Membrane hydrodynamics is intriguing due to an interplay of dimensionalities; momentum travels in the plane of the membrane at short distances, but moves through the outer fluid at larger ones, showing a crossover from 2D to 3D like behavior. Chemical reactions on the surface of a cell, therefore, require a special treatment. While it is possible to perform a simple Smoluchowski-like calculation in 2D to predict reaction rates in membranes, we will see that the expected rates are reduced by an order of magnitude when accounting for hydrodynamic interactions between reactants and targets. A biomembrane, however, is more than just a passive medium. ATP synthase and other proteins produce a great deal of hydrodynamic traffic. In the second part of the talk, we will explore the dynamics of active rotors embedded in a membrane. We will see a power law transition --- from Euler flows at small distances (1/r), to 1/r^2 at large distances. We will derive a Hamiltonian for a discrete system of rotors, find the conserved quantities, and describe a coarse-grained density field of rotors. We will present theory and simulations for the discrete and the continuous cases.
Event Date and Time
Dr. Naomi Oppenheimer, Flatiron Institute at the Simons Foundation