Figure 1.
Schematic of a flexible membrane, with mobile curved membrane complexes (CMC). The membrane (grey solid line) can deform, (a) for example, in the form of a protrusion extending outwards from the cell. For small deformations the membrane shape can be characterized by a continuum field h(x), whose dynamics obey the equation of motion (2.3). (b) The corresponding mean curvature along the membrane is H(x). (c) The CMC will flow within the membrane, or adsorb directly from the cytoplasm, such that they tend to aggregate where their spontaneous curvature H0 best fits the sign and magnitude of the membrane curvature: convex CMC (blue, outwards pointing arcs) flow to the protrusion tip where the curvature is negative, and concave CMC (red, inward pointing arcs) flow towards the most concave parts where the curvature is largest and positive (indicated by the vertical dashed red lines). For CMC that flow in the membrane, the aggregation current Jcurv (equation (2.8)) is indicated by solid arrows. Adsorption of curved CMC from the cytoplasm to the membrane is also curvature-dependent, indicated by the dashed arrows.