Dynamics of DNA-breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem

TL;DR

This paper analyzes DNA bubble dynamics using a weak noise approach, revealing a connection to the quantum Coulomb problem and identifying different regimes of bubble lifetime behavior relative to melting temperature.

Contribution

It introduces a novel mapping of DNA bubble dynamics onto a quantum Coulomb problem and characterizes the finite time singularity and long-term behavior.

Findings

Below melting temperature, bubble closure is a finite time singularity.

At melting temperature, the dynamics show a power law tail.

Above melting temperature, the bubble lifetime is dominated by the lowest bound state.

Abstract

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.