Efficiency of primary saliva secretion: an analysis of parameter dependence in dynamic single-cell and acinus models, with application to aquaporin knockout studies

A Mathematical Exploration of SDH-b Loss in Chromaffin Cells

The succinate dehydrogenase (SDH) is a four-subunit enzyme complex (SDH-a, SDH-b, SDH-c, and SDH-d) central to cell carbon metabolism. The SDH bridges the tricarboxylic acid cycle to the electron transport chain. A pathological loss of the SDH-b subunit leads to a cell-wide signalling cascade that shifts the cell's metabolism into a pseudo-hypoxic state akin to the so-called Warburg effect (or aerobic glycolysis). This trait is a hallmark of phaeochromocytomas, a rare tumour arising from chromaffin cells; a type of cell that lies in the medulla of the adrenal gland. In this study, we leverage the insights from a mathematical model constructed to underpin the metabolic implications of SDH-b dysfunction in phaeochromocytomas. We specifically investigate why chromaffin cells seemingly have the ability to maintain electron transport chain's Complex I function when confronted with the loss of the SDH-b subunit while other cells do not. Our simulations indicate that retention of Complex I is associated with cofactor oxidation, which enables cells to manage mitochondrial swelling and limit the reversal of the adenosine triphosphate synthase, supporting cell fitness, without undergoing lysis. These results support previous hypotheses that point to mitochondrial proton leaks as a critical factor of future research. Moreover, the model asserts that control of the proton gradient across the mitochondrial inner membrane is rate-limiting upon fitness management of SDH-b deficient cells.

Effects of polyphenols in non-centrifugal cane sugar on saliva secretion: in vitro and in vivo experiments and a randomized controlled trial

This study examined the bioactivities and mechanisms of the non-centrifugal cane sugar polyphenols saponarin, schaftoside, and isoschaftoside in the salivary gland and their effects on salivation. In acute isolated C57BL/6N mouse submandibular gland cells, these polyphenols led to a higher increase in intracellular calcium after stimulation with the muscarinic agonist carbachol. Stimulation of these cells with polyphenols enhanced ATP production, aquaporin-5 translocation to the plasma membrane and eliminated intracellular reactive oxygen species generated by H₂O₂. In addition, phosphorylation of endothelial nitric oxide synthase and increased nitric oxide production in vascular endothelial cells were observed. In vivo administration of these polyphenols to C57BL/6N male mice resulted in significantly increased blood flow (saponarin, p = 0.040; isoschaftoside, p = 0.010) and salivation (saponarin, p = 0.031). A randomized controlled trial showed that intake of non-centrifugal cane sugar significantly increased saliva secretion compared with placebo (p = 0.003). These data suggest that non-centrifugal cane sugar polyphenols affect several pathways that support salivation and increase saliva secretion by enhancing vasodilation. Hence, non-centrifugal cane sugar polyphenols can be expected to maintain saliva secretion and improve reduced saliva flow.

Calcium Dynamics and Water Transport in Salivary Acinar Cells

Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.

A Multicellular Model of Primary Saliva Secretion in the Parotid Gland

We construct a three-dimensional anatomically accurate multicellular model of a parotid gland acinus to investigate the influence that the topology of its lumen has on primary fluid secretion. Our model consists of seven individual cells, coupled via a common lumen and intercellular signalling. Each cell is equipped with the intracellular calcium ([Formula: see text])-signalling model developed by Pages et al, Bull Math Biol 81: 1394-1426, 2019. https://doi.org/10.1007/s11538-018-00563-z and the secretion model constructed by Vera-Sigüenza et al., Bull Math Biol 81: 699-721, 2019. https://doi.org/10.1007/s11538-018-0534-z. The work presented here is a continuation of these studies. While previous mathematical research has proven invaluable, to the best of our knowledge, a multicellular modelling approach has never been implemented. Studies have hypothesised the need for a multiscale model to understand the primary secretion process, as acinar cells do not operate on an individual basis. Instead, they form racemous clusters that form intricate water and protein delivery networks that join the acini with the gland's ducts-questions regarding the extent to which the acinus topology influences the efficiency of primary fluid secretion to persist. We found that (1) The topology of the acinus has almost no effect on fluid secretion. (2) A multicellular spatial model of secretion is not necessary when modelling fluid flow. Although the inclusion of intercellular signalling introduces vastly more complex dynamics, the total secretory rate remains fundamentally unchanged. (3) To obtain an acinus, or better yet a gland flow rate estimate, one can multiply the output of a well-stirred single-cell model by the total number of cells required.

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two [Formula: see text] exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by [Formula: see text] movement. Here, a basolateral [Formula: see text] adenosine triphosphatase pump (NaK-ATPase) and a [Formula: see text]-[Formula: see text]-[Formula: see text] cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with [Formula: see text] well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of [Formula: see text] ions from the internal stores of acinar cells, which triggers saliva secretion. [Formula: see text]-dependent [Formula: see text] and [Formula: see text] channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that [Formula: see text] anion exchangers (Ae), coupled with a basolateral [Formula: see text] ([Formula: see text]) (Nhe1) antiporter, regulate intracellular pH and act as a secondary [Formula: see text] uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823-G837, 1992; Melvin et al. in Annu Rev Physiol 67:445-469, 2005. https://doi.org/10.1146/annurev.physiol.67.041703.084745 ). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate [Formula: see text] decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677-10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary [Formula: see text] uptake and thus a key mechanism for saliva secretion. Here, by using 'in-silico' Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger's cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.

Computational modeling of epithelial fluid and ion transport in the parotid duct after transfection of human aquaporin-1

Previous studies have shown that localized delivery of the aquaporin-1 (AQP1) gene to the parotid duct can restore saliva flow in minipigs following irradiation-induced salivary hypofunction. The resulting flow rate and electrochemistry of secreted saliva contradicts current understanding of ductal fluid transport. We hypothesized that changes in expression of ion transport proteins have occurred following AQP1 transfection. We use a mathematical model of ion and fluid transport across the parotid duct epithelial cells to predict the expression profile of ion transporters that are consistent with the experimental measurements of saliva composition and secretion rates. Using a baseline set of parameters, the model reproduces the data for the irradiated, non-AQP1-transfected case. We propose three scenarios which may have occurred after transfection, which differ in the location of the AQP1 gene. The first scenario places AQP1 within nonsecretory cells, and requires that epithelial sodium channel (ENaC) expression is greatly reduced (1.3% of baseline), and ductal bicarbonate concentration is increased from 40.6 to 137.0 mM, to drive water secretion into the duct. The second scenario introduces the AQP1 gene into all ductal cells. The final scenario has AQP1 primarily in the proximal duct cells which secrete water under baseline conditions. We find the change in the remaining cells includes a 95.8% reduction in ENaC expression, enabling us to reproduce all experimental ionic concentrations within 9 mM. These findings provide a mechanistic basis for the observations and will guide the further development of gene transfer therapy for salivary hypofunction.

NEW & NOTEWORTHY

Following transfection of aquaporin into the parotid ducts of minipigs with salivary hypofunction, the resulting increase in salivary flow rates contradicts current understanding of ductal fluid transport. We show that the change in saliva electrochemistry and flow rate can be explained by changes in expression of ion transporters in the ductal cell membranes, using a mathematical model replicating a single parotid duct.

Aquaporins in Salivary Glands: From Basic Research to Clinical Applications

Salivary glands are involved in saliva secretion that ensures proper oral health. Aquaporins are expressed in salivary glands and play a major role in saliva secretion. This review will provide an overview of the salivary gland morphology and physiology of saliva secretion, and focus on the expression, subcellular localization and role of aquaporins under physiological and pathophysiological conditions, as well as clinical applications involving aquaporins. This review is highlighting expression and localization of aquaporins in human, rat and mouse, the most studied species and is pointing out possible difference between major salivary glands, i.e., parotid, submandibular and sublingual glands.

Multiscale modelling of saliva secretion

We review a multiscale model of saliva secretion, describing in brief how the model is constructed and what we have so far learned from it. The model begins at the level of inositol trisphosphate receptors (IPR), and proceeds through the cellular level (with a model of acinar cell calcium dynamics) to the multicellular level (with a model of the acinus), finally to a model of a saliva production unit that includes an acinus and associated duct. The model at the level of the entire salivary gland is not yet completed. Particular results from the model so far include (i) the importance of modal behaviour of IPR, (ii) the relative unimportance of Ca(2+) oscillation frequency as a controller of saliva secretion, (iii) the need for the periodic Ca(2+) waves to be as fast as possible in order to maximise water transport, (iv) the presence of functional K(+) channels in the apical membrane increases saliva secretion, (v) the relative unimportance of acinar spatial structure for isotonic water transport, (vi) the prediction that duct cells are highly depolarised, (vii) the prediction that the secondary saliva takes at least 1mm (from the acinus) to reach ionic equilibrium. We end with a brief discussion of future directions for the model, both in construction and in the study of scientific questions.

A novel biophysical model on calcium and voltage dual dependent gating of calcium-activated chloride channel

Ca(2+)-activated Cl(-) channels (CaCCs) are anion-selective channels and involved in physiological processes such as electrolyte/fluid secretion, smooth muscle excitability, and olfactory perception which critically depend on the Ca(2+) and voltage dual-dependent gating of channels. However, how the Ca(2+) and voltage regulate the gating of CaCCs still unclear. In this work, the authors constructed a biophysical model to illustrate the dual-dependent gating of CaCCs. For validation, we applied our model on both native CaCCs and exogenous TMEM16A which is thought to be the molecular basis of CaCCs. Our data show that the native CaCCs may share universal gating mechanism. We confirmed the assumption that by binding with the channel, Ca(2+) decreases the energy-barrier to open the channel, but not changes the voltage-sensitivity. For TMEM16A, our model indicates that the exogenous channels show different Ca(2+) dependent gating mechanism from the native ones. These results advance the understanding of intracellular Ca(2+) and membrane potential regulation in CaCCs, and shed new light on its function in aspect of physiology and pharmacology.

What do aquaporin knockout studies tell us about fluid transport in epithelia?

The investigation of near-isosmotic water transport in epithelia goes back over 100 years; however, debates over mechanism and pathway remain. Aquaporin (AQP) knockouts have been used by various research groups to test the hypothesis of an osmotic mechanism as well as to explore the paracellular versus transcellular pathway debate. Nonproportional reductions in the water permeability of a water-transporting epithelial cell (e.g., a reduction of around 80-90 %) compared to the reduction in overall water transport rate in the knockout animal (e.g., a reduction of 50-60 %) are commonly found. This nonproportionality has led to controversy over whether AQP knockout studies support or contradict the osmotic mechanism. Arguments raised for and against an interpretation supporting the osmotic mechanism typically have partially specified, implicit, or incorrect assumptions. We present a simple mathematical model of the osmotic mechanism with clear assumptions and, for models based on this mechanism, establish a baseline prediction of AQP knockout studies. We allow for deviations from isotonic/isosmotic conditions and utilize dimensional analysis to reduce the number of parameters that must be considered independently. This enables a single prediction curve to be used for multiple epithelial systems. We find that a simple, transcellular-only osmotic mechanism sufficiently predicts the results of knockout studies and find criticisms of this mechanism to be overstated. We note, however, that AQP knockout studies do not give sufficient information to definitively rule out an additional paracellular pathway.

A quantitative analysis of electrolyte exchange in the salivary duct

A healthy salivary gland secretes saliva in two stages. First, acinar cells generate primary saliva, a plasma-like, isotonic fluid high in Na(+) and Cl(-). In the second stage, the ducts exchange Na(+) and Cl(-) for K(+) and HCO(3)(-), producing a hypotonic final saliva with no apparent loss in volume. We have developed a tool that aims to understand how the ducts achieve this electrolyte exchange while maintaining the same volume. This tool is part of a larger multiscale model of the salivary gland and can be used at the duct or gland level to investigate the effects of genetic and chemical alterations. In this study, we construct a radially symmetric mathematical model of the mouse salivary gland duct, representing the lumen, the cell, and the interstitium. For a given flow and primary saliva composition, we predict the potential differences and the luminal and cytosolic concentrations along a duct. Our model accounts well for experimental data obtained in wild-type animals as well as knockouts and chemical inhibitors. Additionally, the luminal membrane potential of the duct cells is predicted to be very depolarized compared with acinar cells. We investigate the effects of an electrogenic vs. electroneutral anion exchanger in the luminal membrane on concentration and the potential difference across the luminal membrane as well as how impairing the cystic fibrosis transmembrane conductance regulator channel affects other ion transporting mechanisms. Our model suggests the electrogenicity of the anion exchanger has little effect in the submandibular duct.

Modelling the effects of calcium waves and oscillations on saliva secretion

An understanding of Ca(2+) signalling in saliva-secreting acinar cells is important, as Ca(2+) is the second messenger linking stimulation of cells to production of saliva. Ca(2+) signals affect secretion via the ion channels located both apically and basolaterally in the cell. By approximating Ca(2+) waves with periodic functions on the apical and basolateral membranes, we isolate individual wave properties and investigate them for their effect on fluid secretion in a mathematical model of the acinar cell. Mean Ca(2+) concentration is found to be the most significant property in signalling secretion. Wave speed was found to encode a range of secretion rates. Ca(2+) oscillation frequency and amplitude had little effect on fluid secretion.