Large Deviations Analysis for Stochastic Models of Bacterial Evolution

TL;DR

This paper introduces a large deviations theoretical framework for modeling rare genetic shifts in bacterial populations, providing explicit formulas to quantify likely evolutionary paths.

Contribution

It develops a novel large deviations approach for Markov chain models of bacterial evolution, including cost functions and explicit trajectory formulas.

Findings

Explicit formulas for evolutionary trajectories

Cost functions for Markov chain models

Quantitative assessment of rare genetic shifts

Abstract

Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large deviations framework for a class of Markov chains modeling the genetic evolution of bacteria such as E. coli. In particular, we develop the cost function for discrete-time Markov chains which describe the daily evolution of histograms of bacterial populations. We also develop explicit formulas that can be used to numerically quantify the most likely evolutionary trajectories connecting an initial histogram and the target histogram.