Multiscale Modeling and Simulation of Microtubule/Motor Protein Assemblies

Courant Institute of Mathematical Sciences

New York University

We study, through modeling and simulation, the multiscale interactions of microtubules (MTs) and motor-proteins. These elements are the central actors of important self-organized subcellular structures such as the mitotic spindle and the centrosomal MT array, as well as the ingredients of new synthetic "bioactive" liquidcrystalline fluids that are powered by ATP and driven out of equilibrium by motor-protein activity to display turbulent flows and persistent defect dynamics. We start with Brownian dynamics simulations of polar MT ensembles and show that destabilizing active stresses can arise from two different polar interactions between MT pairs. We use this information to develop a continuum Doi-Onsager kinetic theory which we analyze mathematically and use to simulate recent experiments of active nematic flows on immersed surfaces. The simulations exhibit turbulent dynamics and the continuous generation and annihilation of disclination defects. Our analysis shows that the complex dynamics devolves from two linear instabilities, and determines their characteristic length- and time-scales.