Flow-dependent transport in a mathematical model of rat proximal tubule

The mathematical model of rat proximal tubule has been extended to include calculation of microvillous torque and to incorporate torque-dependent solute transport in a compliant tubule. The torque calculation follows that of Du Z, Yan Q, Duan Y, Weinbaum S, Weinstein AM, and Wang T ( Am J Physiol 290: F289–F296, 2006). In the model calculations, torque-dependent scaling of luminal membrane transporter density either as an ensemble or just type 3 Na + /H + exchanger (NHE3) alone had a relatively small impact on overall Na + reabsorption and could produce a lethal derangement of cell volume; coordinated regulation of luminal and peritubular transporters was required to represent the overall impact of luminal flow on Na + reabsorption. When the magnitude of torque-dependent Na + reabsorption in the model agrees with that observed in mouse proximal tubules, the model tubule shows nearly perfect perfusion-absorption balance at high luminal perfusion rates, but enhanced sensitivity of reabsorption at low flow. With a slightly lower coefficient for torque-sensitive transporter insertion, perfusion-absorption balance in the model tubule is closer to observations in the rat over a broader range of inlet flows. In simulation of hyperglycemia, torque-dependent transport attenuated the diuretic effect and brought the model tubule into closer agreement with experimental observation in the rat. The model was also extended to represent finite rates of hydration and dehydration of CO 2 and H 2 CO 3 . With carbonic anhydrase inhibition, torque-dependent transport blunted the diuretic effect and enhanced the shift from paracellular to transcellular NaCl reabsorption. The new features of this model tubule are an important step toward simulation of glomerulotubular balance.