Quasi-two-dimensional clustering of Brownian particles with competitive interactions: Phase diagram, structures, and dynamics

Three-dimensional (3D) bulk dispersions of Brownian particles with competitive short-range attractive (SA) and long-range repulsive (LR) interactions show rich phase behavior, and peculiar diffusion and rheological properties. In comparison, little is known about quasi-two-dimensional (Q2D) SALR dispersions of particles confined to a liquid interface or membrane, despite their biological relevance. For instance, the antagonistic interplay of SA forces (due, e.g., to lipid-mediated depletion, wetting) and LR forces (induced, e.g., by mechanical deformations or membrane fluctuations) in membrane proteins is crucial for forming protein clusters. These clusters, in turn, are pivotal in signal transduction and protein processing. We present mesoscale simulation results on the phase behavior, cluster structures, and dynamics of planar monolayers of SALR Brownian particles embedded in a bulk fluid. Salient differences and similarities between Q2D and 3D SALR particles are highlighted^[1]. Insights on the dynamics of clusters are gained from analyzing mean-squared displacements, cluster correlation and hexagonal order correlation functions, and intermediate scattering functions. Furthermore, we discuss the effects of hydrodynamic interactions on dynamic clustering^[2].