IP3-Mediated Ca2+ Release
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
Ca
2+
is a ubiquitous intracellular secondary messenger, and evidence from several different cell types suggests that an important mode of signalling is through oscillations rather than the maintenance of a steady state level. The oscillatory behaviour of inositol 1,4,5-triphosphate (IP3)-mediated Ca
2+
release has been modelled by Gary W. De Young and Joel Keizer. Their 1992 paper is referenced fully below.
A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca
2+
concentration
, Gary W. De Young and Joel Keizer, 1992,
Proc. Natl. Acad. Sci. USA
, 89, 9895-9899. (A
PDF
of the article is available to subscribers on the PNAS website.)
PubMed ID: 1329108
Several mechanisms have been proposed to explain oscillations of intracellular Ca
2+
concentration in cells. In this study, De Young and Keizer investigate the idea that a biphasic response of the IP3 receptor/channel to cytosolic Ca
2+
may alone be sufficient to induce Ca
2+
oscillations.
They constructed a simplified model of the IP3 receptor/channel by assuming that three equivalent and independent subunits are involved in Ca
2+
conduction. Each subunit has three binding sites: one for IP3, one for Ca
2+
activation, and one for Ca
2+
inactivation. Thus each subunit may exist in eight states with transitions governed by second-order (association) and first-order (dissociation) rate constants (see
below). All three subunits must be in the state S
110
(one IP3 and one activating Ca
2+
bound) for the channel to be open and conducting.
The raw CellML description of the IP3-mediated Ca
2+
release model can be downloaded in various formats as described in
.
A schematic diagram of the kinetics of an IP3 receptor/channel subunit
A schematic diagram of the kinetics of an IP
3
receptor/channel subunit.
$\frac{d \mathrm{x\_010}}{d \mathrm{time}}=\mathrm{V3}-\mathrm{V2}$
$\frac{d \mathrm{Ca\_i}}{d \mathrm{time}}=\mathrm{J1}-\mathrm{J2}\mathrm{J1}=\mathrm{c1}(\mathrm{v1}\mathrm{P\_open}+\mathrm{v2})(\mathrm{Ca\_ER}-\mathrm{Ca\_i})\mathrm{J2}=\frac{\mathrm{v3}\mathrm{Ca\_i}^{2.0}}{\mathrm{Ca\_i}^{2.0}+\mathrm{k3}^{2.0}}$
$\frac{d \mathrm{x\_001}}{d \mathrm{time}}=\mathrm{V1}-\mathrm{V4}$
$\frac{d \mathrm{x\_000}}{d \mathrm{time}}=-\mathrm{V1}-\mathrm{V3}$
$\mathrm{x\_011}=1.0-\mathrm{x\_000}+\mathrm{x\_001}+\mathrm{x\_010}$
$\mathrm{d1}=\mathrm{K\_d1}-\mathrm{IP3\_cold}$
$\mathrm{d2}=\frac{\mathrm{b2}}{\mathrm{a2}}$
$\mathrm{d3}=(\mathrm{K\_d2}-\mathrm{IP3\_cold})(1+\mathrm{d2})-\mathrm{d1}\mathrm{d2}$
$\mathrm{d4}=\frac{\mathrm{d1}\mathrm{d2}}{\mathrm{d3}}$
$\mathrm{d5}=\frac{\mathrm{b5}}{\mathrm{a5}}$
$\frac{d \mathrm{IP3}}{d \mathrm{time}}=\mathrm{v4}\frac{\mathrm{Ca\_i}-1.0\mathrm{k4}}{\mathrm{Ca\_i}+\mathrm{k4}}-\mathrm{Ir}\mathrm{IP3}$
$\mathrm{V1}=\mathrm{a4}(\mathrm{Ca\_i}\mathrm{x\_000}-\mathrm{d4}\mathrm{x\_001})\mathrm{V2}=\mathrm{a4}(\mathrm{Ca\_i}\mathrm{x\_010}-\mathrm{d4}\mathrm{x\_011})\mathrm{V3}=\mathrm{a5}(\mathrm{Ca\_i}\mathrm{x\_000}-\mathrm{d5}\mathrm{x\_010})\mathrm{V4}=\mathrm{a5}(\mathrm{Ca\_i}\mathrm{x\_001}-\mathrm{d5}\mathrm{x\_011})$
$\mathrm{P\_open}=\left(\frac{\mathrm{Ca\_i}\mathrm{IP3}\mathrm{d2}}{(\mathrm{Ca\_i}\mathrm{IP3}+\mathrm{IP3}\mathrm{d2}+\mathrm{d1}\mathrm{d2}+\mathrm{Ca\_i}\mathrm{d3})(\mathrm{Ca\_i}+\mathrm{d5})}\right)^{3.0}$
$\mathrm{Ca\_ER}=\frac{\mathrm{c0}-\mathrm{Ca\_i}}{\mathrm{c1}}$
$\mathrm{b1}=\mathrm{d1}\mathrm{a1}\mathrm{b3}=\mathrm{d3}\mathrm{a3}\mathrm{b4}=\mathrm{d4}\mathrm{a4}$
IP3 receptor dissociation constant
Proportion of IP3 receptor subunits with Ca inactivation site bound.
IP3 receptor binding constant
IP3 receptor binding constant
Time domain
Cytosolic free Ca concentration
IP3 receptor dissociation constant
Ca receptor dissociation constant (activation)
Ca receptor dissociation constant (inhibition)
Cytosolic free Ca concentration
Time domain
Proportion of IP3 receptor subunits with all receptors unbound.
Proportion of IP3 receptor subunits with Ca activation site bound.
Ca receptor binding constant (inhibition)
Proportion of IP3 receptor subunits with all receptors unbound.
Ca receptor binding constant (inhibition)
Ca concentration in the endoplasmic reticulum.
Volume ratio of endoplasmic reticulum and cytosol
Cytosolic free Ca concentration
Time domain
IP3 receptor dissociation constant
Proportion of IP3 receptor subunits with Ca activation and deactivation sites bound.
Proportion of IP3 receptor subunits with Ca activation and deactivation sites bound.
IP3 receptor binding constant
Proportion of IP3 receptor subunits with Ca inactivation site bound.
Concentration of IP3 in the cytosol.
Time domain
IP3 Ca channel
Flow of calcium from endoplasmic reticulum to cytosol across Ca-IP3 receptor.
Flow of calcium from endoplasmic reticulum to cytosol
Outward flux of Ca from Cytosol
Proportion of IP3 receptor subunits with Ca activation site bound.
De Young and Keize assumed that only the state S_110 (one IP3 and
one activating Ca2+ bound) contributes to the conductance and that
all three subunits must be in this state for the channel to be
open. Thus the open probability is proportional to x^3_110.
In their model, De Young and Keizer utilise the Ca2+ conservation
condition to calculate the concentration of calcium ions in the
endoplasmic reticulum (Ca_ER).
IP3 receptor/Ca channel open probability.
Proportion of IP3 receptor subunits with all receptors unbound.
Maximum rate of IP3 production.
https://models.physiomeproject.org/exposure/cd65a6e4500cb8fae8eb0725c1a2db57/deyoung_keizer_1992.cellml/view
Christopher Thompson
A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration
Change in free Ca concentration from Ca binding to unbound subunits and dissociation of Ca from bound inhibition receptor.
Activation constant for ATP-Ca pump
IP3 Ca channel
Flow of calcium from cytosol to endoplasmic reticulum across Ca-IP3 channel.
Flow of calcium from cytosol to endoplasmic reticulum
Cytosol intake of Ca
Ca receptor dissociation constant (activation)
Concentration of IP3 in the cytosol.
Time domain
Proportion of IP3 receptor subunits with Ca inactivation site bound.
Time domain
Max Ca channel flux
Ca receptor dissociation constant (activation)
IP3 loss rate constant
The De Young-Keizer 1992 model of oscillatory calcium release through
the IP3 stimulated channel
IP3 Receptor
The binding kinetics of IP3 and the activation of the receptor by Ca2+ are rapid, ensuring rapid release of Ca2+ after an IP3 pulse. This allows the number of receptor subunit states in the model to be reduced by four. We can eliminate the four receptor subunit states with IP3 bound (S_111, S_100, S_101, S_100). This leaves the reduced system outlined below.
De Young
A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration
Proceedings of the National Academy of Science, USA
calcium dynamics
electrophysiology
signal transduction
ip3 receptor
IP3 Receptor
Cytosolic free Ca concentration
The University of Auckland, Bioengineering Institute
The University of Auckland
The Bioengineering Research Group
Fixed link to diagram.
The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
The model runs in the PCEnv simulator and gives a nice curved output... But not the spiked output published in the original paper.
Ca concentration in the endoplasmic reticulum.
IP3 receptor/channel subunit with 3 unoccupied binding sites
Ca leak flux constant
Ca receptor dissociation constant (activation)
Ca receptor dissociation constant (activation)
Dissociation constant for Ca stimulation of IP3 production.
Ca2+ feedback on the production of inositol 1,4,5-triphosphate (IP3) is described by the equation below, where alpha has a value between 0 and 1.
Ca receptor binding constant (inhibition)
IP3 receptor/channel subunit with an occupied Ca2+ inactivation
binding site
Time domain
Max Ca uptake
IP3 receptor dissociation constant
IP3 receptor dissociation constant
Time domain
Ca receptor binding constant (activation)
Ca receptor binding constant (activation)
Volume ratio of endoplasmic reticulum and cytosol
Ca receptor binding constant (activation)
Proportion of IP3 receptor subunits with Ca activation site bound.
IP3 receptor/channel subunit with an occupied Ca2+ activation binding
site
IP3 receptor/Ca channel open probability.
Total Ca concentration in the cytosol
Volume ratio of endoplasmic reticulum and cytosol
Ca receptor dissociation constant (inhibition)
Ca receptor binding constant (inhibition)
Cytoplasmic oscillations in Ca2+ concentration are described by the
equation below where Ca_i is the cytosolic free Ca2+ concentration,
J1 is the outward flux of Ca2+ and J2 is the inward flux of Ca2+.
Ca receptor binding constant (inhibition)
Change in free Ca concentration from Ca binding to unbound subunits and dissociation of Ca from bound inhibition receptor.
Cytosolic free Ca concentration
IP3 receptor dissociation constant
Ca receptor dissociation constant (activation)