A mathematical model and computer simulation study of insulin sensitive glucose transporter regulation

Endothelial dysfunction due to selective insulin resistance in vascular endothelium: insights from mechanistic modeling

Previously, we have used mathematical modeling to gain mechanistic insights into insulin-stimulated glucose uptake. Phosphatidylinositol 3-kinase (PI3K)-dependent insulin signaling required for metabolic actions of insulin also regulates endothelium-dependent production of the vasodilator nitric oxide (NO). Vasodilation increases blood flow that augments direct metabolic actions of insulin in skeletal muscle. This is counterbalanced by mitogen-activated protein kinase (MAPK)-dependent insulin signaling in endothelium that promotes secretion of the vasoconstrictor endothelin-1 (ET-1). In the present study, we extended our model of metabolic insulin signaling into a dynamic model of insulin signaling in vascular endothelium that explicitly represents opposing PI3K/NO and MAPK/ET-1 pathways. Novel NO and ET-1 subsystems were developed using published and new experimental data to generate model structures/parameters. The signal-response relationships of our model with respect to insulin-stimulated NO production, ET-1 secretion, and resultant vascular tone, agree with published experimental data, independent of those used for model development. Simulations of pathological stimuli directly impairing only insulin-stimulated PI3K/Akt activity predict altered dynamics of NO and ET-1 consistent with endothelial dysfunction in insulin-resistant states. Indeed, modeling pathway-selective impairment of PI3K/Akt pathways consistent with insulin resistance caused by glucotoxicity, lipotoxicity, or inflammation predict diminished NO production and increased ET-1 secretion characteristic of diabetes and endothelial dysfunction. We conclude that our mathematical model of insulin signaling in vascular endothelium supports the hypothesis that pathway-selective insulin resistance accounts, in part, for relationships between insulin resistance and endothelial dysfunction. This may be relevant for developing novel approaches for the treatment of diabetes and its cardiovascular complications.

Insulin signaling - mathematical modeling comes of age

Signaling pathways that only a few years ago appeared simple and understandable, albeit far from complete, have evolved into very complex multi-layered networks of cellular control mechanisms, which in turn are integrated in a similarly complex whole-body level of control mechanisms. This complexity sets limits for classical biochemical reasoning, such that a correct and complete analysis of experimental data while taking the full complexity into account is not possible. In this Opinion we propose that mathematical modeling can be used as a tool in insulin signaling research, and we demonstrate how recent developments in modeling - and the integration of modeling in the experimental process - provide new possibilities to approach and decipher complex biological systems more efficiently.

Modeling of glucose regulation and insulin-signaling pathways

A model of glucose regulation system was combined with a model of insulin-signaling pathways in this study. A feedback loop was added to link the transportation of glucose into cells (by GLUT4 in the insulin-signaling pathways) and the insulin-dependent glucose uptake in the glucose regulation model using the Michaelis-Menten kinetic model. A value of K(m) for GLUT4 was estimated using Genetic Algorithm. The estimated value was found to be 25.3 mM, which was in the range of K(m) values found experimentally from in vivo and in vitro human studies. Based on the results of this study, the combined model enables us to understand the overall dynamics of glucose at the systemic level, monitor the time profile of components in the insulin-signaling pathways at the cellular level and gives a good estimate of the K(m) value of glucose transportation by GLUT4. In conclusion, metabolic modeling such as displayed in this study provides a good predictive method to study the step-by-step reactions in an organism at different levels and should be used in combination with experimental approach to increase our understanding of metabolic disorders such as type 2 diabetes.

A steady state analysis indicates that negative feedback regulation of PTP1B by Akt elicits bistability in insulin-stimulated GLUT4 translocation

Background

The phenomenon of switch-like response to graded input signal is the theme involved in various signaling pathways in living systems. Positive feedback loops or double negative feedback loops embedded with nonlinearity exhibit these switch-like bistable responses. Such feedback regulations exist in insulin signaling pathway as well.

Methods

In the current manuscript, a steady state analysis of the metabolic insulin-signaling pathway is presented. The threshold concentration of insulin required for glucose transporter GLUT4 translocation was studied with variation in system parameters and component concentrations. The dose response curves of GLUT4 translocation at various concentration of insulin obtained by steady state analysis were quantified in-terms of half saturation constant.

Results

We show that, insulin-stimulated GLUT4 translocation can operate as a bistable switch, which ensures that GLUT4 settles between two discrete, but mutually exclusive stable steady states. The threshold concentration of insulin required for GLUT4 translocation changes with variation in system parameters and component concentrations, thus providing insights into possible pathological conditions.

Conclusion

A steady state analysis indicates that negative feedback regulation of phosphatase PTP1B by Akt elicits bistability in insulin-stimulated GLUT4 translocation. The threshold concentration of insulin required for GLUT4 translocation and the corresponding bistable response at different system parameters and component concentrations was compared with reported experimental observations on specific defects in regulation of the system.

A mathematical model of metabolic insulin signaling pathways

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.

Insulin receptor binding kinetics: modeling and simulation studies

Biological actions of insulin regulate glucose metabolism and other essential physiological functions. Binding of insulin to its cell surface receptor initiates signal transduction pathways that mediate cellular responses. Thus, it is of great interest to understand the mechanisms underlying insulin receptor binding kinetics. Interestingly, negative cooperative interactions are observed at high insulin concentrations while positive cooperativity may be present at low insulin concentrations. Clearly, insulin receptor binding kinetics cannot be simply explained by a classical bimolecular reaction. Mature insulin receptors have a dimeric structure capable of binding two molecules of insulin. The binding affinity of the receptor for the second insulin molecule is significantly lower than for the first bound insulin molecule. In addition, insulin receptor aggregation occurs in response to ligand binding and aggregation may also influence binding kinetics. In this study, we develop a mathematical model for insulin receptor binding kinetics that explicitly represents the divalent nature of the insulin receptor and incorporates receptor aggregation into the kinetic model. Model parameters are based upon published data where available. Computer simulations with our model are capable of reproducing both negative and positive cooperativity at the appropriate insulin concentrations. This model may be a useful tool for helping to understand the mechanisms underlying insulin receptor binding and the coupling of receptor binding to downstream signaling events.

Insulin signalling: metabolic pathways and mechanisms for specificity

Biological actions of insulin are mediated by the insulin receptor, a member of a large family of receptor tyrosine kinases (RTK). Signal transduction by the insulin receptor follows a paradigm for RTK signalling. Many intracellular signalling molecules contain multiple modular domains that mediate protein-protein interactions and participate in the formation of signalling complexes. Phosphorylation cascades are also a prominent feature of RTK signalling. Distal pathways are difficult to dissect because branching paths emerge from downstream effectors and several upstream inputs converge upon single branch points. Thus, insulin action is determined by complicated signalling networks rather than simple linear pathways. Interestingly, many signalling molecules downstream from the insulin receptor are also activated by a plethora of RTKs. Therefore, mechanisms that generate specificity are required. In this review we discuss recent advances in the elucidation of specific metabolic insulin signalling pathways related to glucose transport, one of the most distinctive biological actions of insulin. We also present examples of potential mechanisms underlying specificity in insulin signalling including interactions between multiple branching pathways, subcellular compartmentalization, tissue-specific expression of key effectors and modulation of signal frequency and amplitude.

Advances in kinetic analysis of insulin-stimulated GLUT-4 translocation in adipose cells

GLUT-4 is the major insulin-sensitive glucose transporter in muscle and adipose tissue. Regulation of GLUT-4 is an important component of whole body glucose homeostasis. Abnormalities in the regulation of insulin-stimulated reversible translocation of glucose transporters have been observed in various pathological states, including diabetes. Recently, the development of specific photolabels for glucose transporters and the availability of antibodies against the various transporter isoforms have presented the opportunity for detailed kinetic analysis of GLUT-4 regulation. A kinetic analysis of some of the most recent data is presented to demonstrate how this approach can advance the understanding of GLUT-4 regulation. Some areas in which the currently available data limit the ability to resolve certain mechanistic questions are noted. Using a two-compartment model, we show that the mechanism of insulin-stimulated GLUT-4 translocation is likely to involve a large increase in the exocytosis rate of GLUT-4 with a minimal decrease in the endocytosis rate. Mathematical models based on these kinetic analyses are helpful for testing hypotheses and designing experiments to elucidate the molecular and cellular mechanisms of GLUT-4 regulation under normal and pathological conditions. This type of approach may be useful for evaluating the contribution of GLUT-4 regulation to the pathogenesis of diabetes.