Inferring and Modeling Excitable Dynamics in Cell Migration

Living cells continuously move through tissues to fight infections, heal wounds, and build organs during development. Errors in these processes contribute to diseases such as chronic inflammation and cancer metastasis. Although scientists have identified many of the molecules involved in cell movement, it remains difficult to understand how they work together to produce coordinated behavior because only a small fraction of these molecular activities can be observed at any one time. This project seeks to develop new mathematical and computational approaches that reveal the hidden processes controlling cell migration from limited experimental observations. The research combines close collaboration between mathematicians and experimental biologists, using living cells that provide an ideal system for studying the fundamental principles of cell movement. By integrating advanced mathematical methods with quantitative biological experiments, the project will establish new tools for understanding how complex cellular behaviors emerge from interacting molecular networks. These approaches are expected to be broadly applicable to many biological systems in which only incomplete measurements are available. The project will also provide interdisciplinary training for graduate, undergraduate, and high-school students through research experiences, mentoring, and outreach activities, helping to prepare the next generation of scientists working at the interface of mathematics, computation, and biology. The project develops new mathematical foundations for analyzing excitable spatiotemporal dynamics that regulate eukaryotic cell migration. The research focuses on two complementary objectives. First, new constrained neural operator frameworks will be developed to reconstruct unobserved signaling and cytoskeletal fields from partially observed live-cell imaging data. These methods will formulate reconstruction as an inverse problem for nonlinear dynamical systems and incorporate symmetry, locality, and dynamical constraints to improve identifiability, interpretability, and uncertainty quantification. Second, mechanochemically coupled reaction-diffusion models on evolving domains will be developed and analyzed to determine how biochemical signaling, cytoskeletal mechanics, and cell shape jointly regulate wave propagation, stability, and migration behavior. Analytical and computational studies will characterize traveling-wave solutions, bifurcation structure, and parameter sensitivity, while quantitative measurements from Dictyostelium discoideum experiments will provide parameter constraints and independent validation. Together, these integrated approaches establish a mathematical framework that connects partial experimental observations to mechanistic models of excitable biological dynamics. The project advances inverse problems, nonlinear partial differential equations, and mathematical biology while providing broadly applicable methods for analyzing partially observed nonlinear systems. 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.