Our understanding of how neuronal connections in the brain are maintained and reorganized is being revolutionized by new experimental and computational techniques. Neuronal axons terminate onto micron-sized structures known as dendritic spines, which are characterized by their thin necks and bulbous heads, and recent high-resolution 3D images show the fascinating variety of spine morphologies and dynamics. We have used three-dimensional lattice Boltzmann and immersed boundary method simulations to capture the fluid dynamics of vesicle transport into spines using a simplified model. The resulting force estimates are found to be consistent with the physiological density of motor proteins. Resolving the thin lubricating layers between the vesicles and spine poses significant numerical challenges, and we have used lubrication theory to investigate a large region in the geometry-elasticity phase space. Upon including competing molecular motor species that push and pull on the vesicles, we have observed multistable dynamics that neurons could use as a mechanism to control spine growth.
Time permitting, I'll also discuss a model of microfluidic devices that sort cells by deformability, another biological example in which elastic membranes must squeeze through narrow channels. These devices show promise for various medical purposes, e.g. detecting sickle cell anemia and circulating tumor cells. One such device is made up of sequential layers of progressively smaller channels, each layer containing identical channels in parallel. I propose a stochastic model for the failure of microfluidic devices by clogging and present preliminary numerical results. The failure time distribution is investigated analytically in certain limiting cases.