Table 1 Equations and parameters of the model.

Apoptosis Initiation Module
$$Bax=BaxT-BaxmT$$(1) $$\frac{dBaxmT}{dt}=({k}_{f1}+{k}_{f2}\ast Bh3)\ast Bax-{k}_{b}\ast BaxmT$$(2)
$$Baxm=BaxmT-Baxm:Bcl$$(3) $$\frac{dBaxm:Bcl}{dt}={k}_{asXC}\ast Baxm\ast Bcl-{k}_{dsXC}\ast Baxm:bcl2-{k}_{b}\ast Baxm:Bcl$$(4)
$$Bh3=Bh3T-Bh3:Bcl$$(5) $$\frac{dBh3:Bcl}{dt}={k}_{asHC}\ast Bh3\ast Bcl-{k}_{dsHC}\ast Bh3:Bcl2$$(6)
Parameters
$${k}_{f1}=1$$ $${k}_{f2}=300$$ $${k}_{b}=2$$ $${k}_{asXC}=9000$$
$${k}_{dsXC}=0.05$$ $${k}_{asHC}=1000$$ $${k}_{dsXC}=0.01$$
Total BH3 control
$$\frac{Bh3T}{dt}={k}_{sBh3}+{k}_{s2}\ast p53+{k}_{s3}\ast Caspase8-{k}_{dBH3}\ast Bh3T$$(7)
Parameters
$${k}_{sBh3}=0.1$$ $${k}_{2}=0.2$$ $${k}_{3}=1$$ $${k}_{dBh3}=1$$
Caspase 8
$$\frac{dCaspase8}{dt}={k}_{aC8}-({k}_{iC8}+{k}_{i2}\ast cIAP)\ast Caspase8$$(8)
Parameters
$${k}_{aC8}=0.03$$ $${k}_{iC8}=0.1$$ $${k}_{i2}=0.15$$
CIAP
$$\frac{dcIAP}{dt}={k}_{sIAP}+{k}_{sIAP2}\ast \frac{Dru{g}^{n}}{Dru{g}^{n}+{J}^{n}}-{k}_{dIAP}\ast cIAP$$(9)
Parameters
$$J=0.1$$ $${k}_{sIAP}=0.00004$$ $${k}_{sIAP2}=0.016$$ $${k}_{dIAP}=0.004$$
p53
$$wp53={R}_{0}^{p53}+{R}_{p53}^{p53}\ast p53+{R}_{Mdm2}^{p53}\ast Mdm2$$(10) $$wMdm2={R}_{0}^{wMdm2}+{R}_{p53}^{wMdm2}\ast p53$$(11)
$$fp53=\frac{1}{1+{e}^{-\sigma \cdot wp53}}$$(12) $$fMdm2=\frac{1}{1+{e}^{-{\sigma }_{2}\cdot wMdm2}}+\frac{1}{1+{e}^{-\sigma \ast {\rm{R}}\_drug\_effect\ast {\rm{Drug}}}}$$(13)
$$\frac{dp53}{dt}=tsp53\ast (fp53-p53)$$(14) $$\frac{dMdm2}{dt}=tsMdm2\ast (fMdm2-Mdm2)$$(15)
Parameters
$${R}_{0}^{p53}=-0.4$$ $${R}_{p53}^{p53}=2$$ $${R}_{0}^{Mdm2}=-0.55$$ $${R}_{p53}^{Mdm2}=1$$
$${R}_{Mdm2}^{p53}=-1$$ $$tsp53=0.6$$ $$tsMdm2=0.3$$ $$\sigma =5$$
$${\sigma }_{2}=10$$ $$n=10$$
Initial Conditions
$$BaxmT=0.3$$ $$Baxm:Bcl=0.33$$ $$Bh3:Bcl=0.16$$ $$P53=0$$
$$Mdm2=1$$ $$CIAP=0$$ $${R}_{\_drug\_effect}=0.33$$