Mathematical modeling and analysis of in vitro actin filament dynamics and cell blebbing

The dynamics of the actin cytoskeleton are vital for cell motility observed in many biological processes, such as morphogenetic movements during embryotic development, fibroblast migration during wound healing, and chemotactic movements of immune cells. To fulfill specific tasks, motile cells manipulate various actin structures within regions such as the lamellipodium, filopodia and stress fibers. A large pool of regulatory proteins and motor molecules coordinate the dynamic change of these structures to generate mechanical forces.In this thesis, we first investigate the temporal evolution of filament length distribution in a deterministic approach. The change of filament lengths is described by ordinary differential equations, and effects of diverse regulatory mechanisms are explored. We predict that the endwise polymerization alone produces a long-lived Gaussian-like distribution of filament lengths, which eventually evolves to an exponential distribution. The introduction of fragmentation drastically leads to a Bessel-type equilibrium distribution. Our model confirms that profilin proteins slow filament growth, decreases the extent of polymerization, and promote filament treadmilling. Actin monomers are associated with nucleotide ATP. In a filament, ATP can hydrolyze randomly into ADP-Pi, and subsequently release the phoshpate becoming ADP. Random ATP hydrolysis complicates the filament dynamics. The effect is analyzed in a stochastic model where each subunit within a filament is distinguished by associated nucleotide types. We theoretically predict a large length fluctuation occurring around the critical concentration of ATP-actin where the filament tip is bound intermittently by nucleotides ADP and ATP. By implementing an efficient stochastic simulation algorithm, we are able to track the evolution of length and nucleotide profile of single filament.We also investigate the phenomenon of cell blebbing, a typical membrane protrusion driven by actin dynamics and acto-myosin contraction. The major components of blebbing cells are recognized, and models for each component and their interaction are individually considered. Our analysis shows that a simple constraint on the membrane expansion rate relates the dynamic bleb size with the ring constricting the bleb. The properties of equilibrium state of blebbing are probed in a mechanical model whereby a uniform hydrostatic pressure is established by the balance of membrane tension in the contracting and expanding cell domains. We recognize that a potential membrane flow is important in establishing the blebbing equilibrium, and the influence of various flow types is compared.