Quantifying Membrane Curvature Sensing of Peripheral Proteins by Simulated Buckling and Umbrella Sampling

Membrane curvature plays an essential role in the organization and trafficking of membrane associated proteins. Comparison or prediction of the experimentally resolved protein concentrations adopted at different membrane curvatures requires direct quantification of the relative partitioning free energy. Here, we present a highly efficient and simple to implement a free-energy calculation method which is able to directly resolve the relative partitioning free energy of proteins as a direct function of membrane curvature, i.e., a curvature sensing profile, within (coarse-grained) molecular dynamics simulations. We demonstrate its utility by resolving these profiles for two known curvature sensing peptides, namely ALPS and α-synuclein, for a membrane curvature ranging from -1/6.5 to +1/6.5 nm^-1. We illustrate that the difference in relative partitioning (binding) free energy between these two extrema is only about 13 k_BT for both peptides, illustrating that the driving force of curvature sensing is subtle. Furthermore, we illustrate that ALPS and α-synuclein sense curvature via a contrasting mechanism, which is differentially affected by membrane composition. In addition, we demonstrate that the intrinsic spontaneous curvature of both of these peptides lies beyond the range of membrane curvature accessible in micropipette aspiration experiments, being about 1/7 nm ^-1. Our approach offers an efficient and simple to implement in silico tool for exploring and screening the membrane curvature sensing mechanisms of proteins.