Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms
Mark
Hanna
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR to reproduce the published output (figure 4, but using parameters for figure 5 i.e. beta = 1.0 instead of 0.5). The units have been checked and they are consistent.
Model Structure
ABSTRACT: Intracellular Ca2+ oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca2+-induced Ca2+ release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca2+ oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca2+ spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca2+ oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca2+-release channel on a unique intracellular store at high cytosolic Ca2+ concentrations, (ii) taking into account the Ca2+-activated degradation of inositol 1,4,5-trisphosphate (IP3), or (iii) considering explicitly the evolution of the Ca2+ concentration in two different pools, one sensitive and the other one insensitive to IP3. Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP3 into account shows chaotic behaviour.
Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms, Jose A.M. Borghans, Genevieve Dupont, Albert Goldbeter, 1997, Biophysical Chemistry, 66, 25-41. PubMed ID: 17029867
cell diagram
Schematic representation of the one-pool model for Ca2+ oscillations based on CICR.
This component stores information about Calcium ion (Ca2+) concentrations in various cellular compartments
Ca2+ concentration in the cytosol
Ca2+ concentration in the intracellular Ca2+ pool
$\frac{d Z}{d \mathrm{time}}=\mathrm{V\_in}-\mathrm{V\_2}+\mathrm{V\_3}+\mathrm{K\_f}Y-KZ\frac{d Y}{d \mathrm{time}}=\mathrm{V\_2}-\mathrm{V\_3}-\mathrm{K\_f}Y$
Container for Ca2+ flux-related components
Stimulation level
Component for the calculation of V_in
Flux of Ca2+ from the extracellular medium into the cytosol
Passive Ca2+ "leak" from the extracellular medium into the cytosol
Activated Ca2+ transport from the extracellular medium into the cytosol
$\mathrm{V\_in}=\mathrm{v\_0}+\mathrm{v\_1}\mathrm{beta}$
Component for the calculation of V_2
Ca2+ pumping rate into the Ca2+ pool
Maximum Ca2+ pumping rate into the Ca2+ pool
Threshold concentration for Ca2+ pumping into the Ca2+ pool
$\mathrm{V\_2}=\mathrm{V\_M2}\frac{Z^{2}}{\mathrm{K\_2}^{2}+Z^{2}}$
Component for the calculation of V_3
Ca2+ release rate from the Ca2+ pool
Threshold concentration for Ca2+ release
Maximum Ca2+ release rate from the Ca2+ pool
$\mathrm{V\_3}=\mathrm{beta}\mathrm{R\_plus}\mathrm{V\_M3}\frac{Y^{2}}{\mathrm{K\_y}^{2}+Y^{2}}$
Component for the calculation of R_plus
Fraction of activatable channels
Rate at which channels inactivate following binding of Ca2+ to inhibitory site
Rate at which channels activate following unbinding of Ca2+ to inhibitory site
Proportion of channels with Ca2+ bound to the activatory site but not to the inhibitory site
$\mathrm{R\_plus}=\mathrm{gamma}\frac{\mathrm{rho}}{1+\mathrm{gamma}}\frac{d \mathrm{rho}}{d \mathrm{time}}=-(\mathrm{k\_d}Z^{4}\mathrm{rho}\times 1)+\mathrm{k\_r}(1-\mathrm{rho})$
Component for the calculation of gamma
A scaling factor: the number of channels with Ca2+ bound to the activatory site divided by the number of channels without Ca2+ bound to the activatory site.
Kinetic constant for activatory Ca2+ binding
Kinetic constant for deactivatory Ca2+ unbinding
$\mathrm{gamma}=\frac{a}{d}Z^{4}\times 1$
Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms (Model A)
Hanna
Mark
James
mark@hanna.net.nz
The University of Auckland
Auckland Bioengineering Institute
2009-11-30
Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms
Calcium Signalling
Calcium Oscillations
Bursting
Chaos
Calcium Dynamics
17029867
Borghans
Jose
O.M.
Dupont
Genevieve
Goldbeter
Albert
Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms
1997-01-16
Biophysical Chemistry
66
25
41