Thermally activated barrier crossing and stochastic resonance of a flexible polymer chain in a piecewise linear bistable potential

TL;DR

This paper investigates the stochastic resonance and barrier crossing dynamics of a flexible polymer chain in a bistable potential, revealing optimal conditions for signal enhancement and insights into how chain length and coupling affect crossing rates.

Contribution

It introduces a detailed analysis of stochastic resonance and barrier crossing for polymers in bistable potentials, highlighting optimal parameters and contrasting behaviors of different crossing rates.

Findings

Signal to noise ratio peaks at optimal parameters.

Crossing rate for the center of mass decreases with chain length.

Segment crossing rate increases and saturates with chain length.

Abstract

We study the stochastic resonance (SR) of a flexible polymer chain crossing over a piecewise linear bistable potential. The dependence of signal to noise ratio $SNR$ on noise intensity $D$, coupling constant $k$ and polymer length $N$ is studied via two state approximation. We find that the response of signal to the background noise strength is significant at optimum values of $D_{opt}$, $k_{opt}$ and $N_{opt}$ which suggests novel means of manipulating proteins or vesicles. Furthermore, the thermally activated barrier crossing rate $r_{k}$ for the flexible polymer chain is studied. We find that the crossing rate $r_{k}$ exhibits an optimal value at an optimal coupling constant $k_{opt}$; $k_{opt}$ decreases with $N$. As the chain length $N$ increases, the escape rate for the center of mass $r_{k}$ monotonously decreases. On the other hand, the crossing rate for the portion of polymer segment $r_s$ increases and saturates to a constant rate as $N$ steps up.