Murray J. Achs

Gluconeogenesis in rat liver cytosol. I. Computer analysis of experimental data.

Abstract A set of enzyme rate equations have been developed which relate the rates of gluconeogenic enzymes of rat liver cytosol to the concentrations of their substrates, products, and effectors. The gluconeogenic intermediates between phosphoenol pyruvate and glucose-6-phosphate have extremely high turnover rates but the levels do not change markedly when the rate of gluconeogenesis does. In order to reasonably match 14 sets of metabolite data using constant kinetic properties for the enzymes, it was necessary to postulate control of some of the enzymes by molecules other than their substrates, or to slightly correct the apparent substrate concentrations by assuming either random experimental error or compartmentation. Several reversible enzymes appear to maintain their substrate/product ratios very near equilibrium, while others show greater departures from equilibrium because their substrate concentrations are considerably below their respective K m values. Simple expressions to describe these situations were developed. The reported fructose-1,6-diphosphate levels appear to poise the product/substrate ratio for aldolase at a value which would produce glycolysis rather than gluconeogenesis, and drive the fructose-1,6-diphosphatase reaction at rates exceeding the observed net glucose production rates. After a number of approaches to these problems had been explored, the most reasonable hypothesis appeared to be that about 90% of the reported fructose-1,6-disphosphate is bound, compartmented, or otherwise unavailable, and that the phosphofructokinase velocity is roughly inversely related to the glucose production rate and is controlled primarily by the cytosolic citrate concentration. The reported glucose-6-phosphate levels yield the proper rates of glucose production only if it is assumed that a significant portion of the glucose produced by glucose-6-phosphatase is rephosphorylated by hexokinases. It is concluded that the rate of gluconeogenesis is controlled primarily by the net rate of supply of phosphoenolpyruvate, and secondarily by differences in the rates of fructose-1,6-diphosphatase versus phosphofructokinase and glucose-6-phosphatase versus the hexokinases.

Simulation of the detailed regulation of glycolytic oscillation in a heart supernatant preparation

Abstract Regulation of glycolysis during sustained oscillations has been studies by simulating in detail the experimentally observed behavior of a supernatant fraction from beef heart. This preparation exhibits cyclic oscillations in concentrations of all observed glycolytic intermediates and coenzymes. A model consisting of 57 simultaneous differential equations representing 101 chemical reactions was used to simulate the experimental results. Most of the enzyme sub-models composing this are quite similar to those used for a nonoscillating glycolytic simulation. The differential equations were solved numerically by digital computers. An alternative calculation method, which speeds the process of computation by a factor of 100, was used in the later stages of model construction. Phosphofructokinase, primarily under adenine nucleotide control resulting in pulsed-type variations of active concentrations, causes oscillation in this system, although some other enzymes exert a secondary control. The discrepancies found between experimental and computed behavior suggest presently unknown control mechanisms and areas for further experimentation.

A method of calculating time-course behavior of multi-enzyme systems from the enzymatic rate equations☆

Abstract The process of simulating enzyme systems by numerical solution of the corresponding differential equations is often quite slow, as these equations are badly behaved. A much faster method of achieving the same results is described, where the differential equations representing the behavior of an enzyme are replaced by an algebraic rate law. A program for deriving and assembling systems of these rate laws is described. Its applications, limitations, and possible extensions and combinations with other methods are discussed.

Gluconeogenesis in rat liver cytosol. II. Computer simulation of control properties.

Abstract The effect of changes in the adenine nucleotide, pyridine nucleotide, and cytoplasmic citrate concentrations on the rate of gluconeogenesis in perfused rat livers has been evaluated using digital computer models of this pathway. Varying the concentrations of nucleotides or citrate produced pseudocrossovers at enzymes acting between phosphoenolpyruvate and glucose-6-phosphate. However, unless the influx of phosphoenolpyruvate was also appropriately altered, changes in cytosolic nucleotide or citrate levels could not alter the net rate of glucose production without causing massive accumulation or depletion of intermediates. Since such accumulations of intermediates are not seen in vivo , the rate of gluconeogenesis appears to be controlled more by the rate of supply of phosphoenolpyruvate than by effects of adenine or pyridine nucleotides or by cytoplasmic citrate on individual gluconeogenic enzymes beyond enolase. Mechanisms by which the rate of glucose production may be altered by effects on phosphoenolpyruvate carboxykinase and pyruvate kinase are discussed.

Construction of more reliable complex metabolic models without repeated solution of their constituent differential equations

A method is described for constructing metabolic models composed of many nonlinear stiff differential equations. The system being modeled is divided into subunits (where such division is impractical, forcing functions are used), and algebraic relationships for their behavior at an instant in time are derived. Most of the usual searches for correct model structure and parameter sets are then done with the set of these algebraic relationships at different time points, relatively few expensive differential equation solutions being required. The software used, the application to several models of cardiac metabolism, and the significance of models of this type are discussed.

A computer model of pancreatic islet glycolysis

We have modeled an experiment with perifused pancreatic islet cells using our BIOSSIM language. The experiment and the resulting model are concerned with glucose uptake and glycolysis by the beta-cells of pancreatic islets. Although glycolysis appears to be involved in insulin release, we do not have enough information to represent insulin release in detail. The rapid entry of glucose into the beta-cell is promoted by a carrier having a very high tissue capacity. Phosphorylation of glucose by the low affinity enzyme glucokinase appears to be limiting for glycolysis. The effects of several hexose diphosphate activators of phosphofructokinase are modeled. Model behavior is described. The kinetic parameters of the enzyme submodels are given. Because of the difficulties of preparing large amounts of experimental material, information on pancreatic islet metabolism is limited. This model is a plausible explanation of the experimental results. Recent work on the genetically engineered glucose transporter and glucokinase is discussed.

Metabolism of totally ischemic excised dog heart I. Construction of a computer model

Construction and fit to the experimental data of a computer model of glycolysis, the Krebs cycle, and related metabolism in an ischemic dog heart preparation, involving 122 metabolites, 65 enzymes, and 406 chemical reactions, is described. The experimental preparation simulated is a dog heart excised from the body, placed in a beaker of Tyrodes solution, and sampled for 100 min; the model required only moderate modification from models representing perfused rat hearts, and little modification from a model of another ischemic dog heart preparation. Common underlying mechanisms for the ischemia are indicated, although this preparation appears to evolve more slowly with time, perhpas owing to heavy sedation and diffusion-limited transport. Lactate is, at first, exported and then accumulates intracellularly; pH falls, but not as much in the mitochondria as the cytoplasm; redox couples go reduced, but with counterintuitive time courses; calcium phosphate is calculated to precipitate, as often observed in cardiac ischemia.

THE EFFECT OF FRUCTOSE DIPHOSPHATE ACTIVATION OF PYRUVATE KINASE ON GLYCOLYTIC OSCILLATIONS IN BEEF HEART SUPERNATANT: AN EXPERIMENTAL AND SIMULATION STUDY*

Publisher Summary This chapter discusses the simulation of oscillating glycolysis in a beef heart supernatant fraction, and shows how simulation can be used to clarify control mechanisms. The effect of activation of pyruvate kinase by fructose-l,6-diphosphate (FDP) was simulated and verified experimentally. This activation was found to be similar in the glycolyzing system and the isolated enzyme. Deaminodiphosphopyridine nucleotide oscillations have been observed to take place in a concentrated supernatant fraction prepared from beef heart and supplemented with a source of glucose-6-phosphate. At higher, more physiological pH, the same preparation shows active glycolysis but does not oscillate. Straight-forward examination of the experimental data obtained, including concentrations as a function of time for all readily measurable glycolytic intermediates, indicates that oscillations are because of the variations in activity of phosphofructokinase (PFK) under the influence of the adenine nucleotides and perhaps FDP; this is compatible with the properties of the PFK isolated from preparations.