Intracellular-signaling tumor-regression modeling of the pro-apoptotic receptor agonists dulanermin and conatumumab

Abstract

Dulanermin (rhApo2L/TRAIL) and conatumumab bind to transmembrane death receptors and trigger the extrinsic cellular apoptotic pathway through a caspase-signaling cascade resulting in cell death. Tumor size time series data from rodent tumor xenograft (COLO205) studies following administration of either of these two pro-apoptotic receptor agonists (PARAs) were combined to develop a intracellular-signaling tumor-regression model that includes two levels of signaling: upstream signals unique to each compound (representing initiator caspases), and a common downstream apoptosis signal (representing executioner caspases) shared by the two agents. Pharmacokinetic (PK) models for each drug were developed based on plasma concentration data following intravenous and/or intraperitoneal administration of the compounds and were used in the subsequent intracellular-signaling tumor-regression modeling. A model relating the PK of the two PARAs to their respective and common downstream signals, and to the resulting tumor burden was developed using mouse xenograft tumor size measurements from 448 experiments that included a wide range of dose sizes and dosing schedules. Incorporation of a pro-survival signal—consistent with the hypothesis that PARAs may also result in the upregulation of pro-survival factors that can lead to a reduction in effectiveness of PARAs with treatment—resulted in improved predictions of tumor volume data, especially for data from the long-term dosing experiments.

Appendices

Appendix A

This appendix includes the details of the dulanermin and conatumumab treatment groups, with the doses, regimens, and number of animals listed. Table 3 describes the individual dulanermin data, Table 4 describes the average dulanermin data, and Table 5 describes the individual conatumumab data.

Table 3 Dulanermin dosing regimens for tumor xenograft studies with individual data

Table 4 Dulanermin dosing regimens for tumor xenograft studies with average data

Table 5 Conatumumab dosing regimens for tumor xenograft studies with individual data

Appendix B

This appendix includes the details of the dulanermin and conatumumab PK models. Model equations and parameter estimates are provided for both compounds.

A linear two-compartment model described the mean dulanermin IV plasma concentration data (only mean data available). Given these estimates for the disposition parameters, the mean data available following IP administration of dulanermin were described using an absorption model with separate parallel slow and rapid absorption components. The complete pharmacokinetic model for dulanermin is as follows:

$$ \begin{aligned} \frac{d}{dt}x_{1} & = - \left( {k_{10,Dlmn} + k_{12,Dlmn} } \right) \cdot x_{1} + k_{21,Dlmn} \cdot x_{2} + k_{a,Dlmn} \cdot x_{3} \\ & \quad \quad \quad + k_{aa,Dlmn} \cdot x_{5} \, + Dose_{IV} \\ \end{aligned} $$

(10)

$$ \frac{d}{dt}x_{2} = k_{12,Dlmn} \cdot x_{1} - k_{21,Dlmn} \cdot x_{2} $$

(11)

$$ \frac{d}{dt}x_{3} = - k_{a,Dlmn} \cdot x_{3} + F_{2} \cdot Dose_{IP} $$

(12)

$$ \frac{d}{dt}x_{4} = - k_{aa,Dlmn} \cdot x_{4} + F_{1} \cdot Dose_{IP} $$

(13)

$$ \frac{d}{dt}x_{5} = k_{aa,Dlmn} \cdot \left( {x_{4} - x_{5} } \right) $$

(14)

The variables and parameters are defined as follows, along with the values of the model parameter estimates: x ₁ is the amount of dulanermin in the plasma compartment; x ₂ is the amount of drug in the peripheral compartment; x ₃ is the amount of drug in the rapid IP-delivery compartment; x ₄ is the amount of drug in the first slow IP-delivery compartment; x ₅ is the amount of drug in the second slow IP-delivery compartment; k _10,Dlmn is the plasma elimination constant of dulanermin (232/day); k _12,Dlmn (3.76/day)and k _21,Dlmn (10.8/day) are the rate constants between the plasma compartment and the periphery; k _a,Dlmn (18.9/day) is the rate constant for rapid IP delivery; k _aa,Dlmn (19.6/day) is the rate constant for slow IP delivery; F ₁ (0.242) is the IP fraction that is delivered to the first slow IP-delivery compartment; F ₂ (0.097) is the IP fraction that is delivered to the rapid IP-delivery compartment; Dose _IV and Dose _IP represent the IV and IP dosing regimens defined in Appendix A; and V ₁ (48.6 mL/kg) is the plasma volume of distribution. (F _Total (0.339) is the sum of F ₁ and F ₂, and is the total fraction of the IP dose absorbed.) The initial condition of each state is fixed at zero. See Fig. 4 for model fits to the dulanermin plasma concentration data following IV (left panel) and IP (right panel) administration.

Fig. 4

Model fit to mean plasma concentration data for dulanermin following IV administration of 10 mg/kg (left panel) and IP administration of 60 mg/kg (right panel). The solid circles represent the mean of the measured data at each time point; the dashed lines represent the estimated model predictions

A linear two-compartment model was fit to all the median conatumumab plasma concentration data from all the experiments (naïve pooled data analysis). The model parameters and maximum likelihood estimates are given as follows: elimination rate constant, k _10,Cmab  = 0.0913/day; central to peripheral rate constant, k _12,Cmab  = 0.251/day; peripheral to central rate constant, k _21,Cmab  = 0.403/day; intraperitoneal absorption rate into central compartment, k _a,Cmab  = 8.17/day; Dose _IP represents the IP dosing regimens defined in Appendix A; ratio of plasma volume of distribution to fraction of conatumumab absorbed IP (which cannot be distinguished because no separate IV data is available), V/F = 2.99 mL. The initial condition of each state is fixed at zero. See Fig. 5 for selected model fit plots to the conatumumab plasma concentration data following IP administration.

Fig. 5

Sample model fits (2 of 13 experiments shown) to median plasma concentration data for conatumumab given IP (left panel: single dose of 240 mg; right panel: 36.9 mg given twice weekly for 4 weeks). The solid circles represent the median of the measured data at each time point; the dashed lines represent the estimated model predictions