A Three-dimensional Stochastic Spatio-temporal Model of Isotropic Phase of Cell Spreading

Cell motility is important for many physiological processes. The biochemical reactions underlying motility have been well-characterized. Mathematical models, using these biochemical reactions, and focusing on different types of spreading behavior have been constructed and analyzed. We built on these previous models to develop a three-dimensional stochastic model of isotropic spreading of mammalian fibroblasts. Our goal was to determine if a model in which core actin filament remodeling reactions drives the system could capture the dynamic behavior of cells. The model is composed of three actin remodeling reactions that occur stochastically in space and time, and these reactions are regulated by membrane resistance forces. Movement of the leading edge occurs solely due to force constrained-biochemical reactions. Numerical simulations indicate that the model qualitatively captures the experimentally observed isotropic phase of cell spreading behavior. We analyzed the effects of varying branching reaction rate, membrane resistance force and capping protein concentration on the dynamics of isotropic spreading. The simulations allowed us to identify how branching reaction rates and membrane force values cooperate to yield isotropic spreading behavior. The model predicts that increasing capping protein concentration would lead to a linear decrease in average peripheral velocity. We tested this prediction experimentally using varying concentrations of a pharmacologic agent (Cytochalasin D) that caps growing actin filaments. We find that the experimental results agree with the numerical simulations. Thus, a spatio-temporal model of stochastic reactions, when constrained by membrane forces, can yield deterministic behavior as characterized by isotropic cell spreading. Page 2 11/27/2007 Nature Precedings : doi:10.1038/npre.2007.62.2 : Posted 3 Dec 2007