A Mathematical Model of Fluid Transport in an Accurate Reconstruction of Parotid Acinar Cells.

Salivary gland acinar cells use the calcium ([Formula: see text]) ion as a signalling messenger to regulate a diverse range of intracellular processes, including the secretion of primary saliva. Although the underlying mechanisms responsible for saliva secretion are reasonably well understood, the precise role played by spatially heterogeneous intracellular [Formula: see text] signalling in these cells remains uncertain. In this study, we use a mathematical model, based on new and unpublished experimental data from parotid acinar cells (measured in excised lobules of mouse parotid gland), to investigate how the structure of the cell and the spatio-temporal properties of [Formula: see text] signalling influence the production of primary saliva. We combine a new [Formula: see text] signalling model [described in detail in a companion paper: Pages et al. in Bull Math Biol 2018, submitted] with an existing secretion model (Vera-Sigüenza et al. in Bull Math Biol 80:255-282, 2018. https://doi.org/10.1007/s11538-017-0370-6 ) and solve the resultant model in an anatomically accurate three-dimensional cell. Our study yields three principal results. Firstly, we show that spatial heterogeneities of [Formula: see text] concentration in either the apical or basal regions of the cell have no significant effect on the rate of primary saliva secretion. Secondly, in agreement with previous work (Palk et al., in J Theor Biol 305:45-53, 2012. https://doi.org/10.1016/j.jtbi.2012.04.009 ) we show that the frequency of [Formula: see text] oscillation has no significant effect on the rate of primary saliva secretion, which is determined almost entirely by the mean (over time) of the apical and basal [Formula: see text]. Thirdly, it is possible to model the rate of primary saliva secretion as a quasi-steady-state function of the cytosolic [Formula: see text] averaged over the entire cell when modelling the flow rate is the only interest, thus ignoring all the dynamic complexity not only of the fluid secretion mechanism but also of the intracellular heterogeneity of [Formula: see text]. Taken together, our results demonstrate that an accurate multiscale model of primary saliva secretion from a single acinar cell can be constructed by ignoring the vast majority of the spatial and temporal complexity of the underlying mechanisms.