IP3-Mediated Ca2+ Release
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
Ca2+ 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 Ca2+ 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 Ca2+ 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 Ca2+ concentration in cells. In this study, De Young and Keizer investigate the idea that a biphasic response of the IP3 receptor/channel to cytosolic Ca2+ may alone be sufficient to induce Ca2+ oscillations.
They constructed a simplified model of the IP3 receptor/channel by assuming that three equivalent and independent subunits are involved in Ca2+ conduction. Each subunit has three binding sites: one for IP3, one for Ca2+ activation, and one for Ca2+ 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 S110 (one IP3 and one activating Ca2+ bound) for the channel to be open and conducting.
The raw CellML description of the IP3-mediated Ca2+ 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 IP3 receptor/channel subunit.
$\frac{d \mathrm{Ca\_i}}{d \mathrm{time}}=\mathrm{J1}-\mathrm{J2}\mathrm{J1}=\mathrm{c1}(\mathrm{v1}\mathrm{P\_open}+\mathrm{v2})(\mathrm{Ca\_ER}-\mathrm{Ca\_i})\mathrm{J2}=\frac{\mathrm{v3}\mathrm{Ca\_i}^{2.0}}{\mathrm{Ca\_i}^{2.0}+\mathrm{k3}^{2.0}}$
$\mathrm{Ca\_ER}=\frac{\mathrm{c0}-\mathrm{Ca\_i}}{\mathrm{c1}}$
$\frac{d \mathrm{IP3}}{d \mathrm{time}}=\mathrm{v4}\frac{\mathrm{Ca\_i}-1.0\mathrm{k4}}{\mathrm{Ca\_i}+\mathrm{k4}}-\mathrm{Ir}\mathrm{IP3}$
$\mathrm{d1}=\mathrm{K\_d1}-\mathrm{IP3\_cold}$
$\mathrm{d2}=\frac{\mathrm{b2}}{\mathrm{a2}}$
$\mathrm{d3}=(\mathrm{K\_d2}-\mathrm{IP3\_cold})(1+\mathrm{d2})-\mathrm{d1}\mathrm{d2}$
$\mathrm{d4}=\frac{\mathrm{d1}\mathrm{d2}}{\mathrm{d3}}$
$\mathrm{d5}=\frac{\mathrm{b5}}{\mathrm{a5}}$
$\mathrm{P\_open}=\left(\frac{\mathrm{Ca\_i}\mathrm{IP3}\mathrm{d2}}{(\mathrm{Ca\_i}\mathrm{IP3}+\mathrm{IP3}\mathrm{d2}+\mathrm{d1}\mathrm{d2}+\mathrm{Ca\_i}\mathrm{d3})(\mathrm{Ca\_i}+\mathrm{d5})}\right)^{3.0}$
$\frac{d \mathrm{x\_000}}{d \mathrm{time}}=-\mathrm{V1}-\mathrm{V3}$
$\frac{d \mathrm{x\_001}}{d \mathrm{time}}=\mathrm{V1}-\mathrm{V4}$
$\frac{d \mathrm{x\_010}}{d \mathrm{time}}=\mathrm{V3}-\mathrm{V2}$
$\mathrm{x\_011}=1.0-\mathrm{x\_000}+\mathrm{x\_001}+\mathrm{x\_010}$
$\mathrm{V1}=\mathrm{a4}(\mathrm{Ca\_i}\mathrm{x\_000}-\mathrm{d4}\mathrm{x\_001})\mathrm{V2}=\mathrm{a4}(\mathrm{Ca\_i}\mathrm{x\_010}-\mathrm{d4}\mathrm{x\_011})\mathrm{V3}=\mathrm{a5}(\mathrm{Ca\_i}\mathrm{x\_000}-\mathrm{d5}\mathrm{x\_010})\mathrm{V4}=\mathrm{a5}(\mathrm{Ca\_i}\mathrm{x\_001}-\mathrm{d5}\mathrm{x\_011})$
$\mathrm{b1}=\mathrm{d1}\mathrm{a1}\mathrm{b3}=\mathrm{d3}\mathrm{a3}\mathrm{b4}=\mathrm{d4}\mathrm{a4}$
calcium dynamics
electrophysiology
signal transduction
ip3 receptor
IP3 Receptor
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.
The University of Auckland, Bioengineering Institute
1329108
IP3 receptor/channel subunit with 3 unoccupied binding sites
x_000
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).
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.
Catherine
Lloyd
May
IP3 receptor/channel subunit with an occupied Ca2+ activation binding
site
x_010
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+.
Proceedings of the National Academy of Science, USA
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.
keyword
c.lloyd@auckland.ac.nz
2007-05-18T00:00:00+00:00
Catherine
Lloyd
May
Catherine
Lloyd
May
Joel
Keizer
The De Young-Keizer 1992 model of oscillatory calcium release through
the IP3 stimulated channel
IP3 Receptor
IP3 receptor/channel subunit with an occupied Ca2+ inactivation
binding site
x_011
Gary
De Young
W
2007-06-05T09:34:14+12:00
The University of Auckland
The Bioengineering Research Group
Fixed link to diagram.
2007-06-14T11:51:06+12:00
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.
A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration
89
9895
9899
1992-10-15