Living cells in our body receive information through receptors (molecules on their surface) that bind to ligands (other molecules that carry information). An important class of receptors, including the T-cell receptor, bind to ligands that are anchored to the surfaces of other cells. The T-cell receptors themselves are important since they are the site of immunological decision-making, specifically whether or not to mount an immune response against something. Since the 1990s, the presence of the other surface has been speculated to imply forces on the receptor (absent for receptors where the ligand is soluble), but the small, crowded, noisy environment of “in vivo” cell biology has made these forces challenging to observe experimentally.
In this talk, I will present our efforts to understand these forces at the nanometer scale theoretically, using computational fluid dynamics, simple polymer models and theory from dynamical systems. I will discuss four projects: In the first, we develop a method to estimate the effective spring constants of molecules on the cell surface using polymer modeling  and the quantum phenomenon of Forster resonance. In the second, we apply this spring constant to estimate forces and how they influence the T-cell receptor. Surprisingly, we find that the force alters the information processing being done by this receptor, thereby influencing immunological decision making. In the third project, we study the dynamics of surface molecules undergoing simple Brownian motion. While the equilibrium problem is straightforward, the dynamics problem turns out to address a long-standing mathematical problem called the “Capacitance” problem in electrostatics . In the fourth project, we perform simple hydrodynamic estimates to understand the thin layer of water separating the two cell surfaces, and then develop a large-scale computational framework to solve the fluid dynamics problem of two soft, thermally-undulating membranes . The hydrodynamics of the water, long neglected in T-cell biology, appears to play a central role in these cell-cell interactions. Taken together, our work is revealing that forces on receptors lead to nonlinear and sometimes counterintuitive dynamics, and influence how cells process information to perform their biological function.
 Mukhopadhyay, JA, et al., Multisite phosphorylation modulated the T cell receptor. Biophysical Journal 110:1896 (2016)
 Newby and JA, First-passage time to clear the way for receptor-ligand binding. Physical Review Letters 116:128101 (2016)
 Liu, JA, et al., Wrinkling dynamics of fluctuating vesicles in time-dependent viscous flows. Soft Matter 12:5663 (2016)