg(2+) induced an apparent softening of the dsDNA, which was best accounted for by a kink in the region of highest curvature. We tested the effects of all single-nucleotide mismatches on the DNA bending. Remarkably, the propensity to kink correlated with the thermodynamic destabilization of the mismatched DNA relative the perfectly complementary strand, suggesting that the kinked state is locally melted. The molecular vise is exquisitely sensitive to the sequence-dependent linear and nonlinear elastic properties of dsDNA.
Project description: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.
Project description:Elastic tethers, connecting telomeres of all separating anaphase chromosome pairs, lose elasticity when they lengthen during anaphase. Treatment with phosphatase inhibitor CalyculinA causes anaphase chromosomes to move backwards after they reach the poles, suggesting that dephosphorylation causes loss of tether elasticity. We added 50nM CalyculinA to living anaphase crane-fly spermatocytes with different length tethers. When tethers were short, almost all partner chromosomes moved backwards after nearing the poles. When tethers were longer, fewer chromosomes moved backwards. With yet longer tethers none moved backward. This is consistent with tether elasticity being lost by dephosphorylation. 50nM CalyculinA blocks both PP1 and PP2A. To distinguish between PP1 and PP2A we treated cells with short tethers with 50nM okadaic acid which blocks solely PP2A, or with 1µM okadaic acid which blocks both PP1 and PP2A. Only 1µM okadaic acid caused chromosomes to move backward. Thus, tether elasticity is lost because of dephosphorylation by PP1.
Project description:By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.
Project description:Using MP2, CCSD, and B3LYP methods of computational chemistry, we show length dependence in the intrinsic elastic properties of short alkane fragments. For isolated alkane fragments of finite length in the gas phase and zero temperature, the intrinsic elasticity constants are found to vary with the number of carbon atoms and its parity. From extrapolation of the elasticity constants calculations to infinite chain length, and by comparing with in-situ elasticity constant of single poly(ethylene) molecule obtained with atomic force microscopy, we estimate the softening effect of environment on the extension response of the polymer.
Project description:DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart-with the deviation larger for shorter molecules-because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.
Project description:A unique sequence within the giant titin molecule, the PEVK domain, has been suggested to greatly contribute to passive force development of relaxed skeletal muscle during stretch. To explore the nature of PEVK elasticity, we used titin-specific antibodies to stain both ends of the PEVK region in rat psoas myofibrils and determined the region's force-extension relation by combining immunofluorescence and immunoelectron microscopy with isolated myofibril mechanics. We then tried to fit the results with recent models of polymer elasticity. The PEVK segment elongated substantially at sarcomere lengths above 2.4 micro(m) and reached its estimated contour length at approximately 3.5 micro(m). In immunofluorescently labeled sarcomeres stretched and released repeatedly above 3 micro(m), reversible PEVK lengthening could be readily visualized. At extensions near the contour length, the average force per titin molecule was calculated to be approximately 45 pN. Attempts to fit the force-extension curve of the PEVK segment with a standard wormlike chain model of entropic elasticity were successful only for low to moderate extensions. In contrast, the experimental data also could be correctly fitted at high extensions with a modified wormlike chain model that incorporates enthalpic elasticity. Enthalpic contributions are likely to arise from electrostatic stiffening, as evidenced by the ionic-strength dependency of titin-based myofibril stiffness; at high stretch, hydrophobic effects also might become relevant. Thus, at physiological muscle lengths, the PEVK region does not function as a pure entropic spring. Rather, PEVK elasticity may have both entropic and enthalpic origins characterizable by a polymer persistence length and a stretch modulus.