Dynamics of DNA-breathing: Weak noise analysis, finite time singularity, and mapping onto the quantum Coulomb problem
arXiv:0706.4401 · doi:10.1103/PhysRevE.76.061915
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.
12 pages, 10 figures, revtex
References in corpus (17)
- Why is the DNA Denaturation Transition First Order?
- Roles of stiffness and excluded volume in DNA denaturation
- Localization of Denaturation Bubbles in Random DNA Sequences
- DNA bubble dynamics as a quantum Coulomb problem
- Bubble dynamics in DNA
- Sequence sensitivity of breathing dynamics in heteropolymer DNA
- Poland-Scheraga models and the DNA denaturation transition
- Breathing dynamics in heteropolymer DNA
- Loop Dynamics in DNA Denaturation
- A simple model for DNA denaturation
- Canonical phase space approach to the noisy Burgers equation: Probability distributions
- Stochastic approach to DNA breathing dynamics
- Bubble Relaxation Dynamics in Double-Stranded DNA
- Master equation approach to DNA-breathing in heteropolymer DNA
- Power laws and stretched exponentials in a noisy finite-time-singularity model
- Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation
- Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials
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- Resetting transition is governed by an interplay between thermal and potential energy
- Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials
- Determining the DNA stability parameters for the breathing dynamics of heterogeneous DNA by stochastic optimization
- DNA breathing dynamics: Analytic results for distribution functions of relevant Brownian functionals
- Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum
- Dynamics of a bubble formed in double stranded DNA
- Looking into DNA breathing dynamics via quantum physics
- Patterns in the Kardar-Parisi-Zhang equation
- Loop exponent in DNA bubble dynamics
- Bubble merging in breathing DNA as a vicious walker problem in opposite potentials
- Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
- Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA
- Statistical Mechanics of DNA Mutation using SUSY Quantum Mechanics