The network of microfilaments in the cortical cytoplasm of motile tissue cells is capable of producing a sizable repertoire of coherent motions. Locomotion, spreading, phagocytosis, capping and cell clevage are each caused by coordinated spatial and temporal cycles of contraction, polymerization and depolymerization of the cortical network. Forces produced by the cortical network are transmitted to the plasma membrane, to cytoskeletal materials and to external surfaces by specific chemical attachments and by nonspecific viscous interactions. It is notable, that in a given cell type the different forms of motion are produced in a highly controlled manner, each in response to specific stimuli or conditions. The long range objective of this proposal is to advance our understanding of how the various forms of cell motion are produced, triggered and controlled. This will be done by developing, analyzing and testing quantitative mathematical models of the mechanics and chemistry of the motile machinery of nonmuscle cells. As a first step towards this objective, I propose to model the cortical actin network as a fluid composed of """"""""structural units"""""""" that exert short range attractive forces on each other. In contrast to conventional fluids, repulsive forces between the structural units will be neglected in favor of the idea that net chemical breakup of the structural units occurs if their local density rises too high. Models of the type envisioned have not been studied before. Consequently, it will be necessary to investigate the existence, uniqueness and qualitative behavior of periodic, steady and turbulent solutions as well as to develop criteria for the stability and bifurcation of such solutions. It will also be necessary to develop computer codes for the numerical computation of solutions. Ultimately when the behavior of simple contractile gels is adequately understood, detailed modeling of the control and triggering of complex forms of motility will be carried out. Testing of various models will be done by comparing computer generated solutions with data on the distribution and velocity of cytoplasmic markers such as Alpha actinin and of cell surface markers such as con A receptors.
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