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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]