Table 2 Definition, value and units of the vitamin D model parameters taken from³⁶.

\(D^{0}\)

Production of 25(OH)D from diet and sunlight

variable nM/day

\(k_{d}/\delta\)

Maximal rate of conversion of extracellular 25(OH)D to 1,25\(\text {(OH)}_{2}\)D

24 nM/day⁶⁷

\(K_{D}\)

Michaelis Menten constant for extracellular 25(OH)D binding to CYP27B1

1000 nM⁶⁷

\(\delta _{1}\)

\(D^{0}\delta _{1}\) is the maximum production rate of vitamin D dependent upon probiotics

0.3

\(\delta _{2}\)

Degradation of extracellular 25(OH)D

0.048 \(\hbox {day}^{-1}\)⁶⁸

\(\delta _{3}\)

Degradation of extracellular 1,25\(\text {(OH)}_{2}\)D

14.4 \(\hbox {day}^{-1}\)⁶⁸

\(\mu _{f}\)

Proportion of total extracellular 25(OH)D that is free

0.05 %⁶⁷

\(\mu _{a_{f}}\)

Proportion of total extracellular 1,25\(\text {(OH)}_{2}\)D that is free

0.85 %⁶⁷

\(\sigma _{1}\)

Permeability of macrophages to free 25(OH)D or 1,25\(\text {(OH)}_{2}\)D

144 \(\hbox {day}^{-1}\)⁶⁷

\(\sigma _{2}\)

Permeability of epithelial cells to free 25(OH)D or 1,25\(\text {(OH)}_{2}\)D

144 \(\hbox {day}^{-1}\)

\(k_{d_{i}}/\delta\)

Maximal rate of conversion of intracellular 25(OH)D to 1,25\(\text {(OH)}_{2}\)D

24 nM/day⁶⁷

\(K_{D_{i}}\)

Michaelis Menten constant for intracellular 25(OH)D binding to CYP27B1

1000 nM⁶⁷

\(\delta _{4}\)

Degradation of intracellular 25(OH)D

0.048 \(\hbox {day}^{-1}\)⁶⁸

\(\delta _{5}\)

Degradation of intracellular 1,25\(\text {(OH)}_{2}\)D

14.4 \(\hbox {day}^{-1}\)⁶⁸

\(\delta _{6}\)

Rate at which 1,25\(\text {(OH)}_{2}\)D binds to VDR

24\(\times 10^{-7}\) \(\hbox {nM}^{-1}\) \(\hbox {day}^{-1}\)⁶⁷

\(\delta _{7}\)

Rate of degradation of VDR:1,25\(\text {(OH)}_{2}\)D

0.024 \(\hbox {day}^{-1}\)

\(\delta _{8}a/K_{V}\)

Concentration of VDR

1.2 nM⁶⁷

\(K_{V}\)

Saturation constant

1 CFU/day

\(K_{\delta }\)

Saturation constant

5\(\times 10^{8}\) CFU/day