A theoretical study of hepatic glycogen metabolism.

Abstract Hepatic glycogen metabolism is investigated with the aid of a mathematical model under the assumptions of steady state conditions for glucose 6-phosphate, glucose 1-phosphate, and uridine diphosphate glucose, and constant concentrations of adenosine triphosphate, uridine triphosphate, inorganic phosphate, and pyrophosphate. The model, which includes a constant rate of gluconeogenesis, contains 32 input parameters, and is based on enzymatic reaction mechanisms and kinetic data in vitro pertaining to six reactions which interconvert blood glucose and liver glycogen. Calculations in the model have been programmed for the IBM-1620 digital computer. The predicted rates of net glucose production and net glycogen synthesis and the steady state concentrations of glucose-6-P and UDP-glucose compare favorably with experimental observations. The glucose-1-P concentration is shown to be near the equilibrium concentration in the phosphoglucomutase reaction. The predicted glucose threshold for net glycogen synthesis is 90 mg/100 ml, and the predicted glucose threshold for net glucose production is 149 mg/100 ml. The results indicate that the hepatic glycogen system is well stabilized in that a 100-fold change in the glucose concentration, from 5 to 500 mg/100 ml, produces about a 2-fold change in the steady state concentrations of the components and in most enzymatic rates. If the inorganic phosphate concentration is taken as a decreasing function of the glucose concentration, the steady state intermediates are further stabilized but more net glucose production and glycogen synthesis result. It is shown that the rate of gluconeogenesis accounts for the separate hepatic thresholds for net glucose production and net glycogen synthesis and for the latter threshold occurring within the normal glucose concentration range. The results imply that mass action effects are more important than the dependence of glycogen synthetase on glucose-6-P in determining the steady state concentration of UDP-glucose. In the model, phosphoglucomutase and UDP-glucose pyrophosphorylase are near equilibrium, and the amount of either enzyme is not critical. The amount of glucokinase, glucose 6-phosphatase, glycogen synthetase, or phosphorylase is critical even though these enzymes may not be "rate-limiting" on the basis of maximal velocity data. The necessity of considering UDP-glucose pyrophosphorylase as a reversible reaction is established on the basis of maximal velocity data and from the point of view of glycogen synthetase being an effective control point in the system. It is shown that the dependence of glycogen synthetase on glucose-6-P severely limits enzymatic activity but that it allows the enzymatic rate to vary more extensively with changes in the glucose-6-P and UDP-glucose concentrations. The results suggest that the assumption that the reactions occur in a homogeneous phase without compartments is not a good one, and the possibility of two pools of glucose-6-P and glucose-1-P is suggested. A simulation of fasting or diabetes produces results consistent with experimental observation. A simulation of the early effects of glucocorticoid administration raises the question of increased glucose production under conditions of a nonincreasing glucose-6-P concentration.