Mathematical models of cellular movements

University Of California-Davis, Davis CA

Investigators

Abstract

Mogilner 0073828 Three mechanisms - protrusion of the lamellipodial actin network, graded adhesion of the cytoskeleton to the surface, and cytoskeletal contraction - acting in concert are both necessary and sufficient to produce highly effective cell movement. Actual rates and forces of protrusion depend on local concentrations of actin monomers and polymers and a host of actin capping, nucleation, polymerization and adhesion proteins near the cell's leading edge. The investigator derives partial differential equations that couple the chemical kinetics of all these protein concentrations to the model of cytoskeletal mechanics. These equations are solved analytically and quantify molecular mechanisms of protrusion localization at the cell's leading edge and regulation of protrusion rates and forces. Experiments suggest that the force of the cytoskeletal contraction is myosin powered. The investigator models the dynamics of actin filaments and myosin clusters in physical and angular space and describes the actomyosin dynamic contraction mechanism quantitatively. Using this description, the investigator analyzes mechanochemical feedback loops between systems of traction, protrusion and graded adhesion within the frameworks of interactive computer models varying in complexity. These models are applied to migration of fish keratocyte and nematode amoeboid sperm. Comparison of theoretical results with experiment clarify the roles of cytoskeletal, adhesion and membrane systems in cellular movements and concepts of motility, polarizability and directionality. The models allow testing of plausible scenarios of cell movements. Migration of animal cells is a fundamentally important process underlying the phenomena of wound healing, morphogenesis and cancer. Current experimental research is aimed at dissecting the complex processes of migration into simpler phenomena that can be more easily analyzed. The investigator models these motility phenomena theoretically, which will allow biologists to test quantitatively the existing qualitative ideas. Specifically, the investigator examines mathematically the molecular basis and the principles of self-organization of cell mechanics and develops computer models that reproduce the observed patterns of cell locomotion. Results of the modelling will provide a new interdisciplinary level of understanding cell movements and new methods of predicting cell behavior in important medical and technological situations.