Collaborative Research: Spatial Stochastic Rare Events by Asymptotics and Weighted Ensemble Sampling to Understand how Cells Make Space

The surface of a cell is crowded with many different biomolecules. These include receptors and other large protein molecules that enable the cell to sense its environment. For example, cells that function as part of the immune system can sense extra-cellular molecular signals of infection. The cell surface is also a highly dynamic environment, and the movement and interactions of surface molecules play a crucial role in the response to extra-cellular signals. Mathematical modeling enables researchers to study these complex, dynamic, molecular processes in more detail than is currently afforded by experiments. The investigators will develop new mathematical approaches and computer simulation methods tailored to the study of how molecular motion on crowded cell surfaces influences cellular processes. The developed tools will enable researchers to predict the sequence of molecular events that initiate cell-cell interface formation and signaling processes. By enabling computational testing of novel strategies for biomolecular/cellular engineering, these tools will open up new means of discovery in areas such as immunotherapeutics. The investigators will contribute to broadening science participation by training undergraduate researchers in mathematical biology and scientific computing, and will carry out pedagogical activities with middle school students from groups underrepresented in science.

The specific focus of this research will be on modeling stochastic rare events in molecular diffusion. In many circumstances where molecular crowding occurs, un-crowding may also be critical. For example, in T cells, many large surface molecules must evacuate from a local region of the cell surface to allow for the T cell to interact with its target. This collective evacuation is a rare event relative to the timescale of individual molecular diffusion. The goal of this project is to develop a framework to study stochastic evacuation, including in rare event limits, and apply this framework to the T cell surface. Specific aims of this project are to: (1) Develop a combined asymptotic and computational rare event framework to solve diffusional evacuation in simple scenarios. (2) Develop enhanced spatially-distributed rare event methods capable of simulating complex scenarios. (3) Use the developed tools to understand how T cell surface molecules overcome or exploit rare evacuation. The mathematical novelty of this project is: the extension of asymptotic methods to effectively high-dimensional problems; the extension of computational rare event sampling methods, not only handling space but harnessing it; and the creation of synergies between asymptotic and computational approaches in a novel combined framework.