Download Supplementary File S2

SUPPLEMENTARY FILE S2 - PK/PD MODELING
Tumor phosphorylated (p) AKT308 PK/PD model
To generate the PK/PD model tumor pAKT-Thr308 (pAKT308) and plasma PK data from 6 separate
BT474 xenograft studies in mice (n=264) were combined and normalized (biomarker data was
generated using western blot as described in the methods section of the main paper). Free plasma
levels of AZD8835 were calculated based on measured concentrations in plasma using LC-MS/MS
and corrected using a constant free fraction (fu =0.15). A direct response Emax-type model was used
in the PK/PD analysis of normalized tumor pAKT308 versus free concentrations of compound in
plasma. The mathematical equation used to fit the results was:
𝐶𝑛
[eq 1]
𝑝𝐴𝐾𝑇308 = 𝐸0 × [1 − 𝐶 𝑛 +𝐼𝐶 𝑛 ]
50
Where E0= pAKT308 level of the vehicle treated group, C= Free compound concentration in plasma,
IC50= Free compound concentration in plasma that delivers 50% of the max effect and n=sigmoidicity
parameter. The model fit and resulting PK/PD parameters are shown in Supp-PK/PD Fig 1 and SuppPK/PD Table 1 respectively. Models were implemented using naïve pooled approach in Phoenix
WinNonlin, version 6.4.
Supp-PK/PD Figure 1. Effect-concentration PK/PD response of Normalized tumor pAKT308 levels
in mice BT474 xenograft studies to AZD8835 treatment (n=264). A direct Emax-type model was used
for the model fit.
Supp-PK/PD Table 1. PK/PD parameters for model fit of effects of AZD8835 in the Normalized
tumor pAKT308 levels in mice BT474 xenograft studies (n=264).
Parameter
IC50
E0
n
Estimate
0.28
0.86
0.88
Units
uM
-‘--
CV%
17
7.3
4.7
Tumor Cleaved Caspase-3 (CC3) PK/PD model
To generate the PK/PD model tumor CC3 and plasma PK from 8 separate BT474 xenograft studies in
mice (n=314) were combined. AZD8835 doses tested ranged from 25-100 mg/kg (orally), dosing
schedules varied from continuous dosing to multiple intermittent schedules e.g. 2 days on-5 days off
(2d on/5d off), days 1&4 or days 1&8 with administration of drug either once a day (QD) or twice a
day (BID). Tumor CC3 measurements were taken after a single dose or after multiple doses. CC3 was
determined by IHC staining as described in the methods section of the main paper.
Both AZD8835 plasma concentrations and tumor CC3 levels were simultaneously fitted on the final
analysis. Models were implemented using nonlinear mixed effects modelling in Phoenix NLME,
version 1.3. The analysis was conducted using the first order conditional estimation (FOCE-ELS).
Model selection was based on goodness-of-fit plots, the plausibility of the physiological system and
the objective function value provided by Phoenix NLME. Goodness-of-fit plots such as observed
values (DV) versus population predictions (PRED) or versus individual predictions (IPRED), and
conditional weighted residual errors versus time or versus predicted concentrations were used for
graphic assessment of the quality of the model fit.
The plasma AZD8835 concentration data were characterized by a two-compartment PK model
parameterized in terms of absorption rate constant (ka), apparent clearance (CL), the central volume
of distribution (V), distributional clearance (CL2) and the peripheral volume of distribution (V2).
Interindividual variability was included on CL, V1, ka parameters according to a log-normal
distribution of individual parameters. Residual error was characterized with a proportional error
model.
The key components of the PK/PD model used are described in Supp-PK/PD Figure 2 below. Tumor
cells were divided into sensitive and insensitive cells. A sensitive cell can either die providing a CC3
signal or divide and generate 2 insensitive cells. AZD8835 induces cell death resulting in an increase
of the CC3 signal observed after treatment. Mathematical description of the model is provided in
equations 2-7 below.
𝑆𝑡𝑚 (𝐴𝑍𝐷8835) = 1 +
𝑑𝐼𝑛𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒
𝑑𝑡
𝑑𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒
𝑑𝑡
𝑑𝐶𝐶3
𝑑𝑡
𝐸𝑚𝑎𝑥 ×𝐶 𝛾
𝛾
𝐶 𝛾 +𝐸𝐶50
= 2 × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 × 𝑘5 × (1 − 𝑥) − 𝑘5 × 𝐼𝑛𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒
[eq 3]
= 𝑘5 × 𝐼𝑛𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 − 𝑘5 × 𝑥 × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 × 𝑆𝑡𝑚(𝐴𝑍𝐷8835) − 𝑘5 × (1 − 𝑥) × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 [eq 4]
= 𝑘5 × 𝑥 × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 × 𝑆𝑡𝑚(𝐴𝑍𝐷8835) − 𝑘𝑜𝑢𝑡 × 𝐶𝐶3
𝑇𝑐𝑒𝑙𝑙 = 𝐼𝑛𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 + 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐶𝐶3
%𝐶𝐶3 =
[eq 2]
𝐶𝐶3
𝑇𝑐𝑒𝑙𝑙
× 100
[eq 5]
[eq 6]
[eq 7]
Where Emax is the maximum effect, C is the plasma concentration of AZD8835, EC50 is the
concentration required for 50% of the maximum effect (Total concentration in plasma was used in the
model fit, therefore the EC50 represents total concentration and not free concentration as with the
pAKT308) and γ is the sigmoidicity coefficient. k5 is the constant rate of transfer between the
different cell “states”, x is the proportion of sensitive cells that can undergo apoptosis and kout is the
fractional turnover rate for CC3. Tcell represents the total number of cells and %CC3 is the
percentage of cells with a CC3 signal (as the signal measured in these studies by IHC represents the %
of cells showing a strong CC3 signal). %CC3 are the observations that were fitted by the model.
Inter-individual variability was included on kout and x parameters according to a log-normal
distribution of individual parameters. Residual error was characterized with a power (0.5)
proportional error model.
k5 could not be estimated with this data set and was fixed to a value of 0.0071 1/hr. This value was
estimated from tumor growth curves for BT474 xenograft studies based on the tumor volume
doubling time. This k5 value results in the same doubling time in the total number of cells in this
model when unperturbed. Additionally, γ could not be estimated accurately with this dataset.
Sensitivity analysis demonstrated that once a reasonably high value was used the actual value had
little impact on the fit. Therefore a value of 3 was sufficient to provide a steep enough PK/PD
relationship to fit the data.
Initial values for each of the cell populations in the model are required for the model fit and in this
case were obtained from the in vitro cell cycle studies in BT474 described in the main paper.
Proportion of Insensitive cells at the start of the model fit were assumed to be 60% (same as G0/G1
cells from in vitro studies, Figure 1D); proportion of CC3 cells was 0.5% based from signal from
control treated groups in BT474 xenograft studies and the rest were assigned as sensitive cells.
Supp-PK/PD Figure 2. Schematic representation of the CC3 PK/PD model. Refer to equations 2-7
for abbreviations.
”Dead”
[CC3]
K5
x
Insensitive
Cells
K5
K5
kout
Stm (AZD8835)
Sensitive
Cells
(1-x)
The resulting PK/PD parameters of the fit are shown in the Supp-PK/PD Table 2. For the evaluation
of the final model fit, 100 data sets were simulated in Phoenix NLME. The median and the 95 %
prediction intervals of the individual tumor CC3 were superimposed on the respective observed data
(Supp-PK/PD Figure 3).
Supp-PK/PD Figure 3. Visual predictive check of tumor CC3 in mice BT474 xenograft studies
(n=314). One hundred datasets were simulated. Observations are plotted as dots. The thick full line
shows the median, and the thinner blue lines are the 5th and 95th percentiles of the simulated
individual predictions respectively. Different doses and schedules have been separated for clarity: A)
CONTROL; B) 25 mg/kg BID continuous; C) 50 mg/kg BID continuous; D) 50 mg/kg BID 2d on/5d
off, E) 25 mg/kg BID days 1&4; F) 50 mg/kg BID days1&4; G) 100 mg/kg QD day 1&4; H) 100
mg/kg QD days 1&8; I) 100 mg/kg BID days 1&4; J) 100 mg/kg BID days 1&8.
A
B
C
D
E
F
G
H
I
J
Supp-PK/PD Table 2. PK/PD parameters for model fit of effects of AZD8835 in tumor CC3 levels in
mice BT474 xenograft studies (n=314).
Parameter
k5
Estimate
0.0071
Units
1/hr
CV%
FIXED
x
0.24
--
12.2
kout
0.656
1/hr
11.5
Emax
31.4
--
11.9
EC50
1.83
uM
15.4
γ
3
--
FIXED
CC3 Residual proportional (Power 0.5) Error
0.65
--
8.0
Inter Individual Variability (x)
52.2
%
26.0
Inter Individual Variability (kout)
121.2
%
16.4
V
7.61
L/kg
9.6
Cl
1.21
L/(kg*hr)
6.6
V2
1.94
L/kg
12.1
Cl2
0.125
L/(kg*hr)
14.3
Concentration Residual proportional Error tvKa
0.62
--
11.7
Inter Individual Variability (Ka)
63.7
%
30.5
Inter Individual Variability (V)
116.8
%
16.1
Inter Individual Variability (Cl)
68.6
%
19.0
PK parameters
Tumor Volume PK/PD model
To generate the PK/PD model tumor volume and plasma PK from 7 separate BT474-xenograft studies
in mice (n=290) were combined. AZD8835 doses tested ranged from 6-100 mg/kg (orally), dosing
schedules varied from continuous dosing to multiple intermittent schedules e.g. 4 days on-3 days off
(4d on/3d off), 2 days on-5 days off (2d on/5d off), Days 1&4 and Days 1&8 with administration of
drug either once a day (QD) or twice a day (BID). Tumors were measured two-three times weekly by
calliper and volume of tumors calculated using elliptical formula (pi/6 x width x width x length)
Data was analyzed in a sequential manner with AZD8835 plasma concentrations fitted first and then
the tumor volume. Models were implemented using nonlinear mixed effects modelling in Phoenix
NLME, version 1.3. The analysis was conducted using the first order conditional estimation (FOCEELS). Model selection was based on goodness-of-fit plots, the plausibility of the physiological system
and the objective function value provided by Phoenix NLME. Goodness-of-fit plots such as observed
values (DV) versus population predictions (PRED) or versus individual predictions (IPRED), and
conditional weighted residual errors versus time or versus predicted concentrations were used for
graphic assessment of the quality of the model fit.
The plasma AZD8835 concentration data were characterized by a two-compartment PK model
parameterized in terms of absorption rate constant (ka), apparent clearance (CL), the central volume
of distribution (V), distributional clearance (CL2) and the peripheral volume of distribution (V2).
Inter-individual variability was included on all PK parameters according to a log-normal distribution
of individual parameters. Residual error was characterized with a proportional power (0.5) error
model.
The key components of the PK/PD model used are described in Supp-PK/PD Figure 3 below. Tumor
volume is modeled as the sum of cells in three different compartments/states. Healthy cells are
cycling cells that grow following a first order constant rate. Action of AZD8835 in the reduction of
the rate of proliferation is accounted for by means of pAKT308 levels, the lower the levels of pAKT
the slower the proliferation of the cycling cells. Healthy cells are also sent on an irreversible path of
cell death modelled with two transit compartments govern by two first order rates. Once again, the
action of AZD8835 in the cell death part of the model is accounted for by means of CC3, the higher
the CC3 signal the faster the cells are dying.
Supp-PK/PD Figure 3. Schematic representation of the tumor volume PK/PD model. Refer to
equations 1-11 for abbreviations.
L0
Tumour Volume
pAKT
kill
X1
Cycling Cells
X2
Damaged Cells
-
L1
X3
Damaged Cells
L1
Cell Death
kout
CC3
AZD8835
+
Insensitive
Cells
k5 * x
Sensitive Cells
k5
k5 * (1-x)
Mathematical description of the model is provided in equations 8-11 below.
𝑑𝑋1
𝑑𝑡
= 𝐿0 × 𝑋1 × 𝑝𝐴𝐾𝑇308 − 𝑘𝑖𝑙𝑙 × 𝑋1 × 𝐶𝐶3
[eq 8]
𝑑𝑋2
𝑑𝑡
= 𝑘𝑖𝑙𝑙 × 𝑋1 × 𝐶𝐶3 − 𝐿1 × 𝑋2
[eq 9]
𝑑𝑋3
𝑑𝑡
= 𝐿1 × 𝑋2 − 𝐿1 × 𝑋3
[eq 10]
𝑇𝑢𝑚𝑜𝑟 𝑉𝑜𝑙𝑢𝑚𝑒 (𝑇𝑉) = 𝑋1 + 𝑋2 + 𝑋3
[eq 11]
Where L0 is the first order growth rate of healthy cycling cells. Tumor pAKT308 levels are simulated
at each time point and dose of AZD8835 using [eq 1], the PK parameters for each animal and the
PK/PD parameters obtained on the PK/PD modelling of that biomarker. kill is the first order rate for
transfer of healthy cycling cells to the first transit stage of damaged cells. Tumor CC3 levels
are simulated at each time point and dose of AZD8835 using [eq 7], the PK parameters for each
animal and the PK/PD parameters obtained on the PK/PD modelling of that biomarker. L1 is the first
order rate transfer between the two transit compartments of damaged cells. Tumor volume is the sum
of cells on each of the three compartments. Initial conditions assumed that the two damaged cells
compartments were empty at the start of the experiment and therefore the initial tumor volume (W0)
was assigned to healthy cycling cells. W0 was also estimated during the model fit.
Inter-individual variability was included on L0, kill, L1 and W0 parameters according to a log-normal
distribution of individual parameters. Residual error was characterized with an additive error model.
The resulting PK/PD parameters of the fit are shown in the Supp-PK/PD Table 3 (all reported % CV
errors were estimated using a bootstrap method with 100 iterations). For the evaluation of the final
model fit, 100 data sets were simulated in Phoenix NLME. The median and the 95 % prediction
intervals of the individual tumor volume were superimposed on the respective observed data (SuppPK/PD Figure 4).
Supp-PK/PD Table 3. PK/PD parameters for model fit of effects of AZD8835 in tumor volume in
mice BT474 xenograft studies (n=290).
Parameter
Estimate
Units
CV%
Ka
2.74
1/hr
40.1
V
8.94
L/kg
9.4
V2
33.41
L/kg
41.9
Cl
1.14
L/(kg*hr) 10.9
Cl2
3.01
L/(kg*hr) 19.2
k5
0.0071
1/hr
FIXED
x
0.24
-FIXED
kout
0.656
1/hr
FIXED
Emax
31.42
-FIXED
EC50
1.83
uM
FIXED
γ
3
-FIXED
IC50
1.87*
uM
FIXED
n
0.88
-FIXED
E0
1
-FIXED
L0
0.002
1/hr
4.1
kill
0.001
1/hr
11.9
L1
3.37
1/hr
5.7
W0
0.50
cm3
2.6
Concentration Residual proportional (Power 0.5) Error
0.018
-Tumor Volume Residual additive Error
0.10
cm3
Inter-Individual Variability (IIV)
IIV L0
53.7
%
11.2
IIV kill
67.3
%
11.4
IIV L1
28.3
%
38.3
IIV W0
43.9
%
8.0
IIV V
38.1
%
126.7
IIV Cl
111.7
%
16.1
IIV Ka
129.6
%
64.2
IIV V2
41.8
%
176.8
IIV Cl2
6.6
%
77.8
* IC50 for pAKT308 was converted from free to total using fu=0.15 as total drug concentrations in
plasma were used when fitting the tumor volume data
Supp-PK/PD Figure 4. Visual predictive check of tumor volume in mice BT474 xenograft studies
(n=290). One hundred datasets were simulated. Observations are plotted as dots. Red line shows the
median, and black lines are the 5th and 95th percentiles of the simulated individual predictions
respectively. Different doses and schedules have been separated for clarity. A) 6 mg/kg BID; B) 12.5
mg/kg BID 4d on/3d off; C) 12.5 mg/kg BID 5d on/2d off; D) 25 mg/kg BID; E) 25 mg/kg BID 2d
on/5d off; F) 25 mg/kg BID 4d on/3d off; G) 25 mg/kg BID 5d on/2d off; H) 25 mg/kg BID days
1&4; I) 25 mg/kg QD days 1&4; J) 50 mg/kg BID 2d on/3d off; K) 50 mg/kg BID 2d on/5d off; L) 50
mg/kg BID days 1&4; M) 100 mg/kg BID days 1&4 N) 100 mg/kg QD days 1&4; O) Vehicle.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O