Mathematical models of molecular motors: All transport inside the cell is based on an ability of special proteins ó molecular motors ó to convert chemical energy into mechanical work. I derive and solve stochastic differential equations describing mechanochemistry of these proteins in the presence of the brownian movement and predict force-velocity relations and statistical characteristics of the motorís behavior [1].

Computer models of cellular locomotion: Crawling of animals cells is an important part of wound healing, embriogenesis and cancerogenesis. Cytoskeleton (crosslinked meshwork of protein polymers) plays a crucial role in these processes. The central question in the field of cell motility is what is the nature of the forces of protrusion and contraction of the cytoskeleton and how these forces are coordinated. Using the mathematical modeling, I predict the dependencies of cellular velocities, forces and patterns on the essential chemical parameters [2,3]. The models enable me to test, quantitatively, scenaria of the cell movements. Specifically, the models are applicable to chemotaxis, phagocytosis, wound healing, and design principles of nano-scale molecular assemblies.

Nonlocal interactions in biology: Organization of biological motions of groups of animals presents some fascinating examples of pattern formation that is easy to observe, but not so easy to quantify. One of the reasons of the underlying theoretical complexity is a common appearance of long range interactions. This nonlocal character of the biological interactions calls for mathematical description in the form of nonlinear partial integro-differential equations rather than PDEs. I am investigating the role of such interactions in the maintenance of long-lasting groups of organisms, such as birds, fish, and insects [4].

H.-Y. Wang, T. Elston, A. Mogilner, G. Oster, Force generation in RNA Polymerase, Biophysical Journal, 74: 1186-1202 (1998).

A. Mogilner, G. Oster, Cell motility driven by actin polymerization, Biophysical Journal, 71: 3030-3045 (1996).

A. Mogilner, G. Oster, The polymerization ratchet model explains the force-velocity relation for growing microtubules, European Biophysics Journal, 28: 235-242 (1999).

A. Mogilner, L. Edelstein-Keshet, A non-local model for a swarm, Journal of Mathematical Biology, 38: 534-570 (1999).