Mathematical Models for Cell Locomotion

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Mogilner 9707750 Certain kinds of cellular movements are driven by actin polymerization. The most conspicuous examples are the lamellipodia of spreading and migrating embryonic and metastatic cells. A variety of pathogenic bacteria also propel themselves by constructing behind them a polymerized tail of cross-linked actin filaments. Collective cellular movements mediated by cell-cell interactions can generate interesting spatial patterns. These patterns can shed light on intercellular communication and can be used as novel assays for understanding the molecular mechanisms of cell signaling. The goal of this research is to understand at the molecular level (i) the mechanochemical basis of force generation by polymerizing and depolymerizing actin networks, (ii) the mechanisms of spatio-angular cytoskeletal organization, (iii) patterns of collective cell motion. The investigator and his colleagues formulate a mechanochemical theory of how the thermal fluctuations of the filament tips and the membrane can be rectified by actin polymerization to generate a propulsive force. This force is controlled by soluble and transmembrane proteins that stimulate actin polymerization. The investigators also formulate a theory for retrograde flow of lamellar cytoplasm. This theory is based on two sources of contractile force: (i) the contraction of the actin gel that must accompany depolymerization, and (ii) actin filament contraction driven by myosin. The results of these models determine the relative roles of actin polymerization and myosin crosslinking and contraction during cell locomotion. These studies help forge a link between the basic biophysics of cell motility and the chemical control of cell motion. The crawling of cells over surfaces is the basis for the vitally important phenomena of phagocytosis and the migration of metastatic cells. Despite the ubiquity of cellular motions, the molecular mechanisms underlying these movements remain mysterious. The investigators undertake theoretical modeling that provides a solid quantitative basis for understanding the detailed working cycle of the cell's molecular engines. This description provides a new interdisciplinary level of understanding cell movements and new methods of predicting cell behavior in medically and technologically important situations.