Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway.

Content Provider	Europe PMC
Author	Edgington, Matthew P. Tindall, Marcus J.
Abstract	We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.
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ISSN	00928240
Journal	Bulletin of Mathematical Biology [Bull Math Biol]
Volume Number	80
DOI	10.1007/s11538-018-0400-z
PubMed Central reference number	PMC5862969
Issue Number	4
PubMed reference number	29404879
e-ISSN	15229602
Language	English
Publisher	Springer US
Publisher Date	2018-02-05
Publisher Place	New York
Access Restriction	Open
Rights License	Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. © The Author(s) 2018
Subject Keyword	Bacterial chemotaxis Signalling pathway Adaptation Equilibrium Stability analysis Overshoot
Content Type	Text
Resource Type	Article
Subject	Neuroscience Mathematics Biochemistry, Genetics and Molecular Biology Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences