Chapter 28
What drives calcium oscillations in beta-cells? New tasks for cyclic analysis
Leonid E Fridlyand, Louis H. Philipson
Abstract
Insulin secretion is initiated by metabolism-dependent depolarization of the plasma membrane and
regulated in part by oscillations of the plasma membrane potential, which drive oscillations of
cytosolic calcium. Mathematical models have been useful to help understand the key factors
underlying these phenomena. Modeling approaches show that candidates for a pacemaker
underlying the membrane potential bursts and cytosolic Ca2+ oscillations include cyclic changes in
the ratio of ATP to ADP, Ca2+ concentration in the endoplasmic reticulum or cytosolic Na+
concentration. However, additional experiments to evaluate the dynamics of integrated signaling
systems with cyclic analysis using mathematical models is necessary to better understand this
emerging aspect of β-cell physiology.
Key words: beta cell, electrophysiology, calcium, computing modeling, diabetes, oscillations
28.1 Introduction
Insulin secretion from the pancreatic -cell induced by physiological secretagogues,
primarily glucose, is mediated by an elevated cytosolic free calcium concentration ([Ca2+]c). The
metabolism of glucose raises the ratio of ATP to ADP, closing the ATP-sensitive K+ (KATP)
channels. Closure of these channels leads to plasma membrane (PM) depolarization up to a
The University of Chicago, Dept. of Medicine, MC 1027,
5841 S. Maryland Ave., Chicago, IL 60637.
E-mail: lfridlia@medicine.bsd.uchicago.edu, l-philipson@uchicago.edu
1
threshold potential where voltage-dependent Ca2+ channels (VDCC) located on the PM are
activated. Ca2+ influx through VDCCs leads to an increased [Ca2+]c, which triggers the exocytosis
of insulin-containing granules. There is an extensive literature describing β-cell electrical activity
and its relationship to intracellular Ca2+ concentration in intact islets of Langerhans and isolated
islet cells (for recent review see Jacobson and Philipson 2008; Henquin et al. 2009). Mechanisms
of glucose-induced PM depolarization, cytosolic and mitochondrial processes were also considered
in previous chapters.
The β-cell membrane is hyperpolarized at resting potential at low glucose levels ( 3–5 mM)
in islets. When glucose metabolism induces an increased potential across the membrane, a
resultant electrical activity of the pancreatic -cell is usually organized into slow depolarizing
waves, called bursting, with a plateau from which action potentials (AP) rapidly fire. They are
separated by quiescent (resting) periods at potentials below the AP threshold. This bursting
phenomenon regenerates as long as the glucose concentration is elevated and results from the
metabolic processes and electrical activity of ion channels and pumps localized on the β-cell plama
membrane (Ashcroft and Rorsman 1989, Jacobson and Philipson 2008).
Rapid depolarization at the beginning of the burst and a repolarization at the end result in
opening and closing of VDCCs. This leads to cytosolic Ca2+ oscillations which are synchronized
with cyclical spike-burst activity in response to a rise in extracellular glucose (Jacobson and
Philipson 2008, Henquin et al. 2009). These Ca2+ oscillations are intimately connected to multiple
key aspects of β-cell physiology and their regulation continues to be an important area of study.
Increased glucose concentration induces several types of cyclical spike-burst activity and
Ca2+ oscillations in insulin secreting -cells with different periods (Beauvois et al. 2006, Bertram
et al. 2008, Henquin et al. 2009). Oscillations with a period from several seconds to one minute are
usually denoted as “fast.” Ca2+ oscillations with a period ranging from 1 to several minutes and
long bursts are designated as “slow”. Mixed (or compound) Ca2+ oscillations are characterized by
fast oscillations superimposed on slow oscillations. This is due to periodic episodes of fast bursts,
called compound bursting (Bertram et al. 2004, Beauvois et al. 2006).
Fast electrical bursting and cytoplasmic Ca2+ oscillations are usually observed in isolated
mouse islets. Slow and mixed cytoplasmic Ca2+ oscillations are observed both in islets, single cells
and clusters of cells at stimulating glucose concentrations (Gilon et al. 2002, Bertram et al. 2004,
Beauvois et al. 2006).
2
Various experimental and theoretical approaches support the idea that the AP bursts, when
spike activity occurs, and the corresponding [Ca2+]c oscillations reflect a periodic depolarization of
the plasma membrane (Ashcroft and Rorsman 1989, Beauvois et al. 2006, Fridlyand et al. 2009). A
depolarizing component predominates at the beginning of the burst, but the resultant influx of Ca2+
during the burst leads to a progressive increase in outward and/or a decrease in inward cation
currents leading to repolarization and burst termination. Slow depolarization in a resting (silent)
phase should lead to burst re-initiation (Ashcroft and Rorsman 1989, Fridlyand et al. 2009,
Henquin et al. 2009).
After the large depolarizing effect of closing KATP channels, the subsequent generation and
termination of the bursts may be determined by small cyclical changes of any plasma membrane
current (Fridlyand et al. 2009). For this reason, initiation and termination of the bursts results from
activation and deactivation of several electrogenic channels, pumps or exchangers which can be
modulated in turn by numerous intracellular components. A variety of different proposals and
corresponding mathematical models have been advanced underlining the nature of these
components.
In this chapter we discuss an analysis of the proposals to explain these phenomena, together
with the underlying experimental data and the corresponding mathematical models. Bertram and
Sherman (2005) have written a historical review on the development of mathematical modeling of
β–cell oscillatory processes. For this reason we concentrated on recent developments in this field
and new experimental evidence with the goal of understanding how bursting and [Ca2+]c
oscillations can arise. Several illustrative examples are presented below. We consider here only
models for individual β–cells that represent behavior of cells in electrically synchronized normal
islets. Models that treat the effect of electrical coupling can also be found (see for example
Benninger et al. 2008).
Bursting and [Ca2+]c oscillations are easily obtainable phenomenon in isolated mouse islets.
Oscillatory behavior can be changed by numerous hormones, small molecule agonists as well as
toxins. The study of the changes in bursting or [Ca2+]c oscillations could yield a flexible systematic
explanation for the action of different signaling molecules on pancreatic β-cells. However, this
important approach requires a comprehensive knowledge of the pacemaker mechanisms of these
oscillations.
3
Interestingly, the rhythmic variations in insulin secretion from islets are synchronized with
oscillations of the cytoplasmic Ca2+ concentration (Henquin et al. 2009, Tengholm and Gylfe
2009). Whereas pulsatility appears to be a natural function of islets both in vivo and in vitro, it has
been hypothesized that the disruptions in rhythmic function may be an early biomarker of islet
dysfunction leading to diabetes (Tengholm and Gylfe 2009). This emphasizes also the need for
careful study of these oscillatory processes.
28.2 Schematic model
The main components that we consider in this chapter as important for generation of bursting and
cytoplasmic Ca2+ oscillations are summarized in Fig. 28.1. The “complex model” of processes
(from Fridlyand et al. 2003) was used for the following simulations. 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 1”.
(Figure 28.1)
The differential equation describing time-dependent changes in the plasma membrane
potential (Vp) is the current balance equation:
dVp
 Cm   IVCa + ICapump + INaCa + ICRAC + INa + INaK + IKDr + IKCa + IKATP
dt
(28.1)
where Cm is the whole cell membrane capacitance. The plasma membrane currents are listed in
Figure 28.1.
Equations for [Ca2+]c dynamics can be also written as in our model (Fridlyand et al. (2003)):
d[Ca2+]c
IVCa + 2INaCa - 2 I Capump
Jout
  fi   Jer,p + 
dt
2 F Vi
Vi
+ ksg [Ca2+]c
(28.2)
where fi is the fraction of free Ca2+ in cytoplasm, F is Faraday’s constant, Vi is the effective
volume of the cytosolic compartment, Jer,p is flux into the endoplasmic reticulum (ER) through
4
SERCA pumps per cytosol volume, Jout is a Ca2+ leak current from the ER per whole cell and ksg is
a coefficient of the sequestration rate of [Ca2+]c.
The voltage-dependent Ca2+ channel conducts Ca2+ ions into the cell, which raises the
transmembrane voltage, Vp, whereas the K+ channel gates efflux of K+ and restores Vp to a low
level. The temporal interaction of the two channels is sufficient to explain the repetitive spiking
observed in β-cells (see Bertram and Sherman 2005, Fridlyand et al. 2009). However, an inclusion
of additional components was necessary to explain a burst behavior.
28.3 [Ca2+]c as the pacemaker component
Initially, a mechanism with a [Ca2+]c feedback effect was proposed to underlie generation of bursts
and [Ca2+]c oscillations. According to this hypothesis Ca2+ influx during the active phase would
cause a slow rise in [Ca2+]c, which activated Ca2+-activated K+ (KCa) channels (current IKCa in Eq.
28.1) that in turn repolarized the plasma membrane potential until a critical level was attained. This
would shut down the spiking and inactivate VDCCs, leading to a resting phase. A slow decrease in
[Ca2+]c levels in a resting period would lead to decreased current through KCa channels, reinitiating PM depolarization and of the start of a new burst. In this case a cyclical change in [Ca2+]c
is a candidate for an islet pacemaker for burst behavior and [Ca2+]c oscillations per se (Atwater and
al. 1979). For a description of mathematical models incorporating the cyclical activation and
deactivation of KCa channels by bursting-induced elevations in [Ca2+]c see Bertram and Sherman
(2005).
One problem with this hypothesis is that [Ca2+]c should increase slowly during a burst period
leading to a slow increase of current through KCa channels. However, subsequent Ca2+ imaging
data indicates that that the time scale of the [Ca2+]c change is short relative to the oscillation period.
For this and other reasons, this mechanism for [Ca2+]c oscillations was ruled out (see Bertram and
Sherman 2005).
28.4 Role [ATP]/[ADP] ratio as pacemaker
After the large inward currents of KATP channels are mostly inhibited following glucose
metabolism, their small remaining conductance is still comparable with the conductance of other
channels, exchangers and pumps (Smolen and Keizer 1992). KATP channel regulation can thus
participate in the subsequent generation and termination of the bursts. Cyclical changes in the KATP
5
channel conductance were proposed as a mechanism underlying oscillatory behavior of β-cells
(Smolen and Keizer 1992, Magnus and Keizer 1997, Rolland et al. 2002). One possibility is that
the [ATP] to [ADP] ratio slowly decreases when [Ca2+]c increases during a burst, leading to a slow
opening of the remainder KATP channels and PM repolarization. The opposite idea is that the
[ATP]/[ADP] ratio gradually increases during a silent phase, when [Ca2+]c decreases, leading to
further closure of KATP channels and plasma membrane depolarization. New bursts then are
initiated when the plasma membrane depolarizes up to the threshold level (Magnus and Keizer
1997, Rolland et al. 2002). Indeed, the [ATP]/[ADP] ratio drops when [Ca2+]c rises and increases
when [Ca2+]c falls (Detimary et al. 1998, Ainscow and Rutter 2002) indirectly supporting the
proposal that [Ca2+]c oscillations can therefore evoke oscillations in [ATP]/[ADP] ratio and KATP
channel conductance.
Several mathematical models underlining the mechanisms of the [ATP]/[ADP] ratio changes
and attendant [Ca2+]c oscillations were proposed, as follows. Empirical equations for [ATP]/[ADP]
ratio changes were introduced by Smolen and Keizer (1992). In this formulation the [ATP]/[ADP]
ratio decreases slowly with increased [Ca2+]c and increases with decreased [Ca2+]c in simulations
using their empirical equation. Periodic changes in the [ATP]/[ADP] ratio and the corresponding
KATP channel conductances, bursting and [Ca2+]c oscillations were simulated using this model.
Several mechanistic hypotheses underlying the mechanism of how [Ca2+]c effects the
[ATP]/[ADP] ratio were also proposed. A slow decrease in the [ATP]/[ADP] ratio with increased
[Ca2+]c during bursts can result from either stimulation of ATP hydrolysis or inhibition of ATP
production.
[Ca2+]c activated ATP-consumption. Ca2+ activates Ca2+ pumps on the plasma membrane and in
the endoplasmic reticulum (ER), as well as other intracellular reactions that use ATP. In these
cases increased [Ca2+]c can increase ATP consumption and decrease the [ATP]/[ADP] ratio. An
opposite process which increases the [ATP]/[ADP] ratio with decreased ATP consumption can
occur with decreased [Ca2+]c (Rolland et al. 2002, Fridlyand et al. 2003). We illustrate this
mechanism using a mathematical model (Fridlyand et al. 2003) that includes simulation of ATP
consumption due to the work of Ca2+ pumps in the plasma membrane and ER as well as Ca2+activated ATP consumption in some cytosolic processes. The simulated phase relations are
represented in Fig. 28.2 for the conditions when free ADP concentration in the cytoplasm (and the
corresponding [ATP]/[ADP] ratio) is the main slow pacemaker parameter in this complex model.
6
In this case a fast rise in [Ca2+]c during the active phase leads to increased Ca2+-activated ATP
consumption in the cytoplasm. Free ADP increases (and [ATP]/[ADP] ratio decreases) slowly,
opening KATP channels. This in turn leads to a slow IKATP increase and plasma membrane
repolarization, damping of potential spikes and then a corresponding decrease in [Ca2+]c. These
processes have opposite directions after decreased [Ca2+]c in the silent phase. KCa channels serve to
damp depolarization and terminate increased [Ca2+]c arising from the initial part of the active
phase.
(Figure 28.2)
[Ca2+]c supressed ATP-consumption. An earlier proposal suggested that the uptake of Ca2+ by β–
cell mitochondria suppressed the rate of production of ATP because Ca2+ decreased oxidative
phosphorylation resulting in an energy-dissipative effect. This proposal also leads to a decreased
[ATP]/[ADP] ratio with increased [Ca2+]c as in the first case. This allows the possibility of
simulating [Ca2+]c oscillations through the cyclical changes in [ATP]/[ADP] ratio (Magnus and
Keizer 1997). However, recent experimental data favors the opposite idea, as for example it was
pointed out that “the primary role of mitochondrial Ca2+ is the stimulation of oxidative
phosphorylation“ (Brookes et al. 2004).
Hypotheses have been proposed to explain the mechanism of [ATP]/[ADP] ratio oscillations
through glycolytic oscillations. This was suggested to occur by the positive feedback of the
glycolytic
enzyme
phosphofructokinase
product
(fructose
1,6-bisphosphate)
on
phosphofructokinase activity and subsequent depletion of substrate (Tornheim 1997).
Mathematical models were constructed based on this mechanism (Westermark and Lansner 2003,
Bertram et al. 2004).
However, an explanation of the slow [Ca2+]c oscillations on the basis of changes in KATP
channel conductivity involves difficulties. According to this mechanism the conductance of the
KATP channels should oscillate during bursting electrical activity following changes in the
[ATP]/[ADP] ratio. However, KATP channel blockers such as sulfonylurea, which result in
essentially complete IKATP block, do not stop bursting and slow Ca2+ oscillations. Sulfonylurea
drug can even induce Ca2+ oscillations (Miura et al. 1997, Roe et al. 1998). Existence of slow
[Ca2+]c oscillations was also found in a knock-out mouse lacking functional KATP channels (Dufer
7
et al. 2004, Ravier et al. 2009). These results argue against an important role for dynamic changes
in KATP channel conductivity and, consequently, in [ATP]/[ADP] ratios in the generation of slow
Ca2+ oscillations.
28.5 ER Ca2+ as a pacemaker component
The endoplasmic reticulum (ER) is a high-affinity and high-capacity organelle for calcium storage.
The β-cell ER sequesters Ca2+ when the cytosolic Ca2+ level is high and releases it when [Ca2+]c is
low. Ca2+ enters the ER via P-type ATPases (SERCA pumps, primarily SERCA2/3 in β-cells)
using ATP and exits through two ER Ca2+ channels: the inositol 1,4,5 triphosphate receptorchannels (IP3R) and the ryanodine receptor-channels (Fig. 28.1) (Gilon et al. 1999, Maechler et al.
1999, Tengholm et al. 1999, Arredouani et al. 2002).
The ER influences Ca2+ dynamics in many cell types. The ER can play an important role in
creating Ca2+ oscillations through activation of IP3R on ER membranes (Berridge et al. 2009).
Several mathematical models were made underlining this mechanism for different, usually
electrically unexcitable types of cells, resulting in Ca2+ oscillations if the inositol 1,4,5
triphosphate concentration is in the correct range (Shuster et al. 2002, Berridge et al. 2009).
However, β-cells are excitable cells and Ca2+ ion influx from the extracellular space through
VDCCs and pumping by PM Ca2+pumps, along with internal sequestration in ER stores, are the
principal regulators of cytoplasmic Ca2+ homeostasis in these cells (Arredouani et al. 2002,
Fridlyand et al. 2003).
In β-cells, depletion of intracellular Ca2+ stores activates a Ca2+-release activated current
(CRAC) which represents an inward cation current leading to depolarization that potentiates
glucose-induced Ca2+ influx through VDCCs (Worley et al. 1994, Bertram et al. 1995, Roe et al.
1998, Cruz-Cruz et al. 2005). This current represents Na+ influx through nonselective plasma
membrane cation channels, which have been described in insulin secreting β-cells (Roe et al. 1998,
Cruz-Cruz et al. 2005).
Several mathematical models simulate bursting and corresponding [Ca2+]c oscillations on the
basis of this effect. Empirical equations for activation of CRAC currents with decreased [Ca2+]ER
were introduced by Bertram et al. (1995) and Chay (1997). CRAC currents increased with a
decreased [Ca2+]ER and vice versa using these special empirical equations. Periodic changes of
8
[Ca2+]ER, bursting and [Ca2+]c oscillations were simulated in these models (see also Bertran and
Sherman 2005).
We have developed an equation where CRAC represents Na+ influx through some
nonselective cation channels which open with decreased [Ca2+]ER (Fridlyand et al. 2003). The
proposed mechanism is illustrated in Fig. 28.3. In this simulation a rapid [Ca2+]c increase at the
beginning of the active phase led to increased Ca2+ pumping into the ER and slow [Ca2+]ER
accumulation with corresponding closure of nonselective cation channels. This decreased inward
Na+ current through these channels resulted in PM repolarization, a termination of spiking and a
transition to a silent phase. [Ca2+]ER slowly decreases during a silent phase as a result of exit of
Ca2+ from ER, leading to increased of nonselective cation channel conductance, increased inward
Na+ current and PM depolarization. This resulted in subsequent activation of VDCC and a new
burst. In this case [Ca2+]ER is a slow pacemaker component in the mechanism for [Ca2+]c
oscillations.
(Figure 28.3)
However, an argument can be made against all [Ca2+]ER–dependent mechanisms for slow
[Ca2+]c oscillations, since it seems to be at odds with data demonstrating that slow oscillations can
persist in the presence of thapsigargin, the agent that blocks SERCA and empties the ER stores
(Arredouani et al. 2002, Fridlyand et al. 2003) or in a SERCA 3 knock-out mouse (Beauvois et al.
2006).
28.6 Intracellular [Na+] as a slow component in a pacemaker mechanism
Cytosolic Na+ concentration ([Na+]c) changes may play an important role in the generation of
slow Ca2+ oscillations in β-cells (Grapengiesser 1998, Fridlyand et al. 2003). Several components
can regulate Na+ dynamics in β-cells. The electrogenic Na+K+-ATPase extrudes three Na+ ions in
exchange for two K+ ions for each molecule of ATP hydrolyzed generating a net outward flow of
cations through the plasma membrane. This enzyme has high activity in all excitable cells,
including pancreatic β-cells, since it maintains the high K+ concentration in the cytoplasm (Owada
et al. 1999). Like most other cells, the β-cells are equipped with a Na+/Ca2+ exchanger, an
electrogenic transporter located on the PM that couples the exchange of 3Na+ for 1 Ca2+ (Gall et al.
9
1999). A change of cytoplasmic Na+ concentration ([Na+]c) will lead to changes in the inward and
outward currents and therefore in the PM potential.
We proposed a mechanism where [Na+]c is a dynamic pacemaker variable that can govern
bursts and slow [Ca2+]c oscillations even though KATP channels or CRAC do not change their
activity (Fridlyand et al. 2003). Fig. 28.4 illustrates the proposed mechanism using our
mathematical model that includes a description of Na+,K+-ATPase, Na+/Ca2+ exchanger and [Na+]c
dynamics. The following mechanism was responsible for bursting and Ca2+ oscillations: increased
[Ca2+]c during a burst period activates Na+ influx through Na+/Ca2+ exchangers. The resultant
increase in intracellular [Na+]c leads to a slow increase of outward current through electrogenic
Na+-K+ pumps (INaK in Figure 28.1) with corresponding plasma membrane repolarization, and reenters a silent phase. Decreased [Ca2+]c during a silent phase leads to a slow decrease in [Na+]c
because Na+ influx through Na+/Ca2+ exchanger decreases. This leads to a decrease of outward
current through electrogenic Na+-K+ pumps and then in turn to plasma membrane depolarization
and an activation of a burst. A correlation of the model simulations with experimental data shows
that the suggested mechanism with [Na+]c changes can explain bursting and slow [Ca2+]c
oscillations (Fridlyand et al. 2003). However, this mechanism of oscillations remains incompletely
studied.
(Figure 28.4)
28.7 Mechaninistic interactions and compound patterns of bursting and [Ca2+]c oscillations
Different [Ca2+]c oscillations can appear together in the compound (mixed) pattern (Beauvois
et al. 2005, Bertram et al. 2008). The fact that the fast and slow modes of oscillation can occur
together, as in the compound pattern, or separately, as in the fast and slow patterns, strongly argues
that they stem from distinct mechanisms. These mechanisms can be reciprocally linked and are
often co-occurring, but can also proceed largely independently of each other. Mixed oscillations
also occur in isolated cells, suggesting that this peculiar pattern does not result from the sum of
signals produced in distinct β-cells in islets (Gilon et al. 2002).
Modeling approaches show that the compound behavior can be simulated and favors a
scenario where two or more slow variables interact to produce complex oscillations. For example,
Bertram et al. (2004) simulated the fast oscillations by small variations in KATP conductance using
10
an empirical equation connecting the [ATP]/[ADP] ratio with [Ca2+]c changes, whereas the slow
[Ca2+]c oscillations were simulated as metabolic glycolytic oscillations. These two variables
interact to produce compound oscillations, consisting of episodes of bursts separated by long
periods of silence, or “accordion” oscillations, which consist of fast bursts with a slowly
modulated duty cycle. Similar behavior could be achieved by defining the slow and fast variables
in other ways (Bertram et al. 2008). For example, according to a recent mathematical model by
Diederichs (2008), slow [Ca2+]c oscillations in the compound pattern may be a result of a [Ca2+]ER
dependent mechanism while the KATP dependent mechanism may be responsible for fast [Ca2+]c
oscillations superimposed on the top of the slow oscillations.
28.8 Summary
The current mathematical models have great explanatory power. Modeling approaches show
that cyclic changes in [ATP]/[ADP] ratio, concentration of Ca2+ in endoplasmic reticulum or
cytoplasmic Na+ can be pacemakers for bursts and [Ca2+]c oscillations. However, some of the
experimental data are contradictory and often do not support the existing models. Many of the
mechanisms that can control β–cell electrical activity and Ca2+ handling have not been
characterized. A complete identification of physiological variables that drive bursting or Ca2+
oscillations in β-cells and the underlying mechanisms remains elusive. Additional dynamic
experiments and mathematical models are necessary to more fully understand this emerging aspect
of β-cell physiology.
Acknowledgments
This work was supported in part by the NIH (R01 DK48494 to L.H.P.) and by The University of
Chicago Diabetes Research and Training Center (P60 DK20595).
11
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List of abbreviations
AP, action potentials
[Ca2+]c, free calcium concentration
[Ca2+]ER, free calcium concentration in ER
CRAC, Ca2+ -release activated current
ER, endoplasmic reticulum
IP3R, inositol 1,4,5 triphosphate receptor-channels
KATP, ATP-sensitive K+ channels
KCa, Ca2+-activated K+ channels
PM, plasma membrane
VDCC, voltage-dependent Ca2+ channels
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Figure legends
Figure 28.1. General scheme of the main processes involved in bursting and intracellular
Ca2+ oscillations in pancreatic β-cells.
Top: plasma membrane currents: voltage-dependent Ca2+ current (IVCa), a calcium pump current
(ICapump), Na+/Ca2+ exchange current (INaCa), Ca2+ release-activated current (ICRAC); inward Na+
currents (INa); a sodium-potassium pump current (INaK), a delayed rectifying K+ current (IKDr), the
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, SERCA is a calcium pump
in the ER, Ca2+ leaks from ER through the IP3 receptor (IP3R). “ATP” is the free cytosolic form of
ATP, ADPf is the free cytosolic form of ADP. Signals originating from fuel metabolism increase
cytosolic calcium.
Figure 28.2. Slow ATP/ADP ratio changes as a pacemaker. Burst behavior and the oscillation
patterns are illustrated. It was simulated using model (Fridlyand et al. 2003) for conditions when
changes in ATP/ADP ratio and corresponding IKATP are main component determining the
membrane potential cyclic variations by setting: gmCRAN = 2. pS-1 mV, gmKATP = 70,000 pS, gmKCa =
150 pS, gmVCa = 1000 pS, kADP = 0.001 ms, kATP = 0.00002 ms, kATP,Ca = 0.00001 µM-1 ms-1, PCaER
= 0.05 µM-1ms, PIP3 = 0.0004 pl-1 ms, PNaK = 80 fA. All other parameters setting are as in (Fig.3
and Tables from Fridlyand et al. 2003). (a) Action potential (Vp), (b) IKATP, (c) free [ADP] and (d)
[Ca2+]c
Figure 28.3. Slow [Ca2+]ER changes as a pacemaker. Simulations were made as in Figure. 28.2.
Cyclic changes in [Ca2+]ER (and corresponding changes in ICRAN) is main slow parameter in
mechanism of Ca2+ oscillations by setting: gmCRAN = 0.85 pS-1 mV, gmKATP = 10,000 pS, gmVCa =
600 pS, kADP = 0.0003 ms, PNaK = 200 fA. (a) Action potential (Vp), (b) ICRAC, (c) [Ca2+]ER and (d)
[Ca2+]c.
Figure 28.4. Slow [Na+]c changes as a pacemaker. Typical computer simulations were made as in
Figure. 28.2. Slow bursting and the oscillation patterns of Ca2+ and Na+ are illustrated. Cyclic changes
in [Na+]c (and corresponding changes in INaK) is main slow parameter in mechanism of Ca2+
oscillations by setting: kADP = 0.0003 ms, Pleuk = 0.0004 pl-1 ms, PNaK = 1000 fA. All other parameters
setting are as in Fridlyand et al. (2003). (a) Action potential (Vp), (b) INaK, (c) free [Na+]c and (d)
[Ca2+]c.
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