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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