During my undergraduate studies in Novosibirsk State University, Russia, and my Masters degree studies at the Weizmann Institute of Science, Israel, my research work was directed towards deriving rate expressions for chemical reactions in liquid phase that do not obey mass action kinetics. Using nonequilibrium statistical mechanics, I was able to show that the kinetic equations of reaction systems are revealed by investigating the dynamics of many-particle correlations. The resulting equations are usually in integro-differential form, illustrating non-Markovian, or memory functional, kinetics. I applied these equations to analyze transient kinetics and steady state properties of photochemical systems, where non-Markovian effects are essential. Even though all of these studies address kinetics of simple chemical systems, similar non-Markovian effects can be important for the reactions occurring in the crowded cytoplasm of living cells. In these systems many particle correlations can change the governing rate laws significantly.

My interests shifted toward biology as I started my Ph.D. studies at Berkeley. For my dissertation research I joined the theoretical biophysics group of Professor George Oster in the Molecular and Cell Biology Department. This group works on a wide range of physical models for biological systems at different levels of organization, ranging from molecular to intercellular and developmental. My first project was to understand the spatial patterns formed by the gliding myxobacteria Myxococcus xanthus. This project was carried out in close collaboration with Professor Dale Kaiser’s experimental laboratory at Stanford. During starvation-induced development, M. xanthus cells generate a series of spatial patterns by coordinating their motion via a contact-dependent signal. These patterns include traveling density waves (called ‘ripples’) as well as swirling and streaming cell motions that culminate in the formation of multicellular aggregates called fruiting bodies. I was able to explain all of the experimentally observed patterns by constructing a series of mathematical models. These models derive the aggregate behavior from the statistics of how individual cells move and interact with their neighbors. The models were able to make important predictions about inter-cellular signaling and the coordination of cell motility in myxobacteria.

Together with other members of Oster’s lab I have been involved in projects identifying various ways molecular motors convert chemical energy of ATP hydrolysis into mechanical work. In collaboration with Charles Wolgemuth, we proposed mechanisms of propulsion for two classes of wall-less bacteria called mollicutes: the swimming of helical-shaped Spiroplasma, and the gliding motility of Mycoplasma. Coupling of a biochemical cycle, such as ATP hydrolysis or ionic oscillations, to the dynamics of elastic filaments, the models show how propagating deformations generate propulsive forces. The models were able to quantitative fit measured force-velocity relations.

The equations describing developmental waves in myxobacteria are essentially nonlinear. Results of numerical simulations and quantitative analyses of these equations were extended by developing analytic techniques (asymptotic analysis, homogenenisation theory, linear instability analysis). These techniques allow us to reveal the focusing mechanism of the waves. This project is done in collaboration with Professor John Neu (Math Department, Berkeley). The results determine parameters favorable for the wave development and demonstrate the stability of the fully developed nonlinear waves.

One of the important predictions of our models for myxobacteria rippling and aggregation is the existence of a biochemical cycle controlling reversals of gliding direction of each cell. Combining genetic, biochemical and homology data for the proteins controlling reversals in M. xantus, we suggested a signalling circuit which is capable to explain all the essential properties of the myxobacteria reversals.

I am continuing to explore bacterial signaling circuitry during my postdoctoral research in the lab of Professor Michael Savageau (UC Davis). In collaboration with Professor Chester Price (UC Davis) we are looking into mechanisms regulating bacterial gene expression in response to environmental stress. General stress responses in Bacillus subtilis are mediated by the transcription factor sigmaB. The signaling circuit includes an anti-sigma-factor that binds to sigmaB to deactivate it, and its antagonist that releases sigmaB to induce the transcription of the sigmaB-dependent genes. Similar circuits control activation of other transcription factors in Bacillus subtilis as well as in other bacteria. We are in the process of adapting the methodology of mathematically controlled comparison (developed in Michael Savageau’s lab) to identify the design principles of this circuit and to suggest design variations to altered functional demands.