Active Cortical Domains Coupled by Bulk Diffusion Framework for Modeling Spatiotemporal Phenomena in Cell Biology

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Cell growth and division requires cells to polarize by forming distinct compartments with different molecular components. Faulty cell polarization contributes to birth defects or diseases such as cancer. The PI will develop stochastic and deterministic models to better understand how biochemical factors in the cell interact and regulate each other for proper cell function. This project will model the segregation of chemical reactions taking place on cell membranes and in the interior of the cell. Such segregation is thought to give rise to interesting dynamical phenomena, such as oscillations of the central polarity regulator, Cdc42, and establishment of multiple polarity zones. The effects of compartmentalization and geometry on the dynamics of polarization is just beginning to be explored and may lead to novel biological insights of how cell polarity is maintained in cells. The PI’s long term educational goal is to encourage female undergraduate and graduate students to pursue careers in STEM fields, specifically in Applied Mathematics. Broader educational impacts will involve organizing a workshop for undergraduate and graduate students at the University of Notre Dame. The PI will focus on establishment of polarity in fission yeast and budding yeast, two model organisms for understanding how cells integrate polarity and spatial coordination of growth. The current mathematical approach to modeling cell polarity using reaction-diffusion equations does not take into effect the spatial segregation of polarity molecules in the cell. The goal of this project is to model cell signaling occurring during cell polarization by coupling bulk diffusion to active surface-bound chemical species. The PI will apply this bulk- surface PDEs framework to specific scientific aims: (1) Extend the deterministic bulk-cytosol 1D model framework to a spatial stochastic one that describes the inherent noise in the underlying biochemical system, and compare model findings for increasing cell size and molecule number using compartment based SSA approach, (2) Extend the 1D framework to higher dimensions, where cortical domains are modeled as a thin patches to allow for lateral diffusion and the cytosol is modeled as an enclosed volume, and consider effects of cell geometry on intracellular signaling. The educational objectives of this proposal are: 1) organize a workshop for undergraduate women encouraging them to pursue careers in Applied Mathematics and other STEM fields, 2) participate in Women Leaders in STEM program at Notre Dame, 3) develop new materials for graduate course on Mathematical Cell Biology, which will be open to interdisciplinary students, 4) lecture in existing national educational programs such as the q-bio Summer School that introduces students from diverse disciplines such as mathematics, physics, and computer science to modeling in biology. This award is being co-funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and the BIO Division of Molecular and Cellular Biosciences (MCB) through the Cellular Dynamics and Function Cluster.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.