Dimensional Reduction of a Multiscale Continuum Model of Microtubule Gliding Assays

Microtubule gliding assays, in which molecular motors anchored to a plate drive the gliding motion of filaments in a quasi-two-dimensional fluid layer, have been shown to organize into a variety of large-scale patterns. We derive a fully three-dimensional multiscale coarse-grained model of a gliding assay including the evolution of densities of rigid filaments, bound motors, and free motors, coupled to fluid equations. Our model combines continuum theories of polymeric liquids with the force spreading approach of the immersed boundary method. We use dimensional and asymptotic analysis to derive a reduced two-dimensional model and show that, to leading order, the filaments evolve in a plane, similar to what is experimentally observed. We simulate our model numerically with a GPU-based implementation and observe the same qualitative behavior as in experimental work.