Table 3 Definition, baseline values and units for the epithelial barrier and immune response model parameters given in36.
Parameter | Description | Value & Units |
|---|---|---|
\(\epsilon _{1}\) | Proliferation rate of intestinal epithelial cells | \(\mathrm {4.9\times 10}^{-13}\) (ng day)−1 |
\(\epsilon _{2}\) | Rate of repair of damaged epithelial cells by VDR | \(\mathrm {2\times 10}^{9}\) ml/(ng day) |
\(\epsilon _{3}\) | Removal rate of damaged epithelial cells by macrophages | \(\mathrm {3.17\times 10}^{-6}\) ml/day |
\(\epsilon _{4}\) | Damage to epithelial cells by pro-inflammatory mediators | \(\mathrm {2.7\times 10}^{3}\) ml/(ng day) |
\(\epsilon _{5}\) | Damage to epithelial cells by pathogenic bacteria | \(\mathrm {1\times 10}^{-12}\) (CFU day)−1 |
\(\iota _{1}\) | Rate of activation of macrophages by pro-inflammatory cytokines | \(\mathrm {1.35\times 10}^{9}\) (ng day)−1 |
\(\iota _{2}\) | Rate of inhibition of macrophages by anti-inflammatory cytokines | \(\mathrm {1.13\times 10}^{2}\) ml/(ng day) |
\(\iota _{3}\) | Natural death rate of macrophages | 1 day−1 |
\(\iota _{4}\) | Rate that T/B cells are differentiated into T/B regulatory cells in presence of VDR | \(\mathrm {2.38\times 10}^{11}\) (ng day)−1 |
\(\iota _{5}\) | Rate that T/B cells are differentiated into T/B regulatory cells in presence of commensal bacteria | \(\mathrm {8.5\times 10}^{-11}\) (CFU ml day)−1 |
\(\iota _{6}\) | Rate at which differentiation into regulatory cells is inhibited by pathogenic bacteria | \(\mathrm {1\times 10}^{-14}\) CFU−1 |
\(\iota _{7}\) | Combined natural death rate of T/B regulatory cells | 1 day−1 |
\(\iota _{8}\) | Rate of utilisation of metabolites for T-helper cell proliferation | \(\mathrm {2.57\times 10}^{-8}\) (ng ml day)−1 |
\(\iota _{9}\) | Rate of T-helper cell proliferation in response to pro-inflammatory cytokines | \(\mathrm {1.12\times 10}^{9}\) (ng day)−1 |
\(\iota _{10}\) | Rate of T-helper cell proliferation in response to pathogenic bacteria | \(\mathrm {1.05\times 10}^{-7}\) (CFU ml day)−1 |
\(\iota _{11}\) | Rate of inhibition to T helper cell proliferation by VDR | \(\mathrm {4\times 10}^{6}\) ml/ng |
\(\iota _{12}\) | Rate of inhibition to T helper cell proliferation by commensals | \(\mathrm {1\times 10}^{-15}\) CFU−1 |
\(\iota _{13}\) | Natural rate of T-helper cell death | 10 day−1 |
\(\iota _{14}\) | Rate of activation of plasma B cells by bacterial products | \(\mathrm {1.28\times 10}^{-8}\) (ng ml day)−1 |
\(\iota _{15}\) | Rate of maturation of plasma B cells in presence of pro-inflammatory cytokines | \(\mathrm {5\times 10}^{8}\) (ng day)−1 |
\(\iota _{16}\) | Rate of inhibition of plasma B cells by VDR | \(\mathrm {4\times 10}^{8}\) ml/ng |
\(\iota _{17}\) | Natural death rate of plasma B cells | 0.81 day−1 |
\(\alpha _{1}\) | Production rate of anti-inflammatory cytokines by epithelial cells upregulated by VDR | \(\mathrm {7.08\times 10}^{5}\) day−1 |
\(\alpha _{2}\) | Production rate of anti-inflammatory cytokines by T and B regulatory cells stimulated by commensal bacteria | \(\mathrm {2.07\times 10}^{-21}\) ng/(CFU day) |
\(\alpha _{3}\) | Production rate of anti-inflammatory cytokines by macrophages after consuming damaged epithelial cells | \(\mathrm {1.13\times 10}^{-7}\) ng/day |
\(\alpha _{4}\) | Production rate of anti-inflammatory cytokines by macrophages after consuming pathogenic bacteria | \(\mathrm {1.69\times 10}^{-20}\) ng/(CFU day) |
\(\alpha _{5}\) | Natural degradation rate of anti-inflammatory cytokines | \(\mathrm {7.5\times 10}^{2}\) day−1 |
\(\alpha _{6}\) | Production rate of pro-inflammatory cytokines in response to damaged epithelial cells | \(\mathrm {9.3\times 10}^{-18}\) ng/(CFU ml day) |
\(\alpha _{7}\) | Production rate of pro-inflammatory cytokines by activated innate immune cells | \(\mathrm {5.94\times 10}^{-11}\) ng/day |
\(\alpha _{8}\) | Inhibition of pro-inflammatory cytokines by VDR | \(\mathrm {4\times 10}^{7}\) ml/ng |
\(\alpha _{9}\) | Inhibition of pro-inflammatory cytokines by commensals | \(\mathrm {5\times 10}^{-15}\) CFU−1 |
\(\alpha _{10}\) | Production rate of pro-inflammatory cytokines by T helper cells | \(\mathrm {8.78\times 10}^{-24}\) ng/(CFU day) |
\(\alpha _{11}\) | Natural degradation rate of pro-inflammatory cytokines | 1.2 day−1 |
\(\alpha _{c}\) | Rate of pro-inflammatory cytokine release by damaged epithelial cells | \(\mathrm {2.3\times 10}^{-3}\) ng/(ml day) |
\(\alpha _{g}\) | Rate of anti-inflammatory cytokine release by healthy epithelial cells | \(\mathrm {1.77\times 10}^{-3}\) ng/(ml day) |
\(\gamma _{c}\) | Background production rate of pro-inflammatory cytokines | \(\mathrm {3\times 10}^{-4}\) ng/(ml day) |
\(\gamma _{g}\) | Background production rate of anti-inflammatory cytokines | 0.35 ng/(ml day) |
