CAREER: Mathematical Framework for Elucidating Mechanics at Immune Cell Interfaces

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In many biological processes, two or more cells come into physical contact to form a cell-cell interface. Examples in humans include wound healing, tissue development, tumor growth, and some bioengineered diagnostic tools. Experiments have shown that molecules in cell-cell interfaces experience forces (squeezing, pulling) and that these forces influence cell behavior and cellular decision-making. One important example is offered by immune cells, which must attach to the surface of other cells in order to decipher information about disease. Their nanometer size and inaccessible geometry make cell-cell interfaces challenging to explore experimentally. The investigator will develop mathematical equations that predict forces on molecules at cell-cell interfaces, using immune cells as a prototype. Results will have direct implications for understanding immune function, impacting research on autoimmune disease and immunotherapy. Additionally, these mathematical models can be readily generalized to abstract, generic cell-cell interfaces, thereby highlighting the biophysical similarities between biologically disparate systems to help understand the general principles of the cellular tactile sense. In coordination with his research goals, the investigator has an educational goal of using cell mechanics (i.e., forces in cells) as a venue to teach mathematics, biology and physics with tangible, accessible examples to audiences in K-12, undergraduate, graduate and general public education. Unlike cell biology based on biochemistry or genetics, many cell-mechanical phenomena have direct analogies with everyday life that are useful in establishing a three-way correspondence between cell phenomena, everyday intuition of mechanical forces, and their mathematical representation.Of many ways in which cells interact, an increasingly recognized interaction is through the establishment of transient, dynamic cell-cell interfaces. The investigator will develop mathematical models of cell-cell interfaces to describe and predict mechanical forces and their influence on cell signaling. The dynamics at cell-cell interfaces involve an interplay between transport, mechanics and chemical kinetics, and play out over a range of length- and time-scales, necessitating a combination of mathematical techniques: Coupled systems of elliptic, parabolic and stochastic differential equations; computational fluid dynamics of fluid-structure interactions including thermal fluctuations in 3D; Brownian dynamics; and Bayesian statistics to leverage quantitative experimental data from the investigator's collaborators. Specific aims of the investigator through this research are to: (1) Understand how cells overcome and exploit the physical constraints to cell-cell contact, by developing a model that integrates motion of the intracellular and extracellular fluid, Brownian motion of molecules embedded in the cells' membranes, and active forces. (2) Explore the mechanism and evolutionary advantages of molecular clustering at interfaces to address the large class of molecules that aggregate into clusters containing tens to hundreds of molecules. (3) develop, validate and use mesoscale models of large flexible biomolecules to decipher their mechanical properties and biological role. In mesoscale models, individual molecules are represented as combinations of rigid bodies such as rods, spheres and semi-flexible joints undergoing Langevin dynamics. The biological novelty lies in new hypotheses that will emerge from the models, including the hypothesis that within-cluster load sharing can allow for nontrivial kinetics, such as co-operativity, multi-stability and ultra-sensitivity - regulatory modules that have classically been assumed to arise from biochemical reaction networks. The mesoscale models will allow us to access timescales that all-atom molecular dynamics cannot, while capturing details that particle-based simulations miss. Students at all educational levels will gain exposure to contemporary work at the interface of mathematics, biology and physics.