The flux F of a molecule present at concentration C through a circular hole of diameter d on a surface that is adjacent to a fluid that it is diffusing in is given by
F = 4DdC
and the total that can be transferred in the per-pore capacity times the number of pores formed.
Calculate the flux allowed through each pore if the diffusion coefficient D is 10-6 cm2/s, the concentration is 0.1mM and the pore diameter is 1.5nm. With per-pore flux estimated earlier, derive the time constant for transfer of a metabolite from a particular cell to a neighboring cell. Assume that you are dealing with two epithelial cells whose geometry can be approximated as adjacent boxes connected together, with the transfer occurring through n pores.