Analysis of Stochastic Strategies in Bacterial Competence: A Master Equation Approach

Competence is a transiently differentiated state that certain bacterial cells reach when faced with a stressful environment. Entrance into competence can be attributed to the excitability of the dynamics governing the genetic circuit that regulates this cellular behavior. Like many biological behaviors, entrance into competence is a stochastic event. In this case cellular noise is responsible for driving the cell from a vegetative state into competence and back. In this work we present a novel numerical method for the analysis of stochastic biochemical events and use it to study the excitable dynamics responsible for competence in Bacillus subtilis. Starting with a Finite State Projection (FSP) solution of the chemical master equation (CME), we develop efficient numerical tools for accurately computing competence probability. Additionally, we propose a new approach for the sensitivity analysis of stochastic events and utilize it to elucidate the robustness properties of the competence regulatory genetic circuit. We also propose and implement a numerical method to calculate the expected time it takes a cell to return from competence. Although this study is focused on an example of cell-differentiation in Bacillus subtilis, our approach can be applied to a wide range of stochastic phenomena in biological systems.Author Summary: When exposed to stress, organisms react by taking actions that help them protect their DNA. ComK protein is a key regulator which activates hundreds of genes, including the genes encoding the DNA-uptake and recombination systems. In Bacillus subtilis, stress in the environment activates a sequence of chemical reactions that, driven by cellular noise, stochastically increases the level of ComK in some bacterial cells driving them from their original vegetative state into a competent state. Entrance into and exit from competence are stochastic switching events that the cell undergoes. In this work, we present a novel numerical method that allows the analysis of stochastic events in biological systems. We illustrate our method by computing the probability with which Bacillus subtilis enters in competence. We also present a method to analyze the sensitivity of stochastic events. We use this method to study the sensitivity of the probability of entrance in competence with respect to various gene expressions and degradation rates. We finally present a numerical method to calculate the expected time it takes a cell to return from competence. Although we studied the competence regulatory genetic circuit, our approach can be applied to a variety of stochastic events in biological systems.