Localization of lipid density-sensing proteins in fluctuating biomembranes

Proteins like septins that can sense biomembrane curvature on the micron-scale have amphipathic helices that embed themselves into the membrane bilayer. These proteins may be sensing curvature by detecting packing defects in the arrangement of lipids in the membrane. As an initial step to model this lipid defect sensing, we model a diffusing membrane protein with an energetic preference for a particular local lipid density, as well as bending and compressibility moduli that differ from the host membrane. This extends our earlier work on continuum simulations of fluctuating membrane height and lipid density using Fourier Space Brownian Dynamics. We focus on a membrane adhered to a sinusoidal substrate, which induces curvature and leads to differences in the lipid number densities projected by the upper and lower leaflets of the bilayer. Using our simulations, we obtain probability distributions of the protein's position relative to the substrate. We study the dependence of protein localization on various physical parameters of the membrane-protein system. In particular, we investigate how a protein's area compressibility modulus relative to the membrane's can change the protein's ability to localize to regions of the membrane with its preferred lipid density.