Applied Mathematics Seminar: The Lubricated Immersed Boundary Method and Vesicle Transport into Dendritic Spines

Seminar | February 22 | 3:30-4:30 p.m. | 891 Evans Hall

 Thomas Fai, Harvard

 Department of Mathematics

Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We applying this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method.

As another application of lubrication theory, we model the fluid dynamics of vesicle transport into dendritic spines, which are micron-sized structures at which neuronal postsynapses are located. Dendritic spines are characterized by their thin necks and bulbous heads, and recent high-resolution 3D images show a fascinating variety of spine morphologies. Our model, which we validate using 3D lattice Boltzmann simulations, reduces the dynamics of vesicle motion to two essential parameters representing the system geometry and elasticity and allows us to thoroughly explore phase space. Upon including competing molecular motor species that push and pull on vesicles, we observe multistability that we speculate neurons could exploit in order to control spine growth.