Diffusion of molecules on biological membranes of nonplanar form. A theoretical study.

Lateral mobility of molecules on cell membranes has been recently studied by fluorescence photobleaching recovery (FPR) techniques. The interpretation of these results in terms of diffusion along the membranes is based on the assumption that the surface is planar, although biological membranes may have blebs and microvilli. To study the effect of nonplanarity on the diffusion rate, the diffusion equation along curved surfaces was derived and was solved numerically for a "wavy" surface of the form A cos kx cos ky. Calculations show that for k = 10 pi micrometer-1 and a bleached spot of 1 micrometer in diameter, the time dependence of the intensity of fluorescence in the bleached spot depends on A at A less than 0.5 micrometer, while at higher values of A (a and 2 micrometer) the dependence is weak. If one calculates diffusion coefficients from FPR measurements and assumes that the membrane is planar, the resulting diffusion coefficient is not less than about half of the real one. Because of the tortuous shape of the spot boundary, increasing the microvilli length from 0.5 micrometer to 1 or 2 micrometer does not change the diffusion rates. These considerations are valid for times when the diffusion is dominated by molecules that were initially located close to the spot boundary.