Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation
Mark
Hanna
Bioengineering Institute, University of Auckland
Model Status
Runs in PCEnv and COR. Reproduces published output (figures 2a, 2b when the value of 'k' is changed to 6, 4a, 4b when the value of 'beta' is changed to 0.644)
Model Structure
ABSTRACT: In a variety of cells, hormonal or neurotransmitter signals elicit a train of intracellular Ca2+ spikes. The analysis of a minimal model based on Ca2+-induced Ca2+ release from intracellular stores shows how sustained oscillations of cytosolic Ca2+ may develop as a result of a rise in inositol 1,4,5-trisphosphate (InsP3) triggered by external stimulation. This rise elicits the release of a certain amount of Ca2+ from an InsP3-sensitive intracellular store. The subsequent rise in cytosolic Ca2+ in turn triggers the release of Ca2+ from a second store insensitive to InsP3. In contrast to the model proposed by Meyer and Stryer [Meyer, T. & Stryer, L. (1988) Proc. Matl. Acad. Sci. USA 85, 5051-5055], the present model, which contains only two variable, predicts the occurrence of periodic Ca2+ spikes in the absence of InsP3 oscillations. Such results indicate that repetitive Ca2+ spikes evoked by external stimuli do not necessarily require the concomitant, periodic variation of InsP3. The model is closely related to that proposed by Kuba and Takeshita [Kuba, K. & Takeshita, S. (1981) J. Theor. Biol. 93, 1009-1031] for Ca2+ oscillations in sympathetic neurones, based on Ca2+-induced Ca2+ release. We extend their results by showing the minimal conditions in which the latter process gives rise to periodic behaviour and take into account the role of the rise in InsP3 caused by external stimulation. The analysis further shows how signal-induced Ca2+ oscillations might be effectively encoded in terms of their frequency through the phospohorylation of a cellular substrate by a protein kinase activated by cytosolic Ca2+.
Minimla model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation, Albert Goldbeter, Genevieve Dupont, Michael J. Berridge, 1990, Biophysics, 87, 1461-1465. PubMed ID: 2304911
cell diagram
Schematic representation of the mechanism generating Ca2+ oscillations, based on the self-amplified release of Ca2+ from intracellular stores.
This component stores information about Calcium ion (Ca2+) concentrations in various cellular compartments
Ca2+ concentration in the cytosol
Ca2+ concentration in the IP3-insensitive intracellular Ca2+ pool
Influx of Ca2+ into the cell
Efflux of Ca2+ out of the cell
Rate constant for leaky transport of Ca2+ from the IP3-insensitive intracellular Ca2+ pool into the cytosol
Level of external stimulation
Activated flux from extracellular medium into cytosol
$\frac{d Z}{d \mathrm{time}}=\mathrm{v\_0}+\mathrm{v\_1}\mathrm{beta}+-\mathrm{v\_2}+\mathrm{v\_3}+\mathrm{k\_f}Y+-(kZ)\frac{d Y}{d \mathrm{time}}=\mathrm{v\_2}+-\mathrm{v\_3}+-(\mathrm{k\_f}Y)$
Component for the calculation of v_2
Rate of ATP-driven pumping of Ca2+ from the cytosol into the IP3-insensitive store
Maximum rate for v_2
Threshold concentration for pumping of Ca2+ from the cytosol into the IP3-insensitive store
$\mathrm{v\_2}=\mathrm{V\_M2}\frac{Z^{n}}{\mathrm{K\_2}^{n}+Z^{n}}$
Component for the calculation of v_3
Rate of transport from this pool into the cytosol
Maximum rate for v_3
Threshold concentration for Ca2+ release
Threshold concentration for Ca2+ activation
$\mathrm{v\_3}=\mathrm{V\_M3}\frac{Y^{m}}{\mathrm{K\_R}^{m}+Y^{m}}\frac{Z^{p}}{\mathrm{K\_A}^{p}+Z^{p}}$
Component for the calculation of W_star
Fraction of a protein substrate in the phosphorylated form
Total amount of protein substrate
Maximum rate of phosphatase
K_1 = K_m1/W_T, where K_m1 denotes the Michaelis constant of kinase
K_2 = K_m2/W_T, where K_m2 denotes the MIchaelis constant of phosphatase
$\frac{d \mathrm{W\_star}}{d \mathrm{time}}=\frac{\mathrm{v\_P}}{\mathrm{W\_T}}(\frac{\mathrm{v\_K}}{\mathrm{v\_P}}\frac{1-\mathrm{W\_star}}{\mathrm{K\_1}+1+-\mathrm{W\_star}}-\frac{\mathrm{W\_star}}{\mathrm{K\_2}+\mathrm{W\_star}})$
Component for the calculation of v_K
Maximum rate of kinase
Maximum rate of v_K
Constant of activation of the kinase by cytosolic Ca2+
$\mathrm{v\_K}=\mathrm{V\_MK}\frac{Z}{\mathrm{K\_a}+Z}$
Hanna
Mark
James
mark@hanna.net.nz
The University of Auckland
Auckland Bioengineering Institute
2009-12-01
Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation
Calcium Signalling
Calcium Oscillations
Bursting
Calcium Dynamics
2304911
Goldbeter
Albert
Dupont
Genevieve
Berridge
Michael
J.
Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation
1990-02
Biophysics
87
1461
1465