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Table 2 Summary of parameter values

From: Combination therapy for melanoma with BRAF/MEK inhibitor and immune checkpoint inhibitor: a mathematical model

Notation Description Value used References
δ D Diffusion coefficient of DCs 8.64×10−7 cm2 day−1 [65]
δ T Diffusion coefficient of T cells 8.64×10−7 cm2 day−1 [65]
δ M Diffusion coefficient of MDSCs 8.64×10−7 cm2 day−1 [65]
δ C Diffusion coefficient of tumor cells 8.64×10−7 cm2 day−1 [65]
\(\delta _{I_{12}}\) Diffusion coefficient of IL-12 6.05×10−2 cm2 day−1 Estimated
\(\delta _{I_{2}}\) Diffusion coefficient of IL-2 9.58×10−2 cm2 day−1 Estimated
\(\delta _{T_{\beta }}\) Diffusion coefficient of TGF- β 8.52×10−2 cm2 day−1 Estimated
\(\delta _{I_{6}}\) Diffusion coefficient of IL-6 9.03×10−2 cm2 day−1 Estimated
\(\delta _{I_{10}}\) Diffusion coefficient of IL-10 9.11×10−2 cm2 day−1 Estimated
δ A Diffusion coefficient of anti-PD-1 7.85×10−2 cm2 day−1 Estimated
δ B Diffusion coefficient of BRAF/MEKi 3.16×10−1 cm2 day−1 Estimated
σ 0 Flux rate of T 1 and T 8 cells at the boundary 1 cm−1 [65]
χ Chemoattraction coefficient of IL-6 10 cm5/g·day [90, 91]
λ DC Activation rate of DCs by tumor cells 4 g/cm3·day [65]
\(\lambda _{T_{1}I_{12}}\) Activation rate of CD 4+ T cells by IL-12 18.64 day−1 Estimated
\(\lambda _{T_{1}I_{2}}\) Activation rate of CD 4+ T cells by IL-2 0.25 day−1 [65]
\(\lambda _{T_{8}I_{12}}\) Activation rate of CD 8+ T cells by IL-12 16.6 day−1 Estimated
\(\lambda _{T_{8}I_{2}}\) Activation rate of CD 8+ T cells by IL-2 0.25 day−1 [65]
\(\lambda _{T_{r}T_{\beta }}\) Activation rate of Tregs by TGF- β 0.415 day−1 Estimated
\(\lambda _{T_{r}Q}\) Activation rate of Tregs by PD-1-PD-L1 0.083 day−1 Estimated
λ M Activation rate of MDSCs 1.05 day−1 [40]
λ C Growth rate of cancer cells 0.616 day−1 Estimated
λ 0 Growth rate of cancer cells uninhibited (by immune cells) 0.069 day−1 Estimated
\(\lambda _{I_{12}D}\) Production rate of IL-12 by DCs 2.76×10−6 day−1 Estimated
\(\lambda _{I_{12}B}\) Promotion of IL-12 production by BRAF/MEKi 1 Estimated
\(\lambda _{I_{2}T_{1}}\) Production rate of IL-2 by CD 4+ T cells 2.82×10−8 day−1 Estimated
\(\lambda _{T_{\beta } C}\) Production rate of TGF- β by cancer cells 2.18×10−10 day−1 Estimated
\(\lambda _{T_{\beta } T_{r}}\) Production rate of TGF- β by Tregs 5.57×10−9 day−1 [75]
\(\lambda _{T_{\beta } M}\) Production rate of TGF- β by MDSCs 2.18×10−10 day−1 Estimated
\(\lambda _{I_{6} C}\) Production rate of IL-6 by cancer cells 3.54×10−10 day−1 Estimated
\(\lambda _{I_{10} C}\) Production rate of IL-10 by cancer cells 9.10×10−10 day−1 Estimated
\(\lambda _{I_{10} M}\) Production rate of IL-10 by MDSCs 1.82×10−9 day−1 Estimated
η 1 Killing rate of tumor cells by CD 4+ T cells 11.5 day−1·cm3/g Estimated
η 8 Killing rate of tumor cells by CD 8+ T cells 46 day−1·cm3/g Estimated
μ PA Blocking rate of PD-1 by anti-PD-1 6.04×106 cm3/g·day Estimated
μ BC Absorbtion rate of BRAF/MEKi by cancer cells 6.17×10−10 day−1 Estimated
ρ P Expression of PD-1 in T cells 2.49×10−7 Estimated
ρ L Expression of PD-L1 in T cells 5.22×10−7 Estimated
ε C Expression of PD-L1 in tumor cells 0.01 [84]
ε M Expression of PD-L1 in MDSCs 0.005 Estimated
d D Death rate of DCs 0.1 day−1 [65]
\(d_{T_{1}}\) Death rate of CD 4+ T cells 0.197 day−1 [65]
\(d_{T_{8}}\) Death rate of CD 8+ T cells 0.18 day−1 [65]
\(d_{T_{r}}\) Death rate of Tregs 0.2 day−1 [75]
d M Death rate of MDSCs 0.03 day−1 [40]
d C Death rate of tumor cells 0.17 day−1 [65]
\(d_{I_{12}}\) Degradation rate of IL-12 1.38 day−1 [65]
\(d_{I_{2}}\) Degradation rate of IL-2 2.376 day−1 [65]
\(d_{T_{\beta }}\) Degradation rate of TGF- β 499.066 day−1 Estimated
\(d_{I_{6}}\) Degradation rate of IL-6 4.16 day−1 Estimated
\(d_{I_{10}}\) Degradation rate of IL-10 8.32 day−1 Estimated
d A Degradation rate of anti-PD-1 0.046 day−1 [87]
d B Degradation rate of BRAF/MEKi 1.66day−1 Estimated
D 0 Density of inactive DCs 2×10−5 g/cm3 [65]
T 10 Density of naive CD 4+ T cells in tumor 4×10−4 g/cm3 Estimated
T 80 Density of naive CD 8+ T cells in tumor 2×10−4 g/cm3 Estimated
C M Carrying capacity of cancer cells 0.8 g/cm3 [65]
\(\hat T_{1}\) Density of CD 4+ T cells from lymph node 4×10−3 g/cm3 Estimated
\(\hat T_{8}\) Density of CD 8+ T cells from lymph node 2×10−3 g/cm3 Estimated