Ohta–Kawasaki Model Reveals Patterns on Multicomponent Vesicles

We develop a novel mechanochemical modeling framework to investigate shape deformation and pattern formation in multicomponent vesicle membranes. In this approach, membrane morphology is described by a diffuse-interface elastic bending model, while the microphase separation of membrane-associated proteins is captured via an Ohta–Kawasaki (OK) model defined on the evolving membrane surface. The coupled dynamics are governed by an overdamped force-balance equation for the membrane and an OK-type advection–reaction––diffusion equation, enabling the interplay between curvature elasticity and protein-driven active forces. We implement efficient spectral methods to simulate these dynamics in both two- and three-dimensions. Remarkably, our model successfully reproduces a wide spectrum of complex membrane morphologies and microdomain patterns observed in the landmark Nature experiments of Baumgart, Hess, and Webb [ Nature, 425 (2003), pp. 821–824]. This framework integrates curvature mechanics, microphase separation, and active biochemical forcing, providing new insights into the mechanisms of multicomponent vesicles, and offering a practical platform for predictive modeling of biomembrane dynamics.