Fig 1.
Schematic of the two-state receptor model representing PTH to PTH1R binding based on [16].
L(t) = PTH concentration; t = time; T = period; Ra = active receptor concentration; Ri = inactive receptor concentration; Ca = active ligand-receptor complex concentration, Ci = inactive ligand-receptor complex concentration, k±i = kinematic parameters (i ∈ {1, 2, d, r}); α = scaled activity; αR = cellular responsivenes.
Table 1.
Parameter values for the two-state receptor model of PTH-PTH1R as illustrated in Fig 1.
Fig 2.
Schematic representation of the square-wave PTH ligand concentration Lgl (in plasma) vs. time.
γ1 is the peak PTH concentration due to pulsatile glandular secretion, γ0 is the PTH concentration due to tonic glandular secrection, and τ0 and τ1 are the off- and on-phases of pulsatile component. Dark grey area Atonic represents the plasma concentration resulting from a tonic secretion whereas the light grey area Apuls represents the plasma concentration resulting from the pulsatile secretion.
Fig 3.
PTH plasma concentration obtained from the PTH PK model and the simplified square-wave stimulus characterised by the maximum PTH concentration and the on-phase τ1.
Fig 4.
Computational simulation results of two models used to compute scaled activity α and cellular responsiveness αR for the case of combined PTH glandular secretion and external sc daily PTH injection (D = 20μg).
(a) refers to model 1 whereas (b) refers to model 2.
Table 2.
Computed cellular responsiveness for different PTH doses using model 1 and model 2.
Fig 5.
Scaled activity α for healthy person, patient with idiopathic osteoporosis and hyperparathyroidism.
Table 3.
Cellular responsiveness for gland secretion.
Fig 6.
Cellular responsiveness for a healthy person as function of T and τ1; γ1 and τ1; γ1 and T.
The third quantity of the triplet (γ1, τ1, T) results from the optimisation constraint given in Eq (15). Simulation parameters are given in Table 1 and S2 Table.
Fig 7.
Cellular responsiveness computed with model 2 for healthy person, patients with idiopathic osteoporosis and hyperparathyroidism after different doses of PTH sc injection are applied once daily.
Table 4.
Maximum cellular responsiveness for PTH doses administered via sc daily injections.