1 Institute of Theoretical Dynamics and 2 Section on Neurobiology, Physiology, and Behavior, University of California, Davis, California 95616
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ABSTRACT |
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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 -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 -cell; kinetic model
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INTRODUCTION |
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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 -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 (
),
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 -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.
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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.
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D-GLUCOSE DEPENDENCE OF RESPIRATION-RELATED VARIABLES |
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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
and briefly raise Jo.
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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.
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The steep, sigmoidal increase in dehydrogenase activation acts as a
switch for -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).
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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 -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 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.
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D-GLUCOSE DEPENDENCE OF ATP PRODUCTION |
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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 -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).
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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 H2PO4 = 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, -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 ).
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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.
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OSCILLATIONS OF MITOCHONDRIAL VARIABLES |
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Typical time series for the mitochondrial ionic currents and are
shown in Fig. 8. The oscillations of
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
as Ca2+ cycles through
the mitochondria, comparable results have been obtained with a
nonelectrogenic exchange mechanism (28).
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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 . This small depolarization of the
,
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
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 by matrix
Ca2+ cycling has less effect on the
F1F0-ATPase at the elevated
in Fig.
9B.
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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 for a
typical mitochondrial phosphorylation potential (Fig. 10). Notice that the slope of that curve
decreases as
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.
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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 . 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.
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OSCILLATIONS IN MITOCHONDRIAL CALCIUM CONCENTRATION AND THEIR D-GLUCOSE DEPENDENCE |
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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
-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 ).
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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 -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 -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 -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.
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DISCUSSION |
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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 -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
-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 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
-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 .
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 -cells from
ob/ob mice (22), we are unaware of attempts to measure
[Ca2+]m in
-cells under bursting
conditions. We hope that the simulations presented here will encourage
such measurements.
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ACKNOWLEDGEMENTS |
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We thank Dr. A. Sherman for constructive criticism and careful reading of the manuscript.
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FOOTNOTES |
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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.
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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
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
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
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 -cells.
Biochem. J.
294:
35-42,
1993[Medline].
8.
Ereciska, 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
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
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 cell.
Proc. Natl. Acad. Sci. USA
93:
5161-5165,
1996
23.
Letko, G.,
U. Küster,
J. Duszyski,
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
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 -cell Ca2+ handling.
Am. J. Physiol.
273 (Cell Physiol. 42):
C717-C733,
1997
28.
Magnus, G.,
and
J. Keizer.
Model of -cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables.
Am. J. Physiol.
274 (Cell Physiol. 43):
C1158-C1173,
1998
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
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
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 -cell line. Possible role in glucose and agonist-induced insulin secretion.
J. Biol. Chem.
268:
22385-22390,
1993
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
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
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