A dynamic model of saliva secretion

Abstract

We construct a mathematical model of the parotid acinar cell with the aim of investigating how the distribution of K⁺ and Cl⁻ channels affects saliva production. Secretion of fluid is initiated by Ca²⁺ signals acting on Ca²⁺ dependent K⁺ and Cl⁻ channels. The opening of these channels facilitates the movement of Cl⁻ ions into the lumen which water follows by osmosis. We use recent results into both the release of Ca²⁺ from internal stores via the inositol (1,4,5)-trisphosphate receptor (IP₃R) and IP₃ dynamics to create a physiologically realistic Ca²⁺ model which is able to recreate important experimentally observed behaviours seen in parotid acinar cells. We formulate an equivalent electrical circuit diagram for the movement of ions responsible for water flow which enables us to calculate and include distinct apical and basal membrane potentials to the model. We show that maximum saliva production occurs when a small amount of K⁺ conductance is located at the apical membrane, with the majority in the basal membrane. The maximum fluid output is found to coincide with a minimum in the apical membrane potential. The traditional model whereby all Cl⁻ channels are located in the apical membrane is shown to be the most efficient Cl⁻ channel distribution.

Introduction

Saliva production is an important process for both digestion and oral health. Problems with salivation can cause issues with dental cavities, oral pain and infections. In mastication, an adequate supply of saliva is needed to provide lubrication to the mouth and facilitate swallowing. Humans and most mammals possess three major pairs of salivary glands (parotid, sublingual and submandibular). The parotid gland is the largest of these, and is also the only major salivary gland that produces purely serous fluid, with the other glands producing mucous. The structure of the parotid gland consists of bunches of acini connected by ducts. Each acinus comprises several epithelial parotid acinar cells secreting fluid into a shared lumenal cavity. The salivary fluid passes from the lumen of the acini into a branching network of ducts, where it is collected and travels to the mouth. Dysregulation of fluid secretion from the parotid acinar cells can lead to conditions such as xerostomia (dry mouth), where sufferers experience pain with eating and speech because of a lack of saliva.

Fluid is known to travel through the parotid cells by the process of osmosis. Given a membrane impermeable to ions but permeable to water, water will flow from the area of low ionic concentration to that of high concentration. The parotid gland must maintain an ionic gradient, increasing from the interstitium, to the cytoplasm and then into the lumen, to facilitate water movement through the cell to the duct. Whilst maintaining this gradient the acinar cells must avoid accumulation of too much water in the cell, as the cell membrane is incapable of sustaining any significant pressure difference.

Existing models for fluid flow through the parotid acinar cell place K⁺ channels exclusively in the basolateral membrane (Gin et al., 2007, Nauntofte, 1992, Turner et al., 1993, Turner and Sugiya, 2002). However, there is building evidence for the existence of K⁺ channels in the apical membrane (Sørensen et al., 2001 find apical K⁺ channels in frog skin glands, Catalan and Melvin [Unpublished] in parotid acinar). Cook and Young (1989) looked at adding apical K⁺ channels to a model with constant ionic concentrations and steady state currents. We aim to investigate how the distribution of K⁺ channels changes the saliva production of the parotid acinar cell in a dynamic model where salivation is initiated by Ca²⁺ signalling.

We use the currently accepted model for saliva production (see Nauntofte, 1992 for a review) where the movement of Cl⁻ into the cytoplasm and then into the lumen creates a concentration gradient which water follows by osmosis. In this model the basolateral membrane contains a Na⁺–K⁺–2Cl⁻ cotransporter (NKCC), a Na⁺–K⁺–ATPase (NaK) and a K⁺ ion channel. Cl⁻ moves into the cell via the NKCC and then moves through Ca²⁺ sensitive apical Cl⁻ channels into the lumen. The Na⁺ and K⁺ ions are removed from the cell by K⁺ channels and the NaK pump. See Fig. 1 for a diagram of the model used.

Calcium (Ca²⁺) plays a critical role in epithelial tissue as a second messenger activating fluid flow. Previous models have investigated Ca²⁺ signalling in a variety of epithelial tissues including airway epithelium (Sneyd et al., 1995, Warren et al., 2009, Warren et al., 2010). As Ca²⁺ concentration increases in parotid cells the ionic channels at the basal and apical membrane open and fluid production is seen to increase. The salivation process is initiated in the otic ganglion parasympathetic nerve which runs from the brain to the parotid gland. When stimulated, for example when we smell food, these nerves release acetylcholine, which binds to receptors on the cell surface, leading to the production of inositol (1,4,5)-trisphosphate (IP₃) in the cytoplasm. The raised IP₃ concentration releases Ca²⁺ from internal stores in the endoplasmic reticulum (ER). As Ca²⁺ concentration increases in parotid cells the ionic channels at the basal and apical membrane open and fluid production is seen to increase. We create a model for intracellular Ca²⁺ using recent results relating to the release of Ca²⁺ from internal stores via the inositol (1,4,5)-trisphosphate receptor (IP₃R) and the dynamics of IP₃. Feedback of Ca²⁺ on the degradation of IP₃ is the mechanism which our model uses to recreate Ca²⁺ oscillations.

Insight into the role of the K⁺ channel distribution in determining the rate of water transport in the parotid cell is gained by observing the apical and basolateral membrane potentials during simulations with and without the addition of apical K⁺ channels.