Sneyd, Tsaneva-Atanasova, Bruce, Straub, Giovannucci, Yule, 2003
This model contains partial differentials and as such can not currently be solved by existing CellML tools.
ABSTRACT: We construct a mathematical model of Ca(2+) wave propagation in pancreatic and parotid acinar cells. Ca(2+) release is via inositol trisphosphate receptors and ryanodine receptors that are distributed heterogeneously through the cell. The apical and basal regions are separated by a region containing the mitochondria. In response to a whole-cell, homogeneous application of inositol trisphosphate (IP(3)), the model predicts that 1), at lower concentrations of IP(3), the intracellular waves in pancreatic cells begin in the apical region and are actively propagated across the basal region by Ca(2+) release through ryanodine receptors; 2), at higher [IP(3)], the waves in pancreatic and parotid cells are not true waves but rather apparent waves, formed as the result of sequential activation of inositol trisphosphate receptors in the apical and basal regions; 3), the differences in wave propagation in pancreatic and parotid cells can be explained in part by differences in inositol trisphosphate receptor density; 4), in pancreatic cells, increased Ca(2+) uptake by the mitochondria is capable of restricting Ca(2+) responses to the apical region, but that this happens only for a relatively narrow range of [IP(3)]; and 5), at higher [IP(3)], the apical and basal regions of the cell act as coupled Ca(2+) oscillators, with the basal region partially entrained to the apical region.
The original paper reference is cited below:
A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells, J. Sneyd, K. Tsaneva-Atanasova, J. I. E. Bruce, S. V. Straub, D. R. Giovannucci, and D. I. Yule, 2003, Biophysical Journal, 85, 1392-1405. PubMed ID: 12944257
|A simplified diagram of the IPR model, where R represents the free receptor, O is the open state of the channel, A is the activated state of the channel and I1, I2, and S are three inactive states.|
|Schematic diagram of transitions among the four states of the RyR used to describe adaptation. States C1 and C2 are closed states and O1 and O2 represent open states, assumed to have the same single-channel conductance. The k are rate constants: only steps a and b are Ca2+ dependent.|
|Schematic of the model indicating Ca2+ compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca2+ ion movement between the compartments.|