Discrete Persistent Chain Model for Protein Binding on DNA

TL;DR

This paper introduces a discrete persistent chain model to analyze protein binding on DNA, providing analytical and numerical solutions for force-extension behavior and binding fractions, aiding interpretation of experimental data.

Contribution

The paper presents a novel discrete persistent chain model incorporating protein binding states and energy costs, with analytical and numerical solutions for force-extension and binding fractions.

Findings

Analytic expressions for force-extension curves at low force.

Numerical solutions for high-force regimes.

Method to deduce bound protein numbers from experimental data.

Abstract

We describe and solve a discrete persistent chain model of protein binding on DNA, involving an extra sigma_i s at a site i of the DNA. This variable takes the value 1 or 0 depending on whether the site is occupied by a protein or not. In addition, if the site is occupied by a protein, there is an extra energy cost epsilon. For small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA.For higher forces, the model can be solved numerically to obtain force extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of non-specific binding.