Mathematical models of bacterial chemotaxis

Abstract

In response to environmental signals such as light, temperature or chemicals, motile organisms can change their behavior by directed movement toward or away from the signal, by changing their speed of movement and/or frequency of turning. The process is called chemotaxis. E. coli employs chemotaxis to move toward favorable locations. E. coli chemotaxis is a widely studied system. The recent research mainly concentrates on receptor clustering, which is established to account for the dramatic features of the system such as high sensitivity, precise adaptation, and robustness. There are multiple levels of organization of a receptor cluster, and researchers are gaining insights into its structure-function relationship. We hypothesize that multiple-level molecular interactions exist in the receptor cluster, and each of them contributes specific functions to the high-performance signaling. To test it, we first develop a model based on the experimental observation that the most permanent clusters of receptor homodimers are trimers of dimers. We only consider the interactions among dimers within a trimer, called intratrimer interactions. We show that the model can reproduce most of the experimentally-observed behaviors, including excitation, adaptation, high sensitivity, and robustness to parameter variations. In addition, the model makes a number of new predictions as to how the adaptation time varies with the expression level of proteins. Second, we use the approaches of multi-time-scale analysis and mean-field theory to perform model reduction, and obtain two low-dimension models. They successfully capture the output of the original model. Third, we develop a free-energy-based model for a cluster of coupled trimers, emphasizing the interactions among trimers, called intertrimer interactions. We use the model to explain high cooperativity in kinase activity responses by the cheRcheB mutants with overexpression of Tar or Tsr. Last, we develop a stochastic model of adaptation with the mobile CheR and CheB and show some preliminary results.