Semiflexible Chains in Confined Spaces

TL;DR

This paper introduces an analytical mean field-like method to study semiflexible wormlike chains in confined geometries, accurately predicting properties and behaviors relevant to biological systems like DNA in viral capsids.

Contribution

The authors develop a tractable analytical approach for non-interacting WLCs in confinement, accurately reproducing correlation functions and free energy coefficients, and analyzing force-extension behavior.

Findings

Exact correlation functions for confined WLCs are obtained.

Force-extension curves show spatial oscillations under confinement.

Predicted pressures match simulations but are lower than viral DNA pressures.

Abstract

We develop an analytical method for studying the properties of a non-interacting Wormlike Chain (WLC) in confined geometries. The mean field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as $f^{-1}$ at large forces, in contrast to the unconfined chain that approaches the contour length as $f^{-1/2}$. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the MF approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids.