TABLE 1

Parameter estimates for protein network dynamics and cellular response models for JIMT-1 cells in the 2D and 3DD systems

Parameter (Unit)DefinitionEstimateRelative S.E.
(% RSE)
Turnover of measured signaling proteins (h−1)
KsrcTurnover rate constant for pSrc0.23717
KAktTurnover rate constant for pAkt3.3734
KmTORTurnover rate constant for pmTOR0.09422
KcasTurnover rate constant for active caspase-30.0212
Paclitaxel model parameters: 2D system
Kinh (h−1)Turnover rate constant for pAkt inhibitory compartment0.70826
Ip (× 10−1 nM−1)Coefficient of pAkt inhibition by paclitaxel0.1739
 (1/τMP) (×10−1 h−1)Transit rate constant for effect of pAkt on pmTOR due to paclitaxel0.56711
S1PCoefficient of inhibition of pmTOR1a
 (1/τCP) (× 10−1 h−1)Transit rate constant for activation of caspase-3 due to paclitaxel0.69716
kP (nM−1)Slope for activation of caspase-31b
S2PExponent for activation of caspase-30.44518
S3PFeedback coefficient for active caspase-315.366
S4PCoefficient of paclitaxel-mediated cell growth inhibition due to pmTOR1a
kg (× 10−1 h−1)Net growth rate constant for JIMT-1 cells0.0895
kdP (h−1)Death rate constant for JIMT-1 cells due to paclitaxel0.1233
Dasatinib model parameters: 2D system
S1D (× 10−1 nM−1)Coefficient of pSrc inhibition by dasatinib0.1812
S2DCoefficient of inhibition of pAkt due to pSrc0.29328
 (1/τMD) (× 10−1 h−1)Transit rate constant for effect of pAkt on pmTOR due to dasatinib0.70140
S3DCoefficient of inhibition of pmTOR4.7641
kg (× 10−1 h−1)Net growth rate constant for JIMT-1 cells0.0895
S4DCoefficient of dasatinib-mediated cell growth inhibition due to pmTOR10.936
Everolimus model parameters: 2D system
S1E (× 10−1 nM−1)Coefficient of pmTOR inhibition by everolimus0.1514
S2ECoefficient for effect of pAkt on pmTOR1.428
 (1/τSE) (h−1)Transit rate constant for feedback activation effect of pmTOR on pSrc166
S3ECoefficient of feedback activation of pSrc due to pmTOR7.2765
S4ECoefficient of feedback activation of pAkt due to pmTOR1a
S5ECoefficient of effect of pSrc on pAkt1a
kg (× 10−1 h−1)Net growth rate constant for JIMT-1 cells0.0895
S6ECoefficient of everolimus-mediated cell growth inhibition due to pmTOR0.001c
Dasatinib + everolimus model parameters: 2D system
S1DECoefficient for effect of pAkt on pmTOR1.3634
 (1/τCDE) (h−1)Transit rate constant for activation of caspase-3 due to dasatinib + everolimus (D+E)0.9962
kDE (nM−1)Slope for activation of caspase-31b
S2DEExponent for activation of caspase-32.0610
S3DE (× 10−1)Signal modulation coefficient for caspase-3 activation0.26242
kg (h−1)Net growth rate constant for JIMT-1 cells0.0095
S4DECoefficient of D+E–mediated cell growth inhibition due to pmTOR1a
kdDE (h−1)Death rate constant for JIMT-1 cells due to D+E0.12410
Paclitaxel + dasatinib + everolimus simultaneous treatment model parameters: 2D system
S1PDECoefficient for effect of pAkt on pmTOR4.7114
S2PDECoefficient for feedback effect on pAkt due to pmTOR1
 (1/τCPDE) (× 10−1 h−1)Transit rate constant for activation of caspase-3 due to paclitaxel + dasatinib + everolimus (P+D+E)0.12829
kg (h−1)Net growth rate constant for JIMT-1 cells0.0096
S3PDECoefficient of P+D+E–mediated cell growth inhibition due to pmTOR1a
kdPDE (× 10−1 h−1)Death rate constant for JIMT-1 cells due to P+D+E0.7863
Paclitaxel + (dasatinib + everolimus) sequential treatment model parameters: 2D system
 S2P(DE)Coefficient for feedback effect on pAkt due to pmTOR0.094317
 S1P(DE)Coefficient for effect of pAkt on pmTOR1.0127
 kg (h−1)Net growth rate constant for JIMT-1 cells0.0096
 S4PCoefficient of paclitaxel-mediated cell growth inhibition due to pmTOR (before 24 h)1a
 S3PDECoefficient 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)0.7744
 kdPDE (h−1)Death rate constant for JIMT-1 cells due to PDE (after 24 h)0.12410
Paclitaxel + (dasatinib + everolimus) sequential treatment model parameters: 3DD system
λ0 (× 10−2 h−1)Rate constant for exponential growth of JIMT-1 cells0.775
λ1 (h−1)Rate constant for linear growth of JIMT-1 cells7.4159
ΨSwitching factor between exponential and linear growth20d
αPCoefficient for JIMT-1 growth inhibition due to pmTOR (before 24 h)123
βP (h−1)Death rate constant for JIMT-1 due to caspase-3 activity (before 24 h)0.1323
αPDECoefficient for JIMT-1 growth inhibition due to pmTOR (after 24 h)123
βPDE (× 10−1 h−1)Death rate constant for JIMT-1 due to caspase-3 activity (after 24 h)0.8413
Scaling factors for translation of 2D models to the 3DD system
αP/S4P, αPDE/S2PDERatio of cell growth inhibition coefficients in 3DD and 2D1
βP/kdP, βPDE/kdPDERatio of cell death rate constants in 3DD and 2D systems1.07
  • 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).