A Mathematical Model of the Pancreatic Ductal Epithelium Y. Sohma 1, *, M.A. Gray 1 , Y. Imai 2 , B.E. Argent 1 1 Department of Physiological Sciences, University Medical School, Framlington Place, Newcastle upon Tyne NE2 4HH, UK 2 Department of Physiology, Osaka Medical College, Takatsuki Osaka 569, Japan Received: 18 October 1995/Revised: 5 July 1996 Abstract. A mathematical model of the HCO 3 - -secreting pancreatic ductal epithelium was developed using net- work thermodynamics. With a minimal set of assump- tions, the model accurately reproduced the experimen- tally measured membrane potentials, voltage divider ra- tio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO 2 /HCO 3 - -free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO 2 / HCO 3 - -buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K + concentration, and the effect of K + channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na + -free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl - -free ex- tracellular solution and the effect of DIDS on this alka- linization. In addition, the model predicted that the lu- minal Cl - conductance plays a key role in controlling both the HCO 3 - secretory rate and intracellular pH during HCO 3 - secretion. We believe that the model will be help- ful in the analysis of experimental data and improve our understanding of HCO 3 - -transporting mechanisms in pan- creatic duct cells. Key words: Pancreatic duct — Mathematical model — HCO 3 - secretion — Intracellular pH regulation — Cystic fibrosis transmembrane conductance regulator Introduction The ductal epithelial cells of the pancreas form a network of branching tubules whose function is to convey diges- tive enzymes (secreted by the acinar cells) into the in- testine [3, 5]. However, the ducts are not merely passive conduits but also secrete an alkaline fluid, rich in NaHCO 3 , which washes the digestive enzymes down the ductal tree and also partially neutralizes acid chyme en- tering the duodenum from the stomach. The maximum concentration of HCO 3 - found in pancreatic juice depends on the species, and varies between about 70 mM in the rat and 145 mM in cat, dog and humans [3, 5]. The ductal tree forms only a small proportion of the pancreatic mass (2 to 14% depending on species, [3]), and this virtually precludes the direct study of duct cell function in situ. However, in the 1980s a number of groups developed techniques for the isolation of small interlobular and intralobular pancreatic ducts (which are probably the main site of HCO 3 - secretion [3]), and have used electrophysiological and spectrofluorometric tech- niques to study the cellular mechanism of HCO 3 - secre- tion [9, 23, 24, 38]. As a result of these studies, most of which have been performed on ducts isolated from the rat pancreas, the HCO 3 - secretory model shown in Fig. 1 has been proposed [9, 23, 24]. In brief, the initial step in HCO 3 - transport is thought to be diffusion of CO 2 into the duct cell and its hydration to carbonic acid by carbonic anhydrase. The carbonic acid then dissociates into H + and HCO 3 - ions and the proton is translocated back across the basolateral membrane on a Na + /H + exchanger. Ef- fectively, this is the active transport step for HCO 3 - , with the energy being provided by the Na + gradient estab- lished by the Na + /K + ATPase. Once accumulated inside the duct cell, the HCO 3 - ion is then secreted across the apical membrane on a Cl - /HCO 3 - exchanger. The rate at which these exchangers cycle is thought to be controlled by the opening of Cl - channels on the apical plasma membrane. To date, cyclic AMP-activated, cystic fibro- sis transmembrane conductance regulator (CFTR) Cl - channels, and Ca 2+ -activated Cl - channels have been identified on the apical plasma membrane of the duct Correspondence to: B.E. Argent * Present address: Department of Physiology, Osaka Medical College, Takatsuki Osaka 569, Japan J. Membrane Biol. 154, 53–67 (1996) The Journal of Membrane Biology © Springer-Verlag New York Inc. 1996