FIG. 3.

The evolution of membrane vesicle and local protein density (reddish shading) on its surface for the cases of (a) ${𝜀}_{bend}^0=5\text{kJ/mol}$ and C₀ = 0.20 nm⁻¹, (b) ${𝜀}_{bend}^0=10\text{kJ/mol}$ and C₀ = 0.07 nm⁻¹, (c) ${𝜀}_{bend}^0=25\text{kJ/mol}$ and C₀ = 0.40 nm⁻¹, and (d) ${𝜀}_{bend}^0=40\text{kJ/mol}$ and C₀ = 0.20 nm⁻¹. For (a) the semi-regular protein mesh forms from initially disconnected oligomers that span the whole surface of the vesicle. At this relatively low membrane stiffness, the mesh transforms the membrane both locally and globally. At the local scale, the aggregation of the protein results in positive curvature and budding, while the areas of the membrane that are enclosed in the mesh bend inwards, giving rise to negative curvature. The total protein density for the final state is about 15%. For (b), the interconnected protein mesh forms from the very start and coarsens over time. The total protein density for the final state is about 26%. For (c), the small amount of protein aggregates form on the membrane in the beginning, giving rise to oligomerization. However, the influx of the protein is not enough to form an interconnected mesh. Toward the end of the simulation, the long oligomers, with length scale comparable to vesicle diameter, form and break dynamically. The total protein density for the final state is only about 5%. For (d), the short oligomers that first appear start to interconnect into a mesh that spans the whole surface of the vesicle. The areas that are encircled by such mesh start to bend inward. As time progresses, the mesh continues to evolve and the areas with negative curvature tend to aggregate into larger ones. Towards the end of the simulation, the global equilibrium is established, while protein density continues to evolve locally on the membrane surface. The total protein density for the final state is about 9%. The time progresses from left to right. The label in the top left indicates the step in thousand time steps (in some time units τ). The areas of the membrane with non-zero protein local density are colored red, while the rest is colored blue. The scale bar marks 100 nm.