A Model of \(\hbox {Ca}^{2+}\) Dynamics in an Accurate Reconstruction of Parotid Acinar Cells

We have constructed a spatiotemporal model of \(\hbox {Ca}^{2+}\) dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. in J Theor Biol 419:383–393. https://doi.org/10.1016/j.jtbi.2016.04.030, 2017b), which cannot generate realistic \(\hbox {Ca}^{2+}\) oscillations with the new data on IPR distribution, our new model reproduces the \(\hbox {Ca}^{2+}\) dynamics observed in parotid acinar cells. This model is then coupled with a fluid secretion model described in detail in a companion paper: A mathematical model of fluid transport in an accurate reconstruction of a parotid acinar cell (Vera-Siguenza et al. in Bull Math Biol. https://doi.org/10.1007/s11538-018-0534-z, 2018b). Based on the new measurements of IPR distribution, we show that Class I models (where \(\hbox {Ca}^{2+}\) oscillations can occur at constant [\(\hbox {IP}_3\)]) can produce \(\hbox {Ca}^{2+}\) oscillations in parotid acinar cells, whereas Class II models (where [\(\hbox {IP}_3\)] needs to oscillate in order to produce \(\hbox {Ca}^{2+}\) oscillations) are unlikely to do so. In addition, we demonstrate that coupling fluid flow secretion with the \(\hbox {Ca}^{2+}\) signalling model changes the dynamics of the \(\hbox {Ca}^{2+}\) oscillations significantly, which indicates that \(\hbox {Ca}^{2+}\) dynamics and fluid flow cannot be accurately modelled independently. Further, we determine that an active propagation mechanism based on calcium-induced calcium release channels is needed to propagate the \(\hbox {Ca}^{2+}\) wave from the apical region to the basal region of the acinar cell.