Collaborative Research: Experimentally guided mathematics for the mechanochemistry of cell shape dynamics

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An integrated mathematical-experimental effort in cell biology is proposed, focusing on morphology and dynamics of motile cell phenotypes. Specifically, we probe and model the molecular mechanisms of chemical-mechanical transduction, and mechanical feedback to chemical kinetics, with intracellular spatial and temporal resolution of a living cell. The modeling goal is a platform to integrate detailed biological data and test biophysical hypotheses, with a predictive simulation tool for a cell in a specified extracellular environment. The model platform incorporates advances in cell substructure identification and property characterization (bilayer membrane, cortical layer, cytosol and nucleus), coupled with advances in specific signaling molecules, their kinetics, and their role in mechanical activation and deactivation (Rho family of GTPases). The experimental challenges concentrate on achieving spatio-temporal resolution in living cells, so that mechanical-chemical feedback mechanisms can be measured and compared with model simulations. The mathematical challenges lie in a faithful non-equilibrium description and simulation of each cell substructure and its free boundaries, of reacting and diffusing signaling molecular species in deforming substructures, and of the spatio-temporal activation via mechanochemical transduction. A specific cell motility phenotype identified by the Jacobson lab that sustains morphological oscillations with disruption of microtubules is the test-bed for this effort.One impact of this effort is an available platform to simulate living cell morphological dynamics in conjunction with experimental protocols to perturb intracellular chemical or mechanical processes. The oscillation phenotype of the cell is a model system whereby a chemically induced mechanical perturbation (disruption of microtubules) leads to a robust, amplified response that affords hypothesis testing for mechanochemical transduction mechanisms. The model and experimental methods will provide exploratory tools for other cell motility phenotypes and their underlying biochemical and mechanical basis, including dramatic topological changes associated with blebbing and division. The dynamical cell structure simulation tool will be implemented in a high performance computing environment to resolve the complexity of the non-equilibrium, heterogeneous cell. Another impact lies in the training of a new cohort of mathematicians and biologists who learn with and from one another and understand biological principles and experimental methods and the mathematics of modeling, simulation and experimental validation. The outcome of this research will improve the mechanistic understanding of many disorders due to a dysregulation of the cytoskeleton, including cancers.