Unstirred layer effects in osmotic water flow across gallbladder epithelium

The standard one-dimensional model of the unstirred layer is applied in a re-examination of the experimental results of Wright, Smulders and Tormey (Wright, E.M., Smulders, A.P., Tormey, J. McD., 1972, J. Membrane Biol. 7:198) who reported large transients in the osmotic flux of water from the serosal to the mucosal side of rabbit gallbladder epithelium. They initiated osmosis by the addition of sucrose to the mucosal bathing solution (initially, approximately 300 nOsm NaCl) and observed that the initial flux was more than ten times its eventual steady-state value; they interpreted this as a consequence of the piling-up of NaCl in the unstirred tissue layer on the serosal side of the epithelium. The present analysis (both steady-state and unsteady) shows that if measured values of layer thickness delta are used, together with reasonable values of the reduced diffusivity of NaCl in the tissue and of the fraction of tissue available for water flow, then one would predict a discrepancy of only about 10%, not tenfold, between the initial and final values of the flux. Thus the standard model is inconsistent with the observations. Furthermore, Wright et al's results cannot be used to infer that the osmotic permeability of epithelial cell membranes is much larger than steady-state measurements on whole epithelia would indicate. Mucosal-to-serosal flow is also analyzed, and in this case a considerably greater osmotic permeability is predicted; this result is consistent with the observed changes in structure of the lateral intercellular spaces when the direction of flow is reversed.