Models and computation of intracellular signaling in single and collective cell migration

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Many cells respond to stimuli by directed motility. For example, white blood cells (neutrophils) polarize and move persistently towards chemical signals. Cell motility entails dynamic changes in structural proteins of the cytoskeleton (primarily filamentous actin, F-actin). This, in turn, is regulated by proteins that promote assembly and disassembly of the actin network or activity of molecular motors (myosin) that pull on it and reshape it. At the core of the cell-migration regulatory cascades are a family of proteins known as Rho GTPases (e.g. Rac, Rho, Cdc42) to which stimuli from receptors, upstream effectors, and feedback from downstream are funneled. GTPases are activated by GEFs, inactivated by GAPS, and "wired together" by mutual crosstalk. Using mathematical modeling, I propose to investigate how the dynamics of GTPases impacts and scale across three levels of biological organization: subcellular structures (cell edge protrusion, wound repair), cell-cell and cell-matrix interactions, and multicellular tissue dynamics. My methods include ordinary and partial differential equation (ODE, PDE) models to describe spatiotemporal GTPase distributions and cell behaviour. Using nonlinear dynamics, bifurcations, approximation methods and simulations, I characterize solutions and predict how behaviour depends on biologically tunable parameters. I also use abstract theory of reaction-diffusion equations (RDEs) to identify possible behaviour. Scaling up to multiple cells, I adapt the mathematics of "swarms" to the microworld of collective cell dynamics. Cell-cell interaction via adhesion, mechanical or chemical signaling, long filopodia, etc., can be depicted (by integro-PDEs with nonlocal "kernels"). My innovation is to include GTPase activity which affects cell spreading/contractility, and hence the range and strength of interactions (kernel magnitudes, ranges). The analysis is complemented with simulations in one and two spatial dimensions (1D, 2D), that can be directly compared to experimental data from collaborators. My ongoing and new collaborations span the subcellular to tissue scales: (1) With W Bement (Wisconsin, cell wound repair) (2) With JinSeok Park (Yale and USC) and Andre Levchenko (Yale), on cell-ECM interactions and (3) With Cal Roskelley (UBC) and Arnold Hayer (McGill) on cell-cell collisions in vitro; with Paul Kulesa (Stowers, neural crest cells) and with Joy Richman (UBC) on collective cell migration and morphogenesis. Training HQP in interdisciplinary research will take place at all levels, from undergraduates, through graduate students and post-docs, with strong EDI components. My key aims are to link subcellular signaling to the behaviour of single cells, cell groups, and tissues on one hand, and to bridge between abstract mathematics and specific applications on the other hand.