Collective behavior and mixing dynamics in membranes with active inclusions

Eukaryotic cell membranes are a crowded assembly of molecular motors, ion pumps, and other biomolecular machines embedded in the bilayer matrix. Biomimetic membranes made of polymer assemblies also display similar properties, and are promising candidates for drug delivery applications. We investigate the collective behavior of active inclusions in viscous membranes surrounded by a deep subphase ('free' membranes) and in membranes surrounded by a shallow subphase ('confined' membranes). Our simulations show clustering of particles in free and confined membrane systems where 3D fluid viscous stresses dominate. We rationalize this by examining pair interactions in these systems, which reveals unique nonlinear dynamics that result in aggregation. By contrast, pairs are equally likely to aggregate or separate, which translates to large-scale chaotic motion without aggregation in systems where membrane stresses dominate. We also numerically study lipid spatial re-organization ('mixing') due to the flows induced by the inclusions. Mixing dynamics are explored as a function of concentration of active material, passive anchors, and surface viscosities in both free and confined membranes, which we quantify using standard mixing norms.