Basic concepts of Target mediated drug disposition · ”Target mediated drug disposition captures...

TMDD Modelling/Gabrielsson 2012 1 Johan Gabrielsson

Lambertus A. Peletier (Univ Leiden)

[email protected]

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!


”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”


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)


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








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






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

)



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









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


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


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


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


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


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


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


Mixed-order decline

Target route still partly saturated

koff- and kint-driven

decline TMDD

TMDD

Signature profile

17

Changes in ke(RL)


Changes in kon

kon = 0


Changes in koff

20

Changes in dose

0.1 x dose

1 x dose

10 x dose

Repeated iv dosing


Repeated sc dosing


ttdt

m

maxMM

ctdMMlinearL

V/LLCldt

Ld

LK

VCl

V/LLClLClLClIndt

Ld

Case Study 1 – Efalizumab Equations


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!


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


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


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

Basic concepts of Target mediated drug disposition · ”Target mediated drug disposition captures...

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