How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: An entropic stochastic resonance

TL;DR

This study analytically demonstrates how a stretched biopolymer exhibits entropic stochastic resonance, with maximum response amplification at an optimal noise level and chain length, influenced by hydrodynamic interactions and chain undulations.

Contribution

It introduces the concept of entropic stochastic resonance in stretched polymers, highlighting the role of hydrodynamics and chain length in optimizing response to oscillatory signals.

Findings

Power amplification increases with chain length, indicating entropic stochastic resonance.

Hydrodynamic interactions enhance the response, showing polymer cooperativity.

Maximum resonance occurs at an optimal chain length for charged polymers under electric fields.

Abstract

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations.