Parameter (Unit) | Definition | Estimate | Relative S.E. (% RSE) |
---|---|---|---|
Turnover of measured signaling proteins (h−1) | |||
Ksrc | Turnover rate constant for pSrc | 0.237 | 17 |
KAkt | Turnover rate constant for pAkt | 3.37 | 34 |
KmTOR | Turnover rate constant for pmTOR | 0.094 | 22 |
Kcas | Turnover rate constant for active caspase-3 | 0.02 | 12 |
Paclitaxel model parameters: 2D system | |||
Kinh (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/τMP) (×10−1 h−1) | Transit rate constant for effect of pAkt on pmTOR due to paclitaxel | 0.567 | 11 |
S1P | Coefficient of inhibition of pmTOR | 1a | — |
(1/τCP) (× 10−1 h−1) | Transit rate constant for activation of caspase-3 due to paclitaxel | 0.697 | 16 |
kP (nM−1) | Slope for activation of caspase-3 | 1b | — |
S2P | Exponent for activation of caspase-3 | 0.445 | 18 |
S3P | Feedback coefficient for active caspase-3 | 15.3 | 66 |
S4P | Coefficient of paclitaxel-mediated cell growth inhibition due to pmTOR | 1a | — |
kg (× 10−1 h−1) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |
kdP (h−1) | Death rate constant for JIMT-1 cells due to paclitaxel | 0.123 | 3 |
Dasatinib model parameters: 2D system | |||
S1D (× 10−1 nM−1) | Coefficient of pSrc inhibition by dasatinib | 0.181 | 2 |
S2D | Coefficient of inhibition of pAkt due to pSrc | 0.293 | 28 |
(1/τMD) (× 10−1 h−1) | Transit rate constant for effect of pAkt on pmTOR due to dasatinib | 0.701 | 40 |
S3D | Coefficient of inhibition of pmTOR | 4.76 | 41 |
kg (× 10−1 h−1) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |
S4D | Coefficient of dasatinib-mediated cell growth inhibition due to pmTOR | 10.9 | 36 |
Everolimus model parameters: 2D system | |||
S1E (× 10−1 nM−1) | Coefficient of pmTOR inhibition by everolimus | 0.151 | 4 |
S2E | Coefficient for effect of pAkt on pmTOR | 1.42 | 8 |
(1/τSE) (h−1) | Transit rate constant for feedback activation effect of pmTOR on pSrc | 1 | 66 |
S3E | Coefficient of feedback activation of pSrc due to pmTOR | 7.27 | 65 |
S4E | Coefficient of feedback activation of pAkt due to pmTOR | 1a | — |
S5E | Coefficient of effect of pSrc on pAkt | 1a | — |
kg (× 10−1 h−1) | Net growth rate constant for JIMT-1 cells | 0.089 | 5 |
S6E | Coefficient of everolimus-mediated cell growth inhibition due to pmTOR | 0.001c | — |
Dasatinib + everolimus model parameters: 2D system | |||
S1DE | Coefficient for effect of pAkt on pmTOR | 1.36 | 34 |
(1/τCDE) (h−1) | Transit rate constant for activation of caspase-3 due to dasatinib + everolimus (D+E) | 0.996 | 2 |
kDE (nM−1) | Slope for activation of caspase-3 | 1b | — |
S2DE | Exponent for activation of caspase-3 | 2.06 | 10 |
S3DE (× 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 |
S4DE | Coefficient of D+E–mediated cell growth inhibition due to pmTOR | 1a | — |
kdDE (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 | |||
S1PDE | Coefficient for effect of pAkt on pmTOR | 4.71 | 14 |
S2PDE | Coefficient for feedback effect on pAkt due to pmTOR | 1 | — |
(1/τCPDE) (× 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 |
S3PDE | Coefficient of P+D+E–mediated cell growth inhibition due to pmTOR | 1a | — |
kdPDE (× 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 | |||
S2P(DE) | Coefficient for feedback effect on pAkt due to pmTOR | 0.0943 | 17 |
S1P(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 |
S4P | Coefficient of paclitaxel-mediated cell growth inhibition due to pmTOR (before 24 h) | 1a | — |
S3PDE | Coefficient of PDE mediated cell growth inhibition due to pmTOR (after 24 h) | 1a | — |
kdP (× 10−1 h−1) | Death rate constant for JIMT-1 cells due to paclitaxel (before 24 h) | 0.774 | 4 |
kdPDE (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 | |||
λ0 (× 10−2 h−1) | Rate constant for exponential growth of JIMT-1 cells | 0.77 | 5 |
λ1 (h−1) | Rate constant for linear growth of JIMT-1 cells | 7.41 | 59 |
Ψ | Switching factor between exponential and linear growth | 20d | — |
αP | Coefficient for JIMT-1 growth inhibition due to pmTOR (before 24 h) | 1 | 23 |
βP (h−1) | Death rate constant for JIMT-1 due to caspase-3 activity (before 24 h) | 0.132 | 3 |
αPDE | Coefficient for JIMT-1 growth inhibition due to pmTOR (after 24 h) | 1 | 23 |
βPDE (× 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 | |||
αP/S4P, αPDE/S2PDE | Ratio of cell growth inhibition coefficients in 3DD and 2D | 1 | — |
βP/kdP, βPDE/kdPDE | Ratio of cell death rate constants in 3DD and 2D systems | 1.07 | — |
↵a 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.
↵b Slopes (proportionality constants) were fixed to 1 as the exponents used to characterize activation of caspase-3 due to drug concentrations alone were sufficient.
↵c 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.
↵d Fixed factor to allow for a smooth switch from exponential to linear cell growth (Magni et al., 2006).