Mathematical Simulation of Membrane Processes and Metabolic Fluxes of the Pancreatic �-cell (original) (raw)
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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.
Biophysical Journal, 2007
Insulin secretion from pancreatic b-cells is oscillatory, with a typical period of 2-7 min, reflecting oscillations in membrane potential and the cytosolic Ca 21 concentration. Our central hypothesis is that the slow 2-7 min oscillations are due to glycolytic oscillations, whereas faster oscillations that are superimposed are due to Ca 21 feedback onto metabolism or ion channels. We extend a previous mathematical model based on this hypothesis to include a more detailed description of mitochondrial metabolism. We demonstrate that this model can account for typical oscillatory patterns of membrane potential and Ca 21 concentration in islets. It also accounts for temporal data on oxygen consumption in islets. A recent challenge to the notion that glycolytic oscillations drive slow Ca 21 oscillations in islets are data showing that oscillations in Ca 21 , mitochondrial oxygen consumption, and NAD(P)H levels are all terminated by membrane hyperpolarization. We demonstrate that these data are in fact compatible with a model in which glycolytic oscillations are the key player in rhythmic islet activity. Finally, we use the model to address the recent finding that the activity of islets from some mice is uniformly fast, whereas that from islets of other mice is slow. We propose a mechanism for this dichotomy.
Modelling mechanism of calcium oscillations in pancreatic acinar cells
We present a simple model for calcium oscillations in the pancreatic acinar cells. This model is based on the calcium release from two receptors, inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) through the process of calcium induced calcium release (CICR). In pancreatic acinar cells, when the Ca 2+ concentration increases, the mitochondria uptake it very fast to restrict Ca 2+ response in the cell. Afterwards, a much slower release of Ca 2+ from the mitochondria serves as a calcium supply in the cytosol which causes calcium oscillations. In this paper we discuss a possible mechanism for calcium oscillations based on the interplay among the three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosol. Our model predicts that calcium shuttling between ER and mitochondria is a pacemaker role in the generation of Ca 2+ oscillations. We also consider the calcium dependent production and degradation of (1,4,5) inositol-trisphosphate (IP 3 ), which is a key source of intracellular calcium oscillations in pancreatic acinar cells. In this study we are able to predict the different patterns of calcium oscillations in the cell from sinusoidal to raised-baseline, high frequency and lowfrequency baseline spiking.
Phase Analysis of Metabolic Oscillations and Membrane Potential in Pancreatic Islet β-Cells
Biophysical Journal, 2016
Metabolism in islet b-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca 2þ that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured simultaneously with membrane potential bursting to determine the phase relationships between the metabolic oscillations and electrical activity. Our experimental findings suggest that Ca 2þ entry into b-cells stimulates the rate of mitochondrial metabolism, accounting for the depletion of glycolytic intermediates during each oscillatory burst. We also performed Ca 2þ clamp tests in which we clamped membrane potential with the K ATP channel-opener diazoxide and KCl to fix Ca 2þ at an elevated level. These tests confirm that metabolic oscillations do not require Ca 2þ oscillations, but show that Ca 2þ plays a larger role in shaping metabolic oscillations than previously suspected. A dynamical picture of the mechanisms of oscillations emerged that requires the restructuring of contemporary mathematical b-cell models, including our own dual oscillator model. In the companion article, we modified our model to account for these new data.
A simplified model for mitochondrial ATP production
Journal of Theoretical Biology, 2006
Most of the adenosine triphosphate (ATP) synthesized during glucose metabolism is produced in the mitochondria through oxidative phosphorylation. This is a complex reaction powered by the proton gradient across the mitochondrial inner membrane, which is generated by mitochondrial respiration. A detailed model of this reaction, which includes dynamic equations for the key mitochondrial variables, was developed earlier by Magnus and Keizer. However, this model is extraordinarily complicated. We develop a simpler model that captures the behavior of the original model but is easier to use and to understand. We then use it to investigate the mitochondrial responses to glycolytic and calcium input. We use the model to explain experimental observations of the opposite effects of raising cytosolic Ca 2þ in low and high glucose, and to predict the effects of a mutation in the mitochondrial enzyme nicotinamide nucleotide transhydrogenase (Nnt) in pancreatic b-cells.
Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells
Frontiers in Physiology, 2021
Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca2+ initiated by bursts of electrical activity. In parallel with these electrical and Ca2+ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca2+, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this art...
Journal of Biological Chemistry, 2001
Insulin secretion from glucose-stimulated pancreatic -cells is oscillatory, and this is thought to result from oscillations in glucose metabolism. One of the primary metabolic stimulus-secretion coupling factors is the ATP/ADP ratio, which can oscillate as a result of oscillations in glycolysis. Using a novel multiwell culture plate system, we examined oscillations in insulin release and the ATP/ADP ratio in the clonal insulin-secreting cell lines HIT T-15 and INS-1. Insulin secretion from HIT cells grown in multiwell plates oscillated with a period of 4 min, similar to that seen previously in perifusion experiments. Oscillations in the ATP/ADP ratio in cells grown under the same conditions also occurred with a period of 4 min, as did oscillations in [Ca 2؉ ] i monitored by fluorescence microscopy. In INS-1 cells oscillations in insulin secretion, the ATP/ADP ratio, and [Ca 2؉ ] i were also seen, but with a shorter period of about 1.5 min. These observations of oscillations in the ATP/ADP ratio are consistent with their proposed role in driving the oscillations in [Ca 2؉ ] i and insulin secretion. Furthermore, these data show that, at least in the clonal -cell lines, cell contact or even circulatory connection is not necessary for synchronous oscillations induced by a rise in glucose.
A mathematical model of the mitochondrial NADH shuttles and anaplerosis in the pancreatic beta-cell
AJP: Endocrinology and Metabolism, 2006
The pancreatic β-cells respond to an increased glycolytic flux by secreting insulin. The signal propagation goes via mitochondrial metabolism, which relays the signal to different routes. One route is an increased ATP production that, via ATP-sensitive K+ (KATP) channels, modulates the cell membrane potential to allow calcium influx, which triggers insulin secretion. There is also at least one other “amplifying” route whose nature is debated; possible candidates are cytosolic NADPH production or malonyl-CoA production. We have used mathematical modeling to analyze this relay system. The model comprises the mitochondrial NADH shuttles and the mitochondrial metabolism. We found robust signaling toward ATP, malonyl-CoA, and NADPH production. The signal toward NADPH production was particularly strong. Furthermore, the model reproduced the experimental findings that blocking the NADH shuttles attenuates the signaling to ATP production while retaining the rate of glucose oxidation (Eto K,...