Viscoelastic Cytoskeletal-Membrane Mechanics: Hybrid Discrete-Continuum Stochastic Approaches

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

Cells are the fundamental units of life. In cell biology, many biological functions require the generation and coordination of complex mechanical events distributed throughout individual or populations of cells. This includes the generation and control of cellular motions in response to environmental signals of toxins or nutrients, generation of forces during cell division, and regulation of growth within tissues. Understanding of the roles of conditions arising in diseases, development of therapeutics and vaccines, engineering of bioreactors, and development of novel materials calls for advanced quantitative methods for studying cell mechanics. A central challenge in cell mechanics is to understand the principles by which larger scale mechanics arise from the smaller scale molecular-level events. This project develops new mathematical modeling paradigms and simulation software tools for investigating cell mechanics over multiple scales. This includes contributions from cell membranes and the cytoskeleton, which are structures providing the mechanical support maintaining the cell shape and internal organization. The methods capture contributions including the roles of the geometry, elastic structures, fluid mechanics, and fluctuations. Outreach activities are planned for engaging diverse and under-represented students at the University of California Santa Barbara and in the local community. This includes working with local area K-12 schools and colleges on programs to engage students on topics in the sciences, mathematics, and computation. Educational activities are also planned providing unique opportunities to train the next generation of researchers and students on recent emerging quantitative methods at the interface of mathematics and biology. The project addresses challenges in cell mechanics by providing new theoretical and computational stochastic approaches for handling molecular-level interactions and kinetics spanning over a hierarchy of scales. This includes regulation of the viscoelastic mechanics of protein-laiden lipid bilayer membranes, cytoskeletal filament rearrangements driven by cross-linked motor proteins, and cytoskeleton-membrane interactions. The project develops new stochastic computational methods for capturing both continuum and discrete contributions from the elastic mechanics, hydrodynamic coupling, geometry, and fluctuations. Stochastic numerical methods and efficient solvers and samplers are developed for handling the geometry of curved surfaces and general bulk domains. The methods draw on results from differential geometry and formulate unstructured discretizations building on finite element methods and meshless approaches. The methods will be used to study mechanisms underlying the mechanics of cytoskeleton-membrane interactions and in vitro active soft materials consisting of reconstituted cytoskeletal elements. This includes processes playing important roles in blebbing during initiation of cell motility and the generation of cytoskeletal forces. For the introduced modeling approaches and computational methods, software tools also will be developed and released with C++/python interfaces allowing for performing general simulations and analysis of phenomena in cell mechanics, complex fluids, and soft materials. This project is jointly funded by the Mathematical Biology and Computational Mathematics Programs at the Division of Mathematical Sciences and the Physics of Living Systems Program at the Division of Physics. 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.