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

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.

Figure 1

Transcellular fluid secretion. Left: direction of fluid flow. Right: one mechanism, utilizing secretion of chloride, involved in fluid secretion

Figure 2

Efficiency of fluid secretion. Two representations of the behavior of the solution (35) of the quasi-steady-state equation (34) relating fluid flow to chloride current for the large permeability limit (upper bound, blue) and finite permeability (red). The singular (large permeability, α = 0) isosmotic case is an upper bound for fluid secretion and gives a greater flow at a fixed chloride current (1). For fixed chloride current, the dependence of fluid low on the ratio (α) of the chloride and fluid transport parameters can be seen in 2, while the change in shape of the whole solution is illustrated in 1. For small α values, the decrease in fluid flow is roughly proportional, while the rate of decrease is lower for larger α values

Figure 3

Baseline behavior. There are oscillatory shifts to new levels for the ions ([Cl]_i,[Na]_i, [K]_i, [Cl]_l), membrane voltage, total concentrations and cell volume (a-f, respectively)

Figure 4

Simulation plots of fluid secretion for a range of permeabilities. Panel A: L_pa = 1.23 × 10⁻¹⁴ L²J⁻¹s⁻¹, Panel B: L_pa = 1.23 × 10⁻¹⁶ L²J⁻¹s⁻¹, Panel C: L_pa = 1.23 × 10⁻¹⁷ L²J⁻¹s⁻¹. L_pb = 4 * L_pa in all cases. In (a) all the traces are indistinguishable. As the permeability is decreased (panels B and C), the quadratic quasi-steady-state approximation follows the full simulation results, while the linear quasi-steady-state approximation overestimates the secretion, consistent with our prediction of it as an upper bound. In the lower-permeability range, the quadratic steady state slightly overestimates the true water transport rate during rapid spikes

Figure 5

Salivary acinus (not to scale). Cells are arranged about a shared lumenal region (hatched)

Figure 6

Illustration of the comparison of the secretion from n independent cells to the secretion from n lumenally-coupled cells, for fixed chloride currents. For simplicity, the diagram shows the case of three cells when independent compared to the same three cells (with fixed chloride currents) when lumenally-coupled

Figure 7

Individual secretions from differently stimulated cells. Each cell is stimulated differently, but, due to the shared lumen, they secrete saliva at close to the same rate. L_pa = 1.23 × 10⁻¹⁴ L²J⁻¹s⁻¹ and L_pb = 4 * L_pa in all cases

Figure 8

Efficiency of total secretion under coupled conditions. Panel A: L_pa = 1.23 × 10⁻¹⁴ L²J⁻¹s⁻¹, Panel B: L_pa = 1.23 × 10⁻¹⁶ L²J⁻¹s⁻¹, Panel C: L_pa = 1.23 × 10⁻¹⁷ L²J⁻¹s⁻¹. L_pb = 4 * L_pa in all cases

Figure 9

Comparison of the time-averaged total secretion from independent and coupled cells for a range of permeabilities. Top group: L_pa = 1.23 × 10⁻¹⁴ L²J⁻¹s⁻¹, Middle group: L_pa = 1.23 × 10⁻¹⁶ L²J⁻¹s⁻¹, Bottom group: L_pa = 1.23 × 10⁻¹⁷ L²J⁻¹s⁻¹. L_pb = 4 * L_pa in all cases