MODELING IN PHYSIOLOGY
Model of beta -cell mitochondrial calcium handling and electrical activity. II. Mitochondrial variables

Gerhard Magnus1 and Joel Keizer1,2

1 Institute of Theoretical Dynamics and 2 Section on Neurobiology, Physiology, and Behavior, University of California, Davis, California 95616

    ABSTRACT
Top
Abstract
Introduction
Discussion
References

In the preceding article [Am. J. Physiol. 274 (Cell Physiol. 43): C1158-C1173, 1998], we describe the development of a kinetic model for the interaction of mitochondrial Ca2+ handling and electrical activity in the pancreatic beta -cell. Here we describe further results of those simulations, focusing on mitochondrial variables, the rate of respiration, and fluxes of metabolic intermediates as a function of D-glucose concentration. Our simulations predict relatively smooth increases of O2 consumption, adenine nucleotide transport, oxidative phosphorylation, and ATP production by the tricarboxylic acid cycle as D-glucose concentrations are increased from basal to 20 mM. On the other hand, we find that the active fraction of pyruvate dehydrogenase saturates, due to increases in matrix Ca2+, near the onset of bursting electrical activity and that the NADH/NAD+ ratio in the mitochondria increases by roughly an order of magnitude as glucose concentrations are increased. The mitochondrial ATP/ADP ratio increases by factor of <2 between the D-glucose threshold for bursting and continuous spiking. According to our simulations, relatively small changes in mitochondrial membrane potential (~1 mV) caused by uptake of Ca2+ are sufficient to alter the cytoplasmic ATP/ADP ratio and influence ATP-sensitive K+ channels in the plasma membrane. In the simulations, these cyclic changes in the mitochondrial membrane potential are due to synchronization of futile cycle of Ca2+ from the cytoplasm through mitochondria via Ca2+ uniporters and Na+/Ca2+ exchange. Our simulations predict steady mitochondrial Ca2+ concentrations on the order of 0.1 µM at low glucose concentrations that become oscillatory with an amplitude on the order of 0.5 µM during bursting. Abrupt increases in mitochondrial Ca2+ concentration >5 µM may occur during continuous electrical activity.

pancreatic beta -cell; kinetic model

    INTRODUCTION
Top
Abstract
Introduction
Discussion
References

THIS IS THE THIRD ARTICLE in a series exploring the hypothesis that Ca2+ handling by mitochondria plays a role in regulating D-glucose-induced electrical activity in the pancreatic beta -cell. The potential for this type of regulation is significant, because 1) mitochondria produce 90-95% of the ATP in these cells and 2) at basal glucose concentrations the membrane potential is dominated by an ATP-sensitive K+ (KATP) current. In the first article in this series (27) we developed a minimal model of Ca2+ handling that focused on key mitochondrial processes, namely, oxidation of NADH by the respiratory chain, phosphorylation of ADP by the F1F0-ATPase, cotransport of ATP and ADP by the adenine nucleotide translocase, Ca2+ influx via the Ca2+ uniporter, and Ca2+ efflux via Na+/Ca2+ exchange. The minimal model was shown to provide a good representation of state 3 and state 4 mitochondria in suspension. Furthermore, it correctly predicts that phosphorylation of ADP in state 3 is partially inhibited by the electrogenic uptake of Ca2+ via the uniporter. The origin of this inhibition is depolarization of the inner mitochondrial membrane potential (Delta Psi ), which works in concert with the proton gradient to drive ATP synthesis via the F1F0-ATPase.

The second article (28) elaborates the minimal model by including an explicit D-glucose-dependent input of reducing equivalents into the mitochondrial redox complexes at complex I and complex II. This input inherits its glucose dependence from the rate of turnover of D-glucose by glucokinase, which is known to be the proximal glucose sensor in beta -cells. The influence of Ca2+ on mitochondria is further elaborated by addition of a realistic model for the activation of mitochondrial pyruvate dehydrogenase (PDH) by Ca2+. In this form, the model includes the two competing regulatory roles for Ca2+: activation of oxidative phosphorylation by mitochondrial dehydrogenases and its inhibition by futile cycling of Ca2+ via the uniporter and Na+/Ca2+ exchange.

In the companion article (28) we explore the hypothesis that mitochondrial metabolism is involved in the depolarization of the plasma membrane by glucose that precedes bursting electrical activity as well as repolarization of the silent phase during bursting. This is done by constructing a whole cell model that brings together glucose-driven mitochondrial metabolism with a realistic model of plasma membrane ionic currents. Simulations with the model suggest that activation of mitochondrial dehydrogenases by Ca2+ is maximal near the D-glucose threshold for bursting electrical activity (~5-8 mM) and that production of ATP by oxidative phosphorylation is sufficient to depolarize the plasma membrane to activate Ca2+ influx via voltage-gated channels. The resulting rise in the cytosolic Ca2+ concentration ([Ca2+]i) serves in the simulations to slowly depolarize the inner mitochondrial membrane. This, in turn, decreases the rate of mitochondrial ATP production, reactivates the ATP-sensitive K+ current, and terminates the burst. Typical simulations of bursting electrical activity and the associated cytosolic Ca2+ oscillations at 11 mM glucose are given in Fig. 1.


View larger version (32K):
[in this window]
[in a new window]
 
Fig. 1.   A: simulated cytosolic Ca2+ concentration [Ca2+]i and membrane potential oscillations generated by full beta -cell model (28). B: same as A, except that fraction of free mitochondrial Ca2+fm) is increased 1 order of magnitude from 1/3,000 to 1/300.

Here we complete our investigation by examining the mitochondrial fluxes and time-varying mitochondrial concentrations in the model. The six key fluxes between the mitochondria and the cytosol are summarized in Fig. 2. They include respiration-driven proton pumps, the F1F0-ATPase proton-driven phosphorylation of ATP, the adenine nucleotide translocator, a proton leak, and influx and efflux of Ca2+ via the Ca2+ uniporter and Na+/Ca2+ exchange. In the simulations the proton current due to respiration is nearly balanced by proton influx via the F1F0-ATPase, which means that relatively small changes in the Ca2+ currents suffice to depolarize the mitochondrial membrane. Simulations with the model also give the glucose dependence of temporal changes in the mitochondrial ATP/ ADP ([ATP]m/[ADP]m) and NADH/NAD+ ([NADH]m/[NAD+]m) ratios and the mitochondrial Ca2+ concentration ([Ca2+]m). During bursting the simulations predict periodic cycling of Ca2+ into and out of the mitochondria. These synchronized futile cycles are associated with periodic changes in [Ca2+]m, which should be large enough to observe experimentally.


View larger version (20K):
[in this window]
[in a new window]
 
Fig. 2.   Schematic representation of ion fluxes through mitochondrial inner membrane that have been included in full beta -cell model. See Ref. 28 for details.

    D-GLUCOSE DEPENDENCE OF RESPIRATION-RELATED VARIABLES

In Fig. 3 our simulations of the glucose dependence of mitochondrial oxygen consumption ( Jo) (Eq. 5 in Ref. 27) exhibits a steep rise near the threshold for electrical activity. This result is in good agreement with experimental curves for islet respiration and labeled D-glucose oxidation rates (16, 32). The abrupt change in slope of this plot reflects the abrupt increase in activated dehydrogenase levels that accompanies Ca2+ uptake at the onset of electrical activity. The model also predicts small oscillations in oxygen uptake, represented in Fig. 3 as minimum, maximum, and time-average values for the regimens of bursting and continuous spiking. These result from the electrogenic cycling of cytosolic Ca2+ across the mitochondrial inner membrane during each active phase, a periodic effect that tends to lower Delta Psi and briefly raise Jo.


View larger version (14K):
[in this window]
[in a new window]
 
Fig. 3.   O2 consumption rate (Jo) vs. D-glucose concentration as simulated using full beta -cell model (28), showing time averages (bullet ) and minimum and maximum values reached during plasma membrane voltage oscillations (square ). Dashed lines replace unknown abrupt transition between regimens of bursting and continuous spiking.

In the differential equation for the effective mitochondrial NADH concentration ([NADH]m*) (Eq. 22 in Ref. 28), D-glucose appears parametrically only in the production term Jred, whereas oxygen consumption is equal to the rate at which NADH equivalents are oxidized by the respiratory chain enzymes. If Jred is plotted vs. glucose concentration, the relation is nearly identical to that for Jo. Both rates reflect the mass action of glycolytic metabolites, as well as the stimulation of key tricarboxylic acid (TCA) cycle and glycerol phosphate shunt dehydrogenases by Ca2+. The latter amplification of carbohydrate metabolism has been treated in the model as if all the stimulation of glucose metabolism by Ca2+ is due to [Ca2+]m increasing the active fraction of PDH ( fPDHa).

The simulated dependence of fPDHa on glucose concentration is shown in Fig. 4A, along with a corresponding experimental curve for rat islets in Fig. 4B (34). PDH activation in situ is somewhat lower at subthreshold D-glucose concentrations than in the simulations. This is a consequence of slightly higher [Ca2+]i required for activation in the model (28). Indeed, [Ca2+]i has a more direct effect on matrix Ca2+ than does glucose, since [Ca2+]m is responsible for activating fPDHa (Eq. 18 in Ref. 28). A large increase in the fPDHa occurs in the simulations and the experiment once the D-glucose concentration is high enough to initiate Ca2+ influx into the cytosol and, thence, the matrix.


View larger version (15K):
[in this window]
[in a new window]
 
Fig. 4.   A: simulated active fraction of pyruvate dehydrogenase ( fPDHa) with respect to D-glucose concentration ([D-glucose]) as predicted by full beta -cell model (28). Inset: details of transition at threshold for bursting; bullet , average value in a burst; square , maximum and minimum. B: rat islet PDHa content ([PDHa) as measured with respect to D-glucose added to a Krebs-bicarbonate-buffered medium. Total PDH activity is ~400 µU/100 islets, making maximum fPDHa recorded ~50%. Data are from Ref. 34. A and B show saturation of fPDHa near onset of bursting.

The steep, sigmoidal increase in dehydrogenase activation acts as a switch for beta -cell D-glucose metabolism, immediately elevating mitochondrial NADH and ATP production to higher rates once bursting begins. The small deviations from the time averages in Fig. 4A, inset, show that, during bursting, fPDHa is so close to its maximum value that the rate of PDH is only weakly affected by oscillations in [Ca2+]m. The total rate of glycolysis as amplified by the dehydrogenase determines the rate of NADH oxidation and the rate at which ATP is produced by oxidative phosphorylation. Above the threshold for electrical activity the simulations show a negligible influence of plasma membrane ionic currents on the overall level of metabolic activity, producing only small-amplitude oscillations of the metabolic variables around their average values. As shown in Fig. 5, the ratio of the effective NADH to NAD+ concentrations ([NADH]/[NAD+]) is on the order of 0.002-0.02 for suboscillation threshold glucose concentrations and increases by 1 order of magnitude to ~0.2 through the bursting regimen. It then continues to rise for higher levels of stimulation while remaining well below the saturated reduced states associated with state 4 (48).


View larger version (15K):
[in this window]
[in a new window]
 
Fig. 5.   Predicted relation of effective mitochondrial NADH/NAD+ ratio ([NADH]m/[NAD+]m) with respect to added D-glucose, as simulated by full beta -cell model (28): bullet , time average; square , oscillation bounds. Dashed lines replace unknown abrupt transition between regimes of bursting and continuous spiking.

The dose-response relationship between D-glucose and the mitochondrial NAD redox state has not been determined experimentally for insulin-secreting cells. For whole islets, however, sigmoidal increases in the total [NADH]/[NAD+] ratio from a basal level of ~0.1 to ~0.2 at high D-glucose concentrations have been measured (17, 29, 30). Our simulations in Fig. 5 agree well with the whole cell measurements but not at basal glucose. This is, however, in line with evidence that the glycerol phosphate and malate aspartate shunts raise the [NADH]m/[NAD+]m ratio at the expense of the [NADH]/[NAD+] ratio in the cytosol (24, 25, 33). Indeed, the [NADH]/[NAD+] ratio has been measured in liver and heart cells. The results, which range from ~0.002 to 0.04, are consistent with our simulated values at the low glucose concentrations (8, 42). More recent work using clusters of mouse beta -cells show a glucose dose-dependent increase in NAD(P)H autofluorescence, where the bulk of the signal is believed to originate in the mitochondria (7).

The Delta Psi in situ is not directly measurable, although values between 150 and 180 mV for preparations of phosphorylating liver mitochondria in the presence of Ca2+ are typical (3, 5). On the basis of rhodamine-123 fluorescence measurements in intact islets at 20 mM D-glucose, the potential has been estimated as 180 mV, with the inner membrane believed to be significantly depolarized in the absence of metabolic stimulation (7). Our simulations show a variation of ~7 mV, ranging from 158 mV at low D-glucose concentrations to 165 mV during electrical activity.

    D-GLUCOSE DEPENDENCE OF ATP PRODUCTION

Although the rate of synthesis of mitochondrial ATP and its rate of transfer to the cytosol by the adenine nucleotide translocator have not been measured in intact beta -cells, these are integral parts of our model. Figure 6 shows the simulated D-glucose dependence of substrate-level phosphorylation by succinyl-CoA synthase and nucleoside diphosphate kinase (Jp,TCA), F1F0-ATPase activity (Jp,F1), and the adenine nucleotide translocator exchange rate (JANT). As is clear from these plots, substrate-level ATP synthesis makes up ~10% of the total mitochondrial output. The amplitude of the oscillations in JANT is lower than that of Jp,F1. This is due to the fact that JANT depends only on the concentrations of the ionized forms of ATP and ADP, which are quite small, whereas the rate of the F1F0-ATPase depends on the total concentrations of ATP and unbound ADP (27). Despite the attentuation that occurs between the generation of ATP in the mitochondria and its appearance in the cytosol, the amplitude of the adenine nucleotide oscillations in our simulations is still large enough to affect the KATP channel conductance and regulate bursting (28).


View larger version (18K):
[in this window]
[in a new window]
 
Fig. 6.   D-Glucose dependence of islet mitochondrial ATP production and export as simulated by full beta -cell model (28). Time average (bullet ) and oscillation bounds (square ) are shown for rates of adenine nucleotide translocator (JANT), oxidative phosphorylation (Jp,F1), and substrate-level phosphorylation (Jp,TCA). Dashed lines replace unknown abrupt transition between regimes of bursting and continuous spiking.

The P/O ratio, which represents the number of ATP produced for each oxygen atom consumed, serves as a measure of the efficiency of oxidative phosphorylation in mitochondrial preparations. Perfect coupling of NADH oxidation to phosphorylation of ADP means that energy is not dissipated during its transduction from respiration to the proton-motive force and, finally, to ATP. In the absence of dissipation, the stoichiometry of these processes predicts a P/O ratio of 4 [i.e., 6 H+ for oxidation of each 1/2 O by the respiratory chain and 3 H+ for the synthesis of each ATP by the F1F0-ATPase (27)]. That value exceeds the estimate of P/O = 3 on the basis of the stoichiometry of the net chemical reaction for oxidative phosphorylation fueled by NADH (NADH + H+ + 1/2 O2 + 3 ADP + 3 H2PO-4 = NAD+ + 4 H2O + 3 ATP). The simulations reported here give values of the P/O ratio in the more realistic range of 1.9-2.6.

The low efficiency of ATP production by islet mitochondria is a reflection of proton pump slippage and elevated Ca2+ concentrations (28). Considerable inefficiency occurs as a result of pump slippage, which produces excess oxygen consumption with respect to the generated electrochemical energy available for ATP synthesis. Furthermore, the elevated Ca2+ concentrations that are present even during the silent phase tend to divert respiratory energy from oxidative phosphorylation to the futile cycling of mitochondrial Ca2+. This occurs as the increase in the average voltage across the inner membrane increases slippage of the H+ translocation mechanisms due to electron transfer (27, 28). A variation of the latter effect has been observed in mitochondrial preparations challenged by higher external phosphorylation potentials. The resulting transition from state 3 toward state 4 tends to lower the P/O ratio, presumably through the dissipative effects of the more polarized membrane potentials on the proton pumps (47, 50).

Preparations of liver and heart mitochondria using NADH-generating substrates such as pyruvate, beta -hydroxybutyrate, and glutamate give P/O ratios between 2.3 and 3.0 (19, 21, 50). Thus the value of 2.3 calculated from time-averaged values of Jo and Jp,F1 at subthreshold D-glucose concentrations is in reasonable agreement with experiment, whereas inclusion of the substrate-level phosphorylation flux in the calculation, i.e., P/O = (Jp,F1 + Jp,TCA)/Jo, produces an even more credible 2.6. The large increase in oxygen consumption, along with the uptake of Ca2+, lowers the P/O ratio in our simulations to ~2.3 in the bursting regime and to as low as 2.0 during continuous spiking.

In energized mitochondria the adenine nucleotide translocator favors the exchange of cytosolic ADP3- for matrix ATP4-, since the translocator utilizes the inner membrane voltage as a driving force (27). In isolated liver mitochondria, this asymmetry results in [ATP]m/[ADP]m ratios between 1 and 10, about an order of magnitude lower than in the external medium (8, 13). In the presence of external ATP, if the ADP concentration is slowly increased, the resulting transition from state 4 to state 3 tends to further diminish the [ATP]m/[ADP]m ratio toward values closer to <= 1 (2, 23). The [ATP]m/[ADP]m ratio obtained by various fractionation methods from intact cells is generally lower than that measured for organelle preparations. Estimates for rat hepatocytes are ~1 (40, 43, 46), whereas values for [ATP]m/[ADP]m as low as 0.18 have been obtained from the perfused liver (45, 46). These results suggest only small differences between the concentrations of ATP and ADP for mitochondria in situ.

Our simulations of the D-glucose dependence of the [ATP]m/[ADP]m ratio are summarized in Fig. 7A. They exhibit an increase from ~0.75 to 1.0 when glucose is elevated above basal levels. In islets this ratio has been measured in mitochondrial fractions in the absence of glucose to be ~1.8 and ~2.0 when the D-glucose concentration is increased to 16.7 mM (31). Comparable increases (from 1.2 to 1.3) are reported for similar experiments (41). These results, which are only slightly higher than the simulations in Fig. 7A, may be due to our simplifying assumption (28) that total mitochondrial adenine nucleotides are constant (Eq. 26 in Ref. 28) or to the generally higher ATP concentrations measured for rat islets (27). In the simulations the [ATP]m/[ADP]m ratio undergoes small oscillations around 1.0 throughout the bursting regime (Fig. 7A ).


View larger version (13K):
[in this window]
[in a new window]
 
Fig. 7.   Ratio of matrix ATP to ADP concentration [ATP]m/[ADP]m, (A ) and [ATP]m vs. [D-glucose] (B ) for beta -cell mitochondria as simulated using complete model (28): bullet , time averages; square , oscillation bounds.

In our simulations, raising the mitochondrial Pi concentration from 20 to 30-40 mM stimulated mitochondrial ATP synthesis sufficiently to increase duration of the active phase of a burst (not shown). In some cases, this change leads to continuous spiking if there were no parallel elevation of the cytosolic ATP hydrolysis rate (Jhyd) (Eq. 35 in Ref. 28). However, such increases in the mitochondrial ATP synthesis rate are still insufficient to shift the oscillations of the [ATP]m/[ADP]m ratio away from 1 during bursting and have even less effect on the cytosolic adenine nucleotide concentrations. As expected, this increase in Pi also depolarizes the mitochondria and lowers the effective [NADH]m/[NAD+]m ratio due to the increased H+ reuptake and NADH oxidation that accompanies the increase in the rate of ATP production. However, the most dramatic result of increasing Pi concentrations is a decrease in the burst period of >= 4-5 s. This is due to slightly greater efficiency of oxidative phosphorylation (higher P/O ratios), which decreases the time required to generate sufficient ATP to terminate the silent phase.

    OSCILLATIONS OF MITOCHONDRIAL VARIABLES

Typical time series for the mitochondrial ionic currents and Delta Psi are shown in Fig. 8. The oscillations of Delta Psi result from the imbalance of the single negative outward current (JH,res), which is generated by the respiratory chain proton pumps, and the five positive inward currents. As is obvious from Fig. 8, the largest of the inward currents is carried by the ATP synthase (JH,F1), followed by the adenine nucleotide translocator (JANT), the proton leak (JH,leak), the Ca2+ uniporter (2Juni), and an electrogenic Na+/Ca2+ exchanger (JNa+ / Ca2+). Although an electrogenic exchange mechanism enhances the depolarizing effect of the uniporter on Delta Psi as Ca2+ cycles through the mitochondria, comparable results have been obtained with a nonelectrogenic exchange mechanism (28).


View larger version (17K):
[in this window]
[in a new window]
 
Fig. 8.   Simulated time series for inner membrane voltage (Delta Psi ) and positively charged currents of mitochondrial ion transport, as generated by full beta -cell model (28) for 5.6 mM D-glucose. Outward current of respiratory H+ ejection (JH,res) is countered by inward currents of H+ reuptake driving oxidative phosphorylation (JH,F1), ADP3-/ATP4- exchange mediated by adenine nucleotide translocator (JANT), H+ leakage (JH,leak), and futile cycling of Ca2+ (2Juni + JNa+/Ca2+).

Figure 8 is consistent with the hypothesis for bursting described in the previous articles of this series (20, 28). The cycling of mitochondrial Ca2+ induced by the influx of extracellular Ca2+ into the cytosol during the active phase transiently raises the 2Juni + JNa+/Ca2+ current and lowers Delta Psi . This small depolarization of the Delta Psi , which is on the order of 0.8 mV regardless of the level of D-glucose stimulation, is sufficient to diminish respiratory control and increase the proton current (JH,res) associated with electron transfer and oxygen consumption. The smaller values of Delta Psi in the active phase lower JH,F1 as well as JANT.

Simulations of the ATP synthase and oxygen consumption rates, Jp,F1 and Jo, along with the effective ratio of the pyridine nucleotides in the matrix, [NADH]m*/[NAD+]m*, are shown in Fig. 9 for 5.6 mM (A ) and 13.9 mM (B ) D-glucose. In addition to an overall increase in magnitude as a result of heightened TCA cycle activity, the [NADH]m*/[NAD+]m* oscillation also increases in amplitude. The changes in NADH* are relatively smooth during the active phase of a burst. This is due to the relatively slow rates of NADH* production and oxidation, which prevent the NADH*/NAD+* ratio from changing much during an action potential spike. Because an increase in the [NADH]m*/[NAD+]m* ratio increases the rate of oxidation by the respiratory chain, the oxygen consumption rate also increases as D-glucose is elevated. The variation of Jp,F1, on the other hand, is smaller at 13.9 mM D-glucose, since depolarization of Delta Psi by matrix Ca2+ cycling has less effect on the F1F0-ATPase at the elevated Delta Psi in Fig. 9B.


View larger version (25K):
[in this window]
[in a new window]
 
Fig. 9.   Simulated time series for rate of ATP production by oxidative phosphorylation (Jp,F1) and O2 consumption rate (Jo) and [NADH]m* /[NAD+]m* ratio, as generated by complete beta -cell model (28) for [D-glucose] = 5.6 mM (A ) and 13.9 mM (B ).

The source of the decreased amplitude in the oscillation of the ATP synthesis rate as D-glucose concentration is raised from 5.6 to 13.9 mM can be gleaned from the plot of Jp,F1 with respect to Delta Psi for a typical mitochondrial phosphorylation potential (Fig. 10). Notice that the slope of that curve decreases as Delta Psi moves to the right, away from the inflected region. In Fig. 11 the oscillations of mitochondrial ATP are shown for the pair of D-glucose concentrations in Fig. 9 and also reflect the declining amplitude of the Jp,F1 oscillations as metabolic stimulation increases.


View larger version (12K):
[in this window]
[in a new window]
 
Fig. 10.   Rate of F1F0-ATPase-mediated ATP production (Jp,F1) simulated with respect to Delta Psi , with mitochondrial phosphorylation potential (AF1) fixed at 495 mV ([ADP]m = 5.89 nmol/mg protein). Plot uses Eq. 13 and parameter settings given in Table 3 from Ref. 27.


View larger version (13K):
[in this window]
[in a new window]
 
Fig. 11.   Time series for [ATP]m at 5.6 mM (bottom ) and 13.9 mM (top ) D-glucose, as simulated using full beta -cell model (28).

At the start of a burst in Fig. 9, Jo rises abruptly due to the rapid increase in mitochondrial Ca2+ cycling and its depolarizing effect on the membrane voltage. Indeed, Jo is known to be a strictly decreasing function of the mitochondrial membrane voltage (see Fig. 2.8 in Ref. 26) with an extremely large negative slope at physiological values of Delta Psi . The envelope of the high-frequency oscillations in oxygen consumption parallels the [Ca2+]i oscillations and the plasma membrane voltage spikes in Fig. 1B. The slow decline of the average value of Jo during a burst reflects the decline in the effective [NADH]m/[NAD+]m ratio as the increasing values of [NAD+]m* lower the rate of respiration. A dip appears in Jo at the end of the active phase for 5.6 mM D-glucose (Fig. 9A ) but not for 13.9 mM D-glucose (Fig. 9B ). This dip is caused by the rapid rise of the NADH/NAD ratio to the plateau at the lower concentration. The rise in Jo is much slower for 13.9 mM D-glucose, reflecting the saturation of the single electron transfer rate Jres = 2Jo as the [NADH]m*/[NAD+]m* ratio rises. At 13.9 mM glucose the driving force for the NADH oxidation reaction is high and [NADH]m*/[NAD+]m* fluctuations have much less effect on the magnitude of Jres, and therefore the rate of oxygen consumption in the silent phase remains low.

    OSCILLATIONS IN MITOCHONDRIAL CALCIUM CONCENTRATION AND THEIR D-GLUCOSE DEPENDENCE

Below the glucose threshold for bursting, Juni and JNa+/Ca2+ balance at steady state (Fig. 12, A and B ). This corresponds to a futile cycling of beta -cell mitochondrial Ca2+ at a rate of ~2 nmol · min-1 · mg protein-1. The parallel rise of the two fluxes as the D-glucose concentration increases (Fig. 12, A and B ) and the similarity of the phase of the two fluxes with respect the cytosolic and matrix Ca2+ oscillations (Fig. 12C ) show that the futile cycle synchronizes with the bursts. Consistent with the strong dependence of the uniporter on [Ca2+]i (Eq. 19 in Ref. 27), the glucose dose-response curve for Juni is similar to that for [Ca2+]i (Fig. 7A in Ref. 28). The maximum and minimum for both fluxes remain approximately fixed throughout the bursting regime, with the increase in the average values reflecting the longer plateau fraction as continuous spiking is approached. Because the efflux has a hyperbolic dependence on [Ca2+]m (Eq. 21 in Ref. 27), the plot of JNa+/Ca2+ vs. D-glucose concentration in Fig. 12B resembles the analogous plot for [Ca2+]m in Fig. 12D. The greater Ca2+-buffering capacity of the matrix relative to the cytosol attenuates the high-frequency oscillations corresponding to the voltage spikes in the time series for [Ca2+]m and JNa+/Ca2+ (Fig. 12C ).


View larger version (16K):
[in this window]
[in a new window]
 


View larger version (12K):
[in this window]
[in a new window]
 


View larger version (22K):
[in this window]
[in a new window]
 
Fig. 12.   Dependence of Juni (A ) and JNa+/Ca2+ (B ) activity on [D-glucose], as predicted by full beta -cell model (28), plotted in terms of time average values (bullet ) and oscillation bounds (square ). Dashed lines replace unknown abrupt transition between regimes of bursting and continuous spiking. C: simulated time series for Juni and JNa+/Ca2+ and [Ca2+]i and matrix free Ca2+ concentration ([Ca2+]m) at 5.6 mM D-glucose. D: simulated D-glucose dependence of [Ca2+]m.

Although the value of Juni in the model remains far below the maximum values measured for the uniporter in isolated mitochondria, Ca2+ efflux from the matrix is nearly saturated. Thus, at >16.7 mM D-glucose, the simulations no longer predict futile cycles of Ca2+ but rather its continual accumulation. Such a trend could possibly be reversed in vivo by an activation of the mitochondrial permeability transition and its accompanying massive efflux of mitochondrial Ca2+ and phosphate (10), which would also transiently repolarize the plasma membrane and terminate a prolonged phase of continuous spiking.

Although spikes of matrix free Ca2+ as high as 12 µM have recently been measured by fluorescent indicators in insulin-secreting INS-1 cells depolarized by extracellular K+ (39), experimental dose-response curves describing the relation between D-glucose and [Ca2+]m for intact beta -cells or islets are still unavailable. However, the relation between [Ca2+]m and [Ca2+]i has been investigated for other systems, including heart and liver mitochondria and cardiac myocytes. Recent measurements exhibit a strong trend toward lower values of [Ca2+]m concentrations.

Estimates of a 1-5 nmol/mg protein total Ca2+ content for liver mitochondria in situ (36) correspond to free Ca2+ levels of 0.4-2.0 µM on the basis of a 0.03% buffering capacity for mitochondrial Ca2+ and the factor of 1.25 for converting nanomoles per milligram of protein to millimeter in the matrix (27). Comparisons of the Ca2+ requirements for stimulating PDH phosphatase and alpha -ketoglutarate dehydrogenase in coupled heart mitochondria under physiological conditions and in uncoupled mitochondria or extracts predict a two- to threefold concentration gradient across the inner membrane (4, 6). Experiments using fura 2 or indo 1 generally result in lower estimates for the amounts of free Ca2+ available for the activation of the dehydrogenases. By use of fluorescent indicators, heart mitochondria in the presence of physiological levels of Mg2+, Na+, and Ca2+ give [Ca2+]m that are actually lower than those in the external medium. Only when Ca2+ in the external medium exceeds a threshold on the order of 0.5-1.0 µM does the matrix concentration increase significantly (15, 37, 38, 49).

Figure 13 provides a rough comparison of the experimental and simulated dependence of [Ca2+]m on [Ca2+]i. The low affinity for external Ca2+ of the heart mitochondria uniporter is probably responsible for the shift to the right of the experimental curve in Fig. 13A with respect to the simulations in Fig. 13B. In addition, the former experiments, which were carried out with intact cardiac myocytes, used fixed [Ca2+]i (35), whereas the simulations in Fig. 13B use the average [Ca2+]i generated by the beta -cell model for 0.1-22.3 mM D-glucose. If the Ca2+-buffering capacity of the matrix is reduced, as in Fig. 1B, then the theoretical curve in Fig. 13B is shifted upward.


View larger version (11K):
[in this window]
[in a new window]
 
Fig. 13.   A: variations of [Ca2+]m that correspond to manipulations of [Ca2+]i of intact cardiac myocytes. [Ca2+]i was altered to nonphysiological levels by changing level of external Na+ (thereby depolarizing heart cell plasma membrane and opening its Ca2+ channels) and then measured using fluorescent indicator indo 1 (35). B: simulated free [Ca2+]m vs. [Ca2+]i. Both quantities are generated by complete beta -cell model (28) at various levels of D-glucose.

    DISCUSSION
Top
Abstract
Introduction
Discussion
References

Our simulations have explored the hypothesis (20, 26-28) that Ca2+ uptake by mitochondria plays a key role in regulating metabolism and bursting electrical activity in the pancreatic beta -cell. Recent experiments provide support for a regulatory role for Ca2+ in mitochondrial metabolism (10, 11). Abundant evidence is also now available that mitochondria are effective in regulating cytosolic Ca2+ at physiological levels in sympathetic neurons (9), chromaffin cells (1, 14), Xenopus oocytes (18), gonadotrophs (12), oligodendrocytes (44), and T cells (15). In all these cell types, mitochondria interact with agonist-stimulated Ca2+ release and uptake from internal stores to modulate Ca2+ oscillations and waves. Our proposal, which is supported by the simulations presented here, suggests a more central role for mitochondria in the beta -cell, where Ca2+ fluxes are dominated by voltage-gated channels in the plasma membrane. Thus not only are cytoplasmic Ca2+ changes buffered by mitochondria, but the uptake and release of Ca2+ by mitochondria regulate the rate of ATP synthesis.

The mechanism for this regulation is based on the electrogenic properties of Ca2+ uptake and release, which tend to depolarize Delta Psi and reduce the driving force for ATP synthesis. At glucose concentrations below the threshold for bursting, this negative effect of Ca2+ on the rate of ATP synthesis is counteracted by Ca2+ activation of mitochondrial dehydrogenases, especially PDH. This causes depolarization of the plasma membrane by raising cytosolic ATP levels (Fig. 8, A and B in Ref. 28). However, the simulations presented here, which are in line with experiment, show that activation of PDH is nearly maximal at the glucose threshold for bursting (Fig. 4). Thus, above ~5-7 mM D-glucose, elevation of cytosolic Ca2+ by voltage-gated influx through the plasma membrane strongly inhibits ATP synthesis, as shown in Fig. 7. At intermediate glucose concentrations (~5-16 mM), this inhibition is strongly coupled to activation of the KATP channel and produces bursts of electrical activity in the plasma membrane. As shown in Figs. 9-12, bursting leads to oscillations in mitochondrial respiration, mitochondrial synthesis, and transport of ATP, as well as significant changes in [Ca2+]m, all of which are coupled to voltage-gated Ca2+ influx into the beta -cell.

Recent experiments on adrenal chromaffin cells (1) have used voltage-gated pulses of Ca2+ influx to assess Ca2+ entry into mitochondria. When [Ca2+]i is transiently raised to the order of 1.0 µM, those experiments show that sequestration of Ca2+ by the uniporter is complete within <1 s, whereas release occurs over the course of 1-2 min. Although the maximal rate of the uniporter is a factor of 80 greater than that of Na+/Ca2+ exchange in our simulations (28), it is not true during bursting that uptake into the mitochondria is significantly faster than efflux. Figure 12C, for example, shows that Ca2+ uptake during the active phase (average [Ca2+]i of 0.35 µM) is only a factor of 2 faster than that in the silent phase (average [Ca2+]i of 0.2 µM) and that both rates are on the order of a few hundredths micromolar per second. The reason for this difference is easily explained by the allosteric regulation of the uniporter (51). Indeed, in experiments and in our simulations (28), the rate of the uniporter is decreased by a factor of 20-30 when [Ca2+]i is decreased from 1.0 to 0.4 µM at physiological values of Delta Psi .

In the bursting regime the dominant currents into the mitochondria are the F1F0-ATPase proton current and the inward current due to the adenine nucleotide translocator. These are almost completely balanced by the outward proton current associated with respiration, as shown in Fig. 8. The balance of these three currents, which dominate those due to Ca2+ influx and efflux, provide the mechanism for regulation of ATP synthesis by Ca2+ uptake. Indeed, relatively small changes in the inward current (on the order of 5% of that of the F1F0ATPase current) lead to changes in the ATP/ADP ratio that are on the order of 10%. As shown previously (28), these changes are sufficient to trigger bursting electrical activity.

The small, but steady, futile cycling of [Ca2+]m gives rise to steady, low values of [Ca2+]m (~0.1 µM) at low glucose concentrations. This steady behavior is replaced in the bursting regime by oscillations of Ca2+ uptake and release. According to the simulations in Fig. 12C, the maximum value of [Ca2+]m during a burst occurs at the end of the active phase, whereas the minimum occurs at the end of the silent phase. The simulations also predict an amplitude for oscillations in [Ca2+]m on the order of 0.4-0.6 µM, large enough to be detected by current experimental techniques (1). The existence of mitochondrial Ca2+ oscillations of this magnitude and their phase relationship with electrical activity are a robust prediction of the simulations.

A conclusive experimental confirmation of the results of our simulations would require the observation of mitochondrial Ca2+ oscillations that are in phase with oscillations in the conductance of the KATP current (28). Although evidence of the latter has been obtained in clusters of beta -cells from ob/ob mice (22), we are unaware of attempts to measure [Ca2+]m in beta -cells under bursting conditions. We hope that the simulations presented here will encourage such measurements.

    ACKNOWLEDGEMENTS

We thank Dr. A. Sherman for constructive criticism and careful reading of the manuscript.

    FOOTNOTES

This work was supported in part by National Science Fundation Grants BIR-9214381 and BIR-9300799, National Institutes of Health Grant R01-RR-10081, and the Agricultural Experiment Station of the University of California, Davis.

Address for reprint requests: J. Keizer, Institute of Theoretical Dynamics, University of California, Davis, CA 95616.

Received 30 June 1997; accepted in final form 15 December 1997.

    REFERENCES
Top
Abstract
Introduction
Discussion
References

1.   Babcock, D. F., J. Herrington, P. C. Goodwin, Y. B. Park, and B. Hille. Mitochondrial participation in the intracellular Ca2+ network. J. Cell. Biol. 136: 833-844, 1997[Abstract/Free Full Text].

2.   Brawand, F., G. Folly, and P. Walter. Relation between extra- and intramitochondrial ATP/ADP ratios in rat liver mitochondria. Biochim. Biophys. Acta 590: 285-289, 1980[Medline].

3.   Coll, K., S. Joseph, B. Corkey, and J. Williamson. Determination of the matrix free Ca2+ concentration and kinetics of Ca2+ efflux in liver and heart mitochondria. J. Biol. Chem. 257: 8696-8704, 1982[Free Full Text].

4.   Denton, R., and J. McCormack. On the role of the calcium transport cycle in heart and other mammalian mitochondria. FEBS Lett. 119: 1-8, 1980[Medline].

5.   Denton, R., and J. McCormack. Ca2+ transport by mammalian mitochondria and its role in hormone action. Am. J. Physiol. 249 (Endocrinol. Metab. 12): E543-E554, 1985[Abstract/Free Full Text].

6.   Denton, R., J. McCormack, and N. Edgell. Role of calcium ions in the regulation of intramitochondrial metabolism. Biochem. J. 190: 107-117, 1980[Medline].

7.   Duchen, M., P. Smith, and F. Ashcroft. Substrate-dependent changes in mitochondrial function, intracellular free calcium concentration and membrane channels in pancreatic beta -cells. Biochem. J. 294: 35-42, 1993[Medline].

8.   Erecinska, M., and D. Wilson. Regulation of cellular energy metabolism. J. Membr. Biol. 70: 1-14, 1982[Medline].

9.   Friel, D., and R. W. Tsien. An FCCP-sensitive Ca2+ store in bullfrog sympathetic neurons and its participation in stimulus-invoked changes in [Ca2+]i. J. Neurosci. 14: 4007-4024, 1994[Abstract].

10.   Gunter, T., K. Gunter, S.-S. Sheu, and C. Gavin. Mitochondrial calcium transport: physiological and pathological relevance. Am. J. Physiol. 267 (Cell Physiol. 36): C313-C339, 1994[Abstract/Free Full Text].

11.   Hajnòczky, G., L. D. Robb-Gaspers, M. B. Seitz, and A. Thomas. Decoding of cytosolic calcium oscillations in the mitochondria. Cell 82: 415-424, 1995[Medline].

12.   Hehl, S., A. Golard, and B. Hille. Involvement of mitochondria in intracellular calcium sequestration by rat gonadotrophes. Cell Calcium 20: 515-524, 1996[Medline].

13.   Heldt, H., M. Klingenberg, and M. Milovancev. Differences between the ATP/ADP ratios in the mitochondrial matrix and in the extramitochondrial space. Eur. J. Biochem. 30: 434-440, 1972[Medline].

14.   Herrington, J., Y. B. Park, D. F. Babcock, and B. Hille. Dominant role of mitochondria in clearance of large Ca2+ loads from rat adrenal chromaffin cells. Neuron 16: 219-228, 1996[Medline].

15.   Hoth, M., C. M. Fanger, and R. S. Lewis. Mitochondrial regulation of store-operated calcium signaling in T lymphocytes. J. Cell Biol. 137: 633-648, 1997[Abstract/Free Full Text].

16.   Hutton, J., and W. Malaisse. Dynamics of O2 consumption in rat pancreatic islets. Diabetologia 18: 395-405, 1980[Medline].

17.   Hutton, J., A. Sener, A. Herchuelz, I. Atwater, S. Kawazu, A. Boschero, G. Somers, G. Devis, and W. Malaisse. Similarities in the stimulus-secretion coupling mechanisms of glucose- and 2-keto acid-induced insulin release. Endocrinology 106: 203-219, 1980[Abstract].

18.   Jouaville, L. S., F. Ichas, E. L. Holmuhamedov, P. Camacho, and J. D. Lechleiter. Synchronization of calcium waves by mitochondrial substrates in Xenopus laevis oocytes. Nature 377: 348-351, 1995[Medline].

19.   Kaplan, R., and P. Pedersen. Characterization of phosphate efflux pathways in rat liver mitochondria. Biochem. J. 212: 279-288, 1983[Medline].

20.   Keizer, J., and G. Magnus. The ATP-sensitive potassium channel and bursting in the pancreatic beta cell. A theoretical study. Biophys. J. 56: 229-242, 1989[Abstract].

21.   LaNoue, K., F. Jeffries, and G. Radda. Kinetic control of mitochondrial ATP synthesis. Biochemistry 25: 7667-7675, 1986[Medline].

22.   Larsson, O., H. Kindmark, R. Bränström, B. Fredholm, and P.-O. Berggren. Oscillations in KATP channel activity promote oscillation in cytoplasmic free Ca2+ concentration in the pancreatic beta  cell. Proc. Natl. Acad. Sci. USA 93: 5161-5165, 1996[Abstract/Free Full Text].

23.   Letko, G., U. Küster, J. Duszynski, and W. Kunz. Investigation of the dependence of the intramitochondrial [ATP]/[ADP] ratio on the respiration rate. Biochim. Biophys. Acta 593: 196-203, 1980[Medline].

24.   MacDonald, M. High content of mitochondrial glycerol-3-phosphate dehydrogenase in pancreatic islets and its inhibition by diazoxide. J. Biol. Chem. 256: 8287-8290, 1981[Abstract/Free Full Text].

25.   MacDonald, M. Evidence for the malate aspartate shuttle in pancreatic islets. Arch. Biochem. Biophys. 213: 643-649, 1982[Medline].

26.   Magnus, G. A Mitochondria-Based Model for Bursting and Its D-Glucose Dependence in the Pancreatic Beta Cell (PhD thesis). Davis: University of California, 1995.

27.   Magnus, G., and J. Keizer. Minimal model of beta -cell Ca2+ handling. Am. J. Physiol. 273 (Cell Physiol. 42): C717-C733, 1997[Abstract/Free Full Text].

28.   Magnus, G., and J. Keizer. Model of beta -cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables. Am. J. Physiol. 274 (Cell Physiol. 43): C1158-C1173, 1998[Abstract/Free Full Text].

29.   Malaisse, W., J. Hutton, S. Kawazu, A. Herchuelz, I. Valverde, and A. Sener. The stimulus-secretion coupling of glucose-induced insulin release. XXXV. The links between metabolic and cationic events. Diabetologia 16: 331-341, 1979[Medline].

30.   Malaisse, W., F. Malaisse-Lagae, and A. Sener. Coupling factors in nutrient-induced insulin release. Experientia 40: 1035-1043, 1984[Medline].

31.   Malaisse, W., and A. Sener. Glucose-induced changes in cytosolic ATP content in pancreatic islets. Biochim. Biophys. Acta 927: 190-195, 1987[Medline].

32.   Malaisse, W., A. Sener, A. Herchuelz, and J. Hutton. Insulin release: the fuel hypothesis. Metabolism 28: 373-386, 1979[Medline].

33.   Matschinsky, F., A. Ghosh, M. Meglasson, M. Prentki, V. June, and D. von Allman. Metabolic concomitants in pure, pancreatic beta cells during glucose-stimulated insulin secretion. J. Biol. Chem. 261: 14057-14061, 1986[Abstract/Free Full Text].

34.   McCormack, J., E. Longo, and B. Corkey. Glucose-induced activation of pyruvate dehydrogenase in isolated rat pancreatic islets. Biochem. J. 267: 527-530, 1990[Medline].

35.   Miyata, H., H. Silaverman, S. Sollott, E. Lakatta, M. Stern, and R. Hansford. Measurement of mitochondrial free Ca2+ concentration in living single rat cardiac myocytes. Am. J. Physiol. 261 (Heart Circ. Physiol. 30): H1123-H1134, 1991[Abstract/Free Full Text].

36.   Moreno-Sánchez, R. Regulation of oxidative phosphorylation in mitochondria by external free Ca2+ concentrations. J. Biol. Chem. 260: 4028-4034, 1985[Abstract].

37.   Moreno-Sánchez, R., and R. Hansford. Dependence of cardiac mitochondrial pyruvate dehydrogenase activity on inramitochondrial free Ca2+ concentration. Biochem. J. 256: 403-412, 1988[Medline].

38.   Reers, M., R. Kelly, and T. Smith. Calcium and proton activities in rat cardiac mitochondria. Effect of matrix environment on behavior of fluorescent probes. Biochem. J. 257: 131-142, 1989[Medline].

39.   Rutter, G., J.-M. Theler, M. Murgia, C. Wollheim, T. Pozzan, and R. Rizzuto. Stimulated Ca2+ influx raises mitochondrial free Ca2+ to supramicromolar levels in a pancreatic beta -cell line. Possible role in glucose and agonist-induced insulin secretion. J. Biol. Chem. 268: 22385-22390, 1993[Abstract/Free Full Text].

40.   Schwenke, W., S. Soboll, H. Seitz, and H. Sies. Mitochondrial and cytosolic ATP/ADP ratios in rat liver in vivo. Biochem. J. 200: 405-408, 1981[Medline].

41.   Sener, A., J. Rasschaert, and W. Malaisse. Hexose metabolism in pancreatic islets. Participation of Ca2+-sensitive 2-ketoglutarate dehydrogenase in the regulation of mitochondrial function. Biochim. Biophys. Acta 1019: 42-50, 1990[Medline].

42.   Siess, E., D. Brocks, H. Lattke, and O. Wieland. Effects of glucagon on metabolite compartmentation in isolated rat liver cells during gluconeogenesis from lactate. Biochem. J. 166: 225-235, 1977[Medline].

43.   Siess, E., and O. Wieland. Phosphorylation state of cytosolic and mitochondrial adenine nucleotides and of pyruvate dehydrogenase in isolated rat liver cells. Biochem. J. 156: 91-102, 1976[Medline].

44.   Simpson, P. B., and J. T. Russell. Mitochondria support inositol 1,4,5-trisphosphate-mediated Ca2+ waves in cultured oligodendrocytes. J. Biol. Chem. 271: 33493-33501, 1996[Abstract/Free Full Text].

45.   Soboll, S., R. Scholz, and H. Heldt. Subcellular metabolic concentrations. Dependence of mitochondrial and cytosolic ATP systems on the metabolic state of perfused rat liver. Eur. J. Biochem. 87: 377-390, 1978[Abstract].

46.   Soboll, S., H. Seitz, H. Sies, B. Ziegler, and R. Scholz. Effect of long-chain fatty acyl-CoA on mitochondrial and cytosolic ATP/ADP ratios in the intact liver cell. Biochem. J. 220: 371-376, 1984[Medline].

47.   Stucki, J., and P. Walter. Pyruvate metabolism in mitochondria from rat liver. Measured and computer-simulated fluxes. Eur. J. Biochem. 30: 60-72, 1972[Medline].

48.   Tzagoloff, A. Mitochondria. New York: Plenum, 1982, p. 62-180.

49.   Wan, B., K. LaNoue, J. Cheung, and R. Scaduto, Jr. Regulation of citric acid cycle by calcium. J. Biol. Chem. 264: 13430-13439, 1989[Abstract/Free Full Text].

50.   Wilson, D., C. Owen, L. Mela, and L. Weiner. Control of mitochondrial respiration by the phosphate potential. Biochem. Biophys. Res. Commun. 53: 326-333, 1973[Medline].

51.   Wingrove, D., J. Amatruda, and T. Gunter. Glucagon effects on the membrane potential and calcium uptake rate of rat liver mitochondria. J. Biol. Chem. 259: 9390-9394, 1984[Abstract/Free Full Text].


AJP Cell Physiol 274(4):C1174-C1184
0363-6143/98 $5.00 Copyright © 1998 the American Physiological Society