A mathematical study of the role of calcium in the regulation of saliva secretion

Abstract

Xerostomia is estimated to affect 30% of adults over the age of 65. The condition is characterised by a lack of saliva secretion, resulting in a range of health problems. A rise in the concentration of free cytosolic calcium (Ca²⁺) is essential to initiate saliva secretion. We construct mathematical models of saliva secretion and Ca²⁺ dynamics in salivary acinar and duct cells. We investigate how the distribution of K⁺ channels affects the rate of primary saliva secretion. Maximum saliva secretion is hypothesised to occur when a small amount of K⁺ conductance is located in the apical membrane, with the majority in the basolateral membrane. Apical K⁺ channels have since been experimentally located. For a range of applied agonist, the concentration of Ca²⁺ in salivary cells is seen experimentally to oscillate and to travel in waves across the cytosol. We construct a model of Ca2+ oscillations in parotid acinar cells that requires paired oscillations of IP₃. This ODE model reproduces a number of experimentally observed phenomena. The model is later spatially extended. An inhomogeneous distribution of Ca²⁺ channels is shown to produce apical to basal Ca²⁺ waves, as seen experimentally. We investigate how Ca²⁺ wave properties affect the rate of saliva secretion. Mean Ca²⁺ concentration is found to be the most significant property in regulating secretion. Wave speed was found to encode a range of secretion rates. Ca²⁺ oscillation frequency and amplitude had little effect on the fluid secretion rate. Recent experimental results show coupled oscillations of Ca²⁺ and IP3 in HSY cells, a duct cell line. We present a mathematical model of HSY cells in which IP₃ oscillations are not required for the generation of Ca²⁺ oscillations. The inclusion of passive IP₃ oscillations is shown to increase the Ca²⁺ oscillation frequency range and be consistent with the experimental data. These single-cell models provide insight into the regulation of saliva secretion by themselves. They also suggest what is important to include, and what can be simplified in constructing a whole-organ model. With a greater understanding of the regulation of saliva secretion, and the role Ca²⁺ plays, it is hoped that we might learn how salivary gland dysfunction occurs.