Download Lecture 11 (Metabolites)

Metabolite Kinetics
Theoretical Approach
PHM324Y
Guest Lecturer
Dr. Jasmina Novakovic
Apotex Inc, R&D
November 2007
To be consistent
with other slide packs,
in this slide pack
kfm should be km.
Where kfm appears
a note identifying
the change has
been added.
Learning Objectives
Drug fate
Renal and hepatic elimination
Drug-metabolite relationships
Fundamentals of metabolite kinetics
Metabolite concentration versus time
profile
Estimation of relevant rate constants
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Drug Fate









Elimination = clearance
How?
Unchanged or metabolized.
Where?
Excreta. Urine, bile, feces, perspiration…
Clearance renal, mainly unchanged drug
Clearance hepatic = metabolic clearance
Other clearances (e.g. bile)
Liver - the main site of biotransformation. More that
one metabolite can be formed: CLh = CLm1 + CLm2+…
 CLtotal = CLh + CLr + CLother
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Drug-Metabolite Relationships
Important Facts
 Drug = precursor
 Metabolite = successor
 As long as precursor is in the body, the successor will
be there
 Half-life of a metabolite formed from the drug can not
be shorter than parent drug’s half-life
 Conc-time profile of a metabolite: One exponent more
than conc-time profile of the parent drug
 Metabolite is a chemically distinct entity and has its
own volume of distribution and clearance
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Relationship Between Drug and Metabolite
(A) i.v. Doses Given on Separate Occasions
Plasma Conc [mcmoles/L]
Plasma Conc vs Time Profiles
100.000
D2 y = 12.5e-0.1x
10.000
1.000
0.100
-0.25x
M y = 20e
0.010
-0.45x
D1 y = 25e
0.001
0.000
0
4
8
12
16
Time [hours]
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20
24
28
What Can We Learn from i.v. Data?
Parameter
D1
D2
M
Units
Dose
100
100
100
μmoles
Co
25.00
12.50
20.00
μmoles/L
Vd (Dose/Co)
4.00
8.00
5.00
L
K
0.45
0.10
0.25
1/h
CL (Vd*K)
1.80
0.80
1.25
L/h
T1/2 (0.693/K)
1.54
6.93
2.77
h
AUC (Co/K)
55.56
125.00
80.00
μmoles*h/L
CL (Dose/AUC)
1.80
0.80
1.25
L/h
The only way to determine Vd of metabolite.
Metabolite, when given individually, can have longer or
shorter T1/2 than drug. What will be if the metabolite is
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formed in the body?
Relationship Between Drug and Metabolite
(B) Drug was given i.v., the metabolite is formed
Analogy between oral absorption and metabolism
Drug
at absorption site
ka
K
Drug in the body
Absorption
Elimination of Drug
km
kme
kfm
Drug in the body
Metabolism
Metabolite in the body
Elimination of
Metabolite
As long as the drug is in the body, the metabolite will be formed.
2007
What would be Plasma ConcNovember
versus
Time profile of metabolite?
Drug: i.v. bolus, mono-exponential conc vs time profile
Metabolite: Polar, no further metabolites
IV Dose
(Ao)
A Drug
Vd
Urine
ke
kb
Bile
kmf
dA/dt= -K A K = ke + kmf+ kb
kme
Metabolite
Vm
At = Aoe-Kt /Vd
dM/dt = kmf A – kme M
Ct = Co e-Kt
Mt = kmf Ao[ e-Kt – e-kmet]/(kme- K) /Vm
C M(t) = kmf Ao[ e-Kt – e-kmet]/[Vm(kme- K)]
kfm should be km
November 2007
(B) Drug Given i.v., Metabolite Formed in the Body
100.00
D1i.v. K=0.45
1/h
Conc [mcmoles/L]
10.00
1.00
D2i.v K=0.1 1/h
0.10
Metab.i.v.
Km=0.25 1/h
0.01
M from D1
0.00
M from D2
0.00
0
10
20
30
Time [hours]
When K > Km, M terminal phase kinetics follows its own profile
When Km > K, M terminal phase kinetics follows the parent drug profile
The slowest step is rate-limiting
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M T1/2 can’t be shorter than T1/2 of the parent drug
km should be kme
Metabolite Conc. versus Time Profile
(A) Metabolite is given i.v.
(B)
CM =
CM = DoseMetab i.v. e-Km
Drug is given i.v. , metabolite is formed in the body
kmfDoseDrug i.v.
(-kmet) - e(-Kt) )
(e
VM(K-kme)
or
CM =
kmfDoseDrug i.v (-kmet) (-Kt)
-e
)
VM(kme-K) (e
K > kme
kme >K
Note: Different Mol.Wt of parent drug and metabolite!
Use MOLAR doses or correction to calculate CM:
Dose Drug i.v. x (Mol.Wt.Met/Mol.Wt.Drug)
November 2007
kfm should be km
Metabolite Conc. versus Time Profile
Drug is given i.v. , the metabolite is formed in the body
K>kme
CM =
CM =
kmfDoseDrug i.v.
VM(K-kme)
kmfDoseDrug i.v.
VM(K-kme)
(e(-kmet) - e(-Kt) )
If K >> kme
e(-kmet)
kme > K
CM = kmfDoseDrug i.v (e(-kmet) - e(-Kt) )
VM(kme-K)
CM =
kmfDoseDrug i.v e(-Kt)
VM(kme-K)
November 2007
If kme >>K
kfm should be km
The Impact of kfm on the Metabolite Profile
kfm should be km
Conc vs Time Profile: Impact of
kfm
Drug K=0.45 1/h
Plasma Conc [mcmoles/L]
100.000
M kfm=0.2 1/h
10.000
M kfm=0.05 1/h
1.000
0.100
0.010
0.001
0.000
0
5
10
15
20
25
Time [h]
CM and AUC of the metabolite are proportional to kfm
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30
How to Determine K, kme and kmf ?
kfm should be km
100.000
Knowledge on:
 Oral absorption kinetics
 Urinary data analysis
10.000
1.000
0.100
0.010
0.001
0.0
Step 1: Terminal Phase
10.0
15.0
20.0
25.0
30.0
Step 2: Residual Analysis
100.000
100.000
10.000
10.000
1.000
1.000
0.100
0.100
-0.2458x
Line 1: y = 53.84e
0.010
5.0
Residual Line: y = 57.561e-0.517x
0.010
0.001
0.001
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.0
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2.0
4.0
6.0
8.0
10.0
12.0
14.0
We have two exponents. Do we know which is K or kme?
Recall: The slowest step is rate limiting.
Case 2
Case 1
100.000
10.000
10.000
Pl Conc
Pl Conc
100.000
1.000
0.100
1.000
0.100
0.010
0.010
0.001
0.001
0.000
0
5
10
15
20
25
30
0
Time
5
10
15
20
Time
Terminal slope is “K”.
Terminal slope is kme.
“Residual” slope is kme
“Residual” slope is “K”.
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25
30
The Formation Rate Constant kfm and fraction of
drug transformed into metabolite
0.06
0.05
dA/dT
CLtot = CLr +CLmet
CLmet = CLtot-CLr
CLtot =Dose/AUC
CLtot =Vd x K
CLren = Vd x ke
K = ke + kfm
CLmet = Vd x kfm
fmet=CLmet/CLtot = kfm/K
Urinary Excretion Rate vs Cpmid
CLren = slope
0.04
0.03
0.02
0.01
0
0
0.1
0.2
0.3
0.4
Cp m id tim e
Urine
ke
D
kfm should be km
kme
kfm
M
Note:
Metabolic Clearance of Drug = Vd x kfm
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Clearance of Metabolite = Vm x Kmet
0.5
0.6
Some drugs, e.g. Moxifloxacin, form
more than one metabolite
ke
Moxifloxacin
Urine
kmf1
M1
knr
kmf2
M2sec
M2
Bile
Kfm should be km
Subscript 1 & 2 remain
kmf = kmf1 + kmf2 +…
Some metabolites can be further biotransformed to
produce secondary and tertiary metabolites.
Metabolites can be excreted in urine, in bile, or…
November 2007
Mini Quiz
• Q1: Drug dose of 250 mg was given I.V.
bolus. Mol.Wt. of the drug is 200 Da. The
metabolite, conjugate, is formed in the
body and its Mol.Wt. is 350 Da.
• (a) We would like to calculate Cm in the
plasma in ng/mL. What will be the
correction factor?
• b) We would like to calculate Cm in mM.
What should we do?
November 2007
Answers
(a)
• Drug M.Wt. = 200 Da
• Metabolite M.Wt =350 Da
• Correction= 350/200= 1.75
• Dose 250 mg = 250 000 mg, Vm = x L
units mg/L=ng/mL
(b)
• 200 mg = 1 mmol = 1000 mmol
• 250 mg = 1250 mmol
• Vm = x L units mM
November 2007
Mini Quiz, Cont’d
• Q2: Drug t1/2 is 4 h. M1 t1/2 is 1.2 h, and
M2 t1/2 is 7h when given I.V. on a separate
occasions. What will be t1/2 of M1 and M2
when formed in the body from the parent
drug?
November 2007
Mini Quiz, Cont’d
• Q3: “K” of the drug is 0.25 1/h. One
metabolite is formed and kmf is 0.05 1/h.
Another drug, the inducer of metabolism,
was co-administered and kmf is 0.15 1/h.
No change in “K” was observed. What
fraction of the dose was metabolized
before and following the co-administration
of the inducer?
November 2007