Master equation approach to DNA-breathing in heteropolymer DNA

TL;DR

This paper develops a master equation model for DNA-breathing dynamics in heteropolymer DNA, enabling detailed analysis of bubble formation, lifetimes, and relaxation times, validated by stochastic simulations.

Contribution

It introduces a dynamic master equation framework for heteropolymer DNA-breathing, linking free energy models to bubble kinetics and relaxation spectra.

Findings

Derived autocorrelation functions for bubble dynamics

Obtained probability densities for bubble lifetimes

Validated model with Gillespie simulation

Abstract

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.