Dynamics of Competitive Evolution on a Smooth Landscape

TL;DR

This paper investigates the steady-state dynamics of competitive DNA sequence evolution driven by protein binding, revealing a shape-preserving pulse behavior that decelerates to equilibrium, supported by analytical and simulation results.

Contribution

It introduces a continuum mean-field model to explain the pulse dynamics in competitive DNA evolution and shows finite population effects are negligible.

Findings

Pulse behavior decelerates and reaches equilibrium

Analytical results match simulations

Finite population corrections are insignificant

Abstract

We study competitive DNA sequence evolution directed by {\it in vitro} protein binding. The steady-state dynamics of this process is well described by a shape-preserving pulse which decelerates and eventually reaches equilibrium. We explain this dynamical behavior within a continuum mean-field framework. Analytical results obtained on the motion of the pulse agree with simulations. Furthermore, finite population correction to the mean-field results are found to be insignificant.