Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA

TL;DR

This paper develops an analytical formalism to describe force-elongation relations of flexible chain molecules, improving accuracy over previous models, and explores its application in inferring DNA nicking from single-molecule stretching data.

Contribution

It introduces a new analytical approach for finite chain length corrections in wormlike chains, enhancing the understanding of DNA stretching experiments.

Findings

Analytical expressions match numerical data well.

Finite chain length corrections are accurately modeled.

Potential application in DNA nick-counting experiments.

Abstract

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality as the numerical evaluation of Marko's and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests, that our analytical expressions for the finite-chain length corrections are of similar quality. As an application of our results we discuss the possibility of inferring the changing number of nicks in a double-stranded DNA molecule in single-molecule stretching experiments from the accompanying changes in the effective chain length.