Apparent 2-D diffusivity in a ruffled cell membrane

Most biological cell membranes have a microtopology that increases their surface area, including a highly ruffled surface in the case of leukocytes. Thus, molecular membrane diffusivities as measured by fluorescence recovery after photobleaching or other methods are decreased when projected onto a plane. We use a two-dimensional crested cycloid as a parameterized surface to simulate the random-walk diffusion of a molecule within a ruffled membrane. The apparent 2-D diffusivity was then calculated when the ruffled membrane is projected onto a plane. It is shown that the apparent diffusivity decreases as a function of the membrane area, to the −1.4 power.