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Pharmacokinetic model
Parent-metabolite pharmacokinetic modelling has been reported extensively in the
literature [6]. The models usually assume (as here) that the proportion, fmet, of parent
converted to metabolite systemically is the same as for first pass metabolism. This
raises an important parameter identification issue because without iv kinetics data for
the metabolite, this rate of conversion cannot be inferred from PK data resulting from
dosing the parent. In this case iv data were generated for both parent and metabolite
in the CD1 mouse. It was assumed that these iv data were representative of the
disposition of the two molecules in nude and SCID mice.
Figure 1A displays the PK model used to fit PK data in the mouse. Parameters are
defined in Table 1. Two gut compartments (GUT1 and GUT2) were required to fit the
plasma concentration time profiles, adding in a necessary delay between the time of
an oral dose and the time to maximum concentration (Tmax). Both the parent and
metabolite are cleared from their respective central compartments, with a fraction of
parent (osimertinib) being cleared into the active metabolite (AZ5104) of interest.
A flux from the parent GUT1 compartment to the metabolite GUT2 compartment
captures first pass metabolism whereas additional gut metabolism was assumed to
be negligible. The hepatic extraction ratio was calculated using the clearances of
parent, CLp, and metabolite, CLm, and by assuming mouse liver blood flow of 9.12
L/h/kg. This is coupled with fraction absorbed, Fabp, to derived bioavailability of
parent. Two compartment systemic kinetics are used for both parent and metabolite
with CENp and CENm being the central compartments of parent and metabolite and
similarly PERp and PERm being the peripheral compartments
The model is defined as follows, first of all the fraction of absorbed drug passing the
various pre-systemic compartments are defined as follows:
The oral bioavailability of the parent

 CL
f GUT1P ,GUT 2 P  FabP 1  min  P
 QH


,1 

The fraction of the dose metabolised in first pass to AZ5104

 CL  
f GUT1P ,GUT 2 M  FabP  min  P ,1 . f met
 QH  

The fraction of the dose not reaching systemic circulation as parent or metabolite
f GUT1P ,LOST  1  f GUT1P ,GUT 2 P  f GUT1P ,GUT 2 M
The bioavailability of AZ5104

 CL  
f GUT1M ,GUT 2 M  FabM 1  min  M ,1 
 QH  

The fraction of the metabolite dose not absorbed:
f GUT1M , LOST  1  f GUT1M ,GUT 2 M
The distribution volumes are parameterised in terms of the total volume of
distribution and the volume of the central compartment.
V2, P  Vss P  V1, P
V2,M  VssM  V1,M
The fluxes, J, between compartments are then defined as:
J GUT1P ,LOST  f GUT1P ,LOST k ab, P GUT1,P
J GUT1P ,GUT 2 P  f GUT1P ,GUT 2 P k ab,P GUT1,P
J GUT1P ,GUT 2 P  f GUT1P ,GUT 2 M k ab,P GUT1,P
J GUT 2 P ,CENP  k ab,P GUT2, P
 CL
J CENP ,CL   P
 V1, P

CEN P


Q
J CENP , PERP   P
 V1, P

CEN P


Q
J PERP,CENP   P
 V2, P

 PERP


J GUT1M ,LOST  f GUT1M ,LOST k ab,M GUT1,M
J GUT1M ,GUT 2 M  f GUT1M ,GUT 2 M k ab,M GUT1,M
J GUT 2 M ,CENM  k ab,M GUT2,M
 CL
J CENM ,CL   M
 V1,M

CEN M


Q
J CENM , PERM   M
 V1,M

CEN M


Q
J PERM ,CENM   M
 V2,M

 PERM


The differential equations are then defined as follows
dGUT1,P
dt
dGUT2,P
dt
  J GUT1P,LOST  J GUT1P,GUT 2 P  J GUT1P,GUT 2 M
 J GUT1P ,GUT 2 P  J GUT 2 P ,CENP
dCEN P
 J GUT 2 P ,CENP  J PERP,CENP  J CENP , PERP  J CENP ,CL
dt
dPERP
 J CENP , PERP  J PERP,CENP
dt
dGUT1,M
dt
dGUT2,M
dt
  J GUT1M ,LOST  J GUT1M ,GUT 2 M
 J GUT1P,GUT 2 M  J GUT1M ,GUT 2 M  J GUT 2 M ,CENM
dCEN M
 J GUT 2 M ,CENM  f met J CENP ,CL  J PERM ,CENM  J PERM ,CENM  J CENM ,CL
dt
dPERM
 J CENM , PERM  J PERM ,CENM
dt
Predicted plasma concentrations are thus defined as:
CP 
CEN P
V1,P
CM 
CENM
V1,M
For pharmacodynamic and efficacy assessment the assumption is made that free
drug concentration in plasma is in equilibrium with free concentration in tumor. The
predictions are made based upon total predicted concentration corrected for in vitro
measured free fraction (table 1):
C P ,u  f u , p C P
CM ,u  f u ,M CM
Pharmacodynamic Model
Both the parent and active metabolite are considered to bind irreversibly to the ATP
binding pocket of EGFR [4,5] leading to a reduction in the fraction of EGFR that is
phosphorylated (pEGFR). The mechanistic biomarker (pEGFR) reduction following
a single dose of parent compound was measured in PC9, H1975 and A431 mouse
subcutaneous xenografts [5] A simple irreversible binding turnover model (Figure
1B), saturable at high parent and/or metabolite concentrations, was sufficient to
capture the observed pEGFR knock down, as shown in Figure 4. A simpler model,
with second order binding only described by a bilinear term, overestimated the drug
effect at higher concentration. The saturable inactivation model describes the
reversible kinetics of the molecule entering the ATP binding pocket (CPU50,
CMU50) as well as the consequent covalent bond being formed (Kbind) [7]. Only free
drug in tumor is assumed to be available to bind to EGFR, and this is assumed to be
in equilibrium with free concentration in plasma, and so free fraction in mouse
plasma is incorporated into the model. In the absence of in vivo data it was assumed
that the metabolite was 5-fold more potent than parent, this being based upon the
ratio of the in vitro IC50s in H1975 cell line. This assumption was tested in further
pharmacodynamic experiments.
C p ,u
Cm , u





dpEGFR
 K rec 1  pEGFR  pEGFR.K bind  CPU 50 CMU 50 
C p ,u
Cm , u 

dt

1

 CPU 50 CMU 50 
(1)
Efficacy Model
Tumor growth is described using a model [8] developed in house (Fig 1C). Cells in
the outer shell are exposed to oxygen, nutrients and drug and therefore undergo
proliferation and drug-induced cell death. It is assumed cells in the inner core cannot
survive indefinitely and so undergo a “background” cell death rate, but do not
proliferate. (A necrotic core right at the centre of the model can act as a minimum
volume below which the tumor cannot reach if this is required for model fitting
purposes).
A depletion in pEGFR levels is assumed to induce an apoptotic phenotype and
therefore acts via a drug-induced cell death effect rather than by an anti-proliferative
action. This cell death rate in the outer shell cell is proportional to the volume of the
outer shell, given by
death _ rate  f kill .( pEGFR).Vshell
where
f kill  pEGFR  Emax .1  pEGFR if n=1
(2a)
and
 n1 pEGFR  1 

f kill  pEGFR  Emax .
n 1


(2b)
otherwise.
The parameter fkill is the apoptotic effect due to pEGFR depletion. We assume that
when pEGFR levels were at their control values, there was no drug induced cell
death (fkill = 0). And when pEGFR had been depleted to zero the drug effect is
maximal (fkill = Emax). A linear relationship between pEGFR reduction and modelled
cell death was not able to capture the observed tumor growth kinetics, and so we
adopted a nonlinear relation between pEGFR and fkill . This relationship captures a
“threshold” behaviour often observed in biology (see [9] for an example): at small
pEGFR perturbations the system is robust and there is little change in the kill rate,
however when pEGFR is significantly depleted increased cell death occurs. The
dynamics of pEGFR for repeat dosing were simulated based upon the PKPD model
identified from the single dose PKPD experiments. An example of the model fit to the
tumor growth is shown for all three cell lines Figure 4.
The volumes of the shell and core of the tumor, as well as the total tumor volume,
are defined in terms of the shell compartments, S and core compartments, D.
VShell  S a  S d1  S d 2  S d 3
Vcore  Ca  Cd 1  Cd 2  Cd 3
VTumour  VShell  VCore  Vmin
Here subscript a refers to viable cells and d1 through to d3 refers to cells in the
process of dying. The total tumor radius and that of the core is deduced as follows,
assuming it is spherical:
RTumor
 3 

  
VTumor 
  4 

RCore
 3 

  
VCore 
  4 

1
1
3
3
If RTumor is greater than Rdiff then the target volume for the core is
VCore,T arg et 
4
RTumour  Rdiff 3
3
Equilibration between the core of the tumor and the proliferating shell to maintain a
constant proliferating shell thickness was defined as follows:
ACore  4RCore
2
J Transfer  K trans Vcore  VCore,t arg et ACore
The direction of the flux will be dependent whether the core volume is in excess
(current depth of proliferating shell is less than Rdiff) or deficit (proliferating shell
depth greater than Rdiff) of the ideal. If it is in excess then define
Va  C a
Vd 1  C d 1
Vd 2  C d 2
Vd 3  C d 3
Similarly if it is in deficit then define
Va  S a
Vd 1  S d 1
Vd 2  S d 2
Vd 3  S d 3
The differential equations for Tumor growth are the defined as:
dS a
 K growS a  f kill S a  J TransferVa
dt
dS d 1
 f kill S a  K ex S d 1  J TransferVd 1
dt
dS d 2
 K ex S d 1  S d 2   J TransferVd 2
dt
dS d 3
 K ex S d 2  S d 3   J TransferVd 3
dt
dC a
  J TransferVa
dt
dCd 1
  K ex Cd 1  J TransferVd 1
dt
dCd 2
 K ex Cd 1  Cd 2   J TransferVd 2
dt
dCd 2
 K ex C d 2  Cd 3   J TransferVd 3
dt
Supplementary Table 1: All Model parameter estimates and in vitro data used
for model construction. The 95% confidence intervals were calculated using
sampling importance resampling.
Parameter
Interpretation
Units
Value
95% CI
in vitro derived parameters
osimertinib PC9
IC50
Apparent in vitro potency against
pEGFR in Ex19del cell line
nM
17
13, 22
AZ5104 PC9 IC50
Apparent in vitro potency against
pEGFR in Ex19del cell line
nM
2
2, 3
osimertinib H1975
IC50
Apparent in vitro potency against
pEGFR in T790M cell line
nM
15
10, 20
AZ5104 H1975
IC50
Apparent in vitro potency against
pEGFR in T790M cell line
nM
2
2, 4
osimertinib A431
IC50
Apparent in vitro potency against
pEGFR in wild-type cell line
nM
2376, 1193 NA
AZ5104 A431
IC50
Apparent in vitro potency against
pEGFR in wild-type cell line
osimertinib LOVO
IC50
Apparent in vitro potency against
pEGFR in wild-type cell line
AZ5104 LOVO
IC50
Apparent in vitro potency against
pEGFR in wild-type cell line
Not tested
NA
nM
480
320, 720
nM
33
24, 45
osimertinib Mouse
fup
-
3.15
NA
AZ5104 Mouse fup
-
13.0
NA
L/hr/kg
9.12
Fixed
0.0439
Fixed
PK parameters
Qh
Mouse Liver Bllod flow (fixed)
Fup
Free fraction in Plasma Parent(fixed) -
Parameter
Interpretation
Units
Value
95% CI
Fum
Free fraction in Plasma Metabolite
(fixed)
-
0.1147
Fixed
MWp
Molecular weight Parent (fixed)
g/mole
499.62
Fixed
MWm
Molecular weight metabolite (fixed)
g/mole
485.59
Fixed
Fabsp_CD1
Fraction absorbed through gut in
CD1 mice Parent
0.6345
0.00887-0.768
Fabsp_nude
Fraction absorbed through gut in
nude mice Parent
0.12
0.0938-0.536
Fabsp_scid
Fraction absorbed through gut in
scid mice Parent
0.35
0.115-0.375
Kabsp
Rate of absorption Parent
hr-1
0.832
0.635-1.32
Vssp
Volume of distribution Parent
L/kg
4.495
0.003100.0471
V1p
Volume of central compartment
Parent
L/kg
0.209
0.181-0.219
Qp
Distribution clearance Parent
L/hr/kg
4.427
3.23-6.37
CLp
Clearance Parent
L/hr/kg
2.547
2.02-3.46
Fabsm_CD1
Fraction absorbed through gut in
CD1 mice Metabolite
-
0.2933
0.0853-0.541
Fabsm_nude
Fraction absorbed through gut in
nude mice Metabolite
-
0.09701
0.0301-0.311
Fabsm_scid
Fraction absorbed through gut in
scid mice Metabolite
-
0.09701
0.0289-0.345
Kabsm
Rate of absorption Metabolite
hr-1
1.08
0.451-1.89
Vssm
Volume of distribution Metabolite
L/kg
13.7
6.52-22.7
V1m
Volume of central compartment
Metabolite
L/kg
0.2768
0.0316-0.531
Qm
Distribution clearance Metabolite
L/hr/kg
7.66
5.01-8.28
CLm
ClearanceMetabolite
L/hr/kg
4.18
4.06-6.44
Fmet
Fraction of parent cleared to
metabolite
-
0.7
0.536-0.718
CLp +ABT
Fold reduction in CLp in presence of
ABT
-
0.151
0.0790-0.220
CLm+ABT
Fold reduction in CLm in presence of ABT
0.453
0.233-0.876
PD and efficacy parameters
Kpool_A431
Turnover rate of Pool Compartment
hr-1
-
Not estimated
Kbpool_A431
Drug effect on Pool Compartment
hr-1.uM-1 -
Not estimated
Parameter
Interpretation
Units
Value
95% CI
Krec_A431
Turnover rate of phEGFR
hr-1
0.06
0.015-0.0741
Kbind_A431
Maximum binding rate of drug to
EGFR
hr-1
1.07
0.820-1.37
Cpu50_A431
Free potency of parent
uM
0.412
0.203-0.811
mPot_A431
Relative potency of metabolite
-
14.33
Fixed
Kgrow_A431
Growth rate of proliferating cells
hr-1
0.05486
0.0136-0.0721
Emax_A431
Maximum death rate from phEGFR
inhibition
hr-1
0.225
0.104-0.420
N_A431
Power term on fkill
-
10
4.04-188
Vmin_A431
Minimum volume for xenograft
ml
0.1
0.0282-0.410
Kpool_PC9
Turnover rate of Pool Compartment
hr-1
0.0006
0.0003350.00137
Kbpool_PC9
Drug effect on Pool Compartment
hr-1.uM-1 0.035
0.008910.0782
Krec_PC9
Turnover rate of phEGFR
hr-1
0.02508
0.0161-0.0701
Kbind_PC9
Maximum binding rate of drug to
EGFR
hr-1
0.953
0.671-1.34
Cpu50_PC9
Free potency of parent
uM
0.03437
0.0132-0.0793
mPot_PC9
Relative potency of metabolite
-
5.833
Fixed
Kgrow_PC9
Growth rate of proliferating cells
hr-1
0.03601
0.019-0.113
Emax_PC9
Maximum death rate from phEGFR
inhibition
hr-1
0.18
0.0598-0.569
N_PC9
Power term on fkill
-
211
37.4-353
Vmin_PC9
Minimum volume for xenograft
ml
0.06
0.0299-0.284
Kpool_H1975
Turnover rate of Pool Compartment
hr-1
0.00018
0.000070.00067
Kbpool_H1975
Drug effect on Pool Compartment
hr-1.uM-1 0.05
0.0091-0.092
Krec_H1975
Turnover rate of phEGFR
hr-1
0.01809
0.006270.0417
Kbind_H1975
Maximum binding rate of drug to
EGFR
hr-1
1.17
0.87-1.35
Cpu50_H1975
Free potency of parent
uM
0.0106
0.002440.0311
mPot_H1975
Relative potency of metabolite
-
5
Fixed
Kgrow_H1975
Growth rate of proliferating cells
hr-1
0.05447
0.0205-0.116
Emax_H1975
Maximum death rate from phEGFR
inhibition
hr-1
0.15
0.0913-0.736
Parameter
Interpretation
Units
Value
95% CI
N_H1975
Power term on fkill
-
221
56.3-359
Vmin_H1975
Minimum volume for xenograft
ml
0.01
0.004440.0236
Kex
Death delay rate
hr-1
0.2
0.09852-0.998
Ktrans
Transfer rate between shell and core hr-1
1000
Fixed
Rdiff
Depth of proliferating shell
0.03
0.0176-0.148
mm
The above plasma protein binding values were generated using a discovery assay.