# Efficiency of Primary Saliva Secretion: An Analysis of Parameter Dependence in Dynamic Single-Cell and Acinus Models, with Application to Aquaporin Knockout Studies

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## Abstract

Secretion from the salivary glands is driven by osmosis following the establishment of osmotic gradients between the lumen, the cell and the interstitium by active ion transport. We consider a dynamic model of osmotically driven primary saliva secretion and use singular perturbation approaches and scaling assumptions to reduce the model. Our analysis shows that isosmotic secretion is the most efficient secretion regime and that this holds for single isolated cells and for multiple cells assembled into an acinus. For typical parameter variations, we rule out any significant synergistic effect on total water secretion of an acinar arrangement of cells about a single shared lumen. Conditions for the attainment of isosmotic secretion are considered, and we derive an expression for how the concentration gradient between the interstitium and the lumen scales with water- and chloride-transport parameters. Aquaporin knockout studies are interpreted in the context of our analysis and further investigated using simulations of transport efficiency with different membrane water permeabilities. We conclude that recent claims that aquaporin knockout studies can be interpreted as evidence against a simple osmotic mechanism are not supported by our work. Many of the results that we obtain are independent of specific transporter details, and our analysis can be easily extended to apply to models that use other proposed ionic mechanisms of saliva secretion.

## Keywords

Fluid and electrolyte secretion in salivary glands Epithelial transport Mathematical modeling Efficiency Aquaporin## Notes

### Acknowledgement

We thank Ted Begenisich, David Yule and Trevor Shuttleworth at the University of Rochester; James Melvin and Marcelo Catalan at the National Institutes of Health (NIH); and Laurence Palk, Kate Patterson, Katie Sharp, Shawn Means, Ivo Siekmann and Vivien Kirk from the University of Auckland for helpful discussions and feedback. We also thank the anonymous referees for detailed and helpful comments that we feel significantly improved this work. O. M. was supported by the Tertiary Education Commission’s Top Achiever Doctoral Scholarship. This work was supported by NIH grant R01 DE19245-01.

## Supplementary material

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