Multi-body Fluctuation-Induced Forces Between Membrane Proteins: Insights from Mesoscale Simulations

The spatial organization of membrane-associated proteins is essential for a wide range of cellular processes, including signal transduction, endocytosis, and cell adhesion. While protein clustering can be driven by direct short-range forces, indirect interactions mediated by the membrane itself, particularly those arising from thermal shape fluctuations, are potentially sufficient to drive clustering in the absence of direct binding. In this study, we investigate the capacity of fluctuation-induced interactions to induce clustering using mesoscale simulations based on dynamically triangulated surfaces. We examine the roles of protein-induced changes in the local bending rigidity and Gaussian modulus, as well as the effects of protein concentration, identifying a crossover between dispersed and aggregated states that depends on these three parameters. We further explore the influence of surface tension, finding that tension mildly reduces clustering far from the crossover point but has a pronounced effect near it. We generalize these observations to spherical geometries, reporting similar results relevant to experiments involving small unilamellar vesicles (SUVs). Extending the model to systems with two types of stiff inclusions, we show that stiff proteins can serve as clustering centers for less stiff proteins. Finally, we analyze the impact of protein-induced preferred membrane curvature. In this scenario, the combination of fluctuation-mediated clustering and curvature induction can drive membrane shape remodeling. The non-additive nature of fluctuation-induced forces poses a challenge to predicting collective behavior, but our simulations provide a comprehensive framework that unifies previous observations. These findings highlight how a few mesoscale physical parameters can control protein self-organization on membranes, offering insights relevant to both cell biology and the design of membrane-associated nanoparticles.