Bulletin of Mathematical Biology

, Volume 81, Issue 5, pp 1394–1426 | Cite as

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

  • Nathan PagesEmail author
  • Elías Vera-Sigüenza
  • John Rugis
  • Vivien Kirk
  • David I. Yule
  • James Sneyd


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., 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-Sigüenza et al. in Bull Math Biol., 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.


Calcium dynamics Inositol triphosphate receptors Fluid secretion Finite-element modelling Parotid acinar cells 



This work was supported by the National Institutes of Health grant number RO1DE019245-10 and by the Marsden Fund of the Royal Society of New Zealand. High-performance computing facilities and support were provided by the New Zealand eScience Infrastructure (NeSI) funded jointly by NeSI’s collaborator institutions and through the Ministry of Business, Innovation and Employment’s Research Infrastructure programme. Thanks to NVIDIA Corporation for a K40 GPU grant.

Supplementary material

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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand
  2. 2.School of Medicine and DentistryUniversity of Rochester Medical CenterRochesterUSA

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