Density imbalances and free energy of lipid transfer in supported lipid bilayers

Supported lipid bilayers are an abundant research platform for understanding the behavior of real cell membranes as they allow for additional mechanical stability and at the same time have a fundamental structure approximating cell membranes. However, in computer simulations these systems have been studied only rarely up to now. An important property, which cannot be easily determined by molecular dynamics or experiments, is the unsymmetrical density profiles of bilayer leaflets (density imbalance) inflicted on the membrane by the support. This imbalance in the leaflets composition has consequences for membrane structure and phase behavior, and therefore we need to understand it in detail. The free energy can be used to determine the equilibrium structure of a given system. We employ an umbrella sampling approach to obtain the free energy of a lipid crossing the membrane (i.e., lipid flip-flop) as a function of bilayer composition and hence the equilibrium composition of the supported bilayers. In this paper, we use a variant of the coarse-grained Martini model. The results of the free energy calculation lead to a 5% higher density in the proximal leaflet. Recent data obtained by large scale modeling using a water free model suggested that the proximal leaflet had 3.2% more lipids than the distal leaflet [Hoopes et al., J. Chem. Phys. 129, 175102 (2008)]. Our findings are in line with these results. We compare results of the free energy of transport obtained by pulling the lipid across the membrane in different ways. There are small quantitative differences, but the overall picture is consistent. We additionally characterize the intermediate states, which determine the barrier height and therefore the rate of translocation. Calculations on unsupported bilayers are used to validate the approach and to determine the barrier to flip-flop in a free membrane.