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A low dimensional approximation for competence in Bacillus subtilis

A low dimensional approximation for competence in Bacillus subtilis
A low dimensional approximation for competence in Bacillus subtilis
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 two-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 two-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.
1545-5963
272-280
Nguyen, An
69fab095-6fad-4a99-a9c7-83106d5a0dc4
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Nguyen, An
69fab095-6fad-4a99-a9c7-83106d5a0dc4
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698

Nguyen, An, Prugel-Bennett, Adam and Dasmahapatra, Srinandan (2016) A low dimensional approximation for competence in Bacillus subtilis. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 13 (2), 272-280. (doi:10.1109/TCBB.2015.2440275).

Record type: Article

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 two-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 two-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.

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Accepted/In Press date: April 2015
e-pub ahead of print date: 29 June 2015
Published date: March 2016
Organisations: Vision, Learning and Control

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Local EPrints ID: 376760
URI: https://eprints.soton.ac.uk/id/eprint/376760
ISSN: 1545-5963
PURE UUID: 32e1bf2f-7806-4f93-9411-6937ff8469d1

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Date deposited: 08 May 2015 13:26
Last modified: 23 Sep 2019 18:44

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Contributors

Author: An Nguyen
Author: Adam Prugel-Bennett
Author: Srinandan Dasmahapatra

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