A Mathematical Model of Salivary Gland Duct Cells

Abstract

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$$^+$$ + and Cl$$^-$$ - 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.

Simulation of Calcium Dynamics in Realistic Three-Dimensional Domains

“…In previous work [ 27 ], we created artificial striated and intercalated salivary gland duct cells. We performed this by reconstructing a segment of salivary duct from a series of experimental optical slices and growing cells around this ductal skeleton, using a similar method to the one described here.…”

“…Here, we add artificial acini, thus completing a complete “mini-gland” reconstruction as shown in Figure 3 . This reconstruction contains 82 acinar cells (a number of which were used in the simulations reported in this work) as well as 111 duct cells (used in [ 27 ]).…”

“…that we use to guide our reconstruction process ensuring that, on average, our artificial reconstructions are representative of real-world salivary glands. In this work, we use the spatial statistics that we reported in [ 27 ], as well as physics-based “growing”, which ensures that artificially generated cells pack together tightly in a realistic organic fashion.…”

“…For this work, and in [ 27 ], we extracted a representative overall three-dimensional physical outline boundary of a mini-gland from an optical image stack containing 110 slices. However, those particular optical slices highlighted tight junctions and, as such, could not be used to accurately identify individual cell outlines.…”

“…The model equations are identical to those of [ 27 ] and are thus not given in detail again here. Briefly, is produced only at the basolateral membrane and diffuses through the cytoplasm to bind to IPR situated so close to the ClCa on the apical membrane that all IPR fluxes are treated as boundary fluxes on the apical membrane.…”