Bubble Relaxation Dynamics in Double-Stranded DNA
D. J. Bicout (1,2), E. Kats (1,3) (1 - Institut Laue-Langevin,, Grenoble, France; 2 - Biomathematics, Epidemiology, ENVL, Marcy l'Etoile,, France; 3 - L. D. Landau Institute for Theoretical Physics, RAS, Moscow,, Russia.)
TL;DR
This paper provides an exact solution for the dynamics of bubble formation in double-stranded DNA, including finite size effects, and analyzes how these dynamics approximate the continuous model under certain conditions.
Contribution
It introduces an exact solution for the discrete, finite-size bubble relaxation model in DNA, accounting for end effects and deriving key analytic expressions.
Findings
Exact solutions for correlation functions and lifetimes of DNA bubbles.
Finite size effects are significant and well-approximated by the continuous model when a^N << 1.
The model clarifies the influence of opening and closing rates on DNA melting dynamics.
Abstract
The paper deals with the two-state (opening-closing of base pairs) model used to describe the fluctuation dynamics of a single bubble formation. We present an exact solution for the discrete and finite size version of the model that includes end effects and derive analytic expressions of the correlation function, survival probability and lifetimes for the bubble relaxation dynamics. It is shown that the continuous and semi-infinite limit of the model becomes a good approximation to exact result when a^N << 1, where N is bubble size and a, the ratio of opening to closing rates of base pairs, is the control parameter of DNA melting.
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