Bridging the gap between in vitro and in vivo: Dose and schedule predictions for the ATR inhibitor AZD6738

Understanding the therapeutic effect of drug dose and scheduling is critical to inform the design and implementation of clinical trials. The increasing complexity of both mono, and particularly combination therapies presents a substantial challenge in the clinical stages of drug development for oncology. Using a systems pharmacology approach, we have extended an existing PK-PD model of tumor growth with a mechanistic model of the cell cycle, enabling simulation of mono and combination treatment with the ATR inhibitor AZD6738 and ionizing radiation. Using AZD6738, we have developed multi-parametric cell based assays measuring DNA damage and cell cycle transition, providing quantitative data suitable for model calibration. Our in vitro calibrated cell cycle model is predictive of tumor growth observed in in vivo mouse xenograft studies. The model is being used for phase I clinical trial designs for AZD6738, with the aim of improving patient care through quantitative dose and scheduling prediction.


Model Equations
The set of ordinary differential equations used to describe the temporal evolution of the cell population are detailed below: As replication stress is believed to be primarily encountered during DNA synthesis in S phase, cells transitioning from G1 to S are subject to a rate of damage (k2), transitioning from G1 to an S "damaged" (Sd) phase, parallel to the healthy S phase in the cell cycle.
ATR inhibition prevents cells initiating DNA repair which, in this model, accumulates during S phase.
Therefore the transition from the S damaged phase (k3) is inhibited when compound is added to the model. Cells delayed in the damaged state by inhibition of the repair reaction are removed from the system (at rate k4), simulating apoptosis in response to prolonged damage, and a decrease in the total cell population. dG2 dt = k6 · S − k5 · G2 + k IRrepair · S IR + k IRrepair · Sd IR (4) dApoptosis dt = k4 · Sd (5) It was observed in vitro that DNA damage from IR occurs instantaneously and therefore a rate of DNA damage resulting from exposure to radiation was not incorporate into the model. Instead, the initial conditions were set such that the population of cells begins in the damaged version of the cell cycle stages and is repaired at the beginning of the time course simulation. This approach enabled the separation of damage resulting from replication stress from damage induced by radiation, and also separate the repair mechanisms so that ATR inhibition was specific to repairing replication stress induced damage.
Drug was represented with the variable ATRi in the model, and drug binding was modeled using mass action kinetics. Drug concentration was considered to be constant throughout the in vitro experiments.
Drug binding to target in vitro was represented with the reversible reaction (equations 11 and 12).
During the development of the model replication stress and IR damage repair was modeled by damaged cells transitioning back to the same cell cycle phase or into to the next phase. Parameter fitting of both of these approaches returned the same parameter sets and both models were capable of simulating the experimental data. It was therefore concluded that the route taken by repaired cells transitioning back into the cell cycle does not make a significant difference to the behavior of the model. The equations for the tumor shell are as follows: where f i is defined below for each state.
The delay between cells (either background replication stress or IR induced) entering apoptosis and finally being removed from the tumor volume is modeled using a series of transit compartments where A1, A2 and A3 are states for dying cells: The following equations represent the IR damaged compartments: For the necrotic (non-replication) core of the tumor (designated with super-script "C"), the equations are the same as above but for the removal of cell cycle progression. DNA repair is assumed to still occur with the consequence that IR repairing G2/M cells transit back to G1.
The delay between cells (either background replication stress or IR damage induced) that are entering apoptosis and finally being removed from the tumor volume is modeled using a series of transit compartments: The following equations represent the IR damaged compartments in the tumor core: ATR inhibition is assumed constant throughout the tumor volume.
The shell volume is calculated as: The core volume is calculated as: and so the total volume that is compared to the observed tumor volume data is calculated using the following equation: When the total volume of the tumor is such that its radius (R), calculated using: is larger than the diffusion thickness R diff then the total rate of mass transfer between the shell and the core (k Transfer ) is calculated as: where for following equation: is the rate of change of the total volume. Transfer between corresponding states of the cell model in the core and the shell are set as the product of the total mass transfer and the fraction of the volume of the donor compartment, f i , the cell cycle state occupies. If k transfer is positive then the shell is the donor compartment (the tumor is growing) otherwise the donor compartment is the core(the tumor is shrinking).
The observed in vivo γH2AX signal is predicted as: All states in the cell cycle model are initially set to those of the in the in vitro model.
To account for experimental differences between the in vitro and in vivo quantification of γH2AX positive cells, z scaling factors are applied in the model depending on whether it is simulating in vitro or in vivo data sets (see table 2).
To simulate in vivo drug pharmaco-kinetics and pharmaco-dynamics a standard two-compartment model was used to describe gut, central and peripheral clearance [3].
Drug (ATRi) binding was modeled using mass action kinetics where ATR_ATRi represents drug bound to ATR. For in vivo scenario Cp represents drug concentration and the following equations are used: The scaling factor kscale is used to correct the drug concentration for the free fraction after binding to serum albumin and Fu to correct for diffusion of drug from the surrounding plasma into the tumor mass.
For the in vitro scenario drug concentration is considered to be constant and the following equations   In vitro refers to the in vitro time course data with and without washout. IR in vitro is the in vitro time course data measured following IR treatment only. PK parameters were determined from mouse PK studies prior to this work.

Parameter Identifiability
Identifiability of the model was assessed using multi-start parameter estimation in the J2 software package.
As a first step, a parameter sensitivity analysis was performed. J2 computes the parametric sensitivity profiles using the staggered corrector forward sensitivity method [5]. The sensitivities are converted to a scalar metric by evaluating the integral of the absolute value of the profile and are shown in Figure 1 (sorted in decreasing sensitivity of cell count). Sensitivities of both cell count and γH2AX with respect to the estimated parameters are computed. to the same optimal fit. Parameters k i and k 3 were found to be highly correlated, however, the model predictions were found to be insensitive to the different solutions obtained for these two parameters. Given the uniqueness of the estimated parameters, aside from the two highly correlate parameters, we conclude that the best fit parameters were obtained and that the model is identifiable and well constrained by the calibration data.        Parity plots for model simulations and experimental data sets are detailed in figures 7-10.    figure 2a and is included for comparison with the data from the Caspase assay. The data is normalized to the negative control (no drug). The caspase assay was performed separately from the γH2AX assay described in the manuscript, however the cell count dose response behavior is consistent between experiments.