System size effects on the free energy landscapes from molecular dynamics of phase-separating bilayers

The "lipid raft" hypothesis proposes that cell membranes contain distinct domains of varying lipid compositions, where "rafts" of ordered lipids and cholesterol coexist with disordered lipid regions. Experimental and theoretical phase diagrams of model membranes have revealed multiple coexisting phases. Molecular dynamics (MD) simulations can also capture spontaneous phase separation of bilayers. However, these methods merely determine the sign of the free energy change upon phase separation-whether or not it is favorable-but not the amplitude. Recently, we developed a workflow to compute the free energy of phase separation from MD simulations using the weighted ensemble method. However, while theoretical treatments generally focus on infinite systems and experimental measurements on mesoscopic to macroscopic systems, MD simulations are comparatively small. Therefore, if we are to put the results of these calculations into the appropriate context, we need to understand the effects the finite size of the simulation has on the computed free energy landscapes. In this study, we investigate this phenomenon by computing free energy profiles for a model phase-separating system as a function of system size, ranging from 324 to 10 110 lipids. The results suggest that, within the limits of statistical uncertainty, bulk-like behavior emerges once the systems contain roughly 4000 lipids.