Model Status
This CellML model runs in both OpenCell and COR to reproduce the published results. The units have been checked and they are consistent.
Model Structure
ABSTRACT: In response to mechanical stimulation of a single cell, airway epithelial cells in culture exhibit a wave of increased intracellular free Ca2+ concentration that spreads from cell to cell over a limited distance through the culture. We present a detailed analysis of the intercellular wave in a two-dimensional sheet of cells. The model is based on the hypothesis that the wave is the result of diffusion of inositol trisphosphate (IP3) from the stimulated cell. The two-dimensional model agrees well with experimental data and makes the following quantitative predictions: as the distance from the stimulated cells increases, 1) the intercellular delay increases exponentially, 2) the intracellular wave speed decreases exponentially, and 3) the arrival time increases exponentially. Furthermore, 4) a proportion of the cells at the periphery of the response will exhibit waves of decreased amplitude, 5) the intercellular membrane permeability to IP3 must be approximately 2 microns/s or greater, and 6) the ratio of the maximum concentration of IP3 in the stimulated cell to the Km of the IP3 receptor (with respect to IP3) must be approximately 300 or greater. These predictions constitute a rigorous test of the hypothesis that the intercellular Ca2+ waves are mediated by IP3 diffusion.
The original paper is cited below:
Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. J. Sneyd, B.T. Wetton, A.C. Charles and M.J. Sanderson, 1995, American Journal of Physiology, 268, C1537-C1545. PubMed ID: 7611375
Diagram of model
A schematic diagram of the pathway described by the mathematical model.
$\frac{d P}{d \mathrm{time}}=\begin{cases}\mathrm{IPR\_3\_flux}-\frac{\mathrm{V\_p}P\mathrm{k\_p}}{\mathrm{k\_p}+P} & \text{if $\mathrm{time}\le 15$}\\ \frac{-\mathrm{V\_p}P\mathrm{k\_p}}{\mathrm{k\_p}+P} & \text{otherwise}\end{cases}$
$\frac{d c}{d \mathrm{time}}=\mathrm{J\_flux}-\mathrm{J\_pump}+\mathrm{J\_leak}$
$\mathrm{J\_flux}=\mathrm{k\_flux}\mathrm{mu}h(b+\frac{(1-b)c}{\mathrm{k\_1}+c})$
$\mathrm{J\_pump}=\frac{\mathrm{gamma}c^{2}}{\mathrm{k\_gamma}^{2}+c^{2}}$
$\mathrm{J\_leak}=\mathrm{beta}$
$\mathrm{mu}=\frac{P^{3}}{\mathrm{k\_mu}^{3}+P^{3}}$
$\frac{d h}{d \mathrm{time}}=\frac{\frac{\mathrm{k\_2}^{2}}{\mathrm{k\_2}^{2}+c^{2}}-h}{\mathrm{tau\_h}}$
Catherine Lloyd
The Sneyd et al. 1995 model of intercellular calcium waves
SneydJ7611375
This is the CellML description of Sneyd et al.'s mathematical model of intercellular calcium waves
1995-06LiuWei0.12JSandersonMAmerican Journal of PhysiologyThe University of Auckland
Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model
268C1545C15372009-09-29keywordwliu052@aucklanduni.ac.nzCCharlesATWettonBcalcium dynamics