Biological processes that occur at the cellular and molecular level consist of large numbers of interacting elements, are highly nonlinear and generally involve multiple time and spatial scales. The quantitative description of these systems is of great importance but presents large challenges. Different mathematical techniques incorporate varying levels of biological detail into the description of the system. The appropriate modeling approach is dictated by the driving biological problem. We propose to develop and analyze mathematical models of varying complexity to understand the phenomenon of contractility oscillations in spreading cells. ? ? Actomyosin-based cortical contractility is a common feature of eukaryotic cells, but the capability to produce rhythmic contractions is found in only a few cell types such as cardiomyocytes. The mechanisms by which cells transform between smooth, monotonic states and pulsatile states is not understood. These oscillations are governed by a complex mechano-chemical system. Our modeling effort will be fully integrated with an experimental program designed to experimentally measure parameters for the models and test model predictions. The mechanistic details of the models will increase as warranted by the data. The modeling methods will include increasingly complex ordinary differential equation models and spatially-extended models that fully describe the mechonchemical coupling that underlies the observed oscillatory behavior. A a novel course-grained approach (c-map) designed to capture qualitative features of the system, will be developed and validated. This tool, on one hand, will be an intermediate between experiments and physical modeling, determining major requisite elements, their interactions and paths of causality propagation. On the other hand, the c-map will be used as an independent tool to explore the hierarchical organization of cell and the role of uncertainties in the system. ? ? The project has three specific aims: 1) What are the basic necessary elements for generation of oscillations in spreading cells? 2) How do various external mechanochemical inputs to the cell affect oscillatory behavior? 3) How is the biochemical network connected to the constituents and mechanics of the cytoskeleton and how does spatial heterogeneity of cellular elements affect the oscillations? ? ? ? ?
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