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MiS Preprint

Global existence results for complex hyperbolic models of bacterial chemotaxis

Radek Erban and Hyung Ju Hwang


Bacteria are able to respond to environmental signals by changing their rules of movement. When we take into account chemical signals in the environment, this behaviour is often called chemotaxis. At the individual-level, chemotaxis consists of several steps. First, the cell detects the extracellular signal using receptors on its membrane. Then, the cell processes the signal information through the intracellular signal transduction network, and finally it responds by altering its motile behaviour accordingly. At the population level, chemotaxis can lead to aggregation of bacteria, travelling waves or pattern formation, and the important task is to explain the population-level behaviour in terms of individual-based models. It has been previously shown that the transport equation framework is suitable for connecting different levels of modelling of bacterial chemotaxis. In this paper, we couple the transport equation for bacteria with the (parabolic/elliptic) equation for the extracellular signals. We prove global existence of solutions for the general hyperbolic chemotaxis models of cells which process the information about the extracellular signal through the intracellular biochemical network and interact by altering the extracellular signal as well. The conditions for global existence in terms of the properties of the signal transduction model are given.

Dec 12, 2005
Dec 12, 2005
chemotaxis, intracellular transduction, global existence

Related publications

2006 Repository Open Access
Radek Erban and Hyung Ju Hwang

Global existence results for complex hyperbolic models of bacterial chemotaxis

In: Discrete and continuous dynamical systems / B, 6 (2006) 6, pp. 1239-1260