Mathematics Colloquia and Seminars

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Description

Understanding bacterial development requires comprehending of spatio-temporal pattern formation on intracellular (gene expression) scales and multicellular (coordinated cell motility) scales. In this presentation I will describe two examples of mathematical models that help to get insight on the development process. The first part of my talk shows how our model explains traveling wave patterns during starvation induced development of Myxococcus xanthus and leads to predictions on biochemical circuitry that controls the development process. In the second part, I briefly overview our results and current research on organization of regulatory biochemical networks controlling sigma factors in Bacillus subtilis.

Under starvation conditions, a population of myxobacteria aggregates to build a fruiting body whose shape is species-specific and within which the cells sporulate. Early in this process, cells often pass through a "ripple phase" characterized by traveling linear, concentric, and spiral density waves. Based on experimental observation of individual cell motility and intercellular signaling we constructed a mathematical model that successfully reproduces all observed patterns. The model makes testable prediction on motility coordination and signaling system. The results of the model analysis show that pattern formation mechanism exploited by myxobacteria is unlike any other in chemistry or biology. Based on the pattern formation model we were able to construct a model for the biochemical circuit controlling cell reversals. The model explains several aspects of M. xanthus behavior during development and makes testable experimental predictions.

Regulatory networks controlling bacterial gene expression often evolve from a common origin and, therefore, involve homologous proteins and share similar network motifs. For example, in B. subtilis the activities of both the stress response factor sigmaB and the first sporulation-specific factor sigmaF are controlled by similar partner-switching mechanisms. However, clear differences in network organization are apparent: the anti-sigma-factor in the sigmaF network is known to form a long-lived, “dead-end” complex with its antagonist and ADP; and the genes for sigmaB and its network partners lie in a sigmaB-controlled operon, resulting in both positive and negative feedback loops. Here we compare these alternative designs for partner-switching signaling networks. We constructed mathematical models of both networks and performed mathematically controlled comparisons. The results of this analysis show how differences in network organization correlate with different physiological demands.