(Collaborators: B. Mazzag, UC-Davis, and I.Zhulin, Loma Linda University).

Bacterial chemotaxis is the term for biased motion of bacteria toward chemoattractants. Mechanism of chemotaxis is well studied and is based on fast decrease of turning frequency when local conditions get more favorable and slow adaptation to a baseline frequency. As a result, bacteria alternate between longer "runs" up the gradient of chemoattractants and shorter runs down the gradient. Biochemically, this mechanism depends on fast phosphorylation and slow methylation reactions. Because time scale of methylation reactions is of the same order of magnitude, as that of the cellular movement, chemotaxis is the system with memory, and its mathematical description is extremely complicated, except in the case of shallow chemical gradients.

`Energy taxis' (attraction of cells to optimal level of energy related substances, such as oxygen or light) is an alternative bacterial strategy for sensory transduction that is less well understood, but is highly important for bacterial survival. Its two most notable features are:

(i) energy taxis is methylation-independent,

(ii) bacteria involved in energy taxis are able to aggregate into highly localized groups increasing initial density two orders of magnitude in a matter of minutes. Unlike the case of the conventional chemotaxis, signal transduction mechanisms of the energy taxis remain largely elusive. On the other hand, significant experimental data is gathered on the bacterial pattern formation and individual motions. This creates rare situation when mathematical modeling can help to test some plausible hypotheses about biochemical mechanism of the energy.

First, I will demonstrate with the help of Monte Carlo simulations that adaptation mechanisms cannot account for observed high densities of bacterial aggregates. Then a hypothetical protein signaling mechanism sensitive to temporal gradients in intracellular environment will be introduced. Based on this mechanism, we will present the results of analytical and numerical solutions of a model system of non-linear partial differential equations of energy taxis successfully describing the observed bacterial pattern formation. We will discuss how the novel mechanism of energy taxis suggests some clues about signal transduction mechanisms in more complex organisms.

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