Table 2.

Description and values of model parameters

Parameter	Symbol	Value	Reference
Plasma volume	$V_p$	10 mL	Granjon et al. 3
PTH
Maximal rate constant of PTH secretion from the parathyroid gland	${\beta }_{exo}^{PTHg}$	1.034 min−1	estimated (refer to section: STAR Methods:Method details:Parathyroid gland and parathyroid hormone and Figure 2)
Factor controlling the maximal PTH secretion at a given plasma Ca2+ concentration	${\gamma }_{Ca}$	0.15 mM	estimated (refer to section: STAR Methods:Method details:Parathyroid gland and parathyroid hormone and Figure 2)
Factor controlling the maximal PTH secretion at a given plasma Ca2+ concentration	${\gamma }_p$	2	estimated (refer to section: STAR Methods:Method details:Parathyroid gland and parathyroid hormone and Figure 2)
Factor controlling the slope of the PTH secretion curve	$C_m$	3.8 mM	estimated (refer to section: STAR Methods:Method details:Parathyroid gland and parathyroid hormone and Figure 2)
IC50 value of Mg2+ for inhibition of PTH secretion	$K_{low-Mg}$	0.25 mM	Quitterer et al. 14
Basal rate of PTH production in the parathyroid gland	$k_{prod}^{PTHg}$	2.53 pmol/min	estimated
Inhibition of PTH synthesis by 1,25(OH)2D3	${\gamma }_{prod}^{1,25{\left(OH\right)}_2{D}_3}$	0.003 p.m.−1	Stadt et al.4
Rate of degradation of PTH in parathyroid gland	$k_{\mathit{deg}}^{PTHg}$	0.035 min−1	Granjon et al. 3
Degradation rate constant of plasma PTH	$k_{\mathit{deg}}^{PTHp}$	0.081 min−1	estimated
Vitamin D3
Inactive vitamin D3	${\left[25\left(OH\right)D\right]}_p$	25 nM	Granjon et al. 3
Minimum production rate constant of 1,25(OH)2D3	$k_{conv}^{\mathit{min}}$	4.4 x 10−6 min−1	Granjon et al. 3
Maximal increase in 1,25(OH)2D3 production rate	${\delta }_{conv}^{\mathit{max}}$	6 x 10−5 min−1	Granjon et al. 3
Stimulation of 1,25(OH)2D3 production by PTH	$K_{conv}^{PTH}$	3 p.m.	Granjon et al. 3
PTH sensitivity coefficient	$n_{conv}$	6	Granjon et al. 3
Inhibition of 1,25(OH)2D3 production by Ca2+	${\gamma }_{conv}^{Ca}$	0.3 mM−1	Granjon et al. 3
Inhibition of 1,25(OH)2D3 production by itself	${\gamma }_{conv}^{1,25{\left(OH\right)}_2{D}_3}$	1.8 x 10−2 p.m.−1	Granjon et al. 3
Factor controlling the maximal increase in 1,25(OH)2D3 production by Mg2+	${\delta }_{Mg-act}$	6.6	estimated (refer to section: STAR Methods:Method details:Plasma 1,25(OH)2D3 and Figure 3)
Michaelis-Menten constant	$K_{Mg-act}^1$	1.1 mM	estimated (refer to section: STAR Methods:Method details:Plasma 1,25(OH)2D3 and Figure 3)
Michaelis-Menten constant	$K_{Mg-act}^2$	1.2 mM	estimated (refer to section: STAR Methods:Method details:Plasma 1,25(OH)2D3 and Figure 3)
Inhibition of 1,25(OH)2D3 degradation by PTH	${\gamma }_{inact}^{PTH}$	0.52 p.m.−1	Granjon et al. 3
Michaelis-Menten constant	$K_{D3}$	1.7 mM	estimated
Degradation rate constant of 1,25(OH)2D3	$k_{\mathit{deg}}^{1,25{\left(OH\right)}_2{D}_3}$	0.008 min−1	estimated
Kidneys
Minimal fractional reabsorption of Mg2+ in proximal tubule	${\lambda }_{Mg-PT}^0$	0.185	Quamme et al.15
Stimulation of Mg2+ reabsorption in proximal tubule by PTH	${\delta }_{Mg-PT}^{\mathit{max}}$	0.015	estimated
Sensitivity of Mg2+ reabsorption in proximal tubule to PTH	${PTH}_{ref}$	12 p.m.	Granjon et al. 3
Hill coefficient	$n_{PT}$	5	Granjon et al. 3
Minimal fractional reabsorption of Mg2+ in thick ascending limb	${\lambda }_{Mg-TAL}^0$	0.66	Quamme et al.15
Stimulation of Mg2+ reabsorption in thick ascending limb by CaSR	${\delta }_{Mg-CaSR}^{\mathit{max}}$	0.028	estimated
Stimulation of Mg2+ reabsorption in thick ascending limb by PTH	${\delta }_{Mg-PTH}^{\mathit{max}}$	0.012	estimated
Sensitivity of Mg2+ reabsorption in thick ascending limb to Ca2+	${Ca}_{ref}$	1.25 mM	Brown et al. 16
Sensitivity of Mg2+ reabsorption in thick ascending limb to Mg2+	${Mg}_{ref}$	2.5 mM	Brown et al. 16
Hill coefficient	$n_{TAL}$	4	Granjon et al. 3
Sensitivity of Mg2+ reabsorption in thick ascending limb to PTH	$K_{TAL}^{PTH}$	4 p.m.	Stadt et al.4
Minimal fractional reabsorption of Mg2+ in distal convoluted tubule	${\lambda }_{Mg-DCT}^0$	0.08	Quamme et al.15
Stimulation of Mg2+ reabsorption in distal convoluted tubule by PTH and 1,25(OH)2D3	${\delta }_{Mg-DCT}^{\mathit{max}}$	0.02	estimated
Sensitivity of Mg2+ reabsorption in distal convoluted tubule to PTH	$K_{DCT}^{PTH}$	7.25 p.m.	Stadt et al. 4
Sensitivity of Mg2+ reabsorption in distal convoluted tubule to 1,25(OH)2D3	$K_{DCT}^{1,25{\left(OH\right)}_2{D}_3}$	160 p.m.	Stadt et al. 4
Glomerular filtration rate (GFR)	${\mathrm{\Phi }}_{GFR}$	1.25 mL/min	Sadick et al. 17
Intestine
Dietary Mg2+ intake	$I_{Mg}$	0.04 μmol/min	Coudray et al. 13
Maximal rate of active absorption of Mg2+	$V_{active}$	0.764 μmol/min	Hardwick et al.18
Stimulation of active Mg2+ absorption by dietary Mg2+ intake	$K_{active}$	0.17 μmol/min	Hardwick et al.18
Stimulation of Mg2+ absorption by 1,25(OH)2D3	$K_{abs}^{1,25{\left(OH\right)}_2{D}_3}$	100 p.m.	Granjon et al. 3
Bones
Rate of Mg2+ uptake from plasma by fast bone pool	$k_{p-f}^{Mg}$	0.074 min−1	estimated
Rate of Mg2+ release from fast bone pool to plasma	$k_{f-p}^{Mg}$	0.2 x 10−3 min−1	estimated
Rate of accretion into the slow bone pool	${\gamma }_{ac}^{Mg}$	3.98 x 10−4 min−1	estimated
Minimal resorption rate	${\tau }_{res}^{\mathit{min}}$	0.142 x 10−3 mmol/min	Granjon et al. 3
Maximal resorption rate	${\delta }_{res}^{\mathit{max}}$	0.7 x 10−3 mmol/min	Granjon et al. 3
Stimulation of bone resorption by PTH	$K_{res}^{PTHp}$	2.45 p.m.	Granjon et al. 3
Stimulation of bone resorption by 1,25(OH)2D3	$K_{res}^{1,25{\left(OH\right)}_2{D}_3}$	160 p.m.	Granjon et al. 3
Plasma
Fraction of magnesium bound to proteins	${\kappa }_{b-Mg}$	0.3	Jahnen-Dechent et al. 19