A Low Dimensional Approximation For Competence In Bacillus Subtilis

TL;DR

This paper develops low-dimensional stochastic models to accurately capture the competence dynamics of Bacillus subtilis, improving upon adiabatic approximations by incorporating iterative and noise-tuning methods.

Contribution

It introduces a 2D Langevin model with a tunable noise term and an iterative approximation method for better modeling Bacillus subtilis competence dynamics.

Findings

The 2D Langevin model reproduces the bimodal distribution of competence states.

The iterative method accurately approximates the time-course of protein trajectories.

The modified noise term improves the stationary distribution fit.

Abstract

The behaviour of a high dimensional stochastic system described by a Chemical Master Equation (CME) depends on many parameters, rendering explicit simulation an inefficient method for exploring the properties of such models. Capturing their behaviour by low-dimensional models makes analysis of system behaviour tractable. In this paper, we present low dimensional models for the noise-induced excitable dynamics in Bacillus subtilis, whereby a key protein ComK, which drives a complex chain of reactions leading to bacterial competence, gets expressed rapidly in large quantities (competent state) before subsiding to low levels of expression (vegetative state). These rapid reactions suggest the application of an adiabatic approximation of the dynamics of the regulatory model that, however, lead to competence durations that are incorrect by a factor of 2. We apply a modified version of an iterative functional procedure that faithfully approximates the time-course of the trajectories in terms of a 2-dimensional model involving proteins ComK and ComS. Furthermore, in order to describe the bimodal bivariate marginal probability distribution obtained from the Gillespie simulations of the CME, we introduce a tunable multiplicative noise term in a 2-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.