(464d) Activity, Instability and Reorganization within Viscous Membranes

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. Often, particles or biological motors straddling the membrane are active — they convert chemical energy into mechanical work, and generate hydrodynamic disturbances in the surrounding medium. We investigate the collective behavior of such active inclusions in viscous membranes surrounded by a deep subphase (‘free’ membranes) and in membranes surrounded by a shallow subphase (‘confined’ membranes).

We develop a computational platform based on a point-particle model of these active entities, where each particle is approximated as a dipole solution to the Boussinesq-Scriven equation. 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, in systems where membrane stresses dominate, pairs are equally likely to aggregate or separate, which translates to large-scale chaotic motion without aggregation. We also study pattern formation and the stability of these systems by numerically perturbing homogeneous distribution of large collections of active particles, to illustrate how flow-mediated interactions amplify fluctuations as a function of geometry, and the fluid and membrane viscosities.

Finally, we illustrate convective spatial re-organization (‘mixing’) of the lipid field due to the flows induced by the inclusions. We explore mixing dynamics as a function of concentration of active material, passive anchors, surface viscosities in both free and confined membranes, and various activity Peclet numbers. We quantify the mixing dynamics using a mixing norm, and a topological entropy of systems with negligible Brownian forces. Ultimately, these model problems provide the computational framework and an intuitive understanding the conceptual design and analysis of engineered biomimetic interfacial materials.