Stretching weakly bending filaments with spontaneous curvature in two dimensions

TL;DR

This paper investigates how spontaneous curvature influences the mechanical response of weakly bending filaments in two dimensions, providing analytical insights into force-extension behavior and fluctuation widths relevant to biomolecules.

Contribution

It extends the wormlike chain model to include spontaneous curvature, deriving analytical results for force-extension and fluctuations, especially for sinusoidally varying curvature.

Findings

Spontaneous curvature affects force-extension behavior.

Undulations in curvature influence filament flexibility.

Analytical expressions for fluctuation widths are provided.

Abstract

Some important biomolecules (for instance, bacterial FtsZ and eukaryotic DNA) are known to posses spontaneous (intrinsic) curvature. Using a simple extension of the wormlike chain model, we study the response of a weakly bending filament in two dimensions to a pulling force applied at its ends (a configuration common in classical in-vitro experiments and relevant to several in-vivo cell cases). The spontaneous curvature of such a chain or filament can in general be arc-length dependent and we study a case of sinusoidal variation, from which an arbitrary case can be reconstructed via Fourier transformation. We obtain analytic results for the force-extension relationship and the width of transverse fluctuations. We show that spontaneous-curvature undulations can affect the force-extension behavior even in relatively flexible filaments with a persistence length smaller than the contour length.