A Mathematical Model of Salivary Gland Duct Cells.

Saliva is produced in two stages in the salivary glands: the secretion of primary saliva by the acinus and the modification of saliva composition to final saliva by the intercalated and striated ducts. In order to understand the saliva modification process, we develop a mathematical model for the salivary gland duct. The model utilises the realistic 3D structure of the duct reconstructed from an image stack of gland tissue. Immunostaining results show that TMEM16A and aquaporin are expressed in the intercalated duct cells and that ENaC is not. Based on this, the model predicts that the intercalated duct does not absorb Na[Formula: see text] and Cl[Formula: see text] like the striated duct but secretes a small amount of water instead. The input to the duct model is the time-dependent primary saliva generated by an acinar cell model. Our duct model produces final saliva output that agrees with the experimental measurements at various stimulation levels. It also shows realistic biological features such as duct cell volume, cellular concentrations and membrane potentials. Simplification of the model by omission of all detailed 3D structures of the duct makes a negligible difference to the final saliva output. This shows that saliva production is not sensitive to structural variation of the duct.

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.

Image correlation spectroscopy of multiphoton images correlates with collagen mechanical properties.

Multiphoton microscopy (MPM) holds promise as a noninvasive imaging technique for characterizing collagen structure, and thus mechanical properties, through imaging second harmonic generation (SHG) and two-photon fluorescence in engineered and real connective tissues. Controlling polymerization pH to manipulate collagen gel microstructure, we quantified pore and fiber dimensions using both standard methods and image correlation spectroscopy (ICS) on MPM, scanning electron, and darkfield microscopy images. The latter two techniques are used to confirm microstructural measurements made from MPM images. As polymerization pH increased from 5.5 to 8.5, mean fiber diameter decreased from 3.7 +/- 0.7 microm to 1.6 +/- 0.3 microm, the average pore size decreased from 81.7 +/- 3.7 microm(2) to 7.8 +/- 0.4 microm(2), and the pore area fraction decreased from 56.8% +/- 0.8% to 18.0% +/- 1.3% (measured from SHG images), whereas the storage modulus G' and loss modulus G'', components of the shear modulus, increased approximately 33-fold and approximately 16-fold, respectively. A characteristic length scale measured using ICS, W(ICS), correlates well with the mean fiber diameter from SHG images (R(2) = 0.95). Semiflexible network theory predicts a scaling relationship of the collagen gel storage modulus (G') depending upon mesh size and fiber diameter, which are estimated from SHG images using ICS. We conclude that MPM and ICS are an effective combination to assess bulk mechanical properties of collagen hydrogels in a noninvasive, objective, and systematic fashion and may be useful for specific in vivo applications.