A molecular mathematical model of glucose mobilization and uptake.

A new molecular mathematical model is developed by considering the kinetics of GLUT2, GLUT3, and GLUT4, the process of glucose mobilization by glycogen phosphorylase and glycogen synthase in liver, and the dynamics of the insulin signaling pathway. The new model can qualitatively reproduce the experimental glucose and insulin data. It also enables us to use the Bendixson criterion about the existence of periodic orbits of a two-dimensional dynamical system to mathematically predict that the oscillations of glucose and insulin are not caused by liver, instead they would be caused by the mechanism of insulin secretion from pancreatic beta cells. Furthermore it enables us to conduct a parametric sensitivity analysis. The analysis shows that both glucose and insulin are most sensitive to the rate constant for conversion of PI(3,4,5)P(3) to PI(4,5)P(2), the multiplicative factor modulating the rate constant for conversion of PI(3,4,5)P(3) to PI(4,5)P(2), the multiplicative factor that modulates insulin receptor dephosphorylation rate, and the maximum velocity of GLUT4. Moreover, the sensitivity analysis predicts that an increase of the apparent velocity of GLUT4, a combination of elevated mobilization rate of GLUT4 to the plasma membrane and an extended duration of GLUT4 on the plasma membrane, will result in a decrease in the needs of plasma insulin. On the other hand, an increase of the GLUT4 internalization rate results in an elevated demand of insulin to stimulate the mobilization of GLUT4 from the intracellular store to the plasma membrane.

[1]  R. Turner,et al.  Cyclic oscillations of basal plasma glucose and insulin concentrations in human beings. , 1979, The New England journal of medicine.

[2]  A. Ferreira,et al.  Predicting insulin resistance in children: anthropometric and metabolic indicators. , 2008, Jornal de pediatria.

[3]  R N Bergman,et al.  Assessment of insulin sensitivity in vivo. , 1985, Endocrine reviews.

[4]  Hubert Roth,et al.  Glucose appearance in the peripheral circulation and liver glucose output in men after a large 13C starch meal. , 2004, The American journal of clinical nutrition.

[5]  Y. Kuang,et al.  Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. , 2006, Journal of theoretical biology.

[6]  R. M. Lima,et al.  Predição da resistência à insulina em crianças: indicadores antropométricos e metabólicos , 2008 .

[7]  Weijiu Liu,et al.  A theoretic control approach in signal-controlled metabolic pathways. , 2007, Mathematical biosciences and engineering : MBE.

[8]  R. Sherwin,et al.  Renal extraction of glucagon in rats with normal and reduced renal function. , 1977, The American journal of physiology.

[9]  A. Baron,et al.  Evidence for defects in the trafficking and translocation of GLUT4 glucose transporters in skeletal muscle as a cause of human insulin resistance. , 1998, The Journal of clinical investigation.

[10]  R. Wolfe,et al.  Rapid oscillations in plasma insulin, glucagon, and glucose in obese and normal weight humans. , 1982, The Journal of clinical endocrinology and metabolism.

[11]  G. Brandenberger,et al.  Ultradian oscillations of plasma glucose, insulin, and C-peptide in man during continuous enteral nutrition. , 1987, The Journal of clinical endocrinology and metabolism.

[12]  Y. Z. Ider,et al.  Quantitative estimation of insulin sensitivity. , 1979, The American journal of physiology.

[13]  Alessandra Bertoldo,et al.  Interactions Between Delivery, Transport, and Phosphorylation of Glucose in Governing Uptake Into Human Skeletal Muscle , 2006, Diabetes.

[14]  Hua Wu,et al.  Parametric sensitivity in chemical systems , 1999 .

[15]  L C Gatewood,et al.  Model studies of blood-glucose regulation. , 1965, The Bulletin of mathematical biophysics.

[16]  C. J. Goodner,et al.  Insulin, glucagon, and glucose exhibit synchronous, sustained oscillations in fasting monkeys. , 1977, Science.

[17]  Claudio Cobelli,et al.  Minimal model estimation of glucose absorption and insulin sensitivity from oral test: validation with a tracer method. , 2004, American journal of physiology. Endocrinology and metabolism.

[18]  Claudio Cobelli,et al.  A minimal model of insulin secretion and kinetics to assess hepatic insulin extraction. , 2006, American journal of physiology. Endocrinology and metabolism.

[19]  E. Mosekilde,et al.  Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion. , 2000, Journal of theoretical biology.

[20]  M. Birnbaum,et al.  Kinetics of GLUT1 and GLUT4 glucose transporters expressed in Xenopus oocytes. , 1993, The Journal of biological chemistry.

[21]  K. Polonsky,et al.  In vivo pulsatility of pancreatic islet peptides. , 1986, The American journal of physiology.

[22]  J. A. Thomas,et al.  Effects of magnesium on the kinetic properties of bovine heart glycogen synthase D. , 1975, The Journal of biological chemistry.

[23]  C. Kahn.  Membrane receptors for hormones and neurotransmitters , 1976, The Journal of cell biology.

[24]  Claudio Cobelli,et al.  Two-hour seven-sample oral glucose tolerance test and meal protocol: minimal model assessment of beta-cell responsivity and insulin sensitivity in nondiabetic individuals. , 2005, Diabetes.

[25]  P. Lefèbvre,et al.  Renal handling of endogenous glucagon in the dog: comparison with insulin. , 1974, Metabolism: clinical and experimental.

[26]  A. Sherman,et al.  A mathematical model of metabolic insulin signaling pathways. , 2002, American journal of physiology. Endocrinology and metabolism.

[27]  R. Turner,et al.  Brief, Irregular Oscillations of Basal Plasma Insulin and Glucose Concentrations in Diabetic Man , 1981, Diabetes.

[28]  K. Polonsky,et al.  Oscillations in insulin secretion during constant glucose infusion in normal man: relationship to changes in plasma glucose. , 1988, The Journal of clinical endocrinology and metabolism.

[29]  T. Jess,et al.  Kinetic analysis of the liver-type (GLUT2) and brain-type (GLUT3) glucose transporters in Xenopus oocytes: substrate specificities and effects of transport inhibitors. , 1993, The Biochemical journal.

[30]  E. Mosekilde,et al.  Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. , 1991, The American journal of physiology.

[31]  Claudio Cobelli,et al.  The hot IVGTT two-compartment minimal model: an improved version. , 2003, American journal of physiology. Endocrinology and metabolism.

[32]  R. Bergman,et al.  Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. , 1981, The Journal of clinical investigation.

[33]  G. Winston,et al.  Effects of chronic ethanol ingestion on liver glycogen phosphorylase in male and female rats. , 1981, The American journal of clinical nutrition.

[34]  A. Katz,et al.  Glucagon metabolism in the rat. , 1978, The Journal of clinical investigation.

[35]  Fusheng Tang,et al.  Modeling a simplified regulatory system of blood glucose at molecular levels. , 2008, Journal of theoretical biology.

[36]  Claudio Cobelli,et al.  Meal Simulation Model of the Glucose-Insulin System , 2007, IEEE Transactions on Biomedical Engineering.