BPS2026 – Simulation reveals emergent pattern formation of membrane proteins within curved membranes

Cells have highly curved membrane structures ranging from protrusions in the plasma membrane to the mitochondrial cristae and folds of the endoplasmic reticulum. Previous work has shown that processes such as endocytosis, cell migration, and synaptic plasticity are all modulated by membrane curvature. Such studies have been aided by advances in nanofabrication, allowing for controlled induction of membrane curvature on substrates with nanoscale structures such as cylindrical nanopillars. For instance, cells on nanopillars exhibit enhanced clustering of endocytic proteins at regions of high positive (inward) curvature, with downstream effects on mechanotransduction signaling. However, it remains unclear how such curvature-dependent events are initiated. Here, we seek to understand the relationship between membrane curvature and protein microdomain formation. To do so, we use a Cahn-Hilliard system to model aggregation-diffusion of proteins on curved membranes. We test this model for surface geometries that represent the plasma membrane on nanopillars with either spherical or flat caps. We then solve for the predicted protein dynamics using the open-source finite element framework, FEniCS. We find that proteins preferentially aggregate at the hemispherical cap or at the boundary between the cylindrical sidewall and the flat top. This suggests that proteins aggregate at locations with high Gaussian curvature even in the absence of prescribed curvature sensitivity. We anticipate that the spontaneous curvature induced by proteins will further modulate their preferential localization. This approach allows us to understand the initiation of curvature-dependent signaling cascades such as those involved in mechanotransduction.