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
The total that can be transferred is the per pore capacity times the number of pores formed. Calculate the flux allowed though each pore if the diffusion coefficient is 106 cm2=sec, the concentration is 1 mM, and the pore diameter is 1.5 nm. Discuss your results and try to estimate how many pores are needed to reach meaningful cell-to-cell communications. With the per pore flux estimated above, derive the time constant for transfer of a metabolite from a particular cell to a neighboring cell. Assume that these are two epithelial cells whose geometry can be approximated as a box and that the two adjacent boxes are connected with transfer occurring through n pores.