Tunable collective dynamics of inclusions in viscous biological membranes

The typical cell membrane is a crowded assembly of molecular motors and biomolecules embedded in a 2D fluid mosaic. Active molecular motors perform complex cellular tasks by binding, inserting, polymerizing, and changing conformations, inducing disturbance flows in the membrane and the surrounding fluid. These long-ranged hydrodynamic fields perturb neighboring inclusions, potentially leading to coordinated motion. I will build on classic theories of Newtonian fluid dynamics of viscous membranes to illustrate unique oscillations and aggregation dynamics in pairs of active membrane inclusions. The phase behavior of the pair problem reveals the underlying mechanisms and suggests strategies to tune large-scale aggregation. I will also show numerical simulations of large numbers of interacting inclusions whose collective dynamics can be tuned based on these basic insights. If time permits, I will then describe the first steps in the analysis of inclusions in membranes with a nontrivial rheology. Real membranes are often strongly non-Newtonian. I will illustrate a formulation based on the Lorentz reciprocal theorem to asymptotically capture effects of non-constant surface viscosity of phospholipids that comprise most biological membranes. I will highlight the qualitative differences that ensue and potential implications in crowded membranes.