Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints

TL;DR

This paper investigates the entropic elasticity of double-strand DNA under spatial constraints using a discretized WLC model, deriving a transfer matrix approach for efficient numerical analysis of confined DNA configurations.

Contribution

It introduces a discretized WLC model with a transfer matrix method to study DNA elasticity under spatial obstructions, avoiding complex differential equation solutions.

Findings

Validated the approach with DNA confined between parallel plates

Provided a numerically efficient method for modeling constrained DNA

Enhanced understanding of DNA behavior under spatial restrictions

Abstract

The aim of the present paper is the study of the entropic elasticity of the dsDNA molecule, having a cristallographic length L of the order of 10 to 30 persistence lengths A, when it is subject to spatial obstructions. We have not tried to obtain the single molecule partition function by solving a Schodringer-like equation. We prefer to stay within a discretized version of the WLC model with an added one-monomer potential, simulating the spatial constraints. We derived directly from the discretized Boltzmann formula the transfer matrix connecting the partition functions relative to adjacent "effective monomers". We have plugged adequate Dirac delta-functions in the functional integral to ensure that the monomer coordinate and the tangent vector are independent variables. The partition function is, then, given by an iterative process which is both numerically efficient and physically transparent. As a test of our discretized approach, we have studied two configurations involving a dsDNA molecule confined between a pair of parallel plates.