Mathematical models of bacterial chemotaxis

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. When the signal is chemical, the process is called chemotaxis. E. coli employs chemotaxis to find and move toward favorable locations. E. coli chemotaxis is a widely studied molecular system. Our knowledge of the signaling pathway in E. coli chemotaxis has been significantly advanced. The recent research mainly concentrates on receptor clustering. It is established to account for the dramatic features of the system such as high sensitivity in transmembrane signaling, precise adaptation over a wide dynamic range of ligand concentrations, and robustness to quantities of intracellular proteins. To fully understand the mechanism behind the high-performance signaling functions, researchers are gaining insights into the structural basis and functional consequences of the interactions among the networked receptors.;So far, we know that there are multiple levels of organization of a receptor network. First, two receptor monomers bind into a homodimer. Second, three homodimers form a trimer of dimers. Third, trimers cluster together into a patch of thousands of molecules, probably in a hexagonal network. Last, most patches localize at a cell pole. We hypothesize that multiple levels of molecular interactions exist in the receptor network and each of them contributes specific functional features to the high-performance signaling for E. coli chemotaxis.;In this dissertation we use mathematical modeling and computer simulation to study the structure-function relationship in signaling for E. coli chemotaxis. We first develop a model based on the experimental observation that the most permanent clusters of receptor homodimers are trimers of dimers. In the model, 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 various proteins involved in signal transduction. Our results provide a more mechanistically-based explanation of the origin of high sensitivity than previous models, and show that in some situations, higher-order receptor interactions beyond intratrimer interactions, called intertrimer interactions, may not be necessary for chemotactic responses by cells.;The 'trimer-of-dimers'-based model describes the full dynamics and includes 158 differential equations. To simplify and apply it to later work, we use two approaches of multi-time-scale analysis and mean-field theory to perform system reduction, and obtain two low-dimension models, which comprise of only 16 and 4 differential equations, respectively. Both of them successfully capture the main features of the response and show very good agreement with the output of the original model.;The experimental measures on kinase activity response by the cheRcheB mutants with overexpression of Tar or Tsr show high Hill coefficients, even up to 11, which probably suggests that higher-order interactions beyond those within a trimer are involved in responses of these cells. The 'trimer-of-dimers' model does not include higher-order interactions and can hardly predict a Hill coefficient higher than 3. To explain the high cooperativity in these strains, we model the signaling function of a trimer of dimers with a free-energy-based method and then extend the equilibrium model for a single trimer to a model for a cluster of coupled trimers. The new model reproduces the high Hill coefficients observed in a range of experiments, verifying our hypothesis that the extremely high cooperativity is attributed to the intertrimer interactions.;In wild-type cells, the copy number ratio of the receptor to the enzyme CheR or CheB is very high. It is highly possible that a single CheR or CheB performs adaptational modification on many receptors in a short time period, especially when the cell responds to a large stimulus, and that the motility of the two enzymes plays some role in the adaptation phase of chemotaxis. The short distance between neighbored trimers of dimers allows the enzymes to quickly access a large number of receptors. Therefore, receptor clustering provides a physical basis for the feature. We develop a stochastic model, apply the Gillespie algorithm in simulation, and show that a mobile CheR and CheB can make the activity of a large receptor cluster precisely adapt in an appropriate timescale.;In summary, in this dissertation, we intensively study the signal transduction pathway of E. coli chemotaxis with the approach of quantitative modeling and computer simulation. We specially focus on receptor clustering and its relationship with high-performance signaling function. The models we construct and the analyses we conduct deepen our understanding on the specific functions contributed by multiple levels of the structure of a receptor network.