Biological CorrelationsâThe Hansch Approach

6 Substituent-Effect Analyses of the Rates of Metabolism and Excretion of Sulfonamide Drugs

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TOSHIO FUJITA Department of Agricultural Chemistry, Kyoto University, Kyoto, Japan

Analyses of the rates of metabolism and renal excretion of sulfonamide drugs were attempted in terms of their physicochemical properties. Using simple models for acetylation in the liver and excretion from the kidney, expressions for rate constants of both processes were proposed on the basis of free energy related substituent constants. Taking into account the effect of dissociation, logarithmic values of the rate constants correlated with a linear combination of the hydrophobicity constant, π, and the electronegativity pa rameter, ΔpΚ , of the N-1 substituent of sulfanilamide. The information obtained from the correlations should be useful in designing long-acting sulfonamide drugs. Α

T J r e v i o u s l y , w e c o r r e l a t e d bacteriostatic a c t i v i t y a n d structure of v a r i o u s series of N - l substituted s u l f o n a m i d e

drugs w i t h the free

energy

r e l a t e d substituent constants of the N - l substituent ( 1 ). F o r a series o f N - l heterocyclic derivatives, activity data obtained b y K r u g e r - T h i e m e r a n d B i i n g e r ( 3 ) w e r e w e l l c o r r e l a t e d b y E q u a t i o n 1. I n E q u a t i o n 1, C

(1) - 0 . 2 9 6 x + 0.985x + 0 . 6 0 5 Δ ρ ^ 2

η = 17

r = 0.975

2.090

s = 0.223

is t h e m i n i m u m i n h i b i t o r y c o n c e n t r a t i o n i n ^ m o l e / l i t e r , π is the h y d r o p h o b i c i t y constant of t h e N - l substituent d e r i v e d f r o m t h e p a r t i t i o n coefficient, P, w i t h a n i s o b u t y l a l c o h o l - w a t e r system as ττ =

log Ρ (sub-

80

Van Valkenburg; Biological Correlations—The Hansch Approach Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

6.

Metabolism

FUJITA

and Excretion

stituted sulfanilamide) — l o g P

0

of

81

Sulfonamides

(sulfanilamide), and Δ ρ Κ

Α

t r o n e g a t i v i t y p a r a m e t e r o f t h e substituent defined as Δ ρ Κ ( s u l f a n i l a m i d e ) — pK

A

is the elec Α

=

pK ° A

( s u b s t i t u t e d s u l f a n i l a m i d e ). T h e η is the n u m b e r

of points u s e d i n the regression, r is the c o r r e l a t i o n coefficient, a n d s is the s t a n d a r d d e v i a t i o n . A l t h o u g h t h e s e c o n d t e r m o n t h e left is i n t r o d u c e d to correct bacteriostatic a c t i v i t y a c c o r d i n g to t h e extent o f d i s s o c i a t i o n at the e x p e r i m e n t a l p H , E q u a t i o n 1 does n o t necessarily m e a n t h a t t h e m o l e c u l a r species responsible f o r t h e a c t i v i t y is t h e n e u t r a l f o r m . T h e correlation was quite good, a n d information o n the o p t i m u m p K

A

and π

values r e q u i r e d f o r the m a x i m u m a c t i v i t y w a s o b t a i n e d b y t a k i n g p a r t i a l Downloaded by FUDAN UNIV on February 15, 2017 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0114.ch006

differentials o f this e q u a t i o n .

Free state Cp(l-a) Neutral form jr

Cpa

Ionized form

+ LH ] +

Figure 1.

Model for protein

binding

W e also a n a l y z e d t h e b i n d i n g constant o f s u l f o n a m i d e s to h u m a n p l a s m a p r o t e i n ( I ) . I n t h e free, n o n - b o u n d state t h e d r u g s exist as a n e q u i l i b r i u m m i x t u r e of n e u t r a l a n d i o n i z e d forms, o f w h i c h the c o n c e n t r a tions are C (1 F

— a) a n d Cpa, r e s p e c t i v e l y (see F i g u r e 1 ) . I n the b o u n d

state t h e y exist as o n l y o n e m o l e c u l a r species, C .

T h e effective b i n d i n g

B

constant, K, c a n b e expressed b y t h e respective b i n d i n g constants of n e u t r a l a n d i o n i z e d f o r m s : K i a n d K< , as s h o w n i n E q u a t i o n 2. T a k i n g 2

Κ = — = CF

KiK K\ -f- K2 2

into account the d i s s o c i a t i o n e q u i l i b r i u m o f free d r u g s a n d a s s u m i n g t h a t the l o g a r i t h m i c values o f the f u n d a m e n t a l b i n d i n g constants, Ki a n d K , 2

c a n b e d e s c r i b e d b y free energy r e l a t e d parameters, w e d e r i v e d E q u a t i o n 3 for p r o t e i n b i n d i n g ; w h e r e a, p, a n d c are constants w h i c h are d e t e r m i n e d

log Κ + l o g

g i t

rH+]

b y t h e m e t h o d o f least squares.

H + 1

=

+

Ρ Ρ*^ + Δ

F o r 20 N - l heterocyclic

the b i n d i n g d a t a o b t a i n e d b y R i e d e r

(4)

were

&

c

sulfonamides,

best r e p r e s e n t e d b y

E q u a t i o n 4, w h i c h shows that o n l y t h e h y d r o p h o b i c i t y of t h e N - l s u b -


82

BIOLOGICAL CORRELATIONS

log Κ +

log

r

η = 20

^ [H+J

J

= 1.651* -

r = 0.938

T H E HANSCH A P P R O A C H

2.896

(4)

s = 0.365

stituent p l a y s a significant r o l e i n g o v e r n i n g the m o d i f i e d b i n d i n g c o n stant.

E q u a t i o n 3 was also u s e f u l i n e l u c i d a t i n g the s e r u m b i n d i n g of

N - 4 - a c e t y l s u l f a n i l a m i d e s , t h e major metabolites of s u l f o n a m i d e

drugs,

as s h o w n i n E q u a t i o n 5 ( 2 ) .

log Κ +

log

K

a

r

t J


[ t i

η = 5

H + ] J

= 2.029x - 2.860 (±0.651) (±1.126)

r = 0.985

(5)

s = 0.264

I n E q u a t i o n s 4 a n d 5, Κ is the mass-action e q u i l i b r i u m constant of b i n d i n g expressed i n l i t e r s / ^ m o l e (4).

T h e figures i n parentheses are the 9 5 %

confidence intervals. T h e s e r u m p r o t e i n b i n d i n g of s u l f o n a m i d e d r u g s has b e e n c o n s i d e r e d a n i m p o r t a n t factor i n m a i n t a i n i n g a h i g h l e v e l of the d r u g i n the b l o o d since e l i m i n a t i o n of drugs f r o m b l o o d occurs via the n o n - b o u n d molecule.

free

T h e t i m e of d u r a t i o n i n b l o o d or the rate of d r u g e l i m i n a t i o n

( a n t i b a c t e r i a l a c t i v i t y n o t w i t h s t a n d i n g ) is one of the most i m p o r t a n t properties to b e c o n s i d e r e d i n d e s i g n i n g n e w drugs. E n c o u r a g e d b y the correlations o b t a i n e d for bacteriostatic a c t i v i t y a n d p r o t e i n b i n d i n g s h o w n a b o v e , w e a t t e m p t e d to a n a l y z e the rate of e l i m i n a t i o n for s u l f o n a m i d e drugs i n terms of free energy r e l a t e d substituent constants. Methods A c c o r d i n g to N e l s o n ( 5 )

the rate of e l i m i n a t i o n of drugs i n b l o o d

f o l l o w s the first-order k i n e t i c s ; the rate constant of w h i c h is k i,

as s h o w n

E

i n E q u a t i o n 6, w h e r e C is the t o t a l d r u g c o n c e n t r a t i o n i n b l o o d .

Sulfona-

m i d e drugs are e l i m i n a t e d m a i n l y b y t w o routes, one of w h i c h is m e t a b o l i s m i n the l i v e r , a n d the other is r e n a l excretion. T h e rate of h e p a t i c m e t a b o l i s m a n d that of r e n a l excretion also o b e y that the rate constant of e l i m i n a t i o n , k i, E

o r d e r rate constants, k

Me

and k .

m e a s u r i n g the t i m e course

Ex

first-order

kinetics so

comprises the respective

first-

T h e s e constants are e s t i m a t e d

o f d r u g c o n c e n t r a t i o n i n the b l o o d

by

after

a d m i n i s t r a t i o n a n d the r a t i o of i n t e g r a t e d amounts of m e t a b o l i z e d a n d free d r u g i n the u r i n e . F o r most s u l f o n a m i d e d r u g s , the major m e t a b o l i t e


6.

FUJITA

Metabolism

and Excretion

of

83

Sulfonamides

is the N - 4 - a c e t y l d e r i v a t i v e ; thus, w e c a n set the r a t e constant o f h e p a t i c m e t a b o l i s m , k , e q u a l to that o f a c e t y l a t i o n , k Me

fëiôôdl

Free state

C

-,. u l! 2

LB-

Figure 2.

— > Acetylated Product

Liver bound state

K

Serum bound state Downloaded by FUDAN UNIV on February 15, 2017 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0114.ch006

as s h o w n i n E q u a t i o n 6.

Ac>

Model of hepatic acetylation

process

T o correlate the rate constant o f h e p a t i c a c e t y l a t i o n w i t h free e n e r g y r e l a t e d parameters, w e u s e d t h e s i m p l e m o d e l s h o w n i n F i g u r e 2. I n b l o o d , t h e free u n d i s s o c i a t e d a n d t h e free dissociated species a r e i n a d y n a m i c q u i l i b r i u m w i t h each other a n d also w i t h t h e s e r u m p r o t e i n b o u n d state. B o t h the n e u t r a l a n d i o n i z e d forms of free d r u g are also i n a n e q u i l i b r i u m w i t h a l i v e r tissue b o u n d state. W e assume that these b i n d i n g e q u i l i b r i a a r e e s t a b l i s h e d r a t h e r q u i c k l y , that there is a c r i t i c a l r a t e - d e t e r m i n i n g step, fc after the d r u g is b o u n d to l i v e r tissue, a n d t h a t 3

a steady state i n t h e c o n c e n t r a t i o n of t h e l i v e r b o u n d c o m p l e x , C ,

is

LJI

m a i n t a i n e d . I f w e a p p l y E q u a t i o n 2 to this m o d e l , the concentrations o f s e r u m - b o u n d , l i v e r - b o u n d , a n d free d r u g , C ,

C B, a n d C , are r e l a t e d to

PB

L

e a c h other b y E q u a t i o n s 7 a n d 8, w h e r e K

F

K , K / , a n d K ' are t h e

u

2

2

b i n d i n g constants f o r t h e u n i t processes as s h o w n i n F i g u r e 2. F r o m

^PB — π t

C LB =

K

t

dCpB

,

ΚχΚι + K

2

c

(8)

P

dC F

K\K.2

~aT

(7)

^Fl F

(9)

Κι' + Κ ' ~dT 2

dC F dt

K\K% k*C Ki + K

(10)

f

2

E q u a t i o n 7, w e c a n d e r i v e E q u a t i o n 9 f o r t h e rate of decrease of 0 . Ρ ΰ

Since t h e rate o f decrease of C

F

c a n b e expressed b y E q u a t i o n 10, t h e

rate of decrease of the t o t a l c o n c e n t r a t i o n i n the b l o o d , (C

F

+ C ), PB

is

d e s c r i b e d b y E q u a t i o n 11, a n d t h e rate constant o f a c e t y l a t i o n , k , is Ac

d e r i v e d as s h o w n i n E q u a t i o n 12.


84


dC

d{CpB + dt

dt

~

t p

dC dt

CF)


F

y

+

κ{

+

κ;) (H)

V

KTTK?)

+ Ki

KI

-

kz

L

Ki +

κ,

f c 3

KjKj

F o r the l o g a r i t h m i c v a l u e of k

(12)

E q u a t i o n 13 a n d its m o d i f i c a t i o n ,

Ac>

E q u a t i o n 14, w e r e f o r m u l a t e d , w h e r e K °

is the dissociation constant of

A

s u l f a n i l a m i d e , a, p', c', p, a n d c are constants, a n d [ H ] is the h y d r o g e n Downloaded by FUDAN UNIV on February 15, 2017 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0114.ch006

+

i o n c o n c e n t r a t i o n i n the b l o o d .

W e u s e d E q u a t i o n 14 to a n a l y z e the

a c e t y l a t i o n d a t a . T h e second t e r m o n the left of E q u a t i o n 14 expresses the d i s s o c i a t i o n effect of the free d r u g , b u t i t does not m e a n that the n e u t r a l f o r m is o n l y responsible for m e t a b o l i s m .

log k

log

+

Ac

log k

+

Ac

log

[H+] + [H+] +

Κ A K° = αχ +

p' ApK

A

A

[H+] +

Κ A

[H+]

= αχ +

ρ ApK

A

+ e

+ c

(13)

(14)

T h e s e equations are d e r i v e d i n a m a n n e r s i m i l a r to that for E q u a t i o n 3, as p r e v i o u s l y r e p o r t e d ( 1 ), a s s u m i n g that l o g kz c a n b e d e s c r i b e d b y a l i n e a r c o m b i n a t i o n of the free energy r e l a t e d substituent constants.

I Blood I CPB

Cp K / y

».

c

X

3

> Bladder

s

s

Figure 3.

tubule

n

Model of renal excretion

F o r r e n a l excretion, w e u s e d the m o d e l s h o w n i n F i g u r e 3.

Here,

the rate constant for the decrease i n the c o n c e n t r a t i o n of d r u g i n the b l o o d b y g l o m e r u l a r u l t r a f i l t r a t i o n is fci, for the t u b u l a r r e a b s o r p t i o n process is k , a n d for the m o v e m e n t of d r u g f r o m t u b u l e to b l a d d e r is k . 2

s

W e assume that k is m u c h larger t h a n fc a n d that c o n c e n t r a t i o n of the 2

3


6.

Metabolism

FUJITA

and Excretion

of

85

Sulfonamides

d r u g i n the t u b u l e (C buie) is i n a steady state. T h u s , t h e rate constant tU

for t h e w h o l e process of r e n a l e x c r e t i o n c a n be expressed b y E q u a t i o n 15.

=

k

Ex

^ k

(15) 2

W e f u r t h e r assume that the t o t a l v o l u m e of b l o o d , V , is m u c h l a r g e r t h a n that filtered p e r u n i t t i m e , dv.

T h e rate of decrease for the a m o u n t

of free d r u g via g l o m e r u l a r u l t r a f i l t r a t i o n is C dv

at a n y t i m e so that t h e

F

rate of decrease for the c o n c e n t r a t i o n i n b l o o d ( —(dC /dt)o)

is g i v e n as

F

E q u a t i o n 16. T h e r e f o r e , the rate of decrease for the C t a i b y t h e same to


r o u t e c a n b e d e s c r i b e d b y E q u a t i o n 17. T h u s , the r a t e constant, k\> is

- ( T ) (dC\

_

(d£_PB

\dt)

c

described

as dv/V

\

dt

"

Λ \

- F

C

dCA

_

_

dt) ~

+

G

j .

«·>

'G

X

K

K\

*

K

+

*

(

Kx'Kt'

V

\ r

Κ ') 2

\

KÏ + >) K

d v

ν

-

r ~~

(dC \ F

\

)

G

(17) d v

ν

w h i c h is constant t h r o u g h a series of

unless the test o r g a n i s m is c h a n g e d .

DT

compounds;

Since the r a t i o of k to fc w o u l d b e 2

3

p r o p o r t i o n a l to the c o n c e n t r a t i o n of the n e u t r a l d r u g i n the t u b u l e a n d also to its p e r m e a b i l i t y t h r o u g h the t u b u l a r m e m b r a n e , the l o g a r i t h m of c a n b e d e s c r i b e d as E q u a t i o n 18, w h e r e

k /k 2

s

log ^

=

^

log ^

[H ] +

is that of u r i n e i n

r-rj ι-i + log p e r m . + constant

(18)

the t u b u l e . L o g p e r m , c a n be f u r t h e r r e l a t e d to the free e n e r g y r e l a t e d p a r a m e t e r s ; thus, the v a l u e of l o g k

Ex

is expressed b y E q u a t i o n 19 w h i c h

c a n be m o d i f i e d to E q u a t i o n 20, w h e r e a, p, a n d c are constants.

log k

Ex

= log ki -

log k

Ex

log ^

-

log

=

K

log

a

^}^

Ka

+ Jj

+]

H+1

+ «Χ +

= αχ +

ApK

Ç

A

ρΔρ^Α + c

+ c

(19)

(20)

U s i n g E q u a t i o n s 14 a n d 20, w e a n a l y z e d the d a t a s h o w n i n T a b l e s I and II obtained by N o g a m i ( 6 ) , Y a m a z a k i ( 7 ) , a n d K a k e m i (8, 9) t h e i r associates b y the m e t h o d of least squares.

and

W e h a v e not i n c l u d e d

a l l c o m p o u n d s of the o r i g i n a l set i n the analyses since the p h y s i c o c h e m i c a l p a r a m e t e r s of some d e r i v a t i v e s are l a c k i n g .


86



Table I.

Substituent Constants Rat Acetylation Rate h


Compounds

log

Sulfanilamide Acetosulf amine Sulfathiazole Sulfadiazine Sulfamerazine Sulfisoxazole Sulfisomidine Sulfaphenazole Sulfamethoxypyridazine Sulfadimethoxine Sulfisomezole Sulfamonomethoxine

0.00 5.05 3.35 4.30 3.52 5.83 3.07 4.54 3.40 4.40 4.64 4.42

0.00 1.01 0.82 1.11 0.94 2.61 0.39 2.15 1.02 1.86 1.55 1.37

k

Ac

-0.45 -0.36 -1.06 -1.47 -1.33 -1.21 -0.96 -1.00 -1.42 -1.92 -1.38 -1.36

obs.

cale.

-0.45 1.64 -0.58 -0.20 -0.73 1.57 -0.65 0.50 -0.91 -0.55 0.22 0.03

-1.10

d

—

-0.43 -0.19 -0.33 1.04 -0.78 0.66 -0.26 —

0.17 0.02

The rate constant, k , is the value per hour. Derived from the values of pK in Ref. 16.

a

Ac

6

A

Calculated from the "Ubergangszahlen" in Ref. 3 with correction for ionization in the aqueous phase according to the K values obtained by Yamazaki et al., Ref. 16. Calculated by Equation 28. 0

A

d

Table II.

Substituent Constants Rat Excretion Rate h

Compounds Sulfanilamide Acetosulf amine Sulfathiazole Sulfadiazine Sulfamerazine Sulfisoxazole Sulfisomidine Sulfaphenazole Sulfamethoxypyridazine Sulfadimethoxine Sulfisomezole Sulfamonomethoxine

ΔρΚ

Α

0.00 5.05 3.35 4.30 3.52 5.83 3.07 4.54 3.40 4.40 4.64 4.42

6

%

b

0.00 1.01 0.82 1.11 0.94 2.61 0.39 2.15 1.02 1.86 1.55 1.37

x'

c

0.00 1.61 0.68 1.81 1.84 2.56 0.89 2.91 2.14 3.12 1.97 2.13

log k Ex

obs.

-1.18 -0.19 -0.63 -1.14 -1.17 -0.61 -0.64 -1.55 -1.55 -1.92 -1.34 -1.41

-1.18 -1.23 -0.71 -1.58 -1.28 -2.39 -0.69 -2.16 -1.64 -2.43 -2.03 -1.93

cale.

d

-1.06 -1.17 -1.28 -1.41 -1.37 -2.62 -0.91 -2.39 -1.47 -2.13 -1.78 -1.64

The rate constant, ksx, is the value per hour. The same values as in Table I. Calculated from the values of partition coefficient measured using a system of C H C l - p H 7.4 buffer solution (16). Calculated by Equation 38. a

6

c

3

d


6.

Metabolism

FUJITA

and Excretion

87

of Sulfonamides

and Rate of Acetylation" Rat

Rabbit

A cetylation Rate

A cetylation Rate

h

obs.

cale.

-1.41

-1.41

-1.26

— — -1.51 — -1.72

— — -0.24 —1.06

— — -0.28 —1.03

-0.96

-0.65

-0.91

— — -2.28

— — -0.91

— — —0.10


-1.38 -1.74

0.22 -0.35

e

-0.06

« Calculated by Equation Calculated by Equation Calculated by Equation Τ η β acetylation rate is (See Equation 14). 0

Λ

and Rate of Excretion

obs.

calcJ

-0.92 -0.90 -0.47 -0.50 -0.26 -0.87 -1.66 -0.58 -0.61 -1.16 -0.24 -0.55

-0.92 1.10 0.01 0.77 0.34 1.91 -1.35 0.92 -0.10 0.21 1.36 0.84

-1.01

22. 31. 34. obtained from:

obs.

calc.

-1.82

-1.82

-1.81

6

— —

-1.16

-1.60

-1.62

-0.70 -1.02

-2.48 -1.07

-2.65 -1.28

-1.84 -1.34 -1.63

-2.35 -2.03 -2.15

-2.34 -1.96 -1.85

— —

log k

Ac

calc.

-1.45 -1.58 -1.29 -1.51 -1.26 -1.40 -2.27 -1.46 -1.57 -2.52 -1.25 -1.68

-1.45 0.42 -0.81 -0.24 -0.66 1.38 -1.96 0.04 -1.06 -1.15 0.35 -0.29

-1.81

+ log (K

A

—

— —

0

—

-0.89 -0.57 -0.76 1.12 -1.38 0.60 -0.67

—

-0.07 -0.27

- f [H ])/([H+]). +

Human Excretion Rate

h

log kEx

— —

0.58

obs.

Excretion Rate

h

—

—0.79

Ac

Rabbit

Excretion Rate

—

—

-0.06 0.28 0.08 2.02 -0.56 1.49 0.17

log k

0

Rat

— —

h

log k Ac

/

— —

A cetylation Rate

h

log k Ac

Human

h

log k Ex

obs.

calcJ

log k

obs.

calc.

-1.02 -0.28 -0.36 -0.71 -0.68 -0.26 -0.92 -0.72 -0.94 -1.52 -0.65 -0.87

-1.03 -3.68 -2.07 -3.36 -2.56 -4.44 -2.36 -3.61 -2.70 -4.27 -3.64 -3.64

-0.86 -3.49 -2.68 -3.23 -2.81 -4.63 -2.34 -3.86 -2.80 -3.65 -3.59 -3.41

-1.50 -1.45 -1.05 -1.30 -1.90 -1.11 -1.08 -1.64 -2.17 -1.84 -1.39 -1.93

-1.50 -2.15 -1.08 -1.54 -1.95 -2.52 -1.10 -1.99 -2.21 -2.12 -1.80 -2.22

-1.51

Calculated by Equation 44. Calculated by Equation 47. Calculated by Equation 52. The excretion rate is obtained from: (See Equation 20).

Ex

0

—

-1.30 -1.70 -1.84

— —

-2.19 -2.00 -2.32 -1.72 -1.83

e

f

0

Λ

log UEX — log (K

A

+

[H ])/([H+]). +


88



Results and Discussion For

the rate of a c e t y l a t i o n of six s u l f o n a m i d e d r u g s i n the r a t ( 6 )

the h i g h e s t c o r r e l a t i o n w a s o b t a i n e d i n E q u a t i o n 22. I f w e n e g l e c t the s e c o n d t e r m o n the left of the e q u a t i o n a n d a n a l y z e the l o g k

Ac

values

d i r e c t l y w i t h the substituent p a r a m e t e r s , the c o r r e l a t i o n becomes p o o r e r as s h o w n i n E q u a t i o n 25. F o r d a t a o b t a i n e d i n d e p e n d e n t l y o n 10 d r u g s ( 7 ) , E q u a t i o n 28 shows the best c o r r e l a t i o n . A n F test shows t h a t the ΔρΚ

t e r m i n E q u a t i o n 29 is justified o n l y at the 0.75 l e v e l of significance.

Α

F o r 10 d r u g s u s e d w i t h r a b b i t ( 7 ) a n d h u m a n ( 8 ) , E q u a t i o n s 31 a n d 34


s h o w the best c o r r e l a t i o n . Rat (6) ([#+] ,

,

=

, ,

log k

Ac

+ log =

10" · ) 7

4

s

r

6

0.366

0.919

(21)

6

0.222

0.971

(22)

6

0.229

0.977

(23)

6

0.290

0.420

(24)

6

0.244

0.644

(25)

6

0.248

0.738

(26)

10

0.609

0.637

(27)

10

0.411

0.854

(28)

10

0.395

0.884

(29)

10

0.606

0.821

(30)

10

0.468

0.898

(31)

10

0.493

0.901

(32)

J J H +

-1.631 +

=

η [H+]

Κ Λ +

O.B78ApK

A

- 1 . 2 5 5 + 0.876x (±0.432) (±0.299)

=

-1.395 +

0.679π +

0.100Δρ#

=

-1.233 -

=

-1.220 -

0.200*

=

-1.382 +

Ο.ΙΙβΔρ^ -

Λ

log k c A

Rat (7) ([#+] ,

,

, ,

= =

7

,

Ac

= =

4

[H+]

H +

0.308Δρ^

- 1 . 1 0 2 + 0.821x (±0.573) (±0.408) -0.732 +

+ log =

0.428x

J J

A

-1.260 +

, ,

log k

+

K

Rabbit (7) ([#+] ,

A

== 1 0 - · )

log κ Ac + l o g =

0.059ApK

= K

A

1.271x -

0.228Δρ^

10- · ) 7

+

4

[H+]

J J

-1.599 +

H +

0.533ΔρΧ^

- 1 . 0 1 0 + 1.160π (±0.652) (±0.465) -1.170 +

0.989x +

0.098ΔρΧ

Λ


6.

Metabolism

FUJITA

Human

(8) ([#+]

, log k

+

Ac

= = =

log

=

If

A

and Excretion

of

89

Sulfonamides

10~ - ) 7

+

4

[H+]

-2.260 +

0.483Δρ#

Λ

- 1 . 8 1 4 + 1.124x (±0.565) (±0.402) -1.735 +

1.208x -

0.048Δρ^

10

0.627

0.783

(33)

10

0.405

0.916

(34)

10

0.431

0.916

(35)

T h e c o m m o n feature of these correlations is that the ΔρΚ

term

Α


p l a y s n o significant r o l e .

S i n c e N - 4 - a c e t y l a t i o n occurs b y a n u c l e o p h i l i c

attack of the lone p a i r of a r o m a t i c a m i n o n i t r o g e n , w e c o u l d assume that the m o r e the e l e c t r o n - d o n a t i n g p r o p e r t y of the N - l - s u b s t i t u e n t , the faster the r a t e of a c e t y l a t i o n at the N - 4 - p o s i t i o n . H o w e v e r , s e p a r a t e d f r o m the b e n z e n e r i n g b y the S 0 N H 2

g r o u p , the e l e c t r o n i c

effect of the N - l -

substituents m a y not b e w e l l t r a n s m i t t e d to the N - 4 p o s i t i o n (10).

There

fore, the l a c k of a significant r o l e of the Δ ρ Κ ^ t e r m i n these correlations shows that the most i m p o r t a n t factor g o v e r n i n g the r a t e - d e t e r m i n i n g step of the h e p a t i c a c e t y l a t i o n is the h y d r o p h o b i c i t y of t h e d r u g . T h e rate of r e n a l excretion i n the rat (6, E q u a t i o n s 38 a n d 44.

7)

is best c o r r e l a t e d

by

T h e t e r m c o r r e c t i n g the effect of d i s s o c i a t i o n i n

the t u b u l e is m a r k e d l y significant i n this case.

W i t h o u t this t e r m , the

correlation becomes m u c h poorer ( E q u a t i o n s 3 9 - 4 1 ) . E q u a t i o n 47 shows the best c o r r e l a t i o n .

F o r rabbits

T h e coefficient

of the

(7), ΔρΚ

Α

t e r m i n E q u a t i o n 47 is negative, i n contrast to that i n E q u a t i o n s 38 a n d 44.

S i n c e the 9 5 %

confidence i n t e r v a l s of coefficients

s u s c e p t i b i l i t y of the t u b u l a r m e m b r a n e

d o not

to the e l e c t r o n i c

overlap,

structure

of

p e r m e a t i n g d r u g s p r o b a b l y differs b e t w e e n rats a n d r a b b i t s .

Rat (7) ([#+]

log fcjsx -

log

10- · )

K

6

A

+

4

J J

η

s

r

[H+]

H +

=

-0.715 -

0.229ΔρϋΟ

12

0.523

0.556

(36)

=

-0.732 -

0.706x

12

0.324

0.858

(37)

12

0.299

0.893

(38)

= log

,

=

- 1 . 0 6 1 - 0.992x + 0 . 1 7 6 Δ # Λ (±0.602)(±0.483) (±0.242) Ρ

k

Ex

=

-1.254 +

0.037ΔρϋΟ

12

0.521

0.108

(39)

=

-0.913 -

0.160x

12

0.509

0.234

(40)

=

-1.483 -

0.657x +

12

0.455

0.565

(41)

0.Ζ0δΑρΚ

Α


90


Rat (6) ([#+]

, , log k

Ex

=

10- · ) 6

, Κ A + log ^

=

-1.476 -

0.119Δρ#

=

-1.386 -

0.427x


-

Ex

=

, K log

A

η

s

r

7

0.470

0.458

(42)

7

0.332

0.779

(43)

7

0.207

0.937

(44)

[H+] j Α

10 · ) -8

+ ^

H +

8

[Η+] j

=

-0.680 -

0.628Δρ.ΚΆ

12

0.398

0.924

(45)

=

-1.639 -

1.193x

12

0.493

0.880

(46)

12

0.345

0.949

(47)

9

0.377

0.395

(48)

9

0.350

0.520

(49)

9

0.375

0.532

(50)

9

0.272

0.748

(51)

9

0.247

0.830

(52)

=

- 0 . 8 5 8 - 0.512x 0.419Δρ^ (±0.693)(±0.557) (±0.279) (9) ([#+]

Human ,

H +

- 1 . 8 0 7 - 0.988π + 0 . 2 9 8 Δ ρ ί : ^ (±0.563)(±0.589) (±0.279)

Rabbit (7) ([#+] log k

4

-

=


,

,

log k

log

Ex

K

A

=

ΙΟ" ) 60

[H+]

+

J J H +

=

-1.445 -

0.104ApuC

=

-1.443 -

0.316x

=

-1.514 -

0.432π +

=

-1.284 -

0.292π'

=

A

0.058Δρ#Λ

- 1 . 5 1 4 - 0.487π' + 0 . 1 6 3 Δ ρ ^ (±0.572)(±0.372) (±0.252)

F o r h u m a n s ( 9 ) , the c o r r e l a t i o n is n o t as g o o d as those f o u n d for r a b b i t s a n d rats ( E q u a t i o n s 4 8 - 5 0 ) . T h i s m a y be the result of t h e s m a l l v a r i a b i l i t y of values o n the left of the e q u a t i o n a n d of the difference i n the a b i l i t y of p a r t i t i o n coefficient d a t a to define p e r m e a b i l i t y i n the d i f ferent test a n i m a l s . I f w e use ττ' values d e r i v e d f r o m the p a r t i t i o n coeffi cients w i t h a C H C l - w a t e r system i n s t e a d of those f r o m a n i s o b u t y l 3

a l c o h o l - w a t e r system, E q u a t i o n 52 results, w h i c h shows a reasonable correlation.

T h i s is the o n l y e x a m p l e h e r e w h e r e the ττ' v a l u e s f r o m a

C H C l - w a t e r system s h o w a better c o r r e l a t i o n t h a n those f r o m a n i s o b u t y l 3

a l c o h o l - w a t e r system. T h e s u s c e p t i b i l i t y of h u m a n t u b u l a r r e a b s o r p t i o n to the h y d r o p h o b i c i t y of d r u g s m i g h t b e different f r o m those of the rat a n d r a b b i t ; thus, the m o d e l w i t h a C H C l - w a t e r system c o u l d s i m u l a t e 3


6.

Metabolism

FUJITA

and Excretion

of

91

Sulfonamides

the t u b u l a r m e m b r a n e better t h a n the m o d e l w i t h a n i s o b u t y l a l c o h o l w a t e r system. We

o m i t t e d the data for acetosulfamine,

sulfisoxazole,

and

sulfi

s o m i d i n e i n d e r i v i n g E q u a t i o n s 4 8 - 5 2 since a n active t u b u l a r secretion m e c h a n i s m has b e e n p o s t u l a t e d for their r e n a l excretion ( 9 ) w h i c h w o u l d also suggest a f u n c t i o n a l difference of h u m a n t u b u l a r m e m b r a n e

from

those of rats a n d r a b b i t s . I n fact, the d a t a for these three c o m p o u n d s fitted p o o r l y a p r e l i m i n a r y c o r e r l a t i o n w i t h the use of ττ'. T a b l e I gives the results of calculations of the a c e t y l a t i o n rate c o n stants b a s e d o n E q u a t i o n s 22, 28, 3 1 , a n d 34. A c e t o s u l f a m i n e a n d s u l f a d i


m e t h o x i n e are o m i t t e d i n the correlations of 12 c o m p o u n d s for w h i c h the

substituent parameters

are k n o w n

since

preliminary calculations

s h o w e d that the d a t a for these t w o d i d not fit w e l l i n e a c h case. D i f f e r e n t routes for the m e t a b o l i s m of these t w o c o m p o u n d s m i g h t b e operative. I n fact, for s u l f a d i m e t h o x i n e , g l u c u r o n i d e f o r m a t i o n has b e e n s h o w n to o c c u r to a c o n s i d e r a b l e extent, a n d this c a n not be n e g l e c t e d as c o m p a r e d w i t h the a c e t y l a t i o n at l i v e r i n rats (6)

a n d h u m a n s (11).

W e expected

that acetosulfamine w o u l d b e h a v e as a n a c e t y l d o n o r as w e l l as the a c e t y l acceptor. T h u s , the N - 4 - a c e t y l g r o u p of N - 4 - a c e t y l a c e t o s u l f a m i n e m i g h t result not o n l y f r o m a c e t y l - C o A b u t also f r o m the N - l - a c e t y l g r o u p of another acetosulfamine

molecule.

T a b l e I I shows r e n a l excretion d a t a . t a i n e d f r o m E q u a t i o n s 38, 44, 47, a n d 52.

C a l c u l a t e d values w e r e H e r e , the rate constants

ob of

acetosulfamine a n d s u l f a d i m e t h o x i n e are as w e l l c o r r e l a t e d as those of the other c o m p o u n d s for rats a n d r a b b i t s . T h i s c o u l d be e x p e c t e d since the k

Ex

v a l u e is d i r e c t l y d e t e r m i n e d b y the p r o p o r t i o n of the i n t e g r a t e d

a m o u n t of n o n - m e t a b o l i z e d d r u g i n the t o t a l u r i n a r y excreted m a t e r i a l s whereas the k

Ac

v a l u e is d e r i v e d b y a s s u m i n g t h a t metabolites, other t h a n

N - 4 - a c e t y l d e r i v a t i v e s , are n e g l i g i b l e i n the u r i n e . F o r h u m a n s , the rate constant of s u l f a d i m e t h o x i n e is w e l l c o r r e l a t e d w h i l e t h a t of acetosulfa m i n e is not.

T h e latter m a y b e excreted b y a different m e c h a n i s m as

mentioned. T h e r e c o u l d b e alternate models t h a n those u s e d i n the a b o v e d i s cussions of the e l i m i n a t i o n processes. F o r instance, a m o d e l of a c e t y l a t i o n , w h e r e the b i n d i n g e q u i l i b r i a of drugs w i t h s e r u m p r o t e i n a n d l i v e r tissues are s l o w reactions a n d c o m p e t e w i t h each other for drugs, w o u l d result i n a different expression t h a n E q u a t i o n 14. H o w e v e r , analyses of the rates of a c e t y l a t i o n a n d excretion for v a r i o u s test organisms, w h i c h are p h y s i c o c h e m i c a l l y as w e l l as statistically reasonable, are o n l y possible w i t h the present models.

T h e p r o p r i e t y of u s i n g these m o d e l s w o u l d b e

f u r t h e r p r o v e d b y the f o l l o w i n g discussions o n the t i m e of d u r a t i o n . T h e most c o n v e n i e n t p a r a m e t e r w h i c h expresses the t i m e of d u r a t i o n is the v a l u e t , 1/2

w h i c h is i n v e r s e l y p r o p o r t i o n a l to the s u m of the


k

Ac


92


pHurine

pHblood

6.4

7.4

Dependence of log k on p K

Figure 4. and k . Ex


A l t h o u g h t h e values o f l o g k

Ac

and log k

A

Ex

(rat) can be individually

c o r r e l a t e d b y substituent constants, i t w o u l d b e m a t h e m a t i c a l l y as w e l l as p h y s i c o c h e m i c a l l y difficult to a n a l y z e s i m i l a r l y t h e v a l u e of l o g (k

Ac

k ). Ex

W e d i d not t r y t o a n a l y z e t ,

logt ,

b y substituent constants.

or l o g (k

1/2

1/2

+

directly

+ k )

Ac

Ex

Instead, w e c h e c k e d t h e p h y s i c o c h e m i c a l c o n

ditions w h i c h m a k e b o t h the l o g k

Ac

and log k

Ex

s i m u l t a n e o u s l y , so that the v a l u e of t

i/2

values as s m a l l as possible,

w o u l d be maximum.

B y t a k i n g the p a r t i a l differentials o f E q u a t i o n s 28 a n d 38, w e u n d e r s t a n d h o w t h e values o f l o g k

andlog k

Ac

Ex

for the rat vary according

to the variations of the pK a n d π values o f the N - l - s u b s t i t u e n t . E q u a t i o n s A

53 a n d 54 are the p a r t i a l differentials w i t h respect to p K , w h i c h i n d i c a t e A

that plots o f b o t h t h e l o g k values against \)K consist o f t w o phases as A

s h o w n i n F i g u r e 4. T h e l o g k

Ac

v a l u e decreases w i t h a d e c l i n e i n the ipK

A

of d r u g b e y o n d t h e v a l u e o f b l o o d p H w h i l e t h e l o g k

Ex

w i t h a d e c r e a s i n g pK

A

v a l u e increases

value beyond the urinary p H value.

Since the

u r i n a r y p H f o r the rat is a b o u t 6.4 ± 0.2 ( w h i c h is s m a l l e r t h a n that f o r b l o o d w h i c h is ca. 7 . 4 ) , w e w o u l d expect that w h e n t h e p K

A

of a drug

is l o c a t e d b e t w e e n these t w o p H values, b o t h l o g k values o f t h e d r u g w o u l d b e as s m a l l as possible s i m u l t a n e o u s l y . dlog k dpK

K

dlog k dpK

K

A

+ [H+l blood

Ex

A

(53)

A

Ac

A

K

A

+

[H+U

-0.176

(54)

C o m p a r i n g t h e p a r t i a l differentials w i t h respect to π of E q u a t i o n s 28 a n d 38 ( E q u a t i o n s 5 5 a n d 5 6 ) , w e see that t h e d e p e n d e n c e o f b o t h l o g k values o n π is almost opposite.

T h e larger t h e π v a l u e , t h e faster

the rate o f a c e t y l a t i o n a n d t h e s l o w e r that o f excretion. T h u s , w e c o u l d


6.

Metabolism

FUJITA

and Excretion

of

93

Sulfonamides

not expect a h y d r o p h o b i c p r o p e r t y w h i c h w o u l d m a k e b o t h t h e l o g k values as s m a l l as possible.

If, h o w e v e r ,

t h e s m a l l difference

i n the

absolute values b e t w e e n p a r t i a l differentials c o u l d b e g i v e n a m e a n i n g , the l a r g e r the ττ v a l u e , the larger w o u l d b e t h e t i m e o f d u r a t i o n since t h e s u s c e p t i b i l i t y o f t u b u l a r r e a b s o r p t i o n to the h y d r o p h o b i c i t y is larger t h a n that o f h e p a t i c a c e t y l a t i o n . dlog

k

Ac

dlog k dx Downloaded by FUDAN UNIV on February 15, 2017 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0114.ch006

Ex

F i g u r e 5 shows the t

0.821

(55)

-0.992

(56)

values for the rat, o b t a i n e d f o r 12 s u l f o n a m i d e

1/2

drugs ( 7 ) , p l o t t e d against pK . A

cussions are q u a l i t a t i v e l y correct.

T h i s figure shows that t h e a b o v e d i s The pK

A

values o f drugs w h i c h h a v e

•S-monomethoxine •S-diazine

•i S-dimethoxine

S-methoxypyridazine

9 H

10 i H Sulfanilamide

PK

10

A

20

30

t

1/2

Figure 5. p K and time of duration (rat). For acetosulfamine and sulfadimethoxine where different routes of hepatic metabolism are suggested, the t values are expressed by dotted columns. A

1/2


94


T H E HANSCH APPROACH

4H

f S-isoxasole ___-_-_-zj Acetosulfamine

S-monomethoxine S-dimethoxine

S-diazine ^S-thiazole

7 H Downloaded by FUDAN UNIV on February 15, 2017 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0114.ch006

1

• S-merazine S-methoxypyridazine

S-isomidine

1

1

10

20

30

t

|

/

2

Figure 6. p K and time of duration (human). For acetosulfamine, sulfis oxazole, sulfisomidine, and sulfadimethoxine, where different mechanisms of renal excretion and hepatic metabolism are suggested by others, the t values are expressed by blank and dotted columns; see text. A

1/2

longer times o f d u r a t i o n are m o s t l y l o c a t e d i n t h e r a n g e p r e d i c t e d a b o v e —i.e., b e t w e e n t h e u r i n a r y a n d b l o o d p H values, pK

A

= 6 ^ 7.4. T h e

times o f d u r a t i o n o f s u l f a t h i a z o l e a n d sulfisomidine w h i c h are q u i t e short for t h e i r o p t i m u m pK values c a n b e u n d e r s t o o d b y t h e i r s m a l l π values. A

Since u r i n a r y a n d b l o o d p H values are s i m i l a r t o those f o r t h e rat, t h e a b o v e discussion c o u l d also b e a p p l i e d to the t i m e o f d u r a t i o n f o r h u m a n s . F i g u r e 6 shows that w h a t w e expect is also correct f o r t h e t

1/2

data

o b t a i n e d b y R i e d e r a n d others (4, 12). F o r t h e r a b b i t , t h e s i t u a t i o n is different. E q u a t i o n s 31 a n d 4 7 w i t h respect to pK

A

57-60.

P a r t i a l differentials o f

a n d π are g i v e n as E q u a t i o n s

A c c o r d i n g t o E q u a t i o n s 57 a n d 58, w e c a n d r a w b i p h a s i c plots dlog k

Ac

dpK

A

K

A

=

K

A

+ [H+] blood


(57)

6.

Metabolism

FUJITA

and Excretion

of

95

Sulfonamides

log k


pHibloody pH 8.8

7.4 Figure 7.

Dependence of log k on p K

A

(rabbit)

4 -

5 -

6

7H

S-isomidine 8

9

10 H

Sulfanilamide

10

PKA

20

1 1/2

Figure 8. p K and time of duration (rabbit). For acetosulfamine and sulfadimethoxine where different mechanisms of hepatic metabolism are suggested by others, the t values are expressed by dotted columns. A

I / 2


96



for l o g k vs. pK , as s h o w n i n F i g u r e 7. H e r e , t h e u r i n a r y p H , 8.8, is A

h i g h e r t h a n t h a t o f t h e b l o o d , 7.4. H e n c e , w e c o u l d n o t expect a n y o p t i m u m r a n g e for the pK . C o m p a r i s o n o f E q u a t i o n 59 w i t h 6 0 indicates A

dlog k dx

=

1.160

(59)

dlog k dx

=

-0.512

(60)

Ac


Ex

t h a t h e p a t i c a c e t y l a t i o n is m u c h m o r e susceptible t o h y d r o p h o b i c i t y o f the d r u g t h a n is t u b u l a r r e a b s o r p t i o n i n r a b b i t s . T h e r e f o r e , t h e s m a l l e r the π v a l u e o f the N - l - s u b s t i t u e n t , the larger the t\/ v a l u e w o u l d b e c o m e . 2

T h e reason w h y s u l f a n i l a m i d e a n d sulfisomidine, w i t h π values w h i c h are a m o n g the smallest, h a v e l a r g e t

1/2

values ( 7 ) ( F i g u r e 8 ) c a n b e u n d e r

stood o n this basis. A n a l y s e s u s i n g free energy r e l a t e d e l e c t r o n i c a n d h y d r o p h o b i c

sub

stituent constants a r e c a p a b l e o f i l l u s t r a t i n g t h e rate constants o f h e p a t i c a c e t y l a t i o n a n d r e n a l excretion as w e l l as the t i m e of d u r a t i o n o f s u l f o n a m i d e drugs i n v a r i o u s test organisms.

T h e effects o f d r u g d i s s o c i a t i o n

on b i n d i n g e q u i l i b r i a w i t h various macromolecules

and o n permeability

through membranes

d o p l a y i m p o r t a n t roles i n e l i m i n a t i o n processes.

Although w e made

d r a s t i c assumptions i n d e r i v i n g t h e rate

constant

expressions, t h e reasonable correlations o b t a i n e d s h o w that these m o d e l s for t h e d r u g e l i m i n a t i o n processes are p r a c t i c a l l y u s e f u l a n d that other r e c e n t l y p o s t u l a t e d e l i m i n a t i o n processes—i.e., t u b u l a r active

secretion

(9, 13, 14) a n d N - l - g l u c u r o n i d a t i o n f o l l o w e d b y h e p a t o - b i l i a r y excretion (15), need not be considered

( e x c e p t f o r a f e w c o m p o u n d s ) as f a r as

c o m p o u n d s s t u d i e d i n this w o r k are c o n c e r n e d .

T h u s , w e expect that t h e

procedures d e v e l o p e d here w i l l p r o v i d e i n f o r m a t i o n o n the p h y s i c o c h e m i c a l p r o p e r t i e s w h i c h are f u n d a m e n t a l i n o u r search f o r n e w l o n g - a c t i n g derivatives o f the s u l f o n a m i d e f a m i l y as w e l l as other dissociable drugs. Acknowledgment T h e a u t h o r thanks C o r w i n H a n s c h f o r m a n y suggestive a n d f o r m a k i n g t h e regression analyses.

discussions

H e is also g r a t e f u l to M i n o r u

N a k a j i m a f o r his s u p p o r t o f this w o r k .

Literature Cited 1. Fujita, T., Hansch, C., J. Med. Chem. (1967) 10, 991. 2. Fujita, T., J. Med. Chem. (1972) 15, in press.


6.

3. 4. 5. 6. 7. 8. 9. 10.


11. 12. 13. 14. 15. 16.

FUJITA

Metabolism

and Excretion

of

Sulfonamides

97

Krüger-Thiemer, E., Bünger, P., Chemotherapia (1965/1966) 10, 61, 129. Rieder, J., Arzneimittel-Forsch. (1963) 13, 81. Nelson, E., J. Pharm. Sci. (1961) 50, 181. Nogami, H., Hasegawa, Α., Hanano, M., Imaoka, K., Yakugaku Zasssi (1968) 88, 893. Yamazaki, M., Aoki, M., Kamada, Α., Chem. Pharm. Bull. (1968) 16, 707, 721. Kakemi, K., Arita, T., Koizumi, T., Arch. Pract. Pharm. (1965) 25, 22. Koizumi, T., Arita, T., Kakemi, K., Chem. Pharm. Bull. (1964) 12, 428. Yoshioka, M., Hamamoto, K., Kubota, T., J. Chem. Soc., Japan (1963) 84, 412. Bridges, J. W., Kibby, M. R., Walker, S. R., Williams, R. T., Biochem. J. (1969) 111, 167. Zbinden, G., ADVAN. CHEM. SER. (1964) 45, 25. Despopoulos, Α., Callahan, P. X., Am. J. Physiol. (1962) 203, 19. Arita, T., Hori, R., Owada, E., Takahashi, K., Chem. Pharm. Bull. (1969) 17, 2526. Millburn, P., Smith, R. L., Williams, R. T., Biochem. J. (1967) 105, 1283. Yamazaki, M., Aoki, M., Kamada, Α., Yata, N., Arch. Pract. Pharm. (1967) 27, 37.

RECEIVED

June 17, 1971.


Biological CorrelationsâThe Hansch Approach

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