Exact solution of a model DNA-inversion genetic switch with orientational control

TL;DR

This paper presents an exact analytical solution and stochastic analysis of a DNA inversion switch model where recombinase production depends on the switch state, revealing non-Poissonian behavior and correlated flip times.

Contribution

It introduces a simple, exactly solvable model for a DNA inversion switch with orientational control, inspired by the fim switch in E. coli.

Findings

Switch times show a peak in their distribution.

Successive flip times are correlated.

Deviations from Poissonian behavior are observed.

Abstract

DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated.