Active Rods in "Soft" Confinement: Increasing Dispersion via Nematic Alignment*

Cytoskeletal proteins, like actin filaments, play a crucial role in cell rearrangement and motility. When bound to molecular motors on surfaces, filaments act as self-propelled (active) colloidal rods due to the conversion of chemical energy into mechanical work. It is known that surface bound actin forms polar and nematic swarms, even when the particle interactions exhibit only nematic symmetry. Furthermore, surface topography allows for the creation and control of these coherent flows, as seen when directing the generation of forces along a cell surface to undergo cell migration. Despite the importance of this topography – swarming coupling, we have little theoretical understanding of how curved surfaces modulate the motion of individual self-propelled particles, or how that propagates into bulk behavior.

We use theory and simulation to determine how topography influences the behavior and transport swarms by as modeling the topography with a "soft" confining potential field. Using both a Langevin-based particle description and a Smoluchowski-based field description, we demonstrate that self-propelled rods align nematically along the channels and demonstrate an exponential increase in axial dispersion. We show that this increase occurs due to the reduction of rotational diffusivity of the rods in the channels.  Additionally, our work provides a framework for studying rods in any periodic potential field, overcoming the high frequency divergence limitation of traditional multipole expansions.