Nonequilibrium theory of polymer stretching based on the master equation

Abstract

We present a model for fast polymer-stretching experiments. We use the master equation and argue that the end-to-end extension of a polymer molecule can be used as a stochastic variable after appropriate coarse graining. The main effect of increasing pulling speed or force loading rate is a marked hysteresis in the force-extension curve as well as an overall shift of the curve to higher forces when compared to the equilibrium curve. This can be understood in terms of the moments of the transition probability in the master equation. An analysis of the fluctuations and relaxation times is also given in the framework of our theory.

Nonequilibrium dynamics of single polymer molecules: Relaxation close to and far from equilibrium

“…To set the stage for the study of fast relaxation phenomena in single‐polymer molecules, we summarize the pertinent features of the mesoscopic approach of our previous paper 22. In a coarse‐grained approach, one takes the end‐to‐end length of the polymer as the stochastic variable and treats the stretching behavior of single polymer molecules as a Markov process represented by a master equation.…”

“…We first use the master equation approach to study relaxation close to equilibrium. In our previous paper 22, we extracted longitudinal and transverse relaxation times from the equation of motion (8) by setting L = L eq + δ L and expanding around L eq with $\mathop{\alpha}\limits^{\rightarrow}{_1}({\bf L}_{\rm eq},{\bf f})={\bf 0}$ , so that This defines two relaxation times τ ‖ and τ ⊥ in the directions parallel and perpendicular to the applied force. To evaluate the moments of the transition rates analytically, we introduce r = L ′ – L and rewrite expression (12) as …”

“…Going beyond simple approaches to the dynamics of polymer chains such as the Rouse and Zimm models 14, 15, a mesoscopic theory was recently developed that treats conformational changes in the polymer as a Markov process 22. Taking the end‐to‐end length as the stochastic variable, a master equation is set up for which a phenomenological form of the transition probabilities is assumed that reproduces experimental equilibrium relaxation times.…”

“…For the calculation of the latter, we will use the rotationally isomeric state (RIS) model. In the previous paper 22 two simple models, i.e., the freely jointed chain (FJC) and the freely rotating chain (FRC) models, were used and the generalization to more detailed polymer models is straightforward, albeit numerically more involved. The RIS model allows for the chain segments to assume only a discrete set of torsional angles (three in most cases for the trans, gauche(+) and gauche(−) conformers), while bond lengths and angles are fixed.…”

Breaking bonds in the atomic force microscope: Extracting information

“…In such a scenario, one might consider an approach as outlined elsewhere. 17 Restricting ourselves to slow pulling such that the spacer molecule is always in equilibrium, we find 15 TABLE I. Parameters V 0 , ␥, and A for the ubiquitin experiment, the corresponding k off * from the Ritchie-Evans model, and the maximum force f max = ␥V 0 / 2 for each Morse potential. Table I.…”