From signal transduction to spatial pattern formation in E-coli: A paradigm for multiscale modeling in biology

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 [R. Erban and H. G. Othmer, SIAM J. Appl. Math., 65 (2004), pp. 361-391] 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.