Membrane mechanics regulate the cooperativity of proteins in curvature sensing.

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Recruitment of proteins to a membrane surface is critical for many biological processes, such as clathrin-mediated endocytosis and signaling. When interacting with the lipid membrane, many proteins exhibit different affinities to membranes with different curvature, known as curvature sensing. They also generate membrane curvature (curvature induction) by a variety of mechanisms, including the insertion of amphipathic helices. Here we use a continuum membrane model to study how helix insertions can alter the membrane energetics and how the mechanical feedback of the membrane regulates the helix insertions. Our membrane model has two coupled layers of triangular mesh to represent the two monolayers of the bilayer membrane, capturing membrane thickness and tilt. We analyzed the membrane deformation around one helix insertion and compared it to molecular dynamic simulations to optimally define the lipid tilt energies. We then investigate the interactions between insertions and membranes by considering the copy number of insertions and their interval distance, membrane tension or stress before the insertions, membrane curvatures, and lipid composition. Our results showed that multiple insertions exhibit a mechanism of cooperativity; each binding event is not independent of previous events. Our results show that this cooperativity is dependent on membrane tension and curvature. In comparison to experimental data, we validated our simulation results and analyzed the role of lipid flip-flop across the bilayers. Quantifying how protein and membrane interactions feedback on one another is critical for understanding the dynamics and control of proteins that remodel membranes through localization and self-assembly in various cellular processes.