A computer model of pancreatic islet glycolysis

Mathematical model of metabolism and electrophysiology of amino acid and glucose stimulated insulin secretion: in vitro validation using a β-cell line

We integrated biological experimental data with mathematical modelling to gain insights into the role played by L-alanine in amino acid-stimulated insulin secretion (AASIS) and in D-glucose-stimulated insulin secretion (GSIS), details important to the understanding of complex β-cell metabolic coupling relationships. We present an ordinary differential equations (ODEs) based simplified kinetic model of core metabolic processes leading to ATP production (glycolysis, TCA cycle, L-alanine-specific reactions, respiratory chain, ATPase and proton leak) and Ca(2+) handling (essential channels and pumps in the plasma membrane) in pancreatic β-cells and relate these to insulin secretion. Experimental work was performed using a clonal rat insulin-secreting cell line (BRIN-BD11) to measure the consumption or production of a range of important biochemical parameters (D-glucose, L-alanine, ATP, insulin secretion) and Ca(2+) levels. These measurements were then used to validate the theoretical model and fine-tune the parameters. Mathematical modelling was used to predict L-lactate and L-glutamate concentrations following D-glucose and/or L-alanine challenge and Ca(2+) levels upon stimulation with a non metabolizable L-alanine analogue. Experimental data and mathematical model simulations combined suggest that L-alanine produces a potent insulinotropic effect via both a stimulatory impact on β-cell metabolism and as a direct result of the membrane depolarization due to Ca(2+) influx triggered by L-alanine/Na(+) co-transport. Our simulations indicate that both high intracellular ATP and Ca(2+) concentrations are required in order to develop full insulin secretory responses. The model confirmed that K(+) ATP channel independent mechanisms of stimulation of intracellular Ca(2+) levels, via generation of mitochondrial coupling messengers, are essential for promotion of the full and sustained insulin secretion response in β-cells.

A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell

We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.

Mathematical model of beta-cell glucose metabolism and insulin release. I. Glucokinase as glucosensor hypothesis

To quantitatively test the theory that glucokinase controls the rate of glucose metabolism and therefore the rate of insulin secretion, a minimal mathematical model of glycolysis in the pancreatic beta-cell was developed. The model represents our current hypothesis of how the normal beta-cell transduces the glucose signal. In this report, the model was used to address questions regarding the control strength of transport, hexokinase, glucose-6-phosphatase, and phosphofructokinase in the metabolism of glucose. The hypothesis that fructose 6-phosphate and a protein regulator modulate glucokinase activity was evaluated by simulation analysis, as was the possibility that glucose-6-phosphatase, working in concert with phosphofructokinase, can modulate the glucose-sensing system. It was found that, in the absence of glucose-6-phosphatase, transport, hexokinase, and phosphofructokinase do not greatly influence the rate of glucose metabolism unless their activities are dramatically altered from the measured values. Glucose metabolism was profoundly affected by the activity of glucokinase. However, in the presence of glucose-6-phosphatase, the ratio of glucose-6-phosphatase to phosphofructokinase activities was a very important parameter, and this potential control mechanism deserves more attention. The results further support the notion that glucokinase is indeed the glucosensor of the beta-cell and that modeling the system in toto provides quantitative evaluation needed to interpret the experimental tests of hypotheses.