Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis
Ethan
Choi
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model has been built with the differential expressions in Dupont and Goldbeter's 1992 paper. This file is known to run in PCEnv and COR, and variables for constants (vMK) can be altered to produce figure4b, c and figure5b and c (the ratio vMK/vP is held constant at vMK/vP = 20/0.89). The current parameterization is set to reproduce 4b with vMK=100 (note the erratum received in 1995: wT=10 not 1, to replicate figure 5. Initial conditions for Z, Y and Wstar were set by letting the model settle into a steady state.
Model Structure
Abstract: Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca2+-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca2+-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.
model diagram
Schematic diagram of the cell model.
The original paper reference is cited below:
Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis, Dupont G, Goldbeter A 1992, Biophysical Chemistry
41, 257-270. PubMedID: 1316185
This component stores and calculates various parameters for the cell components
$\mathrm{v2}=\frac{\mathrm{VM2}Z^{n}}{\mathrm{KP}^{n}+Z^{n}}\mathrm{v3}=\mathrm{VM3}\frac{Y^{m}}{\mathrm{KR}^{m}+Y^{m}}\frac{Z^{p}}{\mathrm{KA}^{p}+Z^{p}}$
This component stores information about the cytosolic Ca2+
Ca2+ in the cytosol
$\frac{d Z}{d \mathrm{time}}=\mathrm{v0}+\mathrm{v1beta}-\mathrm{v2}+\mathrm{v3}+\mathrm{kf}Y-kZ$
This component stores information about the InsP3-insensitive intracellular store and the Ca2+ in this pool
Ca2+ in the intracellular Ca2+ pool
$\frac{d Y}{d \mathrm{time}}=\mathrm{v2}-\mathrm{v3}-\mathrm{kf}Y$
This component incorporates the reversible phosphorylation by taking into account a protein substrate (total amount denoted by WT)
The fraction of phosphorylated protein (Wstar = [Wstar] /[WT])
$\mathrm{vP}=\mathrm{vMK}\frac{0.89}{20}\frac{d \mathrm{Wstar}}{d \mathrm{time}}=\frac{\mathrm{vP}}{\mathrm{WT}}(\frac{\frac{\mathrm{vK}}{\mathrm{vP}}(1-\mathrm{Wstar})}{\mathrm{K1}+1-\mathrm{Wstar}}-\frac{\mathrm{Wstar}}{\mathrm{K2}+\mathrm{Wstar}})$
This component gives the expression for the kinase reaction rate (vK) assuming kinase is activated by cytosolic Ca2+. In this model (dupont_1992b) the ratio vMK/vP is held constant at vMK/vP = 20/0.89
kinase reaction rate
maximal rate of the kinase
$\mathrm{vK}=\mathrm{vMK}\frac{Z^{q}}{\mathrm{Ka}^{q}+Z^{q}}$
Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis (Model B)
Choi
Ethan
mcho099@aucklanduni.ac.nz
The University of Auckland
Auckland Bioengineering Institute
2009-12-01
Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis
This is the CellML description of Dupont and Goldbeter's mathematical model Protein phosphorylation driven by intracellular calcium oscillations.
Ethan Choi
keyword
Calcium Dynamics
Calcium regulation
Kinase
Calmodulin
Frequency coding
Biochemical oscillations
1316185
Dupont
Genevieve
Goldbeter
Albert
Protein phosphorylation driven by intracellular calcium oscillations: A kinetic analysis
1992-04
Biophysical Chemistry
1316185
42
257
270