Disordered, stretched, and semiflexible biopolymers in two dimensions

TL;DR

This paper investigates how sequence-dependent curvature affects the mechanical properties of two-dimensional semiflexible biopolymers, revealing conditions where disorder influences elasticity and when it can be effectively ignored.

Contribution

It provides exact analytical results for the distribution and effective properties of disordered biopolymers, highlighting the conditions under which sequence disorder impacts elasticity.

Findings

Disorder can be mapped to an equivalent system with renormalized persistence length.

External forces and boundary conditions influence the effect of disorder.

Long, strongly stretched biopolymers are unaffected by sequence disorder.

Abstract

We study the effects of intrinsic sequence-dependent curvature for a two dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system is equivalent to a system with a well-defined intrinsic curvature and a proper renormalized persistence length. We find the exact expression for the distribution function of the equivalent system. However, we show that such an equivalent system does not always exist for the polymer subjected to an external force. We find that under an external force, the effect of sequence-disorder depends upon the averaging order, the degree of disorder, and the experimental conditions, such as the boundary conditions. Furthermore, a short to moderate length biopolymer may be much softer or has a smaller apparent persistent length than what would be expected from the "equivalent system". Moreover, under a strong stretching force and for a long biopolymer, the sequence-disorder is immaterial for elasticity. Finally, the effect of sequence-disorder may depend upon the quantity considered.