A mathematical model of calcium dynamics and saliva secretion

Abstract

Salivary fluid secretion is crucial for preventing problems such as dryness of mouth, difficulty with mastication and swallowing, as well as oral pain and dental cavities. Salivary gland dysfunction is also observed in diseases such as Sjogren's syndrome. For these reasons, it is important to understand the mechanisms underlying salivary secretion and we will do this by constructing a mathematical model of an accepted physiological model of the mechanisms. Fluid flow is driven primarily by the transepithelial movement of chloride and sodium ions into the parotid acinus lumen. The activation of Cl- channels is calcium dependent, with the average elevated calcium concentration during calcium oscillations increasing the conductance of the channels, leading to an outflow of CT". The accumulation of NaCl in the lumen drives water flow by osmosis. We construct a mathematical model of the calcium concentration oscillations and couple this to a model for Cl- efflux. We also construct a model governing fluid flow in an isolated parotid acinar cell, which includes a description of the rate of change of intracellular ion concentrations, cell volume, membrane potential and water flow rate. We find that [Ca2+] oscillations lead to oscillations in fluid flow, and that the rate of fluid flow is regulated by the average calcium concentration and not the frequency of the oscillations. One of the important mechanisms for controlling intracellular calcium dynamics is the release of Ca2+ from the endoplasmic reticulum via the inositol trisphosphate receptor (IPR). Therefore, an understanding of this receptor is necessary for an understanding of calcium oscillations and waves. Based on single-channel data from the type-I IPR and using Bayesian inference and a Markov chain Monte Carlo approach, we show that the most complex time-dependent model that can be unambiguously determined from steady-state data is one with three closed states and one open state, and we determine how the rate constants depend on calcium concentration. Our model is much simpler than current models of the IPR and because the transitions between these states are complex functions of calcium concentration, each model state must correspond to a group of physical states. This model predicts that the increased open probability of the IPR is due to the decrease in long closed times, rather than a rate increase from the closed state to the open state.