An implicit lipid model to simulate reaction-diffusion of proteins binding to membrane surface

Localization of proteins to a membrane surface is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion method is a powerful tool for capturing lipid-specific binding to membrane by treating lipids explicitly as individual diffusable binding sites. However, modeling lipid particles is computationally expensive. Here we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. The kinetics show excellent agreement between our method and the full explicit lipid model. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface. We also utilize this method to describe experimental data of membrane binding and the feedback from the curvature generation. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics.