From signal transduction to spatial pattern formation in E. coli: A paradigm for multi-scale modeling in biology
Radek Erban and Hans Othmer
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Submission date: 10. Jun. 2004
published in: Multiscale modeling and simulation, 3 (2005) 2, p. 362-394
DOI number (of the published article): 10.1137/040603565
MSC-Numbers: 35K10, 92B05
Keywords and phrases: transport equations, chemotaxis equations
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Abstract The collective behavior of bacterial populations provides an example of how cell-level decision-making translates into population-level behavior, and illustrates clearly the difficult multi-scale mathematical problem of incorporating individual-level behavior into population-level models. Here we focus on the flagellated bacterium E. coli, for which a great deal is known about signal detection, transduction and cell-level swimming behavior. We review the biological background on individual and population-level processes and discuss the velocity-jump approach used for describing population-level behavior based on individual-level intracellular processes. In particular, we generalize the moment-based approach to macroscopic equations used earlier to higher dimensions and show how aspects of the signal transduction and response enter into the macroscopic equations. We also discuss computational issues surrounding the bacterial pattern formation problem and technical issues involved in the derivation of macroscopic equations.