Mathematical Modeling and Computational Analysis of Cell and Tissue Movement

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Cell locomotion plays an essential role during embryonic development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms. Movement is a very complex process that involves the spatial and temporal control and integration of a number of sub-processes, including the transduction of chemical or mechanical signals from the environment, intracellular biochemical responses, and translation of the intra- and extracellular signals into a mechanical response. The force for protrusion results from localized polymerization of monomeric actin into cross-linked networks of actin filaments in lamellipodia or bundles of filaments in filopdia or pseudopodia. In order to produce directed cell movement the interaction of the actin sub-networks and force transmission to the substrate must be properly integrated in space and time. Understanding the interplay between the processes involved requires a mathematical model that links molecular-level behavior with macroscopic observations on forces exerted, cell shape, and cell speed, but how to formulate a multiscale model that integrates the microscopic steps into a macroscopic model is poorly understood in this context. This study will focus on a number of simpler problems that will lead to the component modules in an integrated model sequentially. The major issues to be addressed are (i) the dynamic control of the actin network at the leading edge of a cell, (ii) models and analysis of the role of focal adhesion construction and lifetime, and how the level of motor activity and the adhesiveness of the substrate determines the cell speed, (iii) analysis of whole-cell models of simple systems with a view toward understanding how the mechanical balances between various components produces stable steady states of actin turnover, motor activity and cell shape, and whether perturbations of this steady state can lead to polarization and movement in the absence of external signals.Cell movement is an essential process at various stages in the life cycle of most organisms. Early development of multicellular organisms involves individual and collective cell movement, leukocytes must migrate toward sites of infection as part of the immune response, and in cancer directed movement is involved in invasion and metastasis. This research addresses various aspects of cytoskeleton dynamics, the integration of these dynamics with the reaction network of actin-binding and cell-signaling proteins, and the related control mechanisms regulating the mechanical properties of cytoskeletal structures involved in cell motility. Understanding the interplay between the processes involved requires a mathematical model that links molecular-level behavior with macroscopic observations on forces exerted, cell shape, and cell speed, but how to formulate a multiscale model that integrates the microscopic steps into a macroscopic model is poorly understood in this context. Developing such descriptions is a major component of our research effort.