ains and warfarin2

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Jou rna l o f Pha rm aco kine t ics and Biopharmaceut ics , Vol . 1 , No. 6, 1973

K i n e ti cs o f D r u g D r u g I n te r a ct io n s 1

M a l c o l m R o w l a n d 2 a n d S h a i k h B M a t i n 2

Si nce many drug-drug pharmacok i ne t i c i n t e rac t i ons are dependent on t he concent ra t i ons o f t he

i n t e rac ti ng spec ie s, t he degree o f i n te rac t i on shoul d be a graded pheno menon vary i ng w i t h drug

and/ or m e t abol i te concen t ra t ion and t hus drug a dmi n i s t ra t ion and t ime . H ence one shoul d be ab le t o

deve lop predict ive kinet ic models fo r such interactions. A change in drug plasma levels when a

compound i s adm inis tered as a s ingle dose together wi th an other drug can ar i se . from a change

drug c learance , di spla ceme nt f ro m binding s i tes , a change in e l iminat ion rates , or a combina t ion of

any o r al l of these poss ibi li ti es . Th e inter ac t ion of p heno barb i tal and the spa ringly soluble oral

an ti fung al agent , griseofulvin, is one exam ple. A na lysis sho ws tha t there is no change in el imination

hal f- I f e of gr i seofulv in but tha t phen oba rbi tal reduces the ex te nt o f gr i seofulv in absorpt ion rather

than enhances i t s e liminat ion. Sul faph enazo le inhibi ts the me tabol i sm and m arked ly prolongs

t o l bu t ami de p l asma l evel s. A n an t i c i pa t ed sudden drop i n t he exc re t i on ra t e o f t he t o l bu t ami de

meta bol i tes at maxim um sulfonamide plasma leve ls i s assoc iated wi th an almost comp le te block of

t o t bu t ami de ox i da t ion . The i nh i b i tor cons t an t K l f o r t h i s i n t e rac t ion has been ca lcu la ted , a l l ow ing

one to predic t tolbuta mid e and m etabo l i te levels when the inhibi tor is adminis tered. Dr ug-d rug

i n t e rac ti on re su l t ing f rom pro t e i n d i sp lacement has been hypo t hes i zed by a nu mber o f au thors .

How ever , t he po t en t i a t i on o f the an t i coagu l an t war f ar i n in pa t i en t s rece iv ing pheny l bu t azon e i s

more com pl icated than has been envis ioned prev iously . W hi le di splacement occurs , data sugg est that

phenylbutazone pr imari ly ac ts through se lec t ive inhibi t ion to al ter the i someric composi t ion and

pot ency o f the racemi c war f ar i n admin is te red . The war f ar i n-p heny l bu t azo ne i n t e rac t ion s t udy

stresses the importan ce of measuring meta bol i tes as well as intac t drug.

K E Y W O R D S

drug-drug interactions; plasma protein displacement; griseofulvin-pheno-

barbital interactio n; to lbuta mide sulfaphenazo le intera ction; Michaelis Menten kinetics;

inhibitor constants; tolbutamide metabolites; warfarin-phenylbutazone interaction.

O p e n a n y c u r r e n t m e d i c a l j o u r n a l a n d o n e is r e m i n d e d t h a t t h e c o

a d m i n i s t r a t i o n o f t w o o r m o r e d r u g s c a n e i t h e r c a u s e d e l e t e r i o u s e ff ec ts o r

Much of the work reported in this paper was supported by a grant from the National Institutes

of Health, Bethesda, Maryland, NIGMS 16496.

aThis paper was presented by Dr. Rowland at the Conference on Pharmacology and Pharma-

cokinetics: Pro blems and Perspectives, October 30- Nov embe r 1, 1972, at the Foga rty Inter-

nation al Center, Nati onal Institutes of Health, Bethesda, Maryland. This paper, in a slightly

different format, will be published in the Proceedings of the Conference by Plenum Press,

New York.

ZSchool of Phar macy, University o f California, San Francisco, California 94143.

553

9 1973 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication

may be reproduced, stored in a retrieval system,or transmitted, in any form or by any means, electronic, mechanical,

photocopying, microfilming, recording, or otherwise, without written permissionof the publisher.



K i n e t i c s o f D r u g D r u g I n t e r a c t io n s

cy la m ide (14 ) ind ica te so m e o f the com plex i t ie s . Se ll e rs and K oc h-W ese r (15 )

h a v e d i s c u s s e d s e v e r a l q u a n t i t a t i v e a s p e c t s o f t h e a u g m e n t a t i o n o f w a r f a r i n

c o a g u l a t i o n i n d u c e d b y c o n c o m i t a n t c h l o r a l h y d r a t e a d m i n i s tr a t i o n , w h i c h

m i g h t r e s u lt f r o m d i s p l a c e m e n t o f t h e a n t i c o a g u l a n t f r o m b i n d i n g s ite s, b u t

the i r s were equ i l ib r ium ra the r th an k ine t i c cons ide ra t i6ns . Th e in ten t o f the

p r e s e n t r e v i e w is t o i l l u st r a te h o w p h a r m a c o k i n e t i c a n a l y si s l ea d s t o f u r t h e r

ins igh t s r ega rd ing the causes , pos s ib le mech an i sms , a nd d es ign o f fu tu re

expe r ime n ts a im ed a t e luc ida t ing va r ious f ace t s o f d rug in te rac t ions . I t is a l so

t h e i n t e n t t o i ll u s tr a te h o w p r e d i c t i v e p h a r m a c o k i n e t i c m o d e l s o f d r u g

i n t e r a c t io n s c a n b e d e v e l o p e d a n d t h e p o t e n t i a l u t il it y o f s u c h m o d e l s i n

d e c i d in g a p p r o p r i a t e d o s a g e r e g im e n s w h e n a c o m b i n a t i o n o f d r u g s is d e e m e d

a t h e r a p e u t i c n e c e s si ty . F o r t h e m o s t p a r t , t h e e x a m p l e s c h o s e n a r e f r o m t h e

a u t h o r s o w n r e s e a r c h e x p e ri e n ce .

M u c h o f t h e i n t e r p r e t a t io n o f d r u g - d r u g i n t e ra c t i o n s a r i se s fr o m c a r e fu l

m e a s u r e m e n t s o f t h e c o n c e n t r a t i o n t i m e c o u r s e o f a d r u g o r i ts m e t a b o l i te . A

d e c r e a s e i n d r u g p l a s m a l ev e ls w h e n a d m i n i s te r e d a s a si n gl e d o s e t o g e t h e r

w i t h a n o t h e r d r u g c o u l d a r i s e f r o m a r e d u c t i o n i n a b s o r p t i o n ( if t h e d r u g i s

g i v e n o t h e r t h a n i n t ra v e n o u s l y ) , d i s p l a c e m e n t f r o m p l a s m a p r o t e i n s, h a s t e n -

ing o f i ts e l im ina t ion , o r a com bin a t io n o f any o r a l l o f these pos s ib i l it i e s.

K i n e t i c a n a l y s is h a s h e l p e d g r e a t l y in th e i n t e r p r e t a t i o n o f s u c h d a t a a n d h a s

s u g g e s t e d t h e d e s ig n o f f u r th e r e x p e r im e n t s . T h e i n t e r a c t i o n b e t w e e n t h e

spar ing ly so lub le o ra l an t i funga l agen t , g r i s eo fu lv in , and phenobarb i t a l i s

o n e e x a m p l e . B u s h f ie l d e t a l (16 ) had no ted tha t p lasm a l evel s o f g r i s eo fu lv in

f o l lo w i n g a s in g le d o s e o f t h is d r u g w e r e r e d u c e d i n s u b j e c t s c o a d m i n i s t e r e d

p h e n o b a r b i t a l . G r i s e o f u l v i n i s p r i m a r i l y O - d e m e t h y l a t e d t o 6 - d e m e t h y l -

g r i s e o f u l v i n i n m a n , a n d i t w a s p r o p o s e d t h a t p l ~ n o b a r b i t a l h a d s t i m u l a t e d

t h i s o x i d a t i v e p a t h w a y . A n a l y s i s b y R i e g e l m a n

e t a l

( 1 7 ) s h o w e d t h a t t h e r e

wa s no cha nge in the e l im ina t ion ha l f- li fe o f g r i seo fu lv in and l ed the m to

d e s ig n a s t u d y t o p r o v e t h a t p h e n o b a r b i t a l r e d u c e d t h e e x t e n t o f g r i se o f u lv i n

ab so rp t i on r a the r th an e nha nce d i t s e l imina t ion (Fig . 1 ). The r edu ced ab -

s o r p t i o n w a s c o m p l e m e n t e d b y a p r o p o r t i o n a l r e d u c t io n i n t h e c u m u l a t iv e

u r i n a r y e x c r e t i o n o f 6 - d e m e t h y l g r is e o f u lv i n . T h e m e c h a n i s m o f t h e i n t er a c -

t i o n i s p o o r l y u n d e r s t o o d . P r e s u m a b l y , p h e n o b a r b i t a l d i m i n i s h e s t h e r a t e o f

d i s s o l u t i o n o f t h is s p a r i n g l y s o l u b l e a n d i n c o m p l e t e l y a b s o r b e d d r u g , p e r h a p s

b y d e c r e a s i n g g u t m o t i l it y o r i n t e s t in a l t r a n s it t im e . T h e s e d a t a s u g g e st t h a t

a m o r e r a p i d l y d i s s o l v i n g g r i s e o f u l v i n f o r m u l a t i o n s h o u l d o b v i a t e t h e

p r o b l e m . P r o b a b l y , b y t h e s a m e o r a s i m i la r m e c h a n i s m , b a r b i t u r a t e s d e -

c r e a s e t h e a b s o r p t i o n o f t h e s p a ri n g l y s o l u b l e a n t i c o a g u l a n t , d i c o u m a r o l

(18 ) . C l in ica l ly , the danger a r i s es when the ba rb i tu ra te i s w i thd rawn f rom a

p a t i e n t s t a b i l i z e d o n t h i s a n t i c o a g u l a n t - b a r b i t u r a t e c o m b i n a t i o n . I n n o n e

o f t h e s e s t u d ie s w e r e p l a s m a b a r b i t u r a t e c o n c e n t r a t i o n s d e t e r m i n e d , a n d

henc e i t is d i f fi cu lt to kn ow wh e the r the s ever i ty o f the dep re s s ion o f the



556

owland and

M a t i n

INTRAVENOUS 9 9

2.0-- ORAL I I 0

CONTROL WITH

. ~ J ~ PHENOBARBITAL

o

2

0, 0.5

?

o i r r r I J

1 2 3 4 50

HOURS

F ig . 1 . G r i s e o f u l v i n - p h e n o b a r b i t a l i n t e r a c t i o n

i n m a n . N o t e t h a t t h e d i s p o s i t i o n k i n e t i c s o f

g r i s e o f u l v i n g i v e n i n t r a v e n o u s l y a r e u n a f f e c t e d

b y p h e n o b a r b i t a l a d m i n i s t r a t i o n . I n c o n t r a s t ,

b o t h t h e r a t e a n d e x t e n t o f o r a l g r i s e o f u l v i n a r e

d e p r e s s e d f o l l o w i n g p h e n o b a r b i t a l . R e p r o d u c e d

f r o m R i e g e l m a n e t a l 1 7 ) w i t h p e r m i s s i o n o f t h e

c o p y r i g h t o w n e r s .

extent of absorption of either griseofulvin or dicoumarol among or within

subjects could be correlated with the amount of barbiturate in the body.

Nonetheless, some relationship between the effect and the body burden of

barbiturate is anticipated.

A more clearly defined and more readily modeled interaction is that

between the oral hypogtycemic agent, tolbutamide, and a variety of drugs.

Together with the anticoagulants, interactions with the oral hypoglycemic

agents constitute some of the most adverse clinical cases of drug interactions.

Hypoglycemic crises have been reported when patients, stabilized on tol-

butamide, have added sulfaphenazote, dicoumarol, phenylbutazone, or

phenyramidol to their drug therapy 19, 20). In each case cited, clear chemical

data exist showing a slowing a tolbutamide elimination. Many of these

interactions appear to involve inhibition of tolbutamide oxidation to

hydroxytolbutamide, which is virtually obligatory for tolbutamide elimina-

tion in man 21). Hydroxyto lbutamide is partially excreted unchanged, and

the majority is further oxidized to carboxytolbutamide, which is excreted

intact. The oxidation of tolbutamide is the rate-limiting step in the elimina-



Kinetics of Drug Drug Interactions 557

tion of the drug and its metabolites. Subsequent oxidation steps are very

rapid 22). Accordingly, a short time after tolbutamide administrat ion, the

rate of excretion of the sum of the two metabolites equals the rate of tol-

butamide oxidation and offers a very sensitive measure of changing tolbuta-

mide oxidation.

The best-studied interaction is that between the sulfonamide, sulfa-

phenazole, and tolbutamide. While not widely prescribed, sulfaphenazole

is reported to increase the half-life of tolbutamide from the normal 4-8 hr to

values ranging from 24 to 70 hr 22, 23). The clinical crises probably arise

when tolbutamide accumulates upon chronic administrat ion in the presence

of sulfaphenazole. Figures 2 and 3 illustrate the situation when sulfaphenazole

>

z

O

r~

z

o

U

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1.0

4 \ \ \ o B 0 A M o

~ ; . \

9 i ' ~ . ~ " ~

~ " 2 0 4 0 6 0 8 0 1 0 0

T I MF (hou rs )

F ig . 2 . T o l b u t a m i d e - s u l f a p h e n a z o l e i n t e r a c t i o n k i n e t ic s i n m a n .

T h e e x p e r i m e n t a l d a t a ( t o l b u t a m i d e , s u l f a p h e n a z o l e ) a n d t h e

a n a l o g c o m p u t e r g e n e r a t e d c u r v e s ( s o l i d l i n e s ) d e s c r i b e t h e

i n t e r a c t i o n b e t w e e n s u l f a p h e n a z o l e a n d t o l b u t a m i d e . T h e

s u b j ec t r e ce iv e d a n i n t r a v e n o u s b o l u s o f 1 g t o l b u t a m i d e a n d a

1 g ora l susp ens i on of su l faphe nazo l e (Su l fab i dR) 589 hr l a t e r.

F o r c o n v e n i en c e , t h e a m o u n t o f t h e t w o d r u g s i n th e b o d y i s

e x p r e s s e d a s a p e r c e n t a g e o f t h e a d m i n i s t e r e d d o s e . T h e h a l f-

l if e o f t o l b u t a m i d e i n t h e a b s e n c e o f s u l f a p h e n a z o l e i s a p p r o x i -

m a t e l y 7 h r . T h e d o t t e d l i n e s d e p i c t t h e a n t i c i p a t e d r a p i d d e c l i n e

o f t o l b u t a m i d e w h e n a d m i n i s t e r e d a lo n e . T h e d e g r e e o f i n -

h i b i t i o n o f t o l b u t a m i d e o x i d a t i o n c o n t i n u o u s l y c h a n g e s w i t h

t h e a m o u n t o f s u l f a p h e n a zo l e in t h e b o d y . B l o c k is m a x i m a l a t

p e a k s u l f o n a m i d e p l a s m a le ve ls , T h e h a lf - li fe o f s u l f a p h e n a z o l e

i n t h i s sub j ec t i s 12 hr .



8 R ow lan d an d Ma t in

100.0

--~

C o r b o x y t o l b u t a m i d e

.EE 1 0. 0 ~ ~ Hyd roxytolbu tamide o

Z

0

1.0

IX O 0 ~

u

x

0 1 I I

~ 2 0 4 0 6 0 8 0 1 0 0

S

I.V) oral)

TIME hours)

F ig . 3 . T o l b u t a m i d e - s u l f a p h e n a z o l e i n t e r a c t i o n k in e t i c s i n m a n . T h e e x c r e t io n r a t e d a t a

o f h y d r o x y t o l b u t a m i d e a n d c a r b o x y t o l b u t a m i d e f o r t h e s a m e s u b je c t w h o s e p l a s m a d a t a

a r e p o r t r a y e d i n F i g . 2 . A t p e a k p l a s m a s u l f a p h e n a z o l e l ev els , t h e i n h i b i t i o n o f t o l b u t a -

m i d e o x i d a t i o n i s a l m o s t c o m p l e t e, a n d , w i th e s s e n ti a ll y n o f o r m a t i o n o f h y d r o x y t o l -

b u t a m i d e , t h e e x c r e t i o n r a t e o f b o t h t h i s m e t a b o l i t e a n d c a r b o x y t o l b u t a m i d e r a p i d l y

fal l, r ef l ec ti ng t he ve ry sho r t 20-4 0 m i n) ha l f -l i ve s o f the se spec ie s. Bey ond 10 hr a f t e r t he

t o l b u t a m i d e b o l u s , t h e r a t e o f e x c r e t io n o f t h e s e t o l b u t a m i d e m e t a b o l i t e s e q u a l s t h e r a t e

o f to l b u t a m i d e o x i d a t i o n . A s t h e s u l f a p h e n a z o l e b o d y l e v e l s d e c l in e , t h e d e g r e e o f

i n h i b i t io n o f t o l b u t a m i d e o x i d a t i o n d i m i n i sh e s a n d t h e e x c r e t io n r a t e o f t h e m e t a b o l it e s

i n c re a s es . H o w e v e r , e v e n t h o u g h t h e i n h i b i t i o n c o n t i n u a l l y d i m i n i s h e s , s o a l s o d o e s t h e

a m o u n t o f t o l b u t a m i d e i n t h e b o d y , a n d a f t e r 5 0 h r t h e e x c r e t i o n r a te o f m e t a b o l i t e s c o n -

t inual ly dec l ines , a lbe i t s lowly.

is g iven o ra l ly to a sub jec t app rox im ate ly 5 h r a f t e r r ece iv ing an in t r av eno us

b o l u s d o s e o f t o l b u ta m i d e . S u l fa p h e n a z o le m a r k e d l y p r o l o n g e d t o l b u t a m i d e

p lasm a l eve ls , w i th an an t i c ipa ted sudd en d r op in the excre t ion r a te o f the

m e t a b o l i t e s a t m a x i m u m s u l f o n a m i d e p l a s m a l e v el s a s s o c i a t e d w it h a n

a l m o s t c o m p l e t e b l o c k o f t o l b u t a m i d e o x i d a t i o n . T h e h a lf -l iv e s f r o m t h i s

s h a r p ly d e s c e n d in g p o r t i o n o f t h e h y d r o x y a n d c a r b o x y t o l b u t a m i d e u r i n a r y

e x c r e t io n r a t e p l o t s a p p r o x i m a t e d t h e h a lf -l iv e s o f t h e s e m e t a b o l i t e s w h e n

a d m i n i s t e r e d a l o n e 2 2 ). A s t h e r a t i o o f h y d r o x y - to c a r b o x y t o l b u t a m i d e i n

t h e u r i n e r e m a i n e d u n c h a n g e d i n th e p r e s e n c e o f s u l fa p h e n a z o l e , i t a p p e a r s

t h a t t h is s u l f o n a m i d e d o e s n o t i n f lu e n c e th e o x i d a t i o n o r r e n a l c l e a r a n c e o f

h y d r o x y t o l b u t a m i d e i n t h e d o s e r a n g e s t u d i e d . S e p a r a t e s t u d i e s c o n f i r m e d

tha t to lbu tam ide 1 g ) d id no t in f luence su l f aphen azo le e l imina t ion k ine t ic s ,

wh ich is p r inc ipa l ly by NX -g lucuron ida t ion and N 4-ace ty la t ion 24 ).

H u m a n in v i tro l iv e r m i c r o s o m a l s t u d i e s c o n f i rm e d t h a t s u l f a p h e n a z o l e

b loc ks to lb u ta m ide ox id a t ion 19 ) , wh ich , a t l eas t in the r ab b i t 25 ) , i s by

com pet i t ive inh ib i tion . T he k ine t ic s o f com pet i t ive inh ib i t ion o f a g iven

m etab o l i t e s t ep is genera l ly g iven by 26 )

R a te o f m e tab o l i sm = V ,n- S 1 )

S + K i n 1 + I / K I )



K i n e t i c s o f D r u g D r u g I n t e r a c t io n s 5 5 9

where Vm is the maximal velocity of the reaction, Km is the Michaelis-Menten

constant, S is the substrate concentration, I is inhibitor concentration, and

K t

is the inhibitor constant, given by the value of I which increases the apparent

K mof the system by twofold. In the particular case of tolbutamide, the rate of

oxidation to hydroxytolbutamide virtually equals the rate of tolbutamide

elimination. Also, as tolbutamide half-life does not change over 0.5-6.0 g dose

range 27), the concentration of drug at the metabolic site must always be

much smaller than its Kin. With these facts, and knowing that in the absence

of sulfaphenazole the decay of tolbutamide can be described by a first-order

process, rate constant

k r ,

the following simple description can be given for the

elimination kinetics of tolbutamide in the presence of the inhibitor, sulfa-

phenazole :

k r T

Rate of tolbutamide elimination = - d T / d t ) - 1 + I / K ~ ) 2)

where T and I are the amounts oftolbutamide and sulfaphenazole in the body,

and K~ may now be defined as the amount of inhibitor which diminishes the

effective k T by one-half or prolongs the half-life twofold). By measuring all

chemical species, only K~ remains unknown. In the present data, an excellent

fit is obtained when Kt is 200 mg sulfaphenazole Fig. 2). This value of 200 mg

is small compared to the 1-2 g daily dose usually recommended for this

sulfonamide.

Knowing the Kt for sulfaphenazole and the other relevant pharmaco-

kinetic data, the clinical situation can be modeled. Usually, 0.5 g tolbutamide

and 1.0 g sulfaphenazole are given orally twice daily. Initially when only

tolbutamide is given, expected plateau levels are reached within 3-4 half-

lives 28), or 30 hr Fig. 4). When sulfaphenazole is also given, it accumulates

and also blocks tolbutamide oxidation, causing a rise in the level of the

sulfonylurea to approximately seven times its usual level. A time period of 2-3

days is required before this elevated tolbutamide level falls to the level in the

absence of sulfaphenazole, regardless of whether only sulfaphenazole or both

drugs are stopped. These data can adequately explain the elevated tolbuta-

mide levels seen when these two drugs are administered concomitantly for

extended periods 19, 23).

The exact estimate for the new half-life of tolbutamide, and the degree of

accumulation in the presence of a steady level of the inhibitor, is gained from

two equations 29) :

Average amount of drug in the body at the plateau 4)

3 )

1.44 x dose x half-life

dosing interval



5 6 R o w l a nd a nd M a t i n

g

> -

o

Z

7_

E

6

4

i

j

0

~ ':?

7 1 4 2 1

T I M E d a y s)

Fig. 4, To lbutam ide-sulfaph enazole interaction kinetics in m an.

A nalo g computer simulations of the clinical situatio n when

tolbutamide 0.5g, twice daily) is given in the absence and

presence of sulfaphenazole 1.0 g twice daily). The so lid b lack

bars denote the dura tion o f each drug regimen. Having a short

half-life 4-8 hr), plateau levels of tolbuta m ide are reached within

2 days. The sulfaphenazole also rapidly reaches plateau con-

cen tratio n half-life 11~12 hr). In the presence ofsulfaphenazole,

the am ount of tolbuta mid e in the bod y continues to rise until

out put once again equals input. U pon cessation o f sulfaphena-

zole, the decline of tolbu tam ide, whether contin ued solid line)

or stop ped at the same time as sulfaphenazole dott ed line), is

prim arily controlled by the ra te of remov al o f sulfaphenazole .

Consequently, it would take several days before to[butamide

levels once again fe ll into the accepted thera peu tic range.

T h e n e w s t e a d y - s t a t e t o l b u t a m i d e h a l f - li fe i s

T o l b u t a m i d e t l / 2 ( i n h i b i t e d ) = t o l b u t a m i d e tl/2 no rm ,j )

4 )

a v e r a g e a m o u n t o f i n h i b i t o r a t p l a t e a u )

x 1 + K I

I f s u l f a p h e n a z o l e t l / 2 = 1 0 h r , K I = 2 0 0 m g ) 2 5 ) i s g i v e n a s 1 .0 g t w i c e

d a i l y , t h e n a c c o r d i n g t o t h e f i rs t e q u a t i o n , 1.5 g is t h e a v e r a g e a m o u n t o f

i n h i b i t o r a t t h e p l a t e a u a n d t h is l ev e l is r e a c h e d w i t h i n 2 d a y s 4 x

t l / z ) .

S u b s t i t u t i n g t h i s a m o u n t o f t h e i n h i b i t o r i n t o e q u a t i o n 4 in d i c a te s t h a t t h e

n e w h a l f - li f e f o r t o l b u t a m i d e is s e v e n t o e i g h t t i m e s l o n g e r t h a n n o r m a l i .e .,

f r o m 3 5 t o 40 h r i n s t e a d o f 5 h r) . N o w i t w i l l t a k e a p p r o x i m a t e l y 6 d a y s

4 x 1 .5 d a y s ) to r e a c h t h e n e w p l a t e a u w h e n t h e a v e r a g e a m o u n t o f t o l -

b u t a m i d e is s e v e n t o e i g h t t i m e s t h e a v e r a g e p l a t e a u l ev e l i n th e a b s e n c e o f t h e



Kinetics of Drug Drug Interactions 5 6 1

i n h i b it o r . I t w a s g r a t i fy i n g t o n o t e t h a t t h e se p r e d i c t io n s , w h e n a p p r o p r i a t e l y

s c a l e d d o w n , w e r e o b s e r v e d i n a s u b j e c t w h o r e c e i v e d t h e s a m e m u l t i p l e

d o s e s c h e d u l e a s d e p i c t e d i n F i g . 4 w i t h t h e e x c e p t i o n t h a t 0 . 1 g r a t h e r t h a n

0 .5 g t o l b u t a m i d e w a s i n g e s t e d e a c h d a y (2 5) . I f i t w e r e n e c e s s a r y t o g i ve th e s e

t w o d r u g s i n c o m b i n a t i o n , it is a p p a r e n t t h a t t h e d o s a g e s c h e d u l e o f t o l b u t a -

m i d e w o u l d h a v e t o b e r e d u c e d o n e - e i g h t h t o m a i n t a i n e s s e n t ia l ly t h e s a m e

a m o u n t o f t o l b u t a m i d e i n t h e b o d y . I n a n y i n d i v id u a l , t h e d e g re e o f i n te r a c -

t i o n w i ll d e p e n d u p o n t h e d o s a g e r e g i m e n o f e a c h d r u g , t h e h a lf -l if e f o r e a c h

d r u g , a n d t h e K t i n t h a t i n d i v i d u a l . A t t h i s s ta g e , t h e v a r i a t i o n o f K ~ w i t h i n

t h e p o p u l a t i o n is u n k n o w n .

T h e e l i m i n a t i o n o f t o l b u t a m i d e in m a n is a sp e c ia l c a se o f t h e m o r e

g e n e r a l s i t u a t i o n w h e r e d r u g is e l i m i n a t e d b y s e v e r a l p a t h w a y s i n s t e a d o f o n e .

C o n s i d e r i n g t h e m o r e g e n e r a l s i tu a t i o n , o n e c a n d e v e l o p a m o d e l o f d r u g

i n h i b i t i o n i n t e r a c t i o n s i n a n a n a l o g o u s m a n n e r t o t h e t o l b u t a m i d e - s u l f a -

p h e n a z o l e - m a n m o d e l . T h e e q u a t i o n s a r e s i m i l a r t o t h o s e d e r i v e d f o r

s c h e d u l e s o f d r u g s i n p a t ie n t s w i th v a r y i n g d e g re e s o f r e n a l i m p a i r m e n t . O n e

n e e d s t o k n o w t h e f r a c t i o n o f t h e d o s e i n th e b o d y e l i m i n a t e d b y a p a r t i c u l a r

p a t h w a y o f i n t e re s t i n t h e a b s e n c e o f i n h i b i t o r ( j, , ), t h e a m o u n t o f i n h i b i to r ( I ),

a n d t h e i n h i b i t o r c o n s t a n t ( K t ) . T h e r a t i o o f t h e n e w h a lf -l if e o f th e d r u g i n t h e

p r e s e n c e o f i n h i b i to r

( t l / 2 i n h i b i t e d ) t o

t h e n o r m a l h a l f - l i f e

t l / 2

. . . . . 1 )

a n d t h e

rat__iio o f t he s t ea dy -s t a t e a m o u n t o f d r ug be fo re

Ab

. . . . l) a n d a f t e r i n h i b i t i o n

(Abinhib ition) w he n a f ixe d reg im en i s ad m ini s te re d , i s g ive n b y

R = t l 2 i n h i b i t e d / t l / Z

1 =

A b i n h i b i t e d A b 1

5 )

[fm/(1 + I / K , ] +

I

- fro)

T h e i n f lu e n c e o f J ,, a n d

I/K I

o n t h e s e p a r a m e t e r s i s i l lu s t r a t e d i n F i g s . 5 a n d 6 .

U n l e s s t h e t h e r a p e u t i c i n d e x o f t h e d r u g is s m a l l ( F ig . 5), a n a l t e r a t i o n i n t h e

d o s a g e s c h e d u l e o f a d r u g i s u n w a r r a n t e d f o r f , < 0 .5 , e v e n w h e n i n h i b i t i o n

o f t h e p a r t i c u l a r p a t h w a y is c o m p l e t e . A l so , if t h e d o s a g e s c h e d u l e is m a i n -

t a i n e d a n d J~, > 0 .5 , a n a d v e r s e r e a c t i o n m a y b e s e e n b e f o r e th e n e w p l a t e a u

is r e a c h e d o r , if s e e n a t t h e p l a t e a u , it m a y t a k e s o m e t i m e ( 4

x t l / 2 i n h i b i t o r )

a f t e r i n i t i a t i o n o f th e i n h i b i t o r r e g i m e n . A l t e r n a t i v e l y , t o p r e v e n t d r u g

a c c u m u l a t i o n t h e d o s a g e s c h e d u le o f t h e d r u g w ill h av e t o b e r e d u c e d b y

1/R.

T h e s i t u a t io n w ill b e m o r e c o m p l e x w h e n t h e c o n c e n t r a t i o n o f d r u g a t t h e

m e t a b o l i c s i t e i s g r e a t e r t h a n i t s K , , , a n d w h e n b o t h d r u g s a r e c o m p e t i t o r s

o f o n e o r m o r e o f t h e o t h e r ' s p a t h w a y ( s ).

T o l b u t a m i d e , a n a c i d , is s i g n if i c a n tl y b o u n d t o p l a s m a a n d p r e s u m a b l y

t is s u e p r o t e in s . I ts h y p o g l y c e m i c a c t i v i ty p r o b a b l y is a f u n c t i o n o f t h e u n -

b o u n d c o n c e n t r a t i o n i n t h e p l a s m a a n d t is s u e w a t e rs . S u l f a p h e n a z o l e , d i -

c o u m a r o l , a n d p h e n y l b u t a z o n e a re a l so a c id s , h i g h l y b o u n d t o p l a s m a a n d



562 o wl a nd a nd M a t in

2 0

1 0

f m - - I

r n = 0 . 8

_ / ~ ~

m : O . 6

[

I [ f m : O . 4

4 1 0 2 0

I/K I

Fig. 5. The effect of inhibition on the ratio R)

of the new half-life of a drug in the presence of

the inhibitor to the normal half-life, or to the

ratio of the average amount of drug at the

plateau in the presence and absence of the

inhibitor. When all the drug is eliminated by

the inhibited route fm = 1), the ratio changes

dramatically with changes in inhibitor. Below

f,, = 0.5, the maximum increase in the ratio

is twofold and is inconsequential unless the

drug has a narrow therapeutic index or the

metabolite affected plays an important phar-

macological role.

tissue proteins, and are capable of displacing tolbutamide and one anothe r

from albumin in

n v t r o

experiments 19). Because of these associations,

protein binding displacement has been intimated as a contributory cause of

the enhanced hypogly cemia experienced when these drugs are used in

comb inat ion with tolbutamide. However, in the case of tolbutamide, the

contri bution of displacement is prob abl y mino r compare d to inhibition of

oxidation, as many other sulfonamides which displace tolbutamide from

albumin

n v t r o

neither produce prolongation of its half-life nor increase its

effect 23, 30). Nonetheless, it is worthwhile to consider when disp lacement

will significantly influence the pharmacological effect of a drug. To answer

this question, one must know whether displacement is from both plasma a nd

tissue proteins, whether drug clearance depends on the total bound and

unbound) or unbound plasma concentration, and whether the drug is given

on a single occasion or continually.

Appreciable drug displacement occurs when a majo r portio n of the same

binding sites are occupied by the displacing agent. Consequently, to displace

drugs from plasma albumin requires that the plasma conc entra tion of the



Kinetics of Drug Drug Interactions 5 6 3

d i s p l a c e r a p p r o a c h o r e x c e e d 0 .6 m M , t h e c o n c e n t r a t i o n o f p l a s m a a l b u m i n .

F o r a s u b s t a n c e w i t h a m o l e c u l a r w e i g h t o f 3 00 , t h is c o r r e s p o n d s t o

1 80 m g / l it e r. T h e s e p l a s m a c o n c e n t r a t i o n s a r e s e e n w i th s u l f o n a m i d e s a n d

s a l i c y l a t e s , w h i c h a r e c o m m o n l y g i v e n i n g r a m d o s e s a n d w h i c h p o s s e s s

s m a l l v o l u m e s o f d i s t ri b u t i o n . T h e y a r e a l s o r e a c h e d w i t h p h e n y l b u t a z o n e .

A l t h o u g h t h e n o r m a l d o s e o f t h is a n t i - in f l a m m a t o r y a g e n t i s 10 0 m g , o w i n g

t o i t s l o n g h a l f- li fe p h e n y l b u t a z o n e a c c u m u l a t e s t o w e l l o v e r 1 g in t h e b o d y

when g iven th ree t imes da i ly .

P l a s m a c o n c e n t r a t i o n s e x c e e d i n g 0 .6 m ~ l a r e a l s o p r o b a b l y a c h i e v e d

fo l lowing the r ap id in t r av eno us b o lu s l es s than 10 s ec ) o f qu i t e m od es t doses .

The se eve n t s a r e l ike ly f l ee t ing , how ever , a s d i sp lace r m ixes w i th the v ascu la r

sys tem an d d i s t r ibu tes ou t in to the t i ssues . Th e r ap id in jec t ion o f even l a rge r

d o s e s m o r e th a n 1 4 m g / k g ) o f d r u g s w h i c h r e si d e p r i m a r i l y i n p l a s m a m a y

s t i l l on ly p roduce s ign i f i can t r i s es in the unbound concen t r a t ion t r ans ien t ly

a s d i s p l a c e d d r u g m o v e s d o w n t h e n e w l y c r e a t e d c o n c e n t r a t i o n g r a d i e n t

ou t in to the l a rge t is sue wa te r spac e 31 ). Indeed , a s the fo l lowing ca lcu la t ion

wi l l show, d ru g d i sp lac em en t i s un l ike ly to be c l in ica lly s ign i fi can t un les s i t is

d i s p l a c e d f r o m a n d s u b s t a n t i a l l y b o u n d t o b o t h p l a s m a a n d t i s s u e b i n d i n g

s it e s. T h u s t h e f r a c t i o n o f a d r u g i n t h e b o d y b o u n d t o p l a s m a p r o t e i n s is

3 /? /Vd , w here 3 i s the p lasm a vo lu m e in l it e rs , V~ i s the vo lu m e o f d i s t r ibu t ion

of the d rug , a l so expre s sed in lit er s, an d /3 is the f r ac t ion o f d rug in p lasm a

b o u n d t o p l a s m a p r o t e in s . F o r a d r u g l ik e t h e a n t i c o a g u l a n t w a r f a ri n , w h i c h

A M O U N T

~ N O R M )

2 0 I KI=I9

10

I KI=9

J I

20 410 60 80 100

TIME TY2NORM]

[ / K [ = 4

2

1 KI=0

0 I

0 120 140

F i g . 6 . T h e e f fe c t o f in h i b i t i o n o n t h e r a t e o f a c c u m u l a t i o n

o f a d r u g g i v e n o n a f i x e d d o s e - f i x e d i n te r v a l r e g i m e n

w h e n f , , = 1. N o t e t h a t t i m e f o r a c c u m u l a t i o n is ex -

p r e s s e d i n u n i t s o f th e n o r m a l h a lf -l if e. T h e m o r e c o m -

p l e t e t h e b l o c k , t h e l o n g e r t h e h a l f- l if e F i g . 5) a n d t h e

l o n g e r i t t a k e s t o r e a c h t h e n e w p l a t e a u . I n c l i n i c a l

p r a c t ic e , to x i c i ty m a y b e n o t e d b e f o r e t h e n e w p l a t e a u

i s r e a c h e d . T h e s e c a l c u l a t i o n s a s s u m e t h a t t h e i n h i b i t o r

a m o u n t i n th e b o d y is i m m e d i a t e l y a tt a i n e d a n d m a i n -

t a i n e d c o n s t a n t .



5 6 4

o wl a nd a nd

M a t i n

i s h ig h ly bo u nd (/~ = 0 .995) an d w i th a ve ry sm al l Va, a r ou nd 10 l it e r s, t h i s

m e a n s th a t a s m u c h a s 3 0 i n t h e b o d y re s id e s o n th e p l a s m a p r o t e in s .

N o n e t h e l e s s , e v e n i f i t w e r e c o m p l e t e l y d i s p l a c e d o f f i ts p l a s m a b i n d i n g s i te s

(/~ --, 0 ), w i t h a d r a m a t i c d r o p i n t h e t o t a l p l a s m a c o n c e n t r a t i o n , t h i s 3 0

a d d e d t o t h e r e m a i n i n g 70 w o u l d i n cr e as e t h e u n b o u n d c o n c e n t r a t i o n in

t h e b o d y o n l y b y 4 2 ~o. T h i s i n c r e a se i s s m a l l c o m p a r e d t o t h e n o r m a l c h a n g e s

i n t h e u n b o u n d c o n c e n t r a t i o n a s d r u g i s e l im i n a t e d . A n y s u b s t a n t i a l in c r e a se

i n u n b o u n d c o n c e n t r a t io n a b o v e t h a t a n t i c ip a t e d f r o m p l a sm a d i s p la c e m e n t

a u t o m a t i c a l l y i m p l i es t h a t t is s u e b i n d i n g i s s i g n if i ca n t a n d t h a t d i s p l a c e m e n t

m u s t a l so h a v e o c c u r r e d .

T h e p r e c e d i n g c o m m e n t s r e fe r t o s i t u a t i o n s w h e r e t h e d r u g is gi v en o n l y

o n c e i n t h e a b s e n c e o r p r e s e n c e o f t h e s u s p e c t e d d i sp l a c e r. I n d r u g t h e r a p y ,

i t i s m o r e c o m m o n t o g i v e b o t h d r u g a n d d i s p l a c e r o n a m u l t i p l e d o s e

r e gi m e n . T h e c h a n g e s i n th e u n b o u n d c o n c e n t r a t i o n (C I) d e p e n d o n w h e t h e r

d r u g c le a r a n c e d e p e n d s o n C o r t o ta l p l a s m a c o n c e n t r a t i o n (C v ). U p o n a

c o n s t a n t d r u g i n t a k e ( R ~ t h e s t e a d y - s t a t e p l a s m a c o n c e n t r a t i o n (C p~s) is

d e f i n e d b y

R ~

=

C L

C , ,

6 )

w h e r e C L is th e c l e a r a n c e o f t h e d r u g , o r

R ~ = C L C A ~ 7 )

w h e r e c~ is t h e f r a c t io n o f d r u g u n b o u n d i n p la s m a . F o r d r u g s w h i c h a r e s o le l y

c l e a re d b y g l o m e r u l a r f i l tr a t i o n o r f o r d r u g s w h i c h h a v e v e r y l o w e x t r a c t i o n

r a t i o s a c r o s s t h e l i v e r , c l e a r a n c e i s d e p e n d e n t o n t h e u n b o u n d p l a s m a c o n -

c e n t r a t i o n s u c h t h a t

C L = C L m a x 9 ~ ( 8 )

w h e r e C L m , x is e it h e r t h e g l o m e r u l a r f i l tr a t i o n ra t e o r t h e m a x i m u m m e t a b o l i c

c l ea ran ce w he n c~ = 1. D i sp l a cem en t , b y i nc reas ing c~, i nc reases c l ea rance .

B u t s u b s t i t u t i o n o f e q u a t i o n 8 i n t o e q u a t i o n 6

R ~ = C t m a x f s ~ ( 9 )

i n d i c a t e s t h a t a t s t e a d y s t a t e , w h e n r a t e o u t b a l a n c e s r a t e i n , t h e u n b o u n d

c o n c e n t r a t i o n s h o u l d b e c o n s t a n t a n d i n d e p e n d e n t o f th e d e g r e e o f p r o t e in

b i n d i n g . B e t w e e n s t e a d y st a te s , t h e u n b o u n d c o n c e n t r a t i o n m a y b e g re a t e r o r

l e s se r t h an t he Czss , d e p e n d i n g o n w h e t h e r t h e c o n c e n t r a t i o n o f t h e d i s p la c i n g

a g e n t i s r i s in g o r f a l l in g . I n t h o s e c a s e s w h e r e c h a n g e s i n t h e d i s p l a c i n g a g e n t

a r e s l o w , r e l a t i v e t o t h e e l i m i n a t i o n k i n e t i c s o f t h e d i s p l a c e d d r u g , t h e d r u g

m a y b e r e g a r d e d a s b e i n g a t p s e u d o s t e a d y s ta te . T h e n , u p o n c o n s t a n t d r u g



Kinetics of D rug Dru g Interactions 6

t he r apy , t he unb ou nd con cen t r a t i on ( and p r e s um ab l y pha r m aco l og i ca l effect)

s hou l d r em a i n con s t an t a nd app a r en t l y una f f ec t ed by t he d i sp l ac ing agen t .

B o t h l i doca ine (32 ) and pen ic i ll in G a r e app r ec i ab l y bou nd t o p l a s m a

pro te ins (/3 > 0 .5), and ye t each is h igh ly c leared b y the l iver and k idney ,

r e spec ti ve ly . E v i den t l y , r emo va l o f un bo un d d r ug is s o e f fec ti ve t ha t t he d r u g -

p r o t e i n comp l ex d i s soc i a te s a l mos t com pl e t e l y be f o r e l eav ing t he e l i mi na t i ng

o r gan . Fo r d r ugs l i ke the s e, w h i ch have an ex t r ac t i on r a ti o ap p r oa ch i ng 1,

c l ea r ance is una f f ec t ed by p r o t e i n b i nd i ng , and f o r a g iven cons t an t i npu t

R ~ C v , ~ m u s t b e t h e s a m e n o m a t t e r t h e d e g r e e o f b i n d in g c f . equat ion 6) .

Ho we ver , now Cy,, ( and p resu m ab ly ac t iv i ty ) w ill increase dra m at ica l ly w i th

d r ug d i s p l acem en t ( equa t i on 7).

I n p r ac t i ce , t he s i t ua t i on can be much mor e compl i ca t ed t han t ha t

env i s i oned du r i ng t he f o r ego i ng t heo r e ti ca l d is cuss ion . A n exce ll en t exam pl e

is the p o te n t i a t io n of the an t i coa gu lan t e ffec t o f wa r far in in pa t i en t s r ece iv ing

pheny l bu t azone ( 33 ) . W ar f a r i n i s ve r y h i gh l y bound t o a l bumi n and t i s s ue

s ite s, a nd t he ph a r m aco l og i ca l e ff ect p r oba b l y is r e la t ed t o t he u nb ou nd

c i r cu l a t i ng d r ug . Pheny l bu t azone can d i s p l ace w ar f a r i n f r om a l bumi n

in

v i t r o (34), and th i s d i sp lacem ent has bee n sugges ted as the cause of phen yl -

b u t a z o n e a u g m e n t a t i o n o f w a r f a r in a c t iv i ty i n v i v o . I ndeed , w he n s ub j ec t s

r ece i v i ng pheny l bu t azone i nges t a s i ng l e dos e o f w ar f a r i n , t he pe r cen t o f

w ar f a r i n un bo un d i n p l a s m a inc r eas es f r om a con t r o l va l ue o f 0 .4 t o 1 .0

(per sona l observa t ion) . Ho we ver , the e ffec ts on war far in d i spos i t ion b y

phe ny l bu t azon e a r e f a r mo r e com pl ex (F ig . 7 ). T hes e da t a s ugges t an add i -

t i ona l m ech an i s m f o r phe ny l bu t azon e po t en t i a t i on ( 35 ). W ar f a r i n i s ad -

mi n i s t e r ed a s a r acemi c mi x t u r e . T he mor e po t en t i s omer i s e l i mi na t ed

p r i ma r i l y by ox i da t i on t o 7 - hyd r oxyw ar f a r i n and is pa r ti a l ly xeduce d t o t he

SS war far in a lcohol ( a lcohol 2 ) . The l es s po ten t R war far in i s p r imar i ly

r educ ed t o t h e R S a l coh o l ( a lcoho l 1). P r e s en t chem i ca l a s says me as u r e t he

s um o r S and R w ar f a r i n i n p la s ma , w h i l e t he pha r ma co l og i ca l e ff ec t p r i mar i l y

r e f l ec t s t he S w ar f a r i n concen t r a t i on , T he dec r eas ed p r oduc t i on o f t he

7 - hyd r oxyw ar f a r i n and i nc r eased p r od uc t i on o f t he a l coho l 1 (F ig . 7 )

p r o m pt ed t he s ugges t ion t ha t phe ny l b u t azo ne (o r its me t abo l i te s ) mi gh t , in

add i t i on t o d i s p l acem en t , sl ow S w ar f a r i n and has t en R w ar f a r i n (35). H e nce

t h is i n t e r ac t i on m ay a l t e r t he i s omer i c com pos i t i on and po t en cy o f t he d r ug

i n p la s ma , w i t hou t m a t e r i a l ly chang i ng t he t o t a l co nce n t r a t i o n - t i m e p r o fi le

o f t he mi x t u r e .

T h e w a r f a r i n - p h e n y l b u t a z o n e i n te r a c ti o n s t u d y s tr es se s t h e i m p o r t a n c e

o f meas u r i ng me t abo l i t e s a s w e l l a s i n t ac t d r ug . Pha r macok i ne t i c ana l y s i s

a i d s i n t he i n t e r p r e t a t i on o f t h is i n f o r ma t i on . A t p r es en t, one ca nno t m ode l t he

expec t ed chem i ca l and pha r m aco l og i ca l s eque l ae r e s u lt ing f r om t h i s i n t e rac -

t ion . Nonethe les s , i t i s hoped tha t w i th carefu l exper imenta l des ign the

quan t i t a t i ve i n t e r r e l a t i ons h i ps can be a s ce r t a i ned . T hen , w hen cons i de r ed



5 6 6 R o w l a n d a n d M a t i n

o n t r o l

1 0 0 0 0

1 0 0 0 0

P h e n y I b u t a z o n e

T W o . 6 0 r a g .

w - w 9 W o d i r i a

, t - I = A lc o h ol1

] 2 - 2 = A lc o ho l

Z

~ w 7 [ ~ - ~ - 2 7 - H v d r o x y

t O 0 0 - 1 0 0 0

loo loo

g Z

1 1

1 1 3 4 5

1 1 1 1 5

d a y s d a y s

Fig. 7 . Phenylbutazone-warfar in in teract ion in man. In th is subject , the

to ta l p lasma war fa r in concen t ra t ion d id no t change , bu t the metabo l i te

pattern did. Produ ction of 7-hydro xyw arfar in was depressed, but produ c-

t ion an d el imin ation of a lcoh ol 1 were increased.

n e c e s s a r y , a p p r o p r i a t e d o s a g e s c h e d u l e s o f t w o s u c h d r u g s i n c o m b i n a t i o n

m a y b e p r e d i c t e d t h a t w o u l d a c h i e v e t h e d e s i r e d t h e r a p e u t i c r e s p o n s e w i t h

m i n i m a l t o x i c i t y .

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ains and warfarin2

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