Computer Analysis of Glucose Transport Mechanism

Abstract

A simulation study was made to analyse a glucose titration curve to evaluate two hypotheses, i, e., the nephron population theory and the transport kinetic theory. 1 In order to verify the latter hypothesis, glucose titration curves were measured on anesthetized mongrel dogs following infusion of a competitive inhibitor (α-methylglucoside) and phlorizin. Equilibrium constants were calculated from the experimental data using a non-linear regression equation. Mathematical models were disigned for the two theories with an analog computer. 2 On an assumption that the amounts of glucose are calculated by multiple integral of the distribution function of nephron threshold, an analog circuit was established in case of the nephron population theory. The computed results of this model almost corresponded to experimental curves. In case a model was employed in which the glucose transport mechanism was considered to have a first order chemical reaction, the computed results indicated that the equilibrium constant reflected changes of splay and that the amounts of transport carrier determined Tm value. These resuls, however, failed to duplicate experimental curves which showed a slow convergence of splay towards T=Load and a sharp turn to T=Tm. 3 Animal experiments indicated that inhibition of glucose transport by α-methylglucoside and phlorizin resulted in wide spread of the glucose titration curve. With an adoption of the equilibrium constants calculated from control experiments using a non-linear regression, the urinary glucose of healthy adults was quantitatively measured to be higher than real value. The nephron population calculated from expermental data by Shmith's method did not seen adequate in obtaining a desired curve. Therfore either theory alone did not explain why and how the splay developed. 4 A model on the basis of the two theories combined was designed and calculated by the Monte-Carlo method with a digital computer. In a model kidney with hundred nephrons a distribution of GFR, Tm and of epuilibrium constant a nephron was determined by random sampling numbers. The computed results resembled the experimental data in any conditions. As a conclusions it was assumed that the splay of the glucose titration curve might results from combined effects of heterogeneity of the nephron and equilibrium constant of transport.