Effects of Impaired ATP Production and Glucose Sensitivity on Human β-Cell Function: A Simulation Study (original) (raw)
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PLoS ONE, 2013
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 b-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-alaninespecific reactions, respiratory chain, ATPase and proton leak) and Ca 2+ handling (essential channels and pumps in the plasma membrane) in pancreatic b-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 Lglutamate 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 b-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 bcells. Citation: Salvucci M, Neufeld Z, Newsholme P (2013) Mathematical Model of Metabolism and Electrophysiology of Amino Acid and Glucose Stimulated Insulin Secretion: In Vitro Validation Using a b-Cell Line. PLoS ONE 8(3): e52611.
Physics Letters A, 2012
A theoretical approach to the glucose-insulin regulatory system is presented. By means of integrated mathematical modeling and extensive numerical simulations, we probe the cell-level dynamics of the membrane potential, intracellular Ca 2+ concentration, and insulin secretion in pancreatic β-cells, together with the whole-body level glucose-insulin dynamics in the liver, brain, muscle, and adipose tissues. In particular, the three oscillatory modes of insulin secretion are reproduced successfully. Such comprehensive mathematical modeling may provide a theoretical basis for the simultaneous assessment of the β-cell function and insulin resistance in clinical examination.
Mathematical Simulation of Membrane Processes and Metabolic Fluxes of the Pancreatic β-cell
Bulletin of Mathematical Biology, 2006
A new type of equation to describe enzyme-catalyzed reactions was developed, which allows the description of processes both at or near equilibrium and far from equilibrium, as they are both known to occur in the living cell. These equations combine kinetic as well as energetic characteristics within one single equation, and they describe the steady state as well as oscillations, as is shown for the glucose metabolism of the pancreatic β-cell. A simulation of oxidative glucose metabolism could be elaborated, which allows to analyse in detail, how membrane and metabolic oscillations of the pancreatic β-cell are generated, and how they are kinetically coupled. Glucose metabolism shows steady-state behaviour at a resting glucose concentration ([Glu]) of 4 mM. The steady state is switched to the oscillatory state by a first increase of the conductance of the glucokinase-catalyzed reaction at an elevated [Glu] of 10 mM. This is in fact sufficient to decrease the cytosolic adenosine diphosphate concentration ([ADP] c ) at constant intracellular [Ca 2+ ]. The associated changes of the ATP and ADP species can reduce the conductance of ATP-sensitive K + channels (K ATP ), thereby initiating bursts of the cell membrane potential ( c φ) with a concomitant influx of Ca 2+ ions from the extracellular space into the cell. The production of oscillations of [ADP] c , [Ca 2+ ] c , and all other variables, including those of mitochondria, are brought about on the one hand by a [Ca 2+ ] m dependent activation of mitochondrial ATP production, on the other hand by a [Ca 2+ ] c -dependent activation of ATP utilisation in the cytosol. Both processes must be coordinated in such a way that ATP production slightly precedes its utilisation. Oscillatory frequencies (fast/slow) are determined by the conductance (high/low, respectively) of flux through pyruvate dehydrogenase and/or citric acid cycle. The simulation shows that the so-called pyruvate paradox possibly results from a relatively low membrane conductance of β-cells for pyruvate.
Mathematical modeling and simulations of the pathophysiology of Type-2 Diabetes Mellitus
2015 8th International Conference on Biomedical Engineering and Informatics (BMEI), 2015
The pathophysiology of Type 2 Diabetes Mellitus (T2DM) is modelled using a coupled system of non-linear deterministic differential equations. An attempt is made to construct to a clinically plausible mathematical model that incorporates the homeostasis associated with endocrinological regulation of glucose and glycogen levels in the human body, by the hormones, insulin and glucagon. The model variables include the concentrations of glucose in the venous blood plasma, the concentration of glycogen in the liver/tissues, the concentration of the hormone glucagon, and the concentration of insulin in the venous blood plasma. The physiological interactions between the model parameters are depicted by clinically measurable rate constants and biophysically quantifiable stoichiometric coefficients. The processes of gluconeogenesis, glycogenolysis, and pulsatile insulin secretion during type 2 diabetes are modelled using plausible auxiliary functions. Investigative computer simulations are performed to elucidate various hypothetical scenarios of glycemia, patho-physiology of T2DM and insulinoma associated hypoglycemia which results from excessive insulin production probably due to a tumor. This study has demonstrated the necessity of simultaneous monitoring of plasma glucose, glucagon, insulin, and glycogen levels in the proper assessment of the pathophysiology of type 2 diabetes and during determination of the therapeutic efficacy of anti-diabetic drugs.
IEEE Transactions on Biomedical Engineering, 2000
The role of pancreatic -cells is fundamental in the control endocrine system, maintaining the blood glucose homeostasis in a physiological regime, via the glucose-induced release of insulin. An increasing amount of detailed experimental evidences at the cellular and molecular biology levels have been collected on the key factors determining the insulin release by the pancreatic -cells. The direct transposition of such experimental data into accurate mathematical descriptions might contribute to considerably clarify the impact of each cellular component on the global glucose metabolism. Under these perspectives, we model and computer-simulate the stimulus-secretion coupling in -cells by describing four interacting cellular subsystems, consisting in the glucose transport and metabolism, the excitable electrophysiological behavior, the dynamics of the intracellular calcium ions, and the exocytosis of granules containing insulin. We explicit the molecular nature of each subsystem, expressing the mutual relationships and the feedbacks that determine the metabolic-electrophysiological behavior of an isolated -cell. Finally, we discuss the simulation results of the behavior of isolated -cells as well as of population of electrically coupled -cells in Langerhans islets, under physiological and pathological conditions, including noninsulin-dependent diabetes mellitus (NIDDM) and hyperinsulinemic hypoglycaemia (PHHI).
Worldwide, diabetes is affecting 370 million people, causing nearly five million deaths and absorbing more than 471 billion USD per year. Mathematical models have been developed to simulate, analyse and understand the dynamics of β-cells, insulin and glucose. In this paper, we consider the effect of genetic predisposition to diabetes on dynamics of β-cells, glucose and insulin. We assume that the β-cell dynamics is governed by the differential equation: . The model indicates different behaviours according to the presence or absence of genetic predisposition. In presence of predisposition (ε = 1), the model shows three equilibrium points: a stable physiological equilibrium point (G = 100, I = 20, β = 600), a stable trivial pathological equilibrium point (G = 600, I = 0, β = 0) and a saddle point (G = 250, I = 9.8, β = 129.36). In absence of predisposition (ε = 0), the model has only two equilibrium points: an unstable pathological equilibrium point (G = 600, I = 0, β = 0) and a stable physiological equilibrium point (G = 82.6, I = 23, β = 900). In order to see how physical activity, obesity and other factors affect insulin sensitivity, simulations are carried out with different values of insulin induced glucose uptake rate (c), β-cell maximum insulin secretory rate (d) and environmental capacity (K).
Theoretical studies on the electrical activity of pancreatic beta-cells as a function of glucose
Biophysical Journal, 1987
The electrical activity of pancreatic,-cells, which has been closely correlated both with intracellular Ca2" concentration and insulin release, is characterized by a biphasic response to glucose and bursts of spiking action potentials. Recent voltage clamp and single channel patch clamp experiments have identified several transmembrane ionic channels that may play key roles in the electrophysiological behavior of #-cells. There is a hypothesis that Ca2"-activated K+ channels are responsible for both the resting potential during low glucose concentration and the silent phase during bursting. The discovery of the ATP-inactivated K+ channel raises the possibility that the current for this latter K+ channel may dominate the resting potential, while the Ca2"-activated K+ current dominates the silent phase potential between bursts. The recent discovery that Ca2"-activated K+ channels are pH sensitive raises an interesting possibility for the biphasic electrical response. In this paper, numerical methods are presented for evaluating these hypotheses against experimental evidence.
Mathematical modeling of the glucose–insulin system: A review
Mathematical Biosciences, 2013
Mathematical modeling of the glucose-insulin feedback system is necessary to the understanding of the homeostatic control, to analyze experimental data, to identify and quantify relevant biophysical parameters, to design clinical trials and to evaluate diabetes prevention or disease modification therapies. Much work has been made over the last 30 years, and the time now seems ripe to provide a comprehensive review. The one here proposed is focused on the most important clinical/experimental tests performed to understand the mechanism of glucose homeostasis. The review proceeds from models of pancreatic insulin production, with a coarser/finer level of detail ranging over cellular and subcellular scales, to short-term organ/tissue models accounting for the intra-venous and the oral glucose tolerance tests as well as for the euglycemic hyperinsulinemic clamp, to total-body, long-term diabetes models aiming to represent disease progression in terms of b-cell population dynamics over a long period of years.
Mathematical Simulation of Membrane Processes and Metabolic Fluxes of the Pancreatic �-cell
Bull Math Biol, 2006
A new type of equation to describe enzyme-catalyzed reactions was developed, which allows the description of processes both at or near equilibrium and far from equilibrium, as they are both known to occur in the living cell. These equations combine kinetic as well as energetic characteristics within one single equation, and they describe the steady state as well as oscillations, as is shown for the glucose metabolism of the pancreatic β-cell. A simulation of oxidative glucose metabolism could be elaborated, which allows to analyse in detail, how membrane and metabolic oscillations of the pancreatic β-cell are generated, and how they are kinetically coupled. Glucose metabolism shows steady-state behaviour at a resting glucose concentration ([Glu]) of 4 mM. The steady state is switched to the oscillatory state by a first increase of the conductance of the glucokinase-catalyzed reaction at an elevated [Glu] of 10 mM. This is in fact sufficient to decrease the cytosolic adenosine diphosphate concentration ([ADP] c ) at constant intracellular [Ca 2+ ]. The associated changes of the ATP and ADP species can reduce the conductance of ATP-sensitive K + channels (K ATP ), thereby initiating bursts of the cell membrane potential ( c φ) with a concomitant influx of Ca 2+ ions from the extracellular space into the cell. The production of oscillations of [ADP] c , [Ca 2+ ] c , and all other variables, including those of mitochondria, are brought about on the one hand by a [Ca 2+ ] m dependent activation of mitochondrial ATP production, on the other hand by a [Ca 2+ ] c -dependent activation of ATP utilisation in the cytosol. Both processes must be coordinated in such a way that ATP production slightly precedes its utilisation. Oscillatory frequencies (fast/slow) are determined by the conductance (high/low, respectively) of flux through pyruvate dehydrogenase and/or citric acid cycle. The simulation shows that the so-called pyruvate paradox possibly results from a relatively low membrane conductance of β-cells for pyruvate.