Mechanisms of glucose sensing in the pancreatic β-cell

Abstract

Pancreatic β-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm with a subsequent influx of calcium and the eventual secretion of insulin. The mechanisms of glucose sensing in the pancreatic β-cell involve the coupling of cytoplasmic and mitochondrial processes. Our analysis, based on mathematical models of data from multiple sources has implications for β-cell function and the treatment of type 2 diabetes (Fridlyand and Philipson, 2010). This β-cell glucose response model correctly predicts changes in the ATP/ADP ratio, cytoplasmic and mitochondrial calcium levels, and other metabolic parameters in response to alterations in substrate delivery at steady-state and during cytoplasmic calcium oscillations. Here we consider how peculiarities of β-cell pathways that result in dysfunction can be a consequence of specific mechanisms of glucose sensitivity, using our computational systems-based analysis. We found that the mitochondrial membrane potential must be relatively low in β-cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in cellular respiratory activity. Our analysis additionally demonstrates how activity of lactate dehydrogenase, uncoupling proteins, and the redox shuttles all working in concert can regulate β-cell function. We further show that a decreased mitochondrial membrane potential may lead to a low rate of production of reactive oxygen species in β-cells under physiological conditions. This computational systems analysis aids in providing a more complete understanding of the complex process of β-cell glucose sensing.

Introduction

Specific biochemical mechanisms couple an increase in intracellular glucose concentration to insulin secretion in pancreatic β-cells. Increased glucose leads to an increase in the glycolytic flux and an acceleration of mitochondrial NADH production. Oxidation of NADH increases mitochondrial membrane potential and ATP synthesis, decreasing ADP concentration. The increased cytoplasmic ATP/ADP ratio causes closure of ATP-sensitive K⁺ (K_ATP) channels resulting in depolarization of the β-cell plasma membrane. This increase in β-cell membrane potential opens voltage-dependent Ca²⁺ channels (VDCCs) and allows Ca²⁺ influx, raising the intracellular free calcium concentration, a key signal in the initiation of insulin secretion along with release of Ca²⁺ from intracellular stores. The currently accepted paradigm of glucose metabolism and Ca²⁺ handling in the β-cells is summarized in Figure 1.^1–5

Figure 1.

Processes included in the mathematical model for coupling of glucose metabolism to Ca²⁺ handling in β-cells. Glucose equilibrates across the plasma membrane and is phosphorylated by glucokinase. Further, glycolysis produces pyruvate, which enters the mitochondria or is converted by lactate dehydrogenase (LDH) to lactate. Pyruvate in the mitochondria is metabolized in the tricarboxylic acid cycle, which then yields reducing equivalents. Oxidation of NADH by the respiration chain increases mitochondrial membrane potential. The resulting transmembrane electrochemical gradient drives ATP synthesis at ATP-synthase, raising the ATP/ADP ratio. Some of the protons may leak back across the membrane through uncoupling proteins (UCPs). Several shuttle systems are required for the transfer of reducing equivalents from the cytoplasm to the mitochondrial matrix. Increased cytoplasmic ATP/ADP ratio causes closure of ATP-sensitive K⁺ channels with depolarization of the β-cell membrane. This opens voltage gated Ca²⁺ channels and the resultant Ca²⁺ influx increases the cytoplasmic Ca²⁺ concentration. ATP_c and ADP_free are the free cytosolic form of ATP and ADP, G3P is the glyceraldehydes 3-phosphate, PDH is pyruvate dehydrogenase, ANT is the adenine nucleotide translocase, ROS is the reactive oxygen species. Ψ_m is the mitochondrial membrane potential. Solid lines indicate flux of substrates and dashed lines indicate regulating effects, where (+) represents activation and (−) repression.

β-cells are endowed with unique metabolic properties that control insulin secretion in comparison with energy metabolism in other cell types. For example, liver cells maintain a stable ATP/ADP equilibrium while respiring at widely varying rates.⁶ Cardiac myocytes can increase by 3- to 6-fold the rate of cardiac power generation, myocardial oxygen consumption, and ATP turnover in the transition from rest to intense exercise.⁷ Nevertheless, the metabolic stability hypothesis is widely accepted. This argues that at high work states the myocardial ATP and ADP concentrations are maintained at a relatively constant level due to buffering despite the increased turnover rates.^8,9 However, more data are needed to support this hypothesis.¹⁰

The unique character of the β-cell response to glucose is usually attributed solely to glucokinase. Because of its near-dominant control of glycolytic flux, this enzyme is thought to govern the ATP/ADP ratio and insulin secretion almost exclusively; glucokinase is, hence, often referred to as the β-cell, glucose sensor^1,3 that couples the β-cell insulin secretory response to glucose stimulation in the physiological range.

While glucokinase certainly exerts a critical level of control on downstream events, other cytoplasmic and mitochondrial processes also play an essential role in glucose-stimulated insulin secretion (GSIS).^2,5,11 In particular, the relatively high flexibility of the ATP/ADP ratio in β-cells may be accounted for, at least partially, by mitochondrial peculiarities in addition to the properties of glucokinase.^12–14 Often nutrient-stimulated insulin secretion in β-cells is impaired in the diabetic state, which may result from impaired glucose-induced ATP/ADP ratio elevation in β-cells.^13,15 Thus, knowledge of the mechanisms of regulation of ATP production and consumption are central in formulating an understanding of β-cell glucose-sensing and mechanisms of dysfunction in type 2 diabetes.^5,14,16

For these reasons it is critical to develop a comprehensive understanding as to how cytoplasmic and intramitochondrial fuel metabolism is coupled to fuel availability and thereby “sensed” in the β-cell. We have performed a computational analysis of the main processes of β-cell fuel metabolism to quantitatively assess how cytoplasmic ATP/ADP ratio can be controlled by mitochondrial and cytoplasmic processes.¹⁷ Here, we further develop this approach and consider how particular impairments in the mechanisms of β-cell glucose sensitivity can lead to β-cell failure.

Results

Mitochondrial membrane potential (Ψ_m) is maintained primarily by the action of respiration-driven proton pumps in the electron transport chain. These proteins use energy contained in NADH and FADH2 to pump hydrogen ions (H⁺) across the mitochondrial membrane out of the mitochondrial matrix. The dissipation processes for Ψ_m include the activity of the ATP synthase, the phosphate carrier, and proton-leak reactions (Fig. 1).

In an intact cell under physiological high K⁺ the contribution of pH change to the proton-motive force is usually small.^18,19 For simplicity, we suggested that the F1F0 ATPase primarily uses the mitochondrial membrane potential to generate ATP from ADP and Pi by allowing H⁺ ions to flow into the mitochondria.

The dependence of the phosphorylation rate on Ψ_m can be represented as a sigmoid dependence of ATP production on mitochondrial membrane potential.²⁰ We used the data obtained by Brand and colleagues^12,21 for mammalian mitochondria to fit the coefficients for this dependence (Fig. 2). In our model the ATP production rate saturates when Ψ_m is above 150 mV. Using this dependence we found that Ψ_m should be in a range lower than ∼150 mV (where F1F0-ATPase is particularly sensitive to a change of Ψ_m) to obtain a steep response of ATP production with glucose level. In the saturated range (>150 mV) an increase in glucose does not substantially increase Ψ_m and consequently does not lead to a change in ATP production. On the other hand, to provide a maximal F1F0-ATPase productivity, Ψ_m can be in the range above 150 mV (for example in myocytes where a maximal ATP production is necessary).

Figure 2.

Postulated control of the ATP synthase and ROS production by the mitochondrial membrane potential (Ψ_m). The dependence of ATP synthase activity¹⁷ and ROS formation²² on the Ψ_m dependence are represented. The suggested physiological range of Ψ_m for β-cells and muscle cells work is indicated.

Kinetic analysis of our model¹⁷ reveals that decreased Ψ_m into the range lower than 150 mV can be simulated by decreased respiratory activity per unit of ATPase activity. This suggests that mitochondrial glucose sensitivity in β-cells can be a result of decreased respiratory activity compared with F1F0 ATPase activity. This mechanism of decreased respiratory activity leads to a decreased rate of ATP synthesis per unit of F1F0 ATPase. However, this also gives β-cells the ability to adaptively regulate the ATP/ADP ratio in response to changes in glucose concentration (reviewed in ref. 17).

This result helps to explain the data of Affourit and Brand^12,23 which showed that the ATP/ADP ratio was more highly regulated by mitochondria in islet β-cells (studied in INS-1E insulinoma cells) than by mitochondria in skeletal muscle. Also, respiratory activity in isolated β-cell mitochondria was decreased compared with mitochondria from muscle cells. According to our analysis¹⁷ a decreased respiratory activity in β-cell mitochondria is the principal mechanism leading to regulation of the ATP/ADP ratio following changes in applied glucose concentration (see above).

Our model was used to simulate various experimental protocols and it reproduced the simultaneous measurements of multiple constituents within the cytoplasm and mitochondria such as NADH, Ca²⁺ and Ψ_m. For example, steady-state simulations following stepwise increases in glucose concentration are shown in Figure 3. Glucokinase catalyzed the rate-limiting step of glycolysis with a steep dependence on glucose concentration in the range of 4–20 mM. Enhancement of glucose concentration led to an increase in glycolytic flux and pyruvate concentrations. This accelerated pyruvate reduction and decarboxylation, potentiating an increase in [NADH]_m (Fig. 3A). Oxidation of mitochondrial NADH by the respiratory chain additionally influenced Ψ_m, which was dissipated by proton-leak reactions and the activity of the ATP synthase. The net result of these processes is the establishment of an increased Ψ_m in the area of high sensitivity of F1F0-ATPase activity on Ψ_m (at Ψ_m <150 mV) leading to increased ATP production, decreased [ADP]_c, and a corresponding increased ATP/ADP ratio in the cytoplasm (Fig. 3B). Simultaneously, [Ca²⁺]_c and [Ca²⁺]_m increased with increased ATP/ADP ratio (Fig. 3C) and the results of the simulations correspond to experimental data (reviewed in ref. 17).

Figure 3.

Simulated effects of increasing glucose on β-cell metabolism. Extracellular glucose concentration was varied and the steady-state simulations of the model parameters represented. (A) [NADH]_c and [NADH]_m are cytoplasmic and mitochondrial NADH. (B) Ψ_m is the mitochondrial membrane potential, [ATP]/[ADP] is the cytoplasmic ATP/ADP ratio; (C) [Ca²⁺]_c and [Ca²⁺]_m are the concentration of free Ca²⁺ in cytoplasm and mitochondria, respectively.

Discussion

These simulated results suggest an approach to reconciliation of several apparent contradictions between experimental data obtained for living β-cells as opposed to isolated mitochondria. For example, the respiratory control hypothesis for ATP production in intracellular mitochondria was actually based on experiments with isolated mitochondria which found that ADP available to the ATP-synthase is the limiting factor for mitochondrial ATP production.²⁴ That is, the rate of ATP synthesis should decrease with decreased [ADP]_c. However, an increased ATP/ADP ratio (possible due to decreased [ADP]_c) coupled with an increased rate of respiration and oxidative phosphorylation has been firmly established in pancreatic β-cells as a signal for GSIS.^{1,3,13,25–28} Similar results were obtained in our simulation shown in Figure 3. At first glance these data seem inconsistent with the expected inhibition of respiration with decreased ADP concentration.^3,28

Our analysis resolves this apparent contradiction. In our model¹⁷ as glucose increases the ATP synthesis rate is dependent on at least two competing factors: one is a decreased ATP synthesis rate with decreased [ADP]_c, but the other is an increased ATP synthesis rate coupled with an increased Ψ_m. Our simulation shows that glucose-induced enhancement of ATP production with increasing Ψ_m had a greater impact than its decrease as a result of decreasing [ADP]_c. As an important result, ATP synthesis and respiration rate actually increase despite a possible decrease in [ADP]_c and the ATP/ADP ratio increased with a stepwise glucose concentration increase (Fig. 3).

Role of respiration activity.

The regulation of respiratory activity in β-cells may have implications for the development of type 2 diabetes. We have performed an analysis of possible influences of the changes in respiratory activity on glucose sensitivity.¹⁷ As expected, simulation of a suppression of respiratory activity resulted in decreased glucose sensitivity in Ψ_m and ATP/ADP ratio increase (see Fig. 8 from ref. 17) as a consequence of decreased ATP production.

How we can evaluate of the role of increased respiratory activity? For example, Anello et al. examined insulin secretion and mitochondrial function in islets from cadaveric donors with type 2 diabetes and found, as have others, that glucose-stimulation was impaired. While ATP-levels were elevated at low glucose levels, these islets failed to respond to glucose with a rise in the ATP/ADP ratio. Glucose was also less effective in hyperpolarizing the mitochondrial membrane, and the expression of the electron transport chain (ETC) complexes I and V were increased in the diabetic islets.²⁹ According to our model¹⁷ an increased ETC capacity (or maximal respiratory capacity in model) could lead to these metabolic changes because enhanced electron transport should increase Ψ_m even with the resting low glucose conditions. This increases ATP production and [Ca²⁺]_c under low glucose levels but decreases the ability to accelerate ATP production following glucose challenge. This is because the F1F0 ATPase is operating at increased Ψ_m even with low glucose levels and is not able to further increase ATP production (as discussed above). This example and the corresponding theoretical analysis demonstrate that increased ETC capacity can lead to decreased β-cell sensitivity to glucose and may be a possible mechanism of β-cell failure in type 2 diabetes.

Possible role of uncoupling agents and proteins.

The mitochondrial membrane clearly leaks protons, decreasing the energy that can be used to drive ATP synthesis. Up to 20% of the basal metabolic rate may be dissipated in this leak that is always present in mitochondria.³⁰ Part of the leak is also due to uncoupling proteins (UCPs) that exist in mitochondria (Fig. 1), at various levels of expression, to uncouple oxidative phosphorylation among other possible functions. Given their effects on mitochondrial bioenergetics, uncoupling proteins have been implicated in the physiology and pathophysiology of pancreatic β-cells.^5,31,32 Our simulation on the basis of model showed (see Fig. 4 from ref. 17) that at a constant glucose level increased uncoupling protein activity leads to decreases in Ψ_m and [Ca²⁺]_c. This effect of increased activity of uncoupling proteins has been described experimentally.^5,32

Figure 4.

Simulated effect of increasing glucose on [Ca²⁺]_c at different leak activity. To simulate increased leak activity we magnified the proton leak rate two-fold. As expected, one effect was to reduce the inner membrane potential, and thus the ATP/ADP ratio, leading to a change in [Ca²⁺]_c.

However, our simulation also shows a novel aspect of this problem: an ability of uncoupling proteins (and other uncoupling agents) to shift the glucose dependence of the ATP/ADP ratio and [Ca²⁺]_c. This shifting mechanism is characterized by small changes in [Ca²⁺]_c at low and high glucose levels. However, larger differences in the [Ca²⁺]_c response to glucose were found in the glucose sensitive region where [Ca²⁺]_c increases sharply with increased glucose (Fig. 4). This effect of proton leak is only possible when the ATP/ADP ratio can be regulated by changes in Ψ_m, that is, when Ψ_m lies on the sensitive part of the ATP production dependence on Ψ_m (Ψ_m <150 mV). On the other hand, in muscle cells Ψ_m may be maintained at a high level (reviewed in ref. 17) and modest changes in Ψ_m can exert an insignificant effect on the ATP production rate.

This shifting set-point mechanism can regulate GSIS particularly during a fluctuating nutrient supply, for example, when free fatty acids increase uncoupling rates (reviewed in ref. 17). However, this shifting set-point mechanism needs to be tested further in experiments where insulin secretion changes in a glucose sensitive range and not just at low and high glucose concentrations.

Simulations with this model supports the idea that either an under or overexpression of UCP2 may lead to a failure of β-cells to properly respond to glucose. Decreased uncoupling can lead to a prompt increase in ATP production and [Ca²⁺]_c under usually subthreshold glucose levels, i.e., in resting conditions when insulin secretion should be minimal. On other hand, increased uncoupling can eventually lead to a large shift of the response of [Ca²⁺]_c to increases in glucose concentration and a decreased insulin secretion with a glucose increase.

Role of lactate dehydrogenase (LDH) and lactate production.

Very low expression of lactate dehydrogenase (LDH), the enzyme catalyzing the conversion of pyruvate to lactate and NADP to NAD⁺ is an important β-cell property.³³ This arises from the necessity to preferentially channel pyruvate toward mitochondrial metabolism.^1,34 Our computational analysis confirms that low levels of LDH expression is important for channeling pyruvate into mitochondrial metabolism, as increased LDH activity leads to decreased [Ca²⁺]_c responses to increased glucose concentration.¹⁷ However, we also found that net lactate production increases significantly when extracellular glucose is increased, and consequently pyruvate channeling in mitochondria decreases even with low LDH activity.¹⁷ This is because the NAD(P)H/NAD(P)⁺ ratio in the cytoplasm increases significantly with increased glucose concentration (see Fig. 3A). For this reason, low LDH activity can be an effective safeguard preventing mitochondrial overexcitation at high glucose levels, where [Ca²⁺]_c is already saturated and increased Ψ_m can lead to augmented ROS production (see below).

Cytoplasmic NAD(P)H and the role of NADH shuttles.

In our model the main source of NAD(P)H in pancreatic β-cell cytoplasm is the glycolitic glyceraldehyde 3-phosphate dehydrogenase reaction, that uses NAD⁺ as a substrate and produces NAD(P)H (Fig. 1). However, this reaction also can be limiting for glycolysis in β-cells, due to decreased cytoplasmic NAD⁺ availability with low LDH activity.^35,36 It follows that transport of the reducing equivalents derived from glycolysis in β-cells in exchange for mitochondrial NAD⁺, performed primarily by the glycerol phosphate and the malate-aspartate shuttles, is necessary to resupply NAD⁺ in cytoplasm.^2,37 The model simulations of NADH shuttles incorporate this pathway and confirm that these redox shuttles can maintain and restore cytoplasmic NAD(P)H/NAD(P)⁺ ratios in β-cells.¹⁷

We also evaluated the dependence of cytoplasmic NAD(P)H on glucose levels. We found that that NAD(P)H cytoplasmic concentration does not saturated simultaneously with saturation of ATP/ADP ratio or [Ca²⁺]_c and continues to increase with increased glucose concentration increase (Fig. 3). This slow saturation of cytoplasmic NAD(P)H correlates with the important observation that glucose-stimulated insulin secretion continues to increase even when [Ca²⁺]_c has reached a maximal plateau.³⁸ This supports the proposal that cytoplasmic [NADPH/NADP⁺] or related compounds are responsible for an amplifying signal of glucose on insulin secretion beyond that provided by Ca²⁺.^2,39,40

We have also analyzed the possible limiting role of NADH shuttles in the glucose sensing pathway. This in silico study shows that the net transport of mitochondrial NAD⁺ via shuttles into the cytosol can be a limiting factor in a regulation of glycolitic flux, cytosolic NADH/NAD⁺ ratio, ATP/ADP ratio and [Ca²⁺]c in pancreatic β-cells. However, this may only be true when the maximal activity of the shuttles was substantially inhibited from basal conditions, in accord with published data (reviewed in ref. 17).

Fuel supply and regulation of ROS content in β-cells.

In most cells mitochondria represent the primary source of reactive oxygen species (ROS). ROS production in mitochondria depends upon the redox state of ETC complexes. An increased Ψ_m (above ∼150 mV) sharply increases ROS production (Fig. 2).

Interestingly, β-cells inherently have relatively low levels of free-radical detoxifying enzymes such as superoxide dismutase, catalase, thioredoxin and others. However, the β-cell antioxidant systems are sufficient to limit oxidative damage under normal physiological conditions.^41,42 Based on our analysis we can explain this intriguing property of β-cells. Our analysis has shown that β-cells usually work at a relatively low Ψ_m (<150 mV) in contrast with other types of cells (Fig. 2). This leads to a relatively decreased ROS production in mitochondria, and hence, may be a reason why β-cells actually require fewer detoxifying enzymes in normal physiological conditions.

Persistently elevated fuel supplies (glucose or fat) can induce insulin resistance in muscle as a protective adaptation to fuel overload.^43,44 However, several key sensitivity mechanisms in β-cells are presumably adapted to increased glycolitic flux as glucose increases. It therefore seems that the β-cell cannot be completely protected by blocking uptake of excess nutrients. These key mechanisms could be vulnerable to potential excess activation of mitochondrial metabolism and elevated Ψ_m (Fig. 3). The consequence of limited ROS scavenging in the face of an unrestricted nutrient supply system is that β-cells are more vulnerable than other cell types to excess fuel supply. β-cell failure due to excess nutrients could play a critical role in the pathogenesis of type 2 diabetes.^16,45 Therefore, the existence of specific mechanisms for β-cell glucose sensitivity itself could underlie the increased sensitivity of these cells to injury.^16,46

Role of Ca²⁺ handling in mitochondria.

Ca²⁺ influx into the mitochondria is mediated by a Ca²⁺ uniporter that is regulated by the electrochemical gradient. In most cells, including pancreatic β-cells, the main mechanism of Ca²⁺ extrusion from the mitochondria is the Na⁺/Ca²⁺ exchanger (Fig. 1).^47,48

Our model allows an evaluation of the influence of [Ca²⁺]_m changes on GSIS. For example, the results of our simulations showed that increasing mitochondrial [Ca²⁺]_m by inhibiting the Na⁺/Ca²⁺ antiporter did not initially lead to any changes in mitochondrial flux or the corresponding increase in the ATP/ADP ratio and [Ca²⁺]_c. We found that the reason for this insensitivity to [Ca²⁺]_m was that [Ca²⁺]_m is usually above the threshold for activation of mitochondrial processes, so that the respiration rate may follow the glycolytic rate at physiological conditions, rather than the increase in [Ca²⁺]_m.¹⁷

However, a large decrease in [Ca²⁺]_m, due to, for example, a large increase in the maximal velocity of Na⁺/Ca²⁺ exchange, leads in our model to an inhibition of ATP production and a decreased ATP/ADP ratio and [Ca²⁺]_c (Fig. 7 from ref. 17). This analysis shows that β-cell mitochondrial Ca²⁺ handling can play a significant role in the regulation of GSIS only under certain specific conditions that include decreased [Ca²⁺]_m. However, additional studies evaluating Ca²⁺ in β-cell mitochondria and the role it plays in β-cell metabolism is necessary.

Variations in mitochondria operation rates and content.

It has been proposed that a reduction in mitochondrial metabolism and/or cellular content (number or volume) can underlie progression to the decreased GSIS typical of type 2 diabetes.^11,15,16,49 For this reason, we employed our model to simulate the effect of changes in mitochondrial functional activity and/or content.

Our simulations support the proposal that a decrease in mitochondrial function (or content) leads to decreased ATP production, ATP/ADP ratio, and [Ca²⁺]_c response to glucose, together leading to decreased glucose sensitivity (Figs. 8–10 from ref. 17), that could underlie β-cell defects in type 2 diabetes.

Our analysis shows that an increase in mitochondrial content can increase apparent β-cell sensitivity to glucose. This is especially true if the initial content was decreased in comparison with normal physiological conditions, either due to a genetic or physiological basis. This supports the idea that increasing mitochondrial functional activity and/or content may be a possible target for treatment of type 2 diabetes. However, such a therapeutic strategy should be used with caution, since according to our simulation¹⁷ too large an increase in mitochondrial content also leads to increased total proton leak from the mitochondrial population and finally to a decrease of glucose sensitivity even at glucose levels below saturation for insulin secretion.

Metabolic oscillations.

Simulations performed on the basis of our model result in steady-state dependence of metabolic parameters on glucose concentration (Fig. 3) since the equations of the model do not include any oscillatory mechanisms themselves. For this reason the results could be considered as time averaged in comparison with experimental data if the data have oscillatory behavior.

However, oscillations in cytoplasmic and mitochondrial metabolism, membrane potential, intracellular and mitochondrial Ca²⁺ due to increased glucose concentrations have been well described as a specific characteristic of glucose signaling in the β-cell.^13,26,39,50 The source of these oscillations and the orchestration mechanisms are not clearly understood and may reflect multiple processes. We have recently performed detailed analysis of possible mechanisms of oscillatory processes and found that metabolic pathways are unlikely to be pacemakers for [Ca²⁺]_c oscillations in β-cells.⁵⁰ In light of this result, how can we explain the existence of metabolic oscillations in the β-cell?

According to our modeling approach an increase in [Ca²⁺]_c can increase the rate of ATP consumption in cytoplasm (for example, as a consequence of increased rate of ATP-consumption due to work of Ca²⁺ pumps, dependent on Ca²⁺ concentrations) and a decrease in [Ca²⁺]_c can lead to a decreased rate of ATP consumption.^17,50 In this case our dynamic simulations clearly show that the independent [Ca²⁺]_c oscillations can lead to simulation of cyclic [ATP] and [ADP] oscillations in the cytoplasm leading to Ψ_m, mitochondrial NADH and respiratory oscillations that were similar to experimental observations (Fig. 11 from ref. 17). Hence, the experimental data and our simulations suggest that independent [Ca²⁺]_c oscillations can be a pacemaker in the generation of oscillations of mitochondrial and cytoplasmic parameters in β-cells.^17,50 However, it should be noted that in recent work by Merrins et al.⁵¹ oscillations of NADH were found in 34% of islets even in the absence of [Ca²⁺]_c oscillations. These oscillations are clearly independent metabolic oscillations in the absence of global [Ca²⁺]_c oscillations.

Materials and Methods

We have previously described a mathematical model of β-cell sensitivity to glucose.¹⁷ The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca²⁺ handling were also modeled. We have performed a computational analysis of the main processes of β-cell fuel metabolism to quantitatively assess how cytoplasmic ATP/ADP ratio can be controlled by mitochondrial and cytoplasmic processes.¹⁷ Additionally, a simple mathematical model that independently creates [Ca²⁺]_c flux dynamics was developed to simulate the [Ca²⁺]_c oscillations in a model of β-cell sensitivity to glucose.¹⁷ Simulations were performed for an idealized mean individual cell using the software environment from “Virtual Cell” as noted previously in reference ¹⁷.

Conclusion

The sensitivity of the pancreatic β-cell to glucose and other nutrients is critically important for the maintenance of energy homeostasis. Based on simple mechanistic models of key processes, an integrated model we recently described in reference ¹⁷, reproduces the experimental relationships between Ψ_m, respiration, NADH, mitochondrial and cytoplasmic Ca²⁺, the ATP/ADP ratio, and other parameters under various conditions and can additionally explain quantitative, numerical experimental observations. The additional analyses provided here show how peculiarities of β-cell functional activity and a failure in insulin secretion can be with a consequence of specific mechanisms endowing glucose sensitivity.

Further study of the mechanisms of energy metabolism in β-cells with corresponding mathematical models will be crucial in the development of our understanding of the pathophysiology of type 2 diabetes, allowing in the future a more complete understanding of β-cell glucose-sensing and the interactions between the numerous molecular processes that contribute to the physiology of the β-cell.