Simulation and analysis of in vitro DNA evolution

TL;DR

This paper models in vitro DNA evolution by binding to a transcription factor, analyzing different population regimes and providing analytical estimates that match simulations, enhancing understanding of evolutionary dynamics.

Contribution

It introduces a simple model for protein-DNA binding, performs large-scale simulations, and derives analytical estimates for different evolutionary regimes.

Findings

Small populations exhibit a random walk evolution path.

Large populations follow mean-field dynamics.

DNA-protein interaction details influence evolution.

Abstract

We study theoretically the in vitro evolution of a DNA sequence by binding to a transcription factor. Using a simple model of protein-DNA binding and available binding constants for the Mnt protein, we perform large-scale, realistic simulations of evolution starting from a single DNA sequence. We identify different parameter regimes characterized by distinct evolutionary behaviors. For each regime we find analytical estimates which agree well with simulation results. For small population sizes, the DNA evolutional path is a random walk on a smooth landscape. While for large population sizes, the evolution dynamics can be well described by a mean-field theory. We also study how the details of the DNA-protein interaction affect the evolution.