Binding of molecules to DNA and other semiflexible polymers

A theory is presented for the binding of small molecules such as surfactants to semiflexible polymers. The persistence length is assumed to be large compared to the monomer size but much smaller than the total chain length. Such polymers (e.g. DNA) represent an intermediate case between flexible polymers and stiff, rod-like ones, whose association with small molecules was previously studied. The chains are not flexible enough to actively participate in the self-assembly, yet their fluctuations induce long-range attractive interactions between bound molecules. In cases where the binding significantly affects the local chain stiffness, those interactions lead to a very sharp, cooperative association. This scenario is of relevance to the association of DNA with surfactants and compact proteins such as RecA. External tension exerted on the chain is found to significantly modify the binding by suppressing the fluctuation-induced interaction.Comment: 15 pages, 7 figures, RevTex, the published versio

Design principles governing the motility of myosin V

The molecular motor myosin V exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is hand-over-hand stepping by a swinging lever arm movement toward the plus-end of actin filaments, essential to its role as a cellular transporter. However, single-molecule experiments have also shown that the motor "foot stomps", with one hand detaching and rebinding to the same site, and backsteps under sufficient load. Explaining the complete taxonomy of myosin V's load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are still open questions. Starting from a polymer model, we develop an analytical theory to understand the minimal physical properties that govern motor dynamics. In particular, we solve the first-passage problem of the head reaching the target binding site, investigating the competing effects of load pulling back at the motor, strain in the leading head that biases the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. The analytical approach yields a formula for the stall force, identifying the relative contributions of the chemical cycle rates and mechanical features like the bending rigidities of the lever arms. Most importantly, by fully exploring the design space of the motor, we predict that myosin V is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle, and changes in the architecture of the lever arm.Comment: Main text: 15 pages, 5 figures; SI: 15 pages, 5 figure

Dynamics and flow-induced phase separation in polymeric fluids

The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an understanding of how to calculate and classify ``phase diagrams'' for flow-induced transitions. Experimentalists have begun mapping out the phase behavior of wormlike micelles, a ``living'' polymeric system, in flow: these systems undergo transitions into shear-thinning or shear-thickening phases, whose variety is remarkably rich and poorly understood. Polymeric ideas must be extended to include the delicate charge and composition effects which conspire to stabilize the micelles and are strongly influenced by flow.Comment: 6 pages, 2 figures, submitted to Current Opinion in Colloid and Interface Scienc

Affine model of stress stiffening in semiflexible filament networks

We present a revised theoretical study of the affine assumption applied to semiflexible networks. Drawing on simple models of semiflexible worm-like chains we derive an expression for the probability distribution of crosslink separations valid at all separations. This accounts for both entropic and mechanical filament stretching. From this we obtain the free energy density of such networks explicitly as a function of applied strain. We are therefore able to calculate the elastic moduli of such networks for any imposed strain or stress. We find that accounting for the distribution of cross-link separations destroys the simple scaling of modulus with stress that is well known in single chains, and that such scaling is sensitive to the mechanical stretch modulus of individual filaments. We compare this model to three experimental data sets, for networks of different types of filaments, and find that a properly treated affine model can successfully account for the data. We find that for networks of stiffer filaments, such as F-actin, to fit data we require a much smaller effective persistence length than usually assumed to be characteristic of this filament type. We propose that such an effectively reduced rigidity of filaments might be a consequence of network formation.Comment: 11 pages, 9 figure

Morphological Variation in a Toroid Generated from a Single Polymer Chain

A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the width and stiffness of the chain together with the surface energy, which characterizes the segmental interaction parameter. Changes in the thickness and outer/inner radius are interpreted in terms of these parameters. Our theoretical expectation corresponds to the actual morphological changes in a single giant DNA molecule as observed by electron microscopy.Comment: 14 pages, 3 figure

Origin of slow stress relaxation in the cytoskeleton

Dynamically crosslinked semiflexible biopolymers such as the actin cytoskeleton govern the mechanical behavior of living cells. Semiflexible biopolymers nonlinearly stiffen in response to mechanical loads, whereas the crosslinker dynamics allow for stress relaxation over time. Here we show, through rheology and theoretical modeling, that the combined nonlinearity in time and stress leads to an unexpectedly slow stress relaxation, similar to the dynamics of disordered systems close to the glass transition. Our work suggests that transient crosslinking combined with internal stress can explain prior reports of soft glassy rheology of cells, in which the shear modulus increases weakly with frequency.Comment: 6 pages, 4 figure

Free energy of a folded polymer under cylindrical confinement

Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy $F$ is measured as a function of $\lambda$, the end-to-end distance of the polymer. In the case of a flexible linear polymer, $F(\lambda)$ is a linear function in the folded regime with a gradient that scales as $f\equiv |dF/d\lambda| \sim N^0 D^{-1.20\pm 0.01}$ for a tube of diameter $D$ and a polymer of length $N$. This is close to the prediction $f \sim N^0 D^{-1}$ obtained from simple scaling arguments. The discrepancy is due in part to finite-size effects associated with the de-Gennes blob model. A similar discrepancy was observed for the folding of a single arm of a three-arm star polymer. We also examine backfolding of a semiflexible polymer of persistence length $P$ in the classic Odijk regime. In the overlap regime, the derivative scales $f \sim N^0 D^{-1.72\pm 0.02} P^{-0.35\pm 0.01}$, which is close to the prediction $f \sim N^0 D^{-5/3} P^{-1/3}$ obtained from a scaling argument that treats interactions between deflection segments at the second virial level. In addition, the measured free energy cost of forming a hairpin turn is quantitatively consistent with a recent theoretical calculation. Finally, we examine the scaling of $F(\lambda)$ for a confined semiflexible chain in the presence of an S-loop composed of two hairpins. While the predicted scaling of the free energy gradient is the same as that for a single hairpin, we observe a scaling of $f \sim D^{-1.91\pm 0.03} P^{-0.36\pm 0.01}$. Thus, the quantitative discrepancy between this measurement and the predicted scaling is somewhat greater for S-loops than for single hairpins.Comment: 17 papes, 12 figure

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure

Shear-induced unfolding and enzymatic cleavage of full-length VWF multimers

Proteolysis of the multimeric blood coagulation protein von Willebrand Factor (VWF) by ADAMTS13 is crucial for prevention of microvascular thrombosis. ADAMTS13 cleaves VWF within the mechanosensitive A2 domain, which is believed to open under shear flow. Here, we combine Fluorescence Correlation Spectroscopy (FCS) and a microfluidic shear cell to monitor real-time kinetics of full-length VWF proteolysis as a function of shear stress. For comparison, we also measure the Michaelis-Menten kinetics of ADAMTS13 cleavage of wild-type VWF in the absence of shear but partially denaturing conditions. Under shear, ADAMTS13 activity on full-length VWF arises without denaturing agent as evidenced by FCS and gel-based multimer analysis. In agreement with Brownian hydrodynamics simulations, we find a sigmoidal increase of the enzymatic rate as a function of shear at a threshold shear rate 5522/s. The same flow-rate dependence of ADAMTS13 activity we also observe in blood plasma, which is relevant to predict hemostatic dysfunction

Viscoelasticity of reversibly crosslinked networks of semiflexible polymers

We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of wich are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding/unbinding processes. We also develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant-strainrate ramps