Figure 2.

(a) (I) A membrane with an Ω-shape. The color bar represents the initial protein density $\stackrel{\sim }{\sigma }$(S,t = 0). (II) The budded region has a radius of curvature R_c, and the point at which the radial distance is minimal, S_Ω, defines the budded area A_bud. For the Ω-shape, ϕ_max = 5π/6. (b) (I) A dome shape and the initial protein density is shown. (II) The dome region has a radius of curvature R_c and ϕ_max = π/3. The dome area is given by the area of a spherical cap, A_bud = $2\pi R_c^2$ (1 − cos(ϕ_max)). (c) A pearled structure with two buds and the initial protein density is shown. (II) Each bud on the pearl has a radius of curvature R_c and ϕ_max = 9π/10. The neck region has a radius of curvature R_neck. The area of the pearled structure is A_bud = A(S_pearl), at which the radial distance is minimal. (d) (I) A tube with the initial protein density is shown. (II) The tube has a radius R_t and a height L_tube measured from the bottom of the spherical cap to the tube rim. S_tube = πR_c/2 + L_tube, and the tube area is A_bud = A(S_tube). Initially, the total protein density m_tot is the same for all shapes, and it is located at the top of the budding structures. The shapes are axially symmetric and represent shapes commonly observed in biological membranes. To see this figure in color, go online.