Mechanisms of self-organization and aggregation of active particles in viscous membranes

Eukaryotic cell membranes are a crowded assembly of various biomolecular machines embedded in a viscous bilayer matrix. Often, such motors are active — they convert chemical energy into mechanical work and generate hydrodynamic disturbances in the surrounding medium. We investigate the collective behavior of such inclusions in viscous membranes surrounded by a shallow subphase ('confined' membranes). Using our computational platform based on a point-particle approach, we conduct large scale simulations to study the organization of the inclusions into either clusters and/or nematic strings. We quantify pair distribution functions and tie them to disturbance fields around a particle in the plane of the membrane to demonstrate the amplifying role of the surrounding 3D fluid in promoting strings or clusters. We then examine the stability of the string-like structures to demonstrate the role of membrane versus subphase hydrodynamics. We also illustrate the stability of triangular locked clusters that emerge upon increasing confinement or – equivalently – upon increasing subphase viscous stresses, which it emerges is the local arrangement that promotes larger system-spanning clusters. Put together, these results provide valuable insight into how geometric or fluidic parameters can be tuned to achieve desirable collective behavior within biological and biomimetic membranes.