Parameter (Unit) | Definition | Estimate | Relative S.E. (% RSE) |
---|---|---|---|

Turnover of measured signaling proteins (h^{−1}) | |||

K_{src} | Turnover rate constant for pSrc | 0.237 | 17 |

K_{Akt} | Turnover rate constant for pAkt | 3.37 | 34 |

K_{mTOR} | Turnover rate constant for pmTOR | 0.094 | 22 |

K_{cas} | Turnover rate constant for active caspase-3 | 0.02 | 12 |

Paclitaxel model parameters: 2D system | |||

K_{inh} (h^{−1}) | Turnover rate constant for pAkt inhibitory compartment | 0.708 | 26 |

Ip (× 10^{−1} nM^{−1}) | Coefficient of pAkt inhibition by paclitaxel | 0.173 | 9 |

(1/τ_{MP}) (×10^{−1} h^{−1}) | Transit rate constant for effect of pAkt on pmTOR due to paclitaxel | 0.567 | 11 |

S1_{P} | Coefficient of inhibition of pmTOR | 1^{a} | — |

(1/τ_{CP}) (× 10^{−1} h^{−1}) | Transit rate constant for activation of caspase-3 due to paclitaxel | 0.697 | 16 |

k_{P} (nM^{−1}) | Slope for activation of caspase-3 | 1^{b} | — |

S2_{P} | Exponent for activation of caspase-3 | 0.445 | 18 |

S3_{P} | Feedback coefficient for active caspase-3 | 15.3 | 66 |

S4_{P} | Coefficient of paclitaxel-mediated cell growth inhibition due to pmTOR | 1^{a} | — |

kg (× 10^{−1} h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |

kd_{P} (h^{−1}) | Death rate constant for JIMT-1 cells due to paclitaxel | 0.123 | 3 |

Dasatinib model parameters: 2D system | |||

S1_{D} (× 10^{−1} nM^{−1}) | Coefficient of pSrc inhibition by dasatinib | 0.181 | 2 |

S2_{D} | Coefficient of inhibition of pAkt due to pSrc | 0.293 | 28 |

(1/τ_{MD}) (× 10^{−1} h^{−1}) | Transit rate constant for effect of pAkt on pmTOR due to dasatinib | 0.701 | 40 |

S3_{D} | Coefficient of inhibition of pmTOR | 4.76 | 41 |

kg (× 10^{−1} h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |

S4_{D} | Coefficient of dasatinib-mediated cell growth inhibition due to pmTOR | 10.9 | 36 |

Everolimus model parameters: 2D system | |||

S1_{E} (× 10^{−1} nM^{−1}) | Coefficient of pmTOR inhibition by everolimus | 0.151 | 4 |

S2_{E} | Coefficient for effect of pAkt on pmTOR | 1.42 | 8 |

(1/τ_{SE}) (h^{−1}) | Transit rate constant for feedback activation effect of pmTOR on pSrc | 1 | 66 |

S3_{E} | Coefficient of feedback activation of pSrc due to pmTOR | 7.27 | 65 |

S4_{E} | Coefficient of feedback activation of pAkt due to pmTOR | 1^{a} | — |

S5_{E} | Coefficient of effect of pSrc on pAkt | 1^{a} | — |

kg (× 10^{−1} h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |

S6_{E} | Coefficient of everolimus-mediated cell growth inhibition due to pmTOR | 0.001^{c} | — |

Dasatinib + everolimus model parameters: 2D system | |||

S1_{DE} | Coefficient for effect of pAkt on pmTOR | 1.36 | 34 |

(1/τ_{CDE}) (h^{−1}) | Transit rate constant for activation of caspase-3 due to dasatinib + everolimus (D+E) | 0.996 | 2 |

k_{DE} (nM^{−1}) | Slope for activation of caspase-3 | 1^{b} | — |

S2_{DE} | Exponent for activation of caspase-3 | 2.06 | 10 |

S3_{DE} (× 10^{−1}) | Signal modulation coefficient for caspase-3 activation | 0.262 | 42 |

kg (h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.009 | 5 |

S4_{DE} | Coefficient of D+E–mediated cell growth inhibition due to pmTOR | 1^{a} | — |

kd_{DE} (h^{−1}) | Death rate constant for JIMT-1 cells due to D+E | 0.124 | 10 |

Paclitaxel + dasatinib + everolimus simultaneous treatment model parameters: 2D system | |||

S1_{PDE} | Coefficient for effect of pAkt on pmTOR | 4.71 | 14 |

S2_{PDE} | Coefficient for feedback effect on pAkt due to pmTOR | 1 | — |

(1/τ_{CPDE}) (× 10^{−1} h^{−1}) | Transit rate constant for activation of caspase-3 due to paclitaxel + dasatinib + everolimus (P+D+E) | 0.128 | 29 |

kg (h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.009 | 6 |

S3_{PDE} | Coefficient of P+D+E–mediated cell growth inhibition due to pmTOR | 1^{a} | — |

kd_{PDE} (× 10^{−1} h^{−1}) | Death rate constant for JIMT-1 cells due to P+D+E | 0.786 | 3 |

Paclitaxel + (dasatinib + everolimus) sequential treatment model parameters: 2D system | |||

S2_{P(DE)} | Coefficient for feedback effect on pAkt due to pmTOR | 0.0943 | 17 |

S1_{P(DE)} | Coefficient for effect of pAkt on pmTOR | 1.01 | 27 |

kg (h^{−1}) | Net growth rate constant for JIMT-1 cells | 0.009 | 6 |

S4_{P} | Coefficient of paclitaxel-mediated cell growth inhibition due to pmTOR (before 24 h) | 1^{a} | — |

S3_{PDE} | Coefficient of PDE mediated cell growth inhibition due to pmTOR (after 24 h) | 1^{a} | — |

kd_{P} (× 10^{−1} h^{−1}) | Death rate constant for JIMT-1 cells due to paclitaxel (before 24 h) | 0.774 | 4 |

kd_{PDE} (h^{−1}) | Death rate constant for JIMT-1 cells due to PDE (after 24 h) | 0.124 | 10 |

Paclitaxel + (dasatinib + everolimus) sequential treatment model parameters: 3DD system | |||

λ_{0} (× 10^{−2} h^{−1}) | Rate constant for exponential growth of JIMT-1 cells | 0.77 | 5 |

λ_{1} (h^{−1}) | Rate constant for linear growth of JIMT-1 cells | 7.41 | 59 |

Ψ | Switching factor between exponential and linear growth | 20^{d} | — |

α_{P} | Coefficient for JIMT-1 growth inhibition due to pmTOR (before 24 h) | 1 | 23 |

β_{P} (h^{−1}) | Death rate constant for JIMT-1 due to caspase-3 activity (before 24 h) | 0.132 | 3 |

α_{PDE} | Coefficient for JIMT-1 growth inhibition due to pmTOR (after 24 h) | 1 | 23 |

β_{PDE} (× 10^{−1} h^{−1}) | Death rate constant for JIMT-1 due to caspase-3 activity (after 24 h) | 0.841 | 3 |

Scaling factors for translation of 2D models to the 3DD system | |||

α_{P}/S4_{P}, α_{PDE}/S2_{PDE} | Ratio of cell growth inhibition coefficients in 3DD and 2D | 1 | — |

β_{P}/kd_{P,} β_{PDE}/kd_{PDE} | Ratio of cell death rate constants in 3DD and 2D systems | 1.07 | — |

↵

Coefficients were fixed to 1 to indicate a direct/inverse proportionality (as applicable) to the actual magnitude of the activity of a particular protein, without the need of a power coefficient.^{a}↵

Slopes (proportionality constants) were fixed to 1 as the exponents used to characterize activation of caspase-3 due to drug concentrations alone were sufficient.^{b}↵

Coefficient fixed to a relatively low magnitude to indicate minimal effect of activity of a protein. Any decrease in magnitude of this coefficient did not have an impact on model fittings.^{c}↵

Fixed factor to allow for a smooth switch from exponential to linear cell growth (Magni et al., 2006).^{d}