Abstract:
Although the theory of exocrine gland secretion is comprehensive, numerous questions over the specific molecular mechanisms and signalling pathways associated with the transport of water in salivary gland epithelia persist. This thesis addresses some of these questions by combining new experimental data, along with mathematical modelling. One such problem involves exploring to what extent do the calcium (Ca²⁺) signalling heterogeneities, arising from agonist stimulation, impact the way salivary cells transport water. Using a three-dimensional and anatomically accurate mathematical model of secretion, we found that these have no direct effect on their rate of secretion. The result suggests the possibility of modelling cell salivation as a quasi-steady-state function of the cytosolic Ca²⁺ averaged over the entire cell; effectively ignoring all the dynamic complexities, not only of the fluid secretion mechanism but also of the intracellular heterogeneity of Ca²⁺-signalling. We also address how these cells work as a cohort; this is because they form clusters called acini. We assembled an ‘in-silico’ parotid acinus and investigated the influence its lumen’s topology has on the efficiency of fluid secretion. Our simulations demonstrate that a particular luminal topology does not affect secretion efficiency. Furthermore, this type of model may not be necessary when modelling fluid flow rate. Thus, to obtain an acinus, or better yet a gland flow rate estimate, one can multiply the output of a homogeneous single-cell model by the number of cells in a salivary gland. Finally, we study new experimental results that revealed a significant potassium (K⁺) current in the apical pole of acinar cells. These results are controversial, as the concentration of K⁺ in primary saliva has been observed to be relatively low. To reconcile these observations, with the accepted secretion model, we use a single-cell model along with experimental data to propose a framework in which the luminal K⁺ is reabsorbed by the cell via apical NaK-ATPases in exchange for intracellular Na⁺ . We show that placing a sizeable K⁺ current in the apical membrane, along with apical NaK-ATPases, does not lead to a secretion rate that is either increased or decreased. However, the luminal electrolyte concentrations are maintained at physiological levels.