A Theoretical and Experimental Analysis of the Osmotic Transient Phenomenon

James A. Schafer ¹, Clifford S. Patlak ¹, and Thomas E. Andreoli ¹

¹ From the Division of Nephrology, Department of Medicine, and the Department of Physiology and Biophysics, University of Alabama Medical Center, Birmingham, Alabama 35294, and the Section on Theoretical Statistics and Mathematics, National Institute of Mental Health, National Institutes of Health, Bethesda, Maryland 20014

This paper reports a theoretical analysis of osmotic transients and an experimental evaluation both of rapid time resolution of lumen to bath osmosis and of bidirectional steady-state osmosis in isolated rabbit cortical collecting tubules exposed to antidiuretic hormone (ADH). For the case of a membrane in series with unstirred layers, there may be considerable differences between initial and steady-state osmotic flows (i.e., the osmotic transient phenomenon), because the solute concentrations at the interfaces between membrane and unstirred layers may vary with time. A numerical solution of the equation of continuity provided a means for computing these time-dependent values, and, accordingly, the variation of osmotic flow with time for a given set of parameters including: P_f (cm s^–1), the osmotic water permeability coefficient, the bulk phase solute concentrations, the unstirred layer thickness on either side of the membrane, and the fractional areas available for volume flow in the unstirred layers. The analyses provide a quantitative frame of reference for evaluating osmotic transients observed in epithelia in series with asymmetrical unstirred layers and indicate that, for such epithelia, P_f determinations from steady-state osmotic flows may result in gross underestimates of osmotic water permeability. In earlier studies, we suggested that the discrepancy between the ADH-dependent values of P_f and P_DDw (cm s^–1, diffusional water permeability coefficient) was the consequence of cellular constraints to diffusion. In the present experiments, no transients were detectable 20–30 s after initiating ADH-dependent lumen to bath osmosis; and steady-state ADH-dependent osmotic flows from bath to lumen and lumen to bath were linear and symmetrical. An evaluation of these data in terms of the analytical model indicates: First, cellular constraints to diffusion in cortical collecting tubules could be rationalized in terms of a 25-fold reduction in the area of the cell layer available for water transport, possibly due in part to transcellular shunting of osmotic flow; and second, such cellular constraints resulted in relatively small, approximately 15%, underestimates of P_f.

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