Table 1 Equations and parameters of the model.

From: A dynamical framework for complex fractional killing

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
\(BaxmT=0.3\) \(Baxm:Bcl=0.33\) \(Bh3:Bcl=0.16\) \(P53=0\)
\(Mdm2=1\) \(CIAP=0\) \({R}_{\_drug\_effect}=0.33\)