Diffusion time for a lipid probe in the plasma membrane to accumulate in a fused secretory granule with a fusion pore. The following calculations were performed with a diffusion constant of 1 × 10−8 cm2/s for PH-GFP (Hammond et al., 2009). (A) Circular sink. Minimum time for diffusional flow from a planar plasma membrane to supply a fused granule with enough molecules to attain a concentration of one half its final concentration. The calculation from Eq. 5.79 in Crank (1967) assumes that the (fusion pore) ring is a “perfect sink” that instantly and permanently transfers every molecule that hits it into the granule. (B) Shell diffusion. Time to attain a concentration of one half the final concentration at the distal pole of a fused granule (300-nm diameter) if all of the protein that is to enter the granule is distributed at zero time along a ring (fusion pore) of specific radius. The calculation is based on Velez and Axelrod (1988). (C) Time to half fill the granule membrane with plasma membrane probe through the fusion pore. The exact solution to this complex diffusion pathway has been solved (Rubin and Chen, 1990). It was applied to the diffusion of PH-GFP/PI-4,5-P2 from the plasma membrane of a 10.5-µm-radius cell into a fused granule membrane with a radius of 150 nm for fusion pores of radii of 7.5, 15, and 30 nm (red symbols). The three points were fitted with a parabola (red line), which was extrapolated to 2-nm pore radius (blue symbol and blue dashed line).The exact solution requires considerable computational power to extend to other fusion pore dimensions. Instead, the minimum time was estimated for a protein to reach one half of the final concentration by summing (black circles) the analyses in A and B. The minimum estimates of time and the exact solutions are remarkably consistent.
