Tutorial calculations for force-sensing proteins, catch bonding, and other elements of cell--matrix adhesion

The ability of cells to adhere to an extracellular matrix, exert forces on it, and in turn measure those forces is critical to many life processes. As the molecular details have emerged in recent years, they have proven to be quite complex. However, to a physicist, the key elements are familiar: They include entropic elasticity of polymers, catch-bonding, and two-state dynamics as cryptic binding sites pop open under force and hence become available for signaling interactions. Each of those processes can now be experimentally studied in vitro, without the complexity of a living cell. Students can observe all of those phenomena in simple kinetic simulations and compare them to experiment. Along the way, they also gain skills by implementing the stochastic simulation algorithm in a sequence of problems: * Simple Brownian motion; * Brownian motion with a linear potential landscape; * Brownian motion in a potential well with escape; * Brownian motion in a double-well potential, modeling a two-state system. Students directly observe the Einstein relation, emergence of the Boltzmann distribution, Kramers rates, the catch bonding phenomenon, and more. Although this exercise lacks the generality that we might get from a year of equilibrium and nonequilibrium statistical physics, it does illuminate key life processes in about two weeks of an undergraduate course. Most of this material is available in a recently published textbook.