Influence of thermal fluctuations on the association and localization of proteins onto curved membranes

Recently, we derived theoretical limits to how well a single protein could sense membrane curvatures in the presence of thermal fluctuations of the membrane. Here, we extend these results to develop models that predict single-protein association rates to membrane-adhered beads of different curvatures. Referring to experiments on the association of septin proteins, we propose two classes of predictive models: i) for proteins with a maximal association rate to a preferred membrane curvature, and ii) for proteins with enhanced association rates above a threshold curvature. This allows us to connect concepts such as fluctuation variances and sensing limits to experimentally measurable protein association rates. Because proteins may be exploiting asymmetries in lipid packing in the bilayer as a proxy for curvature, we show how an algorithm we developed for simulating lipid density fluctuations in continuum membranes can be used to study the localization of proteins to regions with their preferred lipid density deviations. We then investigate how lipid density fluctuations influence the assembly of multiple proteins on the membrane, while varying parameters such as the membrane's thickness and area compressibility modulus, and the topography of substrates underlying the membrane.