MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Radek Erban and Hans Othmer


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 {\it 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.

MSC Codes:
35K10, 92B05
transport equations, chemotaxis equations

Related publications

2005 Repository Open Access
Radek Erban and Hans G. Othmer

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

In: Multiscale modeling and simulation, 3 (2005) 2, pp. 362-394