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Table 1 Summary of parameter values

From: Prediction of anti-CD25 and 5-FU treatments efficacy for pancreatic cancer using a mathematical model

Parameter

Value

Definition

Units

References

a1

4.3992 × 10−2

Panc02 tumor growth rate

\( \frac{1}{day} \)

Estimated

Cmax

1 × 1010

Maximum sustainable tumor cell population

cell

[19]

b1

3.23 × 10−7

NK-mediated tumor cell kill rate

\( \frac{1}{cell\times day} \)

[19]

c1

1.1 × 10−7

CTL-mediated tumor cell kill rate

\( \frac{1}{cell\times day} \)

[19]

d1

2 × 10−34

Proportional parameter of anti-CD25 treatment for inhibition of anti-immune effects of Treg on CTL-mediated tumor cell killing

\( \frac{1}{cell^3} \)

Estimated

e1

0.345

Rate of the suppressive effect of Treg on CTL-mediated tumor cell killing

\( \frac{1}{cell} \)

[34]

f1

0.286

Rate of the suppressive effect of TGF-β on CTL-mediated tumor cell killing

\( \frac{ml}{ng} \)

[34]

g1

3.5 × 10−2

The apoptosis rate of Panc02 tumor cells by low-dose 5-FU treatment

\( \frac{1}{day} \)

Estimated

h1

2.5 × 105

Proportional parameter of tumor inhibition rate by Treg depletion through anti-CD25 treatment

\( \frac{cell}{day} \)

Estimated

k1

1 × 10−15

Proportional parameter of tumor inhibition rate by Treg depletion through anti-CD25 treatment

\( \frac{1}{cell} \)

Estimated

l1

100

Depth of access of immune cells to the tumor mass

\( {cell}^{\frac{1}{3}} \)

[19]

a2

1.4 × 104

Constant generation source of NK cells

\( \frac{cell}{day} \)

[19]

b2

4.12 × 10−2

The exponential death rate of NK cells

\( \frac{1}{day} \)

[19]

c2

0.125

Maximum of IL-2-mediated NK cell growth

\( \frac{1}{day} \)

[34]

d2

0.3

Steepness coefficient of the IL-2-mediated NK cell growth rate

\( \frac{ng}{ml} \)

[34]

e2

0.125

Maximum of IFN-γ mediated NK cell growth rate

\( \frac{1}{day} \)

[34]

f2

0.3

The steepness coefficient of the IFN-γ-mediated NK cell growth rate

\( \frac{ng}{ml} \)

[34]

g2

1 × 10−9

Inactivation rate of NK cells by tumor cells

\( \frac{1}{day} \)

Estimated close to the value reported in [19]

h2

1 × 10−10

Suppression rate of NK cells by Tregs.

\( \frac{1}{cell\times day} \)

[34]

a3

2 × 10−2

The exponential death rate of CTLs

\( \frac{1}{day} \)

[19]

b3

8 × 10−2

Maximum tumor-mediated CTL recruitment rate

\( \frac{1}{day} \)

Estimated close to the value reported in [19]

c3

2.02 × 1014

Steepness coefficient of the tumor-mediated CTL recruitment curve

cell2

Estimated with regarding the value reported in [19]

d3

1.1 × 10−7

CTL stimulation rate by tumor-NK cells interactions

\( \frac{1}{cell\times day} \)

[19]

e3

1.5 × 10−10

Inactivation rate of CTLs by tumor cells

\( \frac{1}{cell\times day} \)

Estimated close to the value reported in [19]

f3

125 × 10−5

Maximum of IL-2-mediated CTL growth rate

\( \frac{1}{day} \)

Estimated with regarding the value reported in [34]

g3

0.3

The steepness coefficient of the IL-2-mediated CTL growth rate

\( \frac{ng}{ml} \)

[34]

h3

12.5 × 10−2

Maximum of IFN-γ-mediated CTL growth rate

\( \frac{1}{day} \)

[34]

k3

0.3

The steepness coefficient of the IFN-γ-mediated CTL growth rate

\( \frac{ng}{ml} \)

[34]

l3

1 × 10−10

Suppression rate of CTLs by Tregs

\( \frac{1}{cell\times day} \)

[34]

p3

2.5 × 106

The normal number of splenic MDSCs in C57/BL6 mice

cell

[19]

m3

18 × 10−2

Minimal CTL proliferation factor induced by inhibition of MDSCs

---

[19]

n3

6 × 10−3

Parameter for MDSC-induced inhibition of CTL proliferation

\( \frac{1}{cell^2} \)

[19]

a4

1.25 × 106

Normal MDSC production rate

\( \frac{cell}{day} \)

[19]

b4

3.25 × 10−2

MDSCs normal death rate

\( \frac{1}{day} \)

Estimated with regarding the value reported in [19]

b4

8 × 10−2

MDSCs death rate during 5-FU treatment

\( \frac{1}{day} \)

Estimated with regarding the value reported in [19]

c4

0.7 × 107

MDSC expansion coefficient in Panc02 tumor-bearing mice

\( \frac{cell}{day} \)

[19]

d4

1 × 1010

Steepness coefficient of the tumor-mediated MDSC production curve

cell

[19]

a5

3.6 × 105

The production rate of T helper cells in the thymus

\( \frac{cell}{day} \)

[34]

b5

1.2 × 10−3

The exponential death rate of T helper cells based on the half-life

\( \frac{1}{day} \)

[34]

c5

0.125

Maximum IL-2-mediated T helper cell proliferation rate

\( \frac{1}{day} \)

[34]

d5

0.3

Steepness coefficient of the IL-2-mediated T helper cell proliferation curve

\( \frac{ng}{ml} \)

[34]

e5

0.125

Maximum IFN-γ-mediated T helper cell proliferation rate

\( \frac{1}{day} \)

[34]

f5

0.3

Steepness coefficient of the IFN-γ-mediated T helper cell proliferation curve

\( \frac{ng}{ml} \)

[34]

g5

1 × 10−10

Suppression rate of T helper cells by Tregs

\( \frac{1}{cell\times day} \)

[34]

a6

5.6 × 105

The constant production rate of Tregs

\( \frac{cell}{day} \)

[34]

b6

2.3 × 10−2

The exponential death rate of Tregs based on the half-life

\( \frac{1}{\ day} \)

[34]

c6

2 × 10−4

Treg origination rate from CTLs

\( \frac{1}{\ day} \)

[34]

d6

4 × 10−4

Treg origination rate from T helper cells

\( \frac{1}{\ day} \)

[34]

e6

0.125

Maximum IL-2-mediated growth rate of Tregs

\( \frac{1}{day} \)

[34]

f6

0.3

Steepness coefficient of the IL-2-mediated Treg growth curve

\( \frac{ng}{ml} \)

[34]

g6

1 × 10−11

NK-mediated Treg degradation constant rate

\( \frac{1}{cell\times day} \)

[34]

h6

1.5 × 10−11

Constant inhibition rate of Tregs by anti-CD25 treatment

\( \frac{1}{\ day} \)

[34]

\( \frac{{\boldsymbol{\tau}}_{\mathbf{1}}}{{\boldsymbol{\alpha}}_{\mathbf{1}}} \)

2.2483 × 1011

The natural death rate of IL-2 based on its half-life/ constant production rate of IL-2 by T helper cells

\( \frac{cell\times ml}{ng} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{1}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10−13

constant production rate of IFN-γ by CTLs/ Natural death rate of IFN-γ based on its half-life

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{2}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10−13

The secretion rate of IFN-γ by NK cells/degradation rate of IFN-γ based on its half-life

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{3}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10−13

The secretion rate of IFN-γ by T helper cells/degradation rate of IFN-γ based on its half-life

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\lambda}}_{\mathbf{1}}}{{\boldsymbol{\tau}}_{\mathbf{3}}} \)

8.9382 × 10−13

The constant production rate of TGF-β by tumor cells/death rate of TGF-β based on its half-life

\( \frac{ng}{ml\times cell} \)

[34]