Articles in PresS. Am J Physiol Endocrinol Metab (June 28, 2005). doi:10.1152/ajpendo.00595.2004
E-00595-2004.R1
Final Accepted Version
Adenine Nucleotide Regulation in Pancreatic Beta Cells:
Modeling of ATP/ADP - Ca2+ Interactions
Leonid E. Fridlyand, Li Ma, and Louis H. Philipson
Department of Medicine, University of Chicago, Chicago, IL 60637
Running head: Nucleotide regulation in beta cells
Correspondeng author: Louis H. Philipson, M.D., Ph.D.,
Dept of Medicine, MC-1027, The University of Chicago
5841 S. Maryland Ave, Chicago, IL 60637
Ph: 773-702-9180, fax: 773-702-2771
E-mail: [email protected]
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Copyright © 2005 by the American Physiological Society.
Abstract
Glucose metabolism stimulates insulin secretion in pancreatic beta cells. A consequence of
metabolism is an increase in the ratio of ATP to ADP ([ATP]/[ADP]) that contributes to
depolarization of the plasma membrane via inhibition of ATP-sensitive K+ (KATP) channels.
The subsequent activation of calcium channels and increased intracellular calcium leads to
insulin exocytosis. Here we evaluate new data and review the literature on nucleotide pool
regulation, to determine the utility and predictive value of a new mathematical model of ion and
metabolic flux regulation in beta cells. The model relates glucose consumption, nucleotide pool
concentration, respiration, Ca2+ flux, and KATP channel activity. The results support the
hypothesis that beta cells maintain a relatively high [ATP]/[ADP] value even in low glucose and
that dramatically decreased free ADP with only modestly increased ATP follows from glucose
metabolism. We suggest that the mechanism in beta cells that leads to this result can simply
involve keeping the total adenine nucleotide concentration unchanged during a glucose elevation,
if a high [ATP]/[ADP] ratio exits even at low glucose levels. Furthermore, modeling shows that
independent glucose-induced oscillations of intracellular calcium can lead to slow oscillations in
nucleotide concentrations, further predicting an influence of calcium flux on other metabolic
oscillations. The results demonstrate the utility of comprehensive mathematical modeling in
understanding the ramifications of potential defects in beta cell function in diabetes.
Keywords: insulin, islets, KATP, mathematical model, oscillations
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INTRODUCTION
Glucose metabolism leads to insulin secretion in pancreatic β-cells. A consequence of
metabolism is an increase in the ratio of ATP to ADP that contributes to depolarization of the
plasma membrane via inhibition of KATP channels. The subsequent activation of calcium
channels and increased intracellular calcium leads to insulin exocytosis (Fig.1, reviewed in Refs.
3, 17, 53, 63). Glucose rapidly equilibrates across the plasma membrane and is phosphorylated
by glucokinase, which determines metabolic flux through glycolysis and ATP production in
mitochondria. As a result, the concentrations of ATP and ADP reflect the increased concentration
of glucose. The β-cell plasma membrane (PM) contains ATP-sensitive K+ (KATP) channels. In
the absence of glucose, enough KATP channels are open to dictate a hyperpolarized resting
membrane potential (-60 mV) determined by outward K+ flux. In the presence of elevated
glucose, the increase in intracellular [ATP]/[ADP] closes the KATP channels, which in turn
results in depolarization of the plasma membrane. Once the membrane potential is more positive
than about -40 mV, Ca2+ channels open, allowing the influx of extracellular Ca2+. The resulting
rise in cytoplasmic Ca2+ concentration then triggers exocytosis of secretory granules containing
insulin, and insulin secretion can then be further augmented (66).
Changes in [ATP]/[ADP] connect metabolic flux with PM depolarization and Ca2+ flux.
However, the mechanisms of adenine nucleotide regulation and interrelationships with other
metabolic and ionic fluxes in pancreatic β–cells are incompletely understood. Adenine nucleotide
concentrations in pancreatic islets have been determined under a variety of conditions by
enzymatic techniques and high pressure liquid chromatography in cell extracts (25). However,
these measurements report their total intracellular level, whereas nucleotides are distributed
among various intracellular compartments (eg. cytosol, mitochondria, secretory granules), with
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different concentrations and kinetics (19, 41). The concentrations of adenine nucleotides (ATP in
particular) in the individual compartments can in principle be measured by targeted expression of
the ATP-dependent luminescent protein firefly luciferase (2, 50).
Exactly how KATP channels are regulated in vivo by adenine nucleotides is still
unresolved. When pancreatic β-cells are exposed to increasing concentrations of glucose the
activity of KATP channels decreases (3, 63). However, the ATP concentration required to cause
half-maximal inhibition of channel activity is ~10 µM in in vitro experiments. Since intracellular
[ATP] in β-cells is normally in the millimolar range, essentially no channel activity would occur
(63). The other problem is that in most investigations the effect of various substrates, including
those that markedly enhance insulin secretion (such as glucose) on ATP concentration is
relatively small (25, 62). Our studies also lead to this conclusion. Therefore, one might not
expect ATP to be a critical physiologic regulator of KATP channel activity (63).
On the other hand, intracellular free MgADP stimulates KATP channel activity, and it
has been suggested that ADP, or the ratio of ATP to ADP, is responsible for channel regulation
in vivo (3, 14, 44, 63). There have been few estimates of free MgADP in β-cells, but increasing
concentrations of glucose are associated with a decline in the concentration of free ADP in the
range that can inhibit KATP channel activity (29, 62). However, the specific regulatory
mechanisms for the nucleotides regulating KATP are still unclear.
Changes in [ATP]/[ADP] are tightly coupled to oscillations in intracellular free Ca2+
([Ca2+]i), oxygen and glucose consumption in pancreatic β-cells (2, 42). However, intermediate
glucose concentrations induce two main types of [Ca2+]i oscillations in pancreatic β-cells: fast,
where the period ranges from 10 to 30 seconds; and slow, with periods of several minutes (30,
32). Fast [Ca2+]i oscillations can follow very small changes in [ATP]i and other components, and
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they have been difficult to measure and interpret (26, 42). Slow oscillations most likely
constitute a physiological oscillatory pattern in β-cells that may constitute the framework for
pulsatile insulin release observed in vivo (30, 32). For this reason, here we focus only on the slow
oscillations in pancreatic β-cells.
Mathematical analysis of complex systems provides a quantitative framework within
which the control of individual processes, cellular fluxes and metabolite levels can be discussed.
Several mechanisms and corresponding mathematical models have been proposed to connect
changes in [Ca2+]i, with regulation in cytoplasmic [ATP]/[ADP] and metabolic oscillations.
However, the proposed models fall short of a comprehensive explanation of existing data (see
(26) and Discussion). We have recently developed a computational model of the β-cell where a
driving force for slow [Ca2+]i and [ATP]i oscillations is the periodic change in cytoplasmic Na+
concentration (26). Here, we have attempted to uncover the links between the changes in [Ca2+]i,
[ATP]/[ADP] ratio, KATP channel conductivity, respiration, and glucose consumption using a
refined model. The results support the idea that β-cells maintain a relatively high [ATP]/[ADP]
value even in low glucose and that dramatically decreased free ADP with only modestly
increased ATP follows from glucose metabolism. The model was employed to test hypotheses
for a pacemaker underlying high glucose-induced oscillations in intracellular calcium. We found
that these can lead to oscillations in nucleotide concentration, supporting a feedback of calcium
flux on other metabolic oscillations.
Methods and Model
Experimental procedures
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Recombinant baculovirus construction. Recombinant Baculoviruses Shuttle Vector
(pFB-IRES-GFP): The shuttle vector was derived from pFastBac1 (Life Technologies). Plasmid
DNA was digested with SnaBI and NotI to remove the baculovirus Polh promoter sequences and
subcloned with a 1977-nucliotide NsiI-NotI fragment from pIRES2-EGFP (Clontech). The
cytosolic firefly luciferase from plasmid pGL3 control (Promega) was cloned 2421-nucleotide
NheI-BamHI fragments into the pFB-IRES-GFP shuttle vector “Li Ma et al. in preparation”.
Recombinant baculovirus was preparated, amplified and titrated as described previously (47).
Transfection and cell culture. The islet and dispersed islet cells were isolated from
pancreata of 8-10 week-old C57BL/6J mice (The Jackson Laboratory, Bar Harbor, ME) using
collagenase digestion followed by discontinuous Ficoll gradient centrifugation. The islet cells
were dissociated using 0.25mg/ml trypsin. The cells were then plated on the glass cover slips,
incubated and transfected with baculovirus as described (47). GFP expression was determined
using fluorescence microscopy.
Measurement of intracellular ATP. Following transduction with the recombinant
baculovirus, the positive infected cells were visualized by GFP detection. The islet cells were
cultured at 2 mM glucose with DMEM for 2 hours, then incubated in KRB buffer (125 mM
NaCl, 5 mM KCl, 1 mM NaH3PO4, 1 mM MgSO4, 1 mM CaCl2, 500 µM luciferin (Molecular
Probes), 20 mM HEPES and 2mM glucose, pH 7.4) in 5 min. at 37°C. Cell luminescence was
measured in a luminometer. Results are expressed as mean +/- SE unless otherwise stated.
Model development
Glucose consumption. We propose in the present model that glucose phosphorylation by
glucokinase is the only limiting step in glucose consumption in pancreatic β-cells under
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physiological conditions (see 51, 54, 68). Glucose is phosphorylated in a sigmoidal fashion, so
the Hill equation was used to model this process. The MgATP dependence of this reaction could
be well fit to a Michaelis-Menten-type saturation equation (16). Therefore, we employed an
empirically derived rate expression for glucokinase from (16):
Jglu = Pglu
[MgATP]i

[MgATP]i + KmATP
[Glu]hgl

[Glu]hgl + KGhgl
(1)
where Jglu is the glucokinase reaction rate, [Glu] is extracellular D-glucose concentration, Pglu is
the maximum rate of glucose consumption; KmATP is the Michaelis-Menten constant, KG is the
half maximal glucose concentration, and hgl is the Hill coefficient.
The mean measured KG (at physiological glucose levels and MgATP concentration taken
from human β-cells) varies from: 6 mM (72), 8.17 mM (55), to 8.33 mM (16) and “hgl” extends
from 1.57 (55), 1.73 (72) to 1.8 (16). KmATP varies from 0.31 mM (16), 0.58 mM (55) to 0.63
mM (72). In our model the coefficient values were fit to lie inside these bounds (Table 1).
Reduced metabolic compounds and oxidative phosphorylation. To reduce the
complexity of terms we assume that the glucokinase reaction determines the glycolytic flux and
we employ a term for the total pool of intermediate metabolites available for oxidative
phosphorylation. Their lumped synthesis rate is determined by the rate of glucose
phosphorylation. ATP production determinates the consumption rate of these intermediate
metabolites. The total pool of these intermediate metabolites can be described with the kinetic
equation:
d[Re]i
 = KRe JGlu - JOP
dt
(2)
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where [Re]i is the concentration of the intermediate metabolites, KRe is the stoichiometric
coefficient for Re production from glucose, and JOP is the oxidative phosphorylation rate,
measured as the rate of ATP production. The concentration of Re is conveniently expressed in
ATP units, i.e. we assume that one ATP molecule is produced from one molecule of this
intermediate metabolite. Then KRe is determined by the quantity of ATP molecules that is
produced from one glucose molecule, that equals 31 according to present estimations (64).
Oxidative phosphorylation processes use two kinds of metabolic substrates for ATP
synthesis: the reduced equivalents such as NAD(P)H (or FADH2) and free cytosolic MgADP.
The dependence of oxidative phosphorylation (JOP) on free MgADP may be calculated using the
Hill equation (35, 49). Then, an empirical equation can be written, assuming the simplest linear
dependence of reaction rate on [Re]i:
JOP
[MgADPf]ihop
= POP [Re]i −−
KOPhop+ [MgADPf]ihop
(3)
where [MgADPf]i is concentration of free cytosolic MgADP, POP is the maximum rate of ATP
production, KOP is the activation rate constant, and hop is the Hill coefficient.
Recent experimental data suggest that mitochondrial Ca2+ stimulates the oxidative
phosphorylation (7). However, the data on the possible magnitude of this stimulation are
contradictory, because Ca2+ can also have energy-dissipative effects, decreasing oxidative
phosphorylation (15,51,52). The calculated ATP production rate increased by only 18%
following an increase in [Ca2+]i (from 0.02 to 0.6 µM) in a recent model of cardiac mitochondrial
energy metabolism (15). For this reason, we do not take into account effects of Ca2+ on the rate
of ATP production in our model.
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Expressed in terms of [MgADPf]i, the apparent Km of 20 µM was obtained in rat liver
mitochondria (8). A reasonable value for the Hill coefficient can be assumed to be in the range of
1.4 or higher, to establish a slightly sigmoidal activation characteristic (35, 49). In our model
these coefficients were fit as: KOP = 20 µM, and hop = 2. The maximum rate POP was fit to
simulate the observed pattern of [Ca2+]i oscillations (Table 1).
ATP and ADP homeostasis. Islets derive over 95% of their energy supply from
mitochondrial oxidative phosphorylation. The contribution from glycolysis is only about 2%
(25). For this reason the rate of oxidative phosphorylation (Eq. 3) can be used as the ATP
production rate. In ATP hydrolysis (as well as in the creatine kinase reaction) the relevant
reactants are Mg2+-complexes of the nucleotides. Since the overwhelming proportion of cellular
ATP exists as such a complex (over 90% in liver (13)), the error in approximating cytosolic
MgATP by total cytosolic ATP is not significant, and we consider cytoplasmic ATP
concentration to be the measure of MgATP in this article. The majority of ATP is in the free
form in the cytoplasm. However, in contrast to ATP, only a small fraction of total cellular ADP
is free (25, 70).
To account for the proposed critical role of ATPases in ATP consumption (see 20, 40,
67) we previously incorporated equations for ATP consumption by the PM and endoplasmic
reticulum Ca2+ pumps, and by the Na+, K+-ATPase (26). Our model also includes a Ca2+dependent ATP consumption term to account for utilization of ATP during insulin secretion (26).
Then, on the basis of the Eq. 3 for oxidative phosphorylation and Eq. 27 from ref. (26) we can
write the balance equation for [ATP]i:
d[ATP]i
INa,K + ICa,pump
Jer,p
 = JOP −  −  − kATP,Ca [Ca2+]i [ATP]i − kATP [ATP]i
dt
Vi F
2
(4)
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In this expression INa,K is a sodium-potassium pump current, ICa,pump is a PM calcium pump current,
Jer,p is the Ca2+ flux into the ER through Ca2+ pumps per cytosol volume, kATP,Ca is the rate constant
of ATP consumption that accelerates as [Ca2+]i increases, and kATP is the rate constant of sustained
ATP consumption. F is Faraday’s constant and Vi is the cytosol volume. The coefficients were fit as
previously (26). However, for better simulation of the observed pattern of [Ca2+]i oscillations we
increased kATP,Ca from 0.00005 to 0.00008 µM-1 ms-1 increasing the sensitivity of ATP consumption
from [Ca2+]i.
We added the balance equations for free ADP ([ADPf]i) and bound ADP ([ADPb]i) to the
previous model, where the terms of free ADP production correspond to the terms of ATP
consumption in Eq. 4, and the interaction between [ADPf]i and [ADPb]i was described by linear
flux exchange terms:
d[ADPf]i
INa,K + ICa,pump
Jer,p
 =  +  + kATP,Ca [Ca2+]i [ATP]i + kATP [ATP]i
dt
Vi F
2
(5)
+ kADPb [ADPb]i − JOP − kADPf[ADPf]i
d[ADPb]i
 = kADPf [ADPf]i − kADPb [ADPb]i
dt
(6)
where kADPf is the rate constant of ADPb production from ADPf, and kADPf is the rate constant of
ADPf production from ADPb.
The total concentration of ATP and ADP is kept constant during experimental
stimulation. Based on the experimental results by Ghosh et al. (29), we assume that the
concentration of free MgADP in pancreatic β-cells is 1/20 that of total cytosolic ADP. To
calculate [ADPf]i we set the free MgADP to 55% of total free ADP as estimated for rat
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hepatocytes (13). Then [ADPf]i = 1.82×[MgATPf]i, and it can be calculated from Eq. 6 that
kADPb/kADPf ≈ 0.1 in steady-state.
Several circumstances and reactions can determine the time to establish steady-state
concentrations of adenine nucleotide pools in β-cells. In particular, the creatine kinase reaction
can be important. However, according to calculations by Ronner at al. (62) the chemical
equilibrium in free ADP concentration resulting from the creatine kinase reaction is established
within 0.2 s in βHC9 insulin-secreting cells. While no information could be found regarding the
transition time between free and bound ADP and MgADP, this process is not catalytic, and is at
least diffusion-limited. It is unlikely to be fast relative to the creatine kinase reaction. We used
kADPb = 0.02 s-1 and kADPf = 0.2 s-1 as a reasonable estimation, where kADPb/kADPf = 0.1.
ATP-sensitive K+ channels. Free ATP inhibits, while free MgADP activates, KATP
channels (24). However, as discussed above in the Introduction, the regulation of KATP
channels in vivo is not clearly understood, and the current data are inadequate to create a detailed
mathematical model of KATP channel regulation. Therefore, we previously used (26) the draft
kinetic model (34) as modified (51, 52), where free ATP inhibits, while MgADP activates,
KATP channels. However, we unmasked this equation to clearly show the dependence of
channel opening on specific forms of nucleotides. After rearrangement the equation for the
whole cell conductance of KATP channels (Eq. 31 from (51)), can be represented as:
Po (1 + 2 [MgADPf]i /Kdd) + Pd ([MgADPf]i /Kdd)2
OKATP = 
(1 + [MgADPf]i /Kdd)2(1 + 0.45 [MgADPf]i /Ktd+ [ATPf]i /Ktt)
(7)
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where OKATP is the fraction of channels open, [ATPf]i concentration of free ATP in cytoplasm, Po
= 0.08, Pd = 0.89; Kdd, Ktd and Ktt are the respective coefficients representing the affinity of
components to the channels.
After taking into account the initial coefficient values from Hopkins at al. (28) and the
existence of different forms of adenine nucleotides (Table 2 from (51)) we were able to
recalculate the coefficients from the work by Magnus and Keizer (51) as: Kdd = 17 µM, Ktd = 26
µM, and Ktt = 20 µM (26). However, in this article Ktt, representing ATP affinity, was increased
from 20 µM to 50 µM. This was done to incorporate new data showing that phosphorylated
inositol compounds can decrease the sensitivity of KATP channels to ATP (3, 4, 24).
The simulated dependence of the open probability on the overall free concentrations of
both nucleotides in the physiological range of concentrations is shown in Figure 2. At
physiological ATP concentrations OKATP is small and does not depend sharply on [ATP]i. This is
consistent with the data on the weak dependence of OKATP on ATP (see introduction) and with
the evidence suggesting a large excess of KATP channels in β-cell. Therefore only a small part
of the whole KATP channel conductance takes part in the regulation of PM potential at any
physiological ATP level (12).
The simulated data in Fig. 2 correspond to experimental data showing that decreased free
ADP concentration in its physiological range can decrease the open probability of KATP
channels at constant ATP concentrations (34,39). In Eq. 7 we propose that a fall in [ADPf]i can
be the dominant regulator of the open probability of KATP with an increase in glucose levels as
suggested by biochemical studies (24). Recent data (see 3, 4, 24) show KATP channel regulation
is more complex than was proposed by Hopkins at al. (34). For this reason, Eq. 7 is only a useful
approximation of the experimental data.
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Computational aspects. The complete system consists of seven state variables that were
introduced in the previous model (26), and three new variables ([Re]i, [ADPf]i and [ADPb]i). In
total, ten differential equations describe their behavior, including Eq. 2 for [Re]i, Eq. 4 for
[ATP]i, Eq. 5 for [ADPf]i and Eq. 6 for [ADPb]i. Eq. 7 was used for OKATP. The units and
coefficients used in the model are for the most part similar to those used in ref. (26). New and
adjusted coefficients are shown in Table 1. The total concentration of intracellular nucleotides
([ATP]i + [ADPf]i + [ADPb]i) is kept constant during simulations, and it is taken as 4 mM (26).
For computational purposes we considered islets as an assemblage of the component β-cells with
similar properties, and performed computer simulations only for some mean individual cell (26).
Simulations were performed as noted previously using the same software environment (26). A
steady state is achieved with time during simulations, if no sustained oscillations emerge. This
model is available for direct simulation on the website “Virtual Cell” (www.nrcam.uchc.edu) in
“MathModel Database” on the “math workspace” in the library “Fridlyand” with name
“Chicago.2“.
RESULTS
Free ATP measurement. Using baculovirus transduction to express firefly luciferase we
estimated cytosolic free ATP in primary islet ß-cells by monitoring ATP-dependent luciferase
activity in living cells using photon detection (Fig. 3). We found that an increase in glucose
concentration from 2 mM to 14 mM caused only a 19.8 ±7.9% increase in free ATP levels.
Computer simulation. Computer simulation at low glucose concentration ([Glu] = 4.6
mM) with the coefficients from (26) and Table 1 leads to a steady-state [Ca2+]i of ~0.1 µM and
[ATP]i/[ADPtot]i ratio close to 3 (see left part of Fig. 4 and Table 2), where [ADPtot]i is the
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concentration of intracellular ADP ([ADPtot]i = [ADPf]i + [ADPb]i). The corresponding rate of
ATPi production (Jop = 0.218 mM s-1) was similar to that we reported previously for the
simulation of low glucose concentrations (26).
Simulations show slow [Ca2+] oscillations when glucose concentration is above a
threshold level of about 7 mM. A typical computer simulation with the patterns of membrane
potential, calculated concentrations and flux is shown in Fig. 4. As can be seen, a step increase of
[Glu] accelerates glucose uptake, increasing [Re]i and oxidative phosphorylation rate. This
slightly increases relative [ATP]i (about 20%) and sharply decreases [ADPf]i several fold. This
decreased KATP current, leads to depolarization of PM and, via opening of voltage-dependent
Ca2+ channels, to a rise in [Ca2+]i.
The simulations of slow oscillations correlate well with our previous model (see Fig. 3
and 5 from (26)), reliably simulating the basic characteristics of slow Ca2+ oscillations in
pancreatic β-cells. It was also possible to simulate the fast oscillations in this system similarly as
in ref (26) (by decreasing kIP from 0.3 s-1 to 0.1 s-1, not shown).
The simulated phase relations in metabolism during slow oscillations are also illustrated
in Fig. 4. [Ca2+]i elevation during the active phase of oscillations increases ATP consumption in
Ca2+ pumps (PM and ER) and in other reactions (Eq. 4), that increase ADP production. This
causes a small decrease in [ATP]i and a corresponding sharp increase in [ADPf]i. Opposite
processes occur with a [Ca2+]i decrease during oscillations.
The small oscillations in the glucokinase rate (Eq. 1) were secondary to the oscillations in
[ATP]i, since the external glucose concentration is fixed. For this reason the rate of glucose
consumption determined by glucokinase follows the [ATP]i changes (Fig.4.8), out of phase with
[Ca2+]i oscillations.
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Variations in the oxidative phosphorylation rate are determined primarily by the
[MgADPf]i changes (Eq. 3), and this rate increases with [Ca2+]i increase. Concentrations of Re
(Fig. 4.4) begin to decrease near the midpoint of the [Ca2+]i increase due to consumption of
intermediate metabolites for ATP production. As a result the oxidative phosphorylation rate is in
phase with [Ca2+]i oscillations (Fig. 4.7). However, the rate of oxidative phosphorylation
determines the oxygen consumption rate, if oxygen concentration is not limiting. For this reason,
oxygen consumption rate (the inverse of O2 concentration inside an islet) should be in phase with
[Ca2+]i oscillations.
The simulated steady-state [ATP]i and [ADPf]i shown in Fig. 5 (dotted lines) were
generated for different glucose levels. However, slow sustained oscillations of metabolic
parameters emerge beginning at 7 mM glucose, after which no steady-state solution is achieved.
On the other hand, several measurements of free ADP changes were made in rat pancreatic islets
(29, 67) and in β-cell lines (62), where Ca2+ oscillations do not occur or are not as uniform as in
mouse islets. Lack of Ca2+ oscillations in β-cell lines can be explained by decreased expression
of voltage-dependent Ca2+ channels (26). Incorporating this suggestion, steady-state solutions
were also obtained using a decreased Ca2+ channel conductance (gmVCa). This expands the
glucose concentration interval where adenine nucleotide changes can be simulated in steady-state
conditions (Fig.5, solid lines).
DISCUSSION
Regulation of ATP and ADP levels. In early studies ATP levels were determined in total
cell homogenates (cf. 25). However, ATP is concentrated in subcellular domains such as
mitochondria or vesicles (19, 41). Luciferase expression can be targeted to specific
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compartments to measure free ATP (2, 50). Here, we employed recombinant baculovirus to
express firefly luciferase in pancreatic β-cells, enabling estimation of cytoplasmic free [ATP] by
photon detection.
In one study with luciferase in single human β-cells the average increase in relative
intracellular free ATP, expressed in relative light output, was found to be 9% following a step
increase in glucose from 3 mmol/l to 15 mmol/l (2). A similar increase was also observed in
mouse islet β-cells following glucose challenge (2). In living INS-1 insulinoma cells ATPdependent luminescence was increased by a mean of 18% following a glucose step from 2.8 mM
to 12.8 mM (50) and 6% following a glucose step from 3 to 16 mM (1). Similarly, a modest
increase in free cytoplasmic ATP was found in intact rat islets following glucose challenge (1).
Our data are consistent with these measurements (Fig. 2) and lead to the conclusion that
intracellular free ATP concentration increases only modestly with increased glucose
concentration in pancreatic β-cells or islets. All these data are consistent with early evidence,
obtained using homogenized islets (20,25).
Measurements of free ADP by Ghosh et al. (29) indicate that in β-cell rich rat pancreatic
islet cores (with a background of 4 mmol/l amino acid), an increase of glucose from 4 to 8
mmol/l led to a decrease of free MgADP from ~ 44 to ~ 31 µM (pooled data from Table 5 of
work (29)) with no significant change in ATP concentration. Ronner et al. (62) found, for clonal
ßHC9 insulin-secreting cells, that increased glucose concentration was associated with an
exponential decline of the concentration of free ADP from about 50 µM at 0 mM glucose to
about 5 µM at 30 mM glucose, while the concentration of ATP remained nearly constant.
Detimary et al. (19) also concluded that glucose induces larger changes in the [ATP]/[ADP] ratio
16
in the cytoplasmic pool than in the whole cell, and that these changes are largely due to a fall in
ADP concentration.
Recently Sweet et al. (67), evaluated [ATP]i/([ADPf]i [Pi]) in response to glucose, using
measurement of cytochrome c redox state and oxygen consumption in perifused isolated rat
islets. They found this ratio increases up to 10-fold following a glucose step increase from 3 mM
to 20 mM. However, the [Pi] change was not studied. In other experiments the [Pi] change was
insignificant following glucose increase (29). The [Pi] decreased 2-fold following a glucose step
increase from 3 mM to 30 mM (Fig. 5 A from (21)). Even with a 2-fold decrease in [Pi], the 10fold increase of [ATP]i/([ADPf]i [Pi]) in response to glucose means that [ATP]i/[ADPf]i increases
5-fold.
Our simulations also show only a small relative increase in cytosolic ATP in response to
glucose stimulation with a significant fall in relative cytoplasmic [ADPf]i and an increase in
[ATP]i/[ADPtot]i (Fig. 4 and 5) that agrees closely with these published data. A small increase in
the ATP level following glucose stimulation could reflect the greater consumption of ATP by
pancreatic β-cells with increasing glucose concentrations (25). Our model reflects this behavior
where an increased ATP consumption occurs with glucose-induced [Ca2+]i increase (Eq. 4) along
with increased ATP production. However, the initial abrupt decrease of [ADPf]i and increase in
[ATP]i/[ADPtot]i following glucose stimulation in Fig. 4.6 and 5 requires clarification.
We assumed that the total adenine nucleotide concentration is constant during short-term
experiments. In this case, our model leads to a large relative decrease in [ADPtot]i (and
corresponding [ADPf]i and [MgADPf]i) in comparison with small relative [ATP]i increase with
increased glucose, if an initial [ATP]i /[ADPtot]i ratio is considerably more than one, even at low
glucose level. It is best explained in terms of a simple numerical example (following a brief
17
consideration by Sweet et al. (68)): For example, if [ATP]i /[ADPtot]i = 3 and [ATP]i + [ADPtot]i
= 4 mM for low glucose level in our model (Table 2), than [ATP]i = 3 mM and [ADPtot] = 1 mM.
If [ATP]i/[ADPtot]i = 9 for increased glucose and total adenine nucleotide concentration is kept
constant, then [ATP]i = 3.6 mM and [ADPtot]i = 0.4 mM. This means that [ATP]i increases by
only 20%, while [ADPtot]i (and [MgADPf]i ) decreases by 2.5 fold. This is a consequence of the
initial high ATP concentration that cannot be increased significantly if total adenine nucleotide
concentration is kept constant, while the relative ADP concentration may undergo a pronounced
decrease. In a contrasting example, if the concentrations of ATP and ADP are equal ([ATP]i
/[ADPtot]i = 1), then a 20% increase in [ATP]i corresponds to only a 20% decrease in [ADPtot]i.
Our calculations support the suggestion that was previously proposed (see for example
3,14,44,63,68), that decreased free ADP can indeed drive closure of KATP channels at increased
glucose concentrations, if [ATP]i in β-cells is kept nearly constant (however, we are not
addressing the exact KATP nucleotide binding constants here). This decrease in ADP
concentration is a specific property of β-cell stimulus-secretion coupling possibly shared with
other cell types that have a fuel sensing function. In contrast to β-cells, no increase in the
[ATP]/[ADP] value was found in purified rat α-cells following an increase in glucose
concentration (18). Also, muscle work during aerobic exercise leads to increased ADP
concentrations (49).
In addition, our analysis stimulated a search for mechanisms underlying the large
decrease in free ADP concentration when the relative ATP concentration increases only slightly,
which, apparently, has not been previously considered in the literature. We suggest that β-cells
can achieve this aim simply by keeping the total adenine nucleotide concentration unchanged
during a glucose elevation and having a high [ATP]i/[ADPtot]i ratio even at low glucose levels.
18
However, given the lack of appropriate methods to determine absolute values of both cytosolic
[ATP]i and [MgADPf]i or their ratio in real time in specific β-cell compartments this question
invites further investigation.
Mechanisms of metabolic oscillations. We also sought to identify pacemaker candidates
in the interrelationships between Ca2+ and [ATP]/[ADP] oscillations. Using our model we
evaluated three hypotheses relating β-cell calcium and metabolic oscillations. The first
hypothesis to consider is that slow [Ca2+]i oscillations are the driving force for metabolic
oscillations in pancreatic β-cells. Indeed, there are several theoretical studies and mathematical
models proposing that cytoplasmic Ca2+ oscillations can be created independently (9, 10, 28, 30,
31, 60, 65, 73) and thereafter they can stimulate metabolic oscillations (10, 30, 61). For example,
the oscillations of Ca2+ in endoplasmic reticulum could be the pacemaker of cytoplasmic Ca2+
oscillations (9, 28, 60, 73). We also suggested in our model that independent [Ca2+]i oscillations
can drive slow [ATP]/[ADP] ratio changes and corresponding metabolic oscillations in β-cell
(Fig.4, see also (26)). In this case slow [Ca2+]i oscillations can evoke IKATP oscillations through
oscillations in the [ATP] to [ADP] ratio as was proposed (61).
We have also found that essentially any model of independent slow Ca2+ oscillations (for
example: 9, 28, 31, 65, 73), when coupled with Eqs. 1-6, will lead to corresponding ATP, ADP
and metabolic oscillations. For this reason, our explanation of the processes that underlie
metabolic oscillation does not limit the use of this model to the generation of slow Ca2+
oscillations. The results from our modeling can be considered as a general characteristic of
metabolic oscillations when Ca2+ oscillations are a driving force and increased [Ca2+]i during
oscillations leads to increased ATP consumption.
19
Our model is in good agreement with recently published studies favoring this first
hypothesis. For example, simultaneous measurements of oxygen and glucose consumption, the
processes tightly coupled with adenine nucleotide regulation and [Ca2+]i during glucosestimulated oscillations, showed that glucose consumption rate was out of phase with slow [Ca2+]
oscillations (37). O2 consumption rate and [Ca2+]i changes were approximately in phase (37).
This means that increased [Ca2+]i during oscillations is accompanied by a decreased glucose
consumption rate and by an increased respiration rate. The mechanism of this phenomenon is as
yet unknown (42). However, these data are in accord with our model simulation (see Results,
Fig. 4), and could be explained by a decrease in ATP and an increase in free ADP concentrations
with [Ca2+]i increase during the appropriate phase of slow oscillations. However, [Ca2+]i and
changes in [ATP]i/[ADP]i ratio have not yet been measured simultaneously during oscillations.
In intact INS-1 insulinoma cells, citrate and ATP oscillations are in phase with each other
(48). Citrate changes can be evaluated in our model through a variation of the total pool of
intermediate metabolites (Re) that oscillates in phase with ATP (Fig. 4). This can be explained
by an increased consumption of the reduced molecules for oxidative phosphorylation in phase
with [Ca2+]i increases during oscillations (see Results).
Glucose-induced NAD(P)H and [Ca2+]i slow oscillations were measured simultaneously
in mouse pancreatic islets (46). It was found that these oscillations were nearly in phase although
NAD(P)H oscillations preceded those of calcium by about 0.1 of a period. In our model
NAD(P)H concentration is included as a component of the total pool Re, as is citrate. Similarly,
as is the case for citrate, such NAD(P)H oscillations ([Re]i changes in the model) are nearly in
phase with [Ca2+]i slightly preceding [Ca2+]i changes (see Fig. 4), also in reasonable
correspondence with the data.
20
The concept that slow metabolic oscillations could be driven by cytoplasmic Ca2+
oscillations has previously been dismissed based on the proposal that such a scenario would
contradict observations that increases in metabolism lead to Ca2+ influx and insulin secretion
(69). Indeed, the [ATP]/[ADP] ratio (11, 20), NADH levels (59), and respiration (25, 37) all
increase before an increase in [Ca2+]i following glucose stimulation. At first glance these data are
in contradiction with our suggestion.
However, as was pointed out by Kennedy et al. (42), creation of oscillations by changes
in metabolism does not prove that these metabolic variations are the real pacemaker of
oscillations. We have shown in Fig. 4 (left part) that our simulated glucose challenge leads at
first to a slow increase in [ATP]i, [Re]i and oxidative phosphorylation rate and to a decrease in
free ADP and [Na+]i before a creation of Ca2+ oscillations, i.e. this behavior corresponds to the
experimental data. However, these slow processes are necessary to depolarize the PM to the
threshold for calcium influx when slow Ca2+ oscillations emerge. Then the driving force for slow
[Ca2+]i oscillations is the periodic changes of some mediator (for example, cytoplasmic Na+
concentration in our model). Our calculations show clearly that during oscillations the opposite
changes in concentrations of some metabolites could occur compared with initial respond to
external stimulation. For example, ATP concentration decreases and free ADP concentration
increases with [Ca2+]i increase during oscillations (Fig. 4), i.e. this is opposite to the changes
during the initial glucose-induced [Ca2+]i increase. On the other hand, [Re]i increase is
accompanied by [Ca2+]i increase both during oscillations and after simulation of glucose increase
(Fig. 4.4). This shows clearly that data obtained by changing metabolism should be used with
care for interpretation of the oscillation processes.
21
In conclusion, our mathematical modeling shows that slow [Ca2+]i oscillations can be the
driving force for metabolic oscillations in pancreatic β-cells. We can also pointed out that
although the mechanisms underlying Ca2+ oscillations, which are independent of [ATP]/[ADP]
value changes, were considered in several mathematical models (9, 28, 65, 73), these did not
include a detailed analysis connecting metabolic changes with Ca2+ oscillations.
The second hypothesis suggests that some metabolic pathways serve as a pacemaker and
inherently oscillate to give rise to oscillations in [ATP]/[ADP], [Ca2+]i and respiration (5, 38, 58,
69). For example, oscillations in glycolysis could lead to [ATP]/[ADP] oscillations which
influence KATP channel conductance serving as a pacemaker of slow Ca2+ oscillations (6, 69,
71). This possibility was recently analyzed in detail using mathematical modeling (6, 71).
The third hypothesis assumes an interaction between the [ATP]i/[ADPf]i, [Ca2+]i and
KATP channels as the mechanism underlying oscillatory behavior of β-cells. Here [Ca2+]i
increase during the active phase leads to [ATP]i/[ADPtot]i decrease via [Ca2+]i-induced decreases
in ATP production (43, 51, 52) or by an increase in ATP consumption (2, 20, 56). In turn,
changes in [ATP]/[ADP] cause decreased KATP channel conductance leading to plasma
membrane repolarization and Ca2+ channel closing. [Ca2+]i decrease during a resting phase of
oscillations acts in the opposite direction, stimulating a new cycle. This mechanism can create
sustained Ca2+ oscillations (2, 20, 51, 52, 56).
However, in the most computationally developed model by Magnus and Kaizer (51,52),
that used this hypothesis, it was suggested “that the uptake of Ca2+ by β–cell mitochondria
suppressed the rate of production of ATP via oxidative phosphorylation” (51). Recent
experimental data contradict this conclusion, and favor the opposite, for e.g. in a recent review it
was pointed out that “the primary role of mitochondrial Ca2+ is the stimulation of oxidative
22
phosphorylation“ (7). Decreased oxidative phosphorylation following [Ca2+]i increase in the
model of Magnus and Kaiser (51, 52) leads directly to the conclusion that oxygen consumption
should decrease with increased [Ca2+]i during the active phase of oscillations if we incorporate
the experimental evidence that oxygen consumption accounts for the oxidative phosphorylation
rate in vivo. However, this conclusion seems contrary to the experimental evidence by Jung et al.
(37) considered above, that oxygen consumption increases with increased [Ca2+]i during slow
oscillations. Decreased ATP production with increased Ca2+ was also used in other model (6),
casting some doubt on the result of these simulations.
The second and third hypotheses above propose that regulation of KATP channel
conductance by [ATP]/[ADP] changes play a decisive role in driving slow Ca2+ oscillations.
However, KATP channel blockers such as tolbutamide can create slow bursting and Ca2+
oscillations at low glucose concentrations in pancreatic islets (33, 45), in single β-cells or β-cell
clusters isolated from mouse islets (23, 36), and in βTC3-neo cells (60). The existence of slow
Ca2+ oscillations was found in SUR1-/- knock-out mouse lacking functional KATP channels (22).
These results using KATP channel blockers and knock-out mouse models argue against a
important role of KATP channel conductivity in slow Ca2+oscillations. This contradicts the
second and third hypotheses, where Ca2+ oscillations can be created only if oscillations in
[ATP]/[ADP] lead to oscillations in conductance of KATP channels. This mechanism could not
work if KATP channels are blocked. Furthermore, stimulation of slow Ca2+oscillations by KATP
channel blockers at low glucose level is opposite to the proposal that oscillations in glycolysis
could lead to [ATP]/[ADP] oscillations which influence KATP channel conductance (second
hypothesis) since, apparently, these oscillations could not exist at low glucose levels (6, 71).
23
Because the second and third hypotheses cannot explain these critical experiments with KATP
channel blockers, we believe that they are incorrect and will not be further considered here.
However, it should be pointed out that mainly fast oscillations were considered in many
models (28, 51, 52, 56). According to Kanno et al. (40), KATP channel modulation could take
part in the creation of β-cell fast [Ca2+]i oscillations, which we do not consider in this article (see
Introduction). This means that appropriate simulation of fast metabolic and Ca2+ oscillations on
the basis of the second and third hypotheses is possible, however it is not taken into
consideration here.
In our model slow Ca2+ oscillations can be still simulated with considerable decrease in
KATP conductance that is accompanied by the corresponding shift of glucose level from which a
simulation of oscillations takes place to a region of lower glucose concentration. For example, 10
fold decrease of KATP conductance (from 24 to 2.4 nS) still permits us to simulate the slow Ca2+
oscillations at 8 mM glucose, however, the concentration of glucose from which these oscillation
could be created was shifted from 7 mM to 4.2 mM (not shown). These simulations correlate
well with experimental data on KATP channel blocker action described above. This effect is
possible in our model because KATP channels serve as a trigger of Ca2+ oscillations at their
closing not as a pacemaker. In this case, closing of KATP channels by specific blockers at low
glucose levels should create oscillations similar to that causing by increased glucose (as, for
example, we have demonstrated in experiments (60)).
Conclusion. By employing mouse β-cells expressing firefly luciferase we found that a
glucose challenge caused only about 20% increase in free ATP levels, confirming previous
measurements and highlighting the potential importance of free ADP in glucose signaling. The
integrated β-cell mathematical model we developed reproduces key experimental relationships
24
among ATP, ADP and cytoplasmic Ca2+ changes. Variations in steady-state concentrations after
glucose challenge are also in good agreement with published data. We used the model to test the
proposal that slow Ca2+ oscillations are the driving force of metabolic oscillations in pancreatic
β-cells. We found that considerable experimental data on oscillations in glucose consumption,
metabolites, mitochondrial respiration and ATP concentrations was also reflected in the
simulations from the mathematical model. This analysis supports the hypothesis that ATP and
particularly free ADP can be the critical regulators of glucose-stimulated calcium flux. Since
most ATP production (up to 95%) occurs in mitochondria, this view supports the recent
suggestion that subtle variation in mitochondrial function could underlie β-cell defects in Type 2
diabetes (57). The glucose-dependent changes in [ATP]/[ADP] levels could also underlie the
development of oxidative stress in pancreatic β-cells (27).
25
GRANTS
This work was partially supported by NIH grants DK48494, DK20595, DK44840
26
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Table 1. Standard parameter values added or changed in expanded model (see text for
explanations).
Symbol
Description
Value
Pglu
Maximum rate of glucose consumption
0.025 µM/ms
KmATP
Michaelis-Menten constant for ATP
500 µM
KG
Half-activation glucose level
7 mM
hgl
Hill coefficient (Eq. 1)
1.7
KRe
Stoichiometric coefficient (Eq. 2)
31
POP
Maximum rate of ATP production
0.0002 ms-1
KOP
Activation rate constant for free MgADP
20µM
hop
Hill coefficient (Eq. 3)
2
kATP,Ca
Rate constant of [Ca2+]i dependent ATP
0.00008 µM-1 ms-1
consumption (Eq. 4)
kADPf
Rate constant of ADPb production from
0.0002 ms-1
ADPf (Eq. 6)
kADPb
Rate constant of ADPf production from
0.00002 ms-1
ADPb (Eq. 6)
Ktt
Dissociation constant (Eq. 7)
50 µM
36
Table 2. PM potential and intracellular ion concentrations at steady-state
at the simulation of low glucose concentration (4.6 mM).
Symbol
Value
V
-57 mV
[Ca2+]i
0.107 µM
[Ca2+]ER
34.3 µM
[IP3]i
0.5 µM
[ATP]i
2985µM
[ADPf]i
92µM
[ADPb]i
923µM .
[Na+]i
7281µM
[Re]i
1261µM
n
0.00123
37
FIGURE LEGENDS
Fig. 1. Schematic diagram of currents and ion fluxes through the PM and endoplasmic reticulum
(ER) membrane, and the mechanisms of the adenine nucleotides regulation that have been
included in the whole β-cell model. Top: plasma membrane currents: voltage-dependent Ca2+
current (IVCa), a calcium pump current (ICa,pump), Na+/Ca2+ exchange current (INa,Ca), Ca2+ releaseactivated nonselective cation current (ICRAN); inward Na+ currents (INa); a sodium-potassium
pump current (INa,K), a delayed rectifying K+ current (IKDr), the voltage-independent small
conductance Ca2+-activated K+ current (IKCa), ATP-sensitive K+ current (IKATP). ksg is a
coefficient of the sequestration rate of Ca2+ by the secretory granules, Jer,p is an uptake of Ca2+
by ER, Jout is Ca2+ leak current from ER. IP3, inositol 1,4,5-trisphosphate. ATP is free cytosolic
form of ATP, ADPf is free cytosolic ADP and MgADP, ADPb is bound cytosolic ADP and
MgADP. Solid lines indicate flux of metabolic substrates, and dashed lines indicate inhibitory
effects of ATP and stimulatory influence of free ADP on KATP channel conductance.
Fig. 2. Simulated equilibrium fraction of open KATP channels (OKATP) calculated using Eq. 7
with respect to concentration of unbound cytosolic ADP ([ADPf]i) for various concentrations
cytosolic ATP ([ATP]i). (1) [ATP]i = 3000 µM, (2) [ATP]i = 4000 µM.
Fig. 3. Relative intracellular ATP measurements in mouse pancreatic β-cells. The photon output
is shown during incubation with 2 mM glucose and after transition to 14 mM glucose. Results
are average of three independent experiments. Data represent means ± SE.
Fig. 4. Glucose-induced slow electrical bursting and [Ca2+]i oscillations were simulated at a step
increase of the glucose concentration from 4.6 to 8 mM at arrow in (1) at initial concentration as
in Table 2; all other parameter setting are standard (Table 1, 2). PNaK was taken as 400 fA and
gmVCa as 670 pS. (1) [Ca2+]i; (2) Membrane potential; (3) [Na+]i; (4) [Re]i; (5) [ATP]i; (6)
38
[ADPf]i; (7) oxidative phosphorylation rate, (JOP, Eq. 3); (8) glucokinase reaction rate, (Jglu, Eq.
1).
Fig. 5. Steady-state simulation of [ATP]i (1) and (2) [ADPf]i vs. glucose concentration as
calculated using the full β-cell model. All other parameter setting are as in Fig. 4 (dotted lines).
For simulation of β–cell lines the voltage-dependent Ca2+ channel conductance was decreased
(gmVCa = 450 pS) (solid lines).
39
Ca2+o
Na+o

IVCa ICa,pump INa,Ca ICRAN INa
ksg
IP3
Ca2+i
Jout
Na
Jer,p
Ca2+ER
Endoplasmic
reticulum
+
INa,K
i
ADPf
ADPb
CYTOSOL
Figure 1
K+o

IKDr IKCa IKATP
K+i
ATP
glucose (Glu)
glucose
(+)
(–)
Glucokinase
Intermediate
metabolites (Re)
Oxidative
phosphorylation
OKATP (relative)
0.015
1
0.01
2
0.005
0
0
20
40
[ADPf]i (µM)
Figure 2
60
80
100
1000
Photon/Second
800
600
400
2mM
14 mM Glucose
200
0
0
5
10
Time (Minute)
Figure 3
15
20
3
4
5
6
7
8
[Re]i (µM) [Na+]i (mM) V (mV) [Ca2+]i (µM)
2
Jglu (µM/ms) JOP (µM/ms) [ADPf]i (µM) [ATP]i (mM)
1
1
0.5
0
0
–50
–100
10
4
10
5
0
4
3.5
3
100
50
0
1.0
0.5
0.
0.0125
0.0124
0.01
≈
≈
0.
0
100
200
300
Time (s)
Figure 4
400
500
200
(1), [ATP]i (µM)
1
2000
100
2
0
(2), [ADPf]i (µM)
4000
0
5
10
15
[Glu] (mM)
Figure 5
1