The volcano effect in bacterial chemotaxis

A population-level model of bacterial chemotaxis is derived from a simple bacterial-level model of behavior. This model, to be contrasted with the Keller-Segel equations, exhibits behavior we refer to as the ''volcano effect'': steady-state bacterial aggregation forming a ring of higher density some distance away from an optimal environment. The model is derived, as in Erban and Othmer (2004) [1], from a transport equation in a state space including the internal biochemical variables of the bacteria and then simplified with a truncation at low moments with respect to these variables. We compare the solutions of the model to stochastic simulations of many bacteria, as well as the classic Keller-Segel model. This model captures behavior that the Keller-Segel model is unable to resolve, and sheds light on two different mechanisms that can cause a volcano effect.

[1]  H. Berg,et al.  Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking , 1972, Nature.

[2]  M. Brenner,et al.  Motility of Escherichia coli cells in clusters formed by chemotactic aggregation , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[3]  L. Segel,et al.  Model for chemotaxis. , 1971, Journal of theoretical biology.

[4]  Radek Erban,et al.  From Signal Transduction to Spatial Pattern Formation in E. coli: A Paradigm for Multiscale Modeling in Biology , 2005 .

[5]  B. Perthame,et al.  Kinetic Models for Chemotaxis and their Drift-Diffusion Limits , 2004 .

[6]  H. Berg,et al.  Adaptation kinetics in bacterial chemotaxis , 1983, Journal of bacteriology.

[7]  P. K. Maini,et al.  Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations , 2008, Bulletin of mathematical biology.

[8]  J. Murray,et al.  A minimal mechanism for bacterial pattern formation , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  H. Berg,et al.  Complex patterns formed by motile cells of Escherichia coli , 1991, Nature.

[10]  D. Brown,et al.  Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. , 1974, Antibiotics and chemotherapy.

[11]  Radek Erban,et al.  From Individual to Collective Behavior in Bacterial Chemotaxis , 2004, SIAM J. Appl. Math..

[12]  Dennis Bray,et al.  The Chemotactic Behavior of Computer-Based Surrogate Bacteria , 2007, Current Biology.

[13]  J. Adler.  A method for measuring chemotaxis and use of the method to determine optimum conditions for chemotaxis by Escherichia coli. , 1973, Journal of general microbiology.