TMDD Modelling/Gabrielsson 2012 1 Johan Gabrielsson
Lambertus A. Peletier (Univ Leiden)
Basic concepts of Target mediated
drug disposition
”Target mediated drug disposition captures the capacity
limited binding and saturation of a drug-’target’ complex,
where a significant portion of the drug binds to its target, such
that this interaction impacts the disposition of the drug per se”
Peletier & Gabrielsson, 2009
TMDD Modelling/Gabrielsson 2012 2
Objectives
• Give some background to TMDD
• What type of models are available?
• Parameter (identifiability) challenges
• Discuss clearance mechanisms
• Focus on available circulating target
• Analysis of L, R and RL. Not Ltot & Rtot
• Demo of Maxsim2
• Remember where you have the pharmacological concentration range!
TMDD Modelling/Gabrielsson 2012 3
”Target mediated drug disposition
captures the capacity limited binding
and saturation of a drug-’target’
complex, where a significant portion of
the drug binds to its target, such that
this interaction impacts the disposition
of the drug per se”
TMDD Modelling/Gabrielsson 2012 4
Target mediated drug disposition - consequences
Cle
ara
nce
Concentration (L) Time
Co
nce
ntr
ation
(L
)
Linear PK
Linear PK
A) Rapid 2-order
decline
B) Slow 1-order disposition
Target route saturated
C) Mixed-order disposition
Target route partly saturated
D) koff and ke(RL)-driven disposition
Target Mediated Drug Disposition
CL(L) + TMDD
CL(L)
Effective concentration range
Predicted human dose = Ce x CL(L)
TMDD Modelling/Gabrielsson 2012 5
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Con
ce
ntr
atio
n (
mg/L
)
0R
on
)RL(eoff
mk
kkK
on
off
dk
kK
Target mediated drug disposition – Data (L)
A) Rapid 2-order decline
B) Slow 1-order disposition
Target route saturated
C) Mixed-order disposition
Target route partly saturated
D) koff and ke(RL)-driven disposition
Target Mediated Drug Disposition
TMDD Modelling/Gabrielsson 2012 6
on
off
d
on
)RL(eoff
m
in)RL(emax
)RL(eoffon
offonoutin
ttddt
offonctddL)L(L
k
kK
k
kkK
kkRV
RLkRLkRLkdt
RLd
RLkRLkRkkdt
Rd
V/LClLCldt
Ld
RLkRLkV/LClLClLClLClIndt
Ld
0
Equations - TMDD
Time
Co
nce
ntr
ation
(L
)
Linear PK
Linear PK
A) Rapid 2-order
decline
B) Slow 1-order disposition
Target route saturated
C) Mixed-order disposition
Target route partly saturated
TMDD Modelling/Gabrielsson 2012 7
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Target mediated drug disposition – Data (L)
0R
on
)RL(eoff
mk
kkK
on
off
dk
kK
Con
ce
ntr
atio
n (
mg/L
)
A) Rapid 2-order decline
TMDD Modelling/Gabrielsson 2012 8
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Con
ce
ntr
atio
n (
mg/L
)
Target mediated drug disposition – Data (L&R)
0R
on
)RL(eoff
mk
kkK
on
off
dk
kK
A) Rapid 2-order decline
B) Slow 1-order disposition
Target route saturated
C) Mixed-order disposition
Target route partly saturated
D) koff and ke(RL)-driven disposition
Target Mediated Drug Disposition
TMDD Modelling/Gabrielsson 2012 9
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Co
nce
ntr
atio
n (
..)
Target mediated drug disposition – Data (L&R&RL)
0R
on
)RL(eoff
mk
kkK
on
off
dk
kK
TMDD Modelling/Gabrielsson 2012 10
Parameter Estimate CV%
CL 0.001 1
KON 0.099 17
KOFF 0.001 27
VT 0.101 2
CLD 0.003 4
KOUT 0.009 6
R0 12. 4
KERL 0.002 27
Parameter Estimate CV%
CL 0.001 1
KON 0.092 2
KOFF 0.001 13
VT 0.100 2
CLD 0.003 3
KOUT 0.009 2
R0 12. 1
KERL 0.002 23
Parameter Estimate CV%
CL 0.001 1
KON 0.096 1
KOFF 0.001 3
VT 0.100 1
CLD 0.003 3
KOUT 0.009 2
R0 12. 1
KERL 0.003 2
Ligand only Ligand & traget Ligand & traget & complex
Target mediated drug disposition – Results
• Known model & parameters
• Several dose levels
• Low variability
• A) Ligand
• B) Ligand & Target
• C) Ligand & Target & Complex info
TMDD Modelling/Gabrielsson 2012 11
TMDD Modelling/Gabrielsson 2012 12
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Con
ce
ntr
atio
n (
mg/L
)
Input
Vc
Cld
Cld
1.
Vt
CK
VCl
m
max
Non-linear PK
Linear PK
Michaelis-Menten does not mimick TMDD
TMDD Modelling/Gabrielsson 2012 13
Lin + Michaelis-Menten does not mimick TMDD
0.001
0.01
0.1
1
10
100
1000
0 100 200 300 400 500 600
Time (h)
Con
ce
ntr
atio
n (
mg/L
) Non-linear PK
Linear PK
Input
Vc
Cld
Cld
1.
Vt
CK
VCl
m
max
linCl
on
)RL(eoff
mk
kkK
Linear PK
TMDD Modelling/Gabrielsson 2012 14
TMDD Modelling/Gabrielsson 2011 15
Lig
an
d C
oncentr
ation
Time
RLkdt
dL .A on
LV
CLLk
dt
dLB
c
L
Le )(
)( .
d
in)L(eKL
LkLk
dt
dL .C
Lkdt
dL .D )RL(e
Concentr
ation
Time
Rapid 2-order decline
Slow 1-order decline
Target route saturated
Mixed-order decline
Target route still partly saturated
koff- and kint-driven
decline TMDD
TMDD
Signature profile
TMDD Modelling/Gabrielsson 2011 16
17
Changes in ke(RL)
TMDD Modelling/Gabrielsson 2011 18
Changes in kon
kon = 0
TMDD Modelling/Gabrielsson 2011 19
Changes in koff
20
Changes in dose
0.1 x dose
1 x dose
10 x dose
Repeated iv dosing
TMDD Modelling/Gabrielsson 2011 21
Repeated sc dosing
TMDD Modelling/Gabrielsson 2012 22
ttdt
m
maxMM
ctdMMlinearL
V/LLCldt
Ld
LK
VCl
V/LLClLClLClIndt
Ld
Case Study 1 – Efalizumab Equations
TMDD Modelling/Gabrielsson 2012 23
Case Study 1 - Efalizumab
Michaelis-Menten approximation Parameter Initial estimate Final estimate CV%
Vc (L) 0.0572 14
Vt (L) 0.0447 20
Vmax (mg·h-1
) 0.0359 7
Km (mg·L-1
) 0.0393 53
Cld (L·h-1
) 0.0512 45
CleH (L·h-1
) 0.0067 7
Note, no shallow
terminal phase!
TMDD Modelling/Gabrielsson 2012 24
TMDD Modelling/Gabrielsson 2012 25
NCA Analysis
1 Cl_pred 0.0196 1
2 Cl_pred 0.0035 x 3
3 Cl_pred 0.0020 x 10
4 Cl_pred 0.0017 x 30
1-
.
1-1-
1-1-
.
marmoset
marmosetlinear,marmosetlinear,man
hL ..
.CL Low
.CL High
.kg .
gkhL .
gkhL .
BWBWClCl
4200360
0360
420
60
7060
00170
01960
70
750
750
mg.....oseD Low
mg....oseD High
hL .
hL .Lmg .CLCDose
1-
-1
predicted,maneman420
036010 1
TMDD Modelling/Gabrielsson 2012 26
PK Acute PD
Sim
PK
Sim
Chron PD
Sim
Acute TK Chron TK
Sim
Points to consider - Design
CL
Vmax
Km
EC50
Kd
R0
kout
EC50
Kd
R0
kout
Effective concentration range
Predicted human dose
TMDD Modelling/Gabrielsson 2012 27
Conclusions – TMDD models
• Model never better than data – Remember pharmacological concentration range!
• Requires several concentration-time courses
• Approx. of Vc often works well (0.05 L·kg-1) & parameterize target with R0 and
kout
• Identifiability problems (L, R, LR) Estimation of ke(RL) requires R and/or RL
• L and R (and RL) information improves parameter estimates and their precision
• Let design be an iterative process – simulate design
• Mechanistic interpretation of parms requires adequate experimental design and
information about L, R and RL