- Email: [email protected]
Chapter 34. The Use of Substituent Constants in Drug Design
347
Chapter 34. The U s e of S u b s t i t u e n t C o n s t a n t s i n Drug Design Corwin Hansch, Pomona C o l l e g e , Claremont, C a l i f o r n i a The s u b j e c t of s t r u c t u r e - a c t i v i t y r e l a t i o n s i n m e d i c i n a l chemistry is almost boundless. Few p a p e r s a r e now published without some d i s c u s s i o n of t h i s problem. The work considered i n t h i s review i s l i m i t e d t o t h a t concerned w i t h mathematical c o r r e l a t i o n s between s t r u c t u r e and activity. The u s e of physical-chemical r e f e r e n c e systems t o s e r v e a s scales w i t h which one could d i s c u s s i n q u a n t i t a t i v e t e r m s t h e r e l a t i o n between b i o l o g i c a l a c t i v i t y and chemical s t r u c t u r e e x c i t e d g r e a t i n t e r e s t a t t h e t u r n of t h e c e n t u r y . C. R i c h e t , J . Traube, H . Fiihner and e s p e c i a l l y H . Meyer and E. Overton gave t h r u s t t o t h i s movement. It was observed, almost e n t i r e l y i n a l i p h a t i c systems, t h a t as one i n c r e a s e d t h e c h a i n l e n g t h i n a homologous series a r e g u l a r i n c r e a s e i n a s t a n d a r d b i o l o g i c a l response o c c u r r e d . L i n e a r r e l a t i o n s between a s t a n d a r d r e s p o n s e and t h e number of carbon atoms i n t h e c h a i n , w a t e r s o l u b i l i t y , s u r f a c e t e n s i o n lowering a b i l i t y , vapor p r e s s u r e and o i l - w a t e r p a r t i t i o n c o e f f i c i e n t s were o f t e n found i n many d i f f e r e n t tests. An example of t h i s t y p e of c o r r e l a t i o n u s i n g p a r t i t i o n c o e f f i c i e n t s coming from t h e work of Overton is : l o g 1 / C = 0.858 logP
+
0.837
n = 28
r = 0.978
(1)
I n eq 1, C r e p r e s e n t s t h e molar c o n c e n t r a t i o n of v a r i o u s a l c o h o l s , k e t o n e s and esters producing i s o n a r c o s i s i n t a d p o l e s , P i s t h e octanol-water part i t i o n c o e f f i c i e n t , n i s t h e number of d a t a used i n f i n d i n g t h e c o n s t a n t s v i a t h e method of least s q u a r e s , and r i s t h e c o r r e l a t i o n c o e f f i c i e n t . The c o n s t a n t s i n eq 1 are s l i g h t l y d i f f e r e n t from t h o s e published' and t h e c o r r e l a t i o n is a l i t t l e b e t t e r because of t h e u s e of imprpved P v a l u e s . An important advance w a s made by Ferguson2y3 who showed t h a t t h e following generalization holds. ci = kAi l / n
I n eq 2 , Ci is t h e c o n c e n t r a t i o n of t h e ithmember of a series producing a n e q u i v a l e n t response, k and n are t h e c o n s t a n t s , and A. i s a p h y s i c a l 1 chemical d i s t r i b u t i o n c o n s t a n t of t h e above mentioned k i n d . Ferguson p o i n t e d o u t t h a t f o r n o n s p e c i f i c n a r c o t i c s i n s t a t e s of e q u i l i b r i u m , biol o g i c a l a c t i v i t y i s r e l a t e d t o thermodynamic a c t i v i t y . Ferguson's approach was extended by Brink and Post-._-nak4 and i t i s now e v i d e n t t h a t t h e r e a r e many i n s t a n c e s where e q u a l d e g r e e s of n a r c o s i s a r e caused by molecules having e q u a l thermodynamic a c t i v i t i e s . Other approaches t o e x p l a i n i n g t h e e f f e c t of n a r c o t i c a c t i v i t y i n terms of physical-chemical - ~ Mullinsg McGowan u s i n g parachor parameters are t h o s e of M c G ~ w a n ~and and Mullins u s i n g H i l d e b r a n d ' s s o l u b i l i t y parameter and m o l a l volume, have
.
3 48 -
Sect. VI
-
Topics in C h e m i s t r y
S m i s sman, Ed.
assembled e v i d e n c e t o s u p p o r t t h e view t h a t t h e m o l e c u l a r volume of t h e n a r c o t i c is of c r i t i c a l importance i n d e t e r m i n i n g n a r c o s i s . PaulinglO and Miller'' have s u g g e s t e d t h a t a n e s t h e t i c potency i s r e l a t e d t o t h e a b i l i t y of a n e s t h e t i c s t o form h y d r a t e s . M i l l e r , Paton and Smith' and o t h e r s have c r i t i c i z e d t h e Pauling-Miller view. Agin, Hersh and Holtzman14 have shown t h a t eq 3 g i v e s an e x c e l l e n t c o r r e l a t i o n f o r t h e r e l a t i o n between minimum b l o c k i n g c o n c e n t r a t i o n (MBC) of 3 9 l o c a l a n e s t h e t i c s i n f r o g s a r t o r i u s muscle w i t h p o l a r i z a b i l i t y (a) and t h e i o n i z a t i o n p o t e n t i a l (I) of t h e d r u g s . Zahradnik15, i n a s y s t e m a t i c s t u d y u s i n g mice and c a r e f u l l y cont r o l l e d c o n d i t i o n s , developed a set of c o n s t a n t s f o r a l k y l groups from t h e l i n e a r Hammett-like p o s t u l a t e thattftog (T./T,,) = aB where T r e p r e 1 s e n t s t h e molar c o n c e n t r a t i o n of t h e i member of a set of a l i p k a t i c cong e n e r s producing a s t a n d a r d b i o l o g i c a l r e s p o n s e and T~~ i s t h e concentrat i o n of t h e e t h y l d e r i v a t i v e . 6 i s a c o n s t a n t c h a r a c t e r i s t i c of t h e subs t i t u e n t ( R of RX) and a i s a c o n s t a n t c h a r a c t e r i s t i c of t h e system. The c o n s t a n t B w a s determined f o r 25 R groups and a w a s e v a l u a t e d f o r 39 d i f f e r e n t b i o l o g i c a l systems. While t h i s s i n g l e parameter approach works w e l l f o r i n h i b i t o r y s t u d i e s of homologous groups of a l i p h a t i c compounds where h i g h l y s p e c i f i c e l e c t r o n i c and s t e r i c e f f e c t s are n o t c r i t i c a l , i t h a s n o t been extended t o more complex systems. The above i d e a s have provided i n s i g h t i n t o n o n s p e c i f i c b i o l o g i c a l i n h i b i t i o n s ; however, t h i s knowledge h a s n o t been of g r e a t h e l p i n t h e des i g n and m o d i f i c a t i o n of d r u g s of h i g h s p e c i f i c i t y . Two approaches have been emerging i n r e c e n t y e a r s t o supplement t h e m e d i c i n a l c h e m i s t s ' i n t u i t i o n on t h e e f f e c t of s u b s t i t u e n t v a r i a t i o n on drug a c t i v i t y . I n one aproach de novo s u b s t i t u e n t c o n s t a n t s have been d e r i v e d by simply f i n d i n g t h e " b e s t numbers'' t o go w i t h g i v e n s u b s t i t u e n t s on a p a r t i c u l a r drug a c t i n g i n a s t a n d a r d t e s t . The o t h e r approach h a s used s u b s t i t u e n t cons t a n t s d e r i v e d from model n o n b i o l o g i c a l systems. The f i r s t work on t h e former of t h e s e two t r a c k s a p p e a r s t o b e t h a t of B r u i c e , Kharasch and Winzlerl working w i t h t h y r o x i n e d e r i v a t i v e s . T h e i r ,approach has been s t a t e d i n more g e n e r a l terms by F r e e and Wilson17. The method can b e ill u s t r a t e d w i t h t h e i r example f o r a s e t of t e t r a c y c l i n e (I) a n a l o g s . The r e l a t i v e b i o l o g i c a l a c t i v i t y f o r each d e r i v a t i v e c a n be formulated a s t h e l i n e a r combination of t h e c o n t r i b u t i o n of each of t h e groups r e p r e s e n t e d by X , Y and R: Biological a c t i v i t y = p
+
a[X.] 1
+ c[Ril
+
bEY.1 1
(1)
One can w r i t e a set of s i m u l t a n e o u s e q u a t i o n s , one f o r each compound t e s t e d , t h e s o l u t i o n of which g i v e s t h e c o n t r i b u t i o n t o t h e a c t i v i t y f o r each a [ X i ] , e t c . T a b l e I l i s t s t h e r e s u l t s f o r t h e t e t r a c y c l i n e s .
Table I X
R
a[Hl a[CH3]
75
b[C11
84
-112
b[Brl
-16
349 -
Hansch
Drug Design
Chap. 3 4
Y
c “Hz
I
123 18
c [ CH3CONHI
!J =
161
-218 Of t h e t o t a l of 1 8 p o s s i b l e d e r i v a t i v e s r e s u l t i n g from d i f f e r e n t combinat i o n s of R, X and Y , 10 had been t e s t e d . Presumably, a c t i v i t i e s f o r t h e o t h e r e i g h t can b e c a l c u l a t e d from t h e s u b s t i t u e n t c o n s t a n t s i n T a b l e I . The method i s of g r e a t e s t v a l u e when a l a r g e group of d e r i v a t i v e s and f u n c t i o n s i s i n v o l v e d . There a r e of c o u r s e many o b j e c t i o n s t h a t come t o mind i n c o n s i d e r i n g t h e above t e c h n i q u e . Modern c h e m i s t r y h a s l o n g recognized t h e g r e a t importance of s t e r i c and e l e c t r o n i c e f f e c t s of s u b s t i t u e n t s on r a t e and e q u i l i b r i u m p r o c e s s e s 1 8 . From t h e Meyer-Overton work and from more r e c e n t t h e hydrophobic bonding power of funct i o n a l groups i s s e e n t o b e a v e r y i m p o r t a n t s u b s t i t u e n t e f f e c t . These t h r e e e f f e c t s a r e lumped i n t o each of t h e c o n s t a n t s under R, X and Y of T a b l e I . Hence i t would seem t h a t i n g e n e r a l , c o n s t a n t s d e r i v e d f o r one s e t of congeners w i l l n o t b e u s e f u l f o r a n o t h e r set c a u s i n g a d i f f e r e n t b i o l o g i c a l r e s p o n s e . N e v e r t h e l e s s , t h i s e m p i r i c a l method of d e r i v i n g cons t a n t s f o r t h e r e l a t i v e e f f e c t s of chemical groups on b i o l o g i c a l a c t i v i t y i s bound t o b e more h e l p f u l i n t h e long run t h a n unguided i n t u i t i o n . Purc e l l 3 4 has been s t u d y i n g t h e Free-Wilson method. Some i n f o r m a t i o n i s a l r e a d y i n hand t o show t h a t such e m p i r i c a l cons t a n t s are r e l a t e d t o more fundamental p a r a m e t e r s . C i l e n t o and Berenholc have shownz6 t h a t t h e r e i s a good l i n e a r c o r r e l a t i o n between f(X) o b t a i n e d f o r 1 6 t h y r o x i n e a n a l o g s (11) and t h e n e g a t i v e l o g a r i t h m of t h e l i f e t i m e of t h e phosphorescent s t a t e ( e q u i v a l e n t t o t h e t r i p l e t t o s i n g l e t t r a n s i t i o n i n n a p h t h a l e n e a n a l o g s ) f o r t h e f i v e f u n c t i o n s where X = H , CH3, C l , B r , I. They conclude t h a t t h e s t r o n g T+S t r a n s i t i o n i n d i i o d o t y r o s i n e and t h y r o x i n e d e r i v a t i v e s makes t h e s e compounds v e r y e f f i c i e n t i n t h e t r a n s f e r of t r i p l e t - s t a t e energy. Using t h e subx s t i t u e n t o f o r t h e e l e c t r o n i c e f f e c t and / \ H \ n f o r t h e hydrophobic e f f e c t z 7 of /WH,CHNH,COOH .-.\-R /-.\s u b s t i t u e n t s , i t i s s e e n from eq 4 t h a t f(X’) d e r i v e d by B r u i c e e t a l . x’/ X/ (11) i s i n f a c t r e l a t e d t o t h e s e more fundamental c o n s t a n t s .
\.-.
<-
f(X’)
It h a s of t h y r o x i n e t h e u s e of B been shown30
-
= 0.3081~
0.5640
- 1.672
n = 7
r
=
0.934
(4)
been shown28 t h a t IT and o c a n b e used t o r a t i o n a l i z e t h e SAR a n a l o g s and J ~ r g e n s e n *h~a s t e s t e d t h e p r e d i c t i v e v a l u e of and IT w i t h a t e r t - b u t y l a n a l o g of t h y r o x i n e . It h a s a l s o t h a t Zahradnik‘s $ c o n s t a n t s a r e l i n e a r l y r e l a t e d t o IT.
Kopeck; and Bozek31,32 have a l s o been s t u d y i n g t h e u t i l i t y of emp i r i c a l s u b s t i t u e n t c o n s t a n t s i n an i n v e s t i g a t i o n of t h e t o x i c i t y of d i s u b s t i t u t e d benzenes. I n t h e i r e q u a t i o n (5) t h e y have used a n i n t e r a c t i o n
3 50 -
Sect. VI
-
Topics i n Chemistry
Smi s sman, Ed.
term of t h e t y p e d i s c u s s e d by Miller33 f o r t h e l i n e a r combination of terms i n t h e f o r m u l a t i o n of m a t h e m a t i c a l m o d e l s .
I n eq. 5 , HH r e p r e s e n t s benzene and XY a d i s u b s t i t u t e d d e r i v a t i v e . Quite good c o r r e l a t i o n s w e r e o b t a i n e d u s i n g eq 5 f o r n o n s p e c i f i c t o x i c i t y . The c o n s t a n t bX i s s t a t e d t o b e l i n e a r l y r e l a t e d t o f(X’) of Bruice e t a l . Puree1136 , following t h i s g e n e r a l approach, h a s s t u d i e d amides which are i n h i b i t o r s of c h o l i n e s t e r a s e . P u r ~ e 1 Y 136~ and ~ co-workers have a l s o i n v e s t i g a t e d a v a r i e t y of p h y s i c a l chemical parameters t o r a t i o n a l i z e t h e SAR f o r these inhibitors. A f t e r t h e r a t h e r i n t e n s e work on t h e c o r r e l a t i o n of b i o l o g i c a l act i v i t y w i t h p a r t i t i o n c o e f f i c i e n t s of t h e e a r l y y e a r s of t h i s c e n t u r y had reached a s t a n d s t i l l , new hope f o r r a t i o n a l i z i n g t h e b i o l o g i c a l a c t i v i t y of o r g a n i c compounds appeared i n t h e work of H a m m e t t 3 7 . The H a m m e t t equat i o n and o t h e r v a r i a t i o n s of i t 1 a ~ 3 a have proved t o be v e r y s u c c e s s f u l i n c o r r e l a t i n g chemical r e a c t i v i t y w i t h t h e e l e c t r o n i c o r s t e r i c e f f e c t s of s u b s t i t u e n t s f o r t h e r e a c t i o n s of o r g a n i c compounds i n homogeneous solut i o n s . Although a good many a t t e m p t s have been made39’47 t o apply t h e H a m m e t t e q u a t i o n t o biochemical systems, t h e r e s u l t s have, w i t h few except i o n s , been d i s a p p o i n t i n g . Such a n e x c e p t i o n i s seen i n t h e enzymatic hyd r o l y s i s of phenyl s u l f a t e s 3 9 from which eq 6 r e s u l t s 2 4 . l o g l / K m = 0.9300
+
2.522
n = 10
r = 0.931
(6)
I n eq 6, K i s t h e Michaelis c o n s t a n t . Good c o r r e l a t i o n w i t h o w a s a l s o The b e s t l i n e a r r e l a t i o n s w i t h o have been found uso b t a i n e d wyth Vmax. i n g more o r less pure enzymes. The l a c k of s u c c e s s w i t h o i n biochemical s t e r i c i n t e r a c t i o n s of s u b s t i t systems h a s g e n e r a l l y been a t t r i b ~ t e dt o~ ~ u e n t s w i t h t h e enzyme o r l i p o p r o t e i n membranes. Recent work21-25 would i n d i c a t e t h a t w h i l e s t e r i c i n t e r a c t i o n s are extremely i m p o r t a n t , t h e conc e p t of lock-and-key f i t of enzyme and s u b s t r a t e h a s been over-emphasized a t t h e expense of hydrophobic bonding. The importance t o t h e m e d i c i n a l chemist of t h e more f l e x i b l e c h a r a c t e r of enzymes which is emerging from t h e work of Koshlandlt9 and others5O h a s been analyzed by Belleau51. A most important new concept f o r t h e d e s i g n e r of drugs is t h a t of t h e hydrophobic bond19 y 2 0 ,s2. The view of Hansch and co-workers is t h a t i f a s u i t a b l e parameter can be formulated f o r t h i s , t h e n by means of t h e w e l l known c o n s t a n t s 1 8 o , a+, O-, o*, and E,, many of t h e powerful t o o l s of p h y s i c a l o r g a n i c chemistry might b e brought t o b e a r on m e d i c i n a l chemic a l problems. To t h i s end octanol-water p a r t i t i o n c o e f f i c i e n t s (P) have Y ~ a d~ d i t. i v e - c o n s t i t u t i v e been s t u d i e d as a r e f e r e n c e standard1 Y ~ ~ The n a t u r e of l o g P and IT (IT = logP - logP where P r e f e r s t o a p a r e n t moleX H H c u l e and P t o a d e r i v a t i v e ) means t h a t from a r e l a t i v e l y few v a l u e s Of X l o g P, many o t h e r s can b e calculated1,24,27,53,54. The u s e f u l n e s s of t h e s e parameters f o r measuring binding of n e u t r a l molecules w i t h p r o t e i n s i s i l l u s t r a t e d i n eq 7 - 2 .
Drug Design
Chap. 34 l o g 1 / C = 0.71 logP l o g 1 / C = 0.58 logP
+
+ +
Hansch
351 -
1.51
n = 17
r = 0.950
(7)
2.40
n = 4
r = 0.961
(8)
n = 19
r
(9)
l o g 1 / C = 0 . 6 8 1 ~ 3.48
= 0.962
I n eq 7-9, C is t h e molar c o n c e n t r a t i o n of compound n e c e s s a r y t o produce a 1-to-1 complex w i t h bovine hemog1obin2l (eq 7 ) and bovine serum albumin (eq 8 and 9 ) . Equation 7 c o r r e l a t e s t h e binding of 1 7 m i s c e l l a n e o u s compounds ( e . g . , phenols, a n i l i n e s , naphthalene) and eq 8 c o r r e l a t e s t h e binding of 4 barbiturate^^^. I n eq 9 , t h e comparative c o n s t a n t IT i s used55 t o c o r r e l a t e t h e binding of phenols by serum albumin. The s l o p e s of t h e t h r e e e q u a t i o n s a r e s u r p r i s i n g l y c l o s e , i n d i c a t i n g t h a t t h e binding of n e u t r a l molecules t o two d i f f e r e n t p r o t e i n s can be q u a n t i t a t i v e l y def i n e d u s i n g l o g P o r IT as hydrophobic bonding c o n s t a n t s . For t h e s e s i t u a t i o n s no h i g h l y s p e c i f i c s t e r i c o r e l e c t r o n i c parameters a r e n e c e s s a r y t o rationalize the results. Going t o t h e n e x t more complex s i t u a t i o n , t h a t of enzymic r e a c t i o n s , i t can be shown t h a t t h e l i n e a r combination of IT and 0 can account f o r t h e s u b s t i t u e n t e f f e c t s i n t h e h y d r o l y s i s of phenyl g l u c o s i d e s by e m ~ l s i n ~ ~ . Using r e g r e s s i o n a n a l y s i s , eq 10-13 are d e r i v e d t o i l l u s t r a t e how one can f a c t o r s u b s t i t u e n t e f f e c t s on a biochemical r e a c t i o n . P a r a Groups
Meta Groups
+ 0.331~+
l o g Ke = 0.52a
2.03
l o g Ke =
0.620
+
+ 1.63 0 . 1 2 ~+ 0.96 +
1.80
l o g Ke = 0.95a l o g Ke =
1.59
n = 8
r = 0.753
(10)
n = 8
r = 0.921
(11)
n = 6
r = 0.949
(12)
n = 6
r = 0.963
(13)
Ke r e p r e s e n t s t h e e q u i l i b r i u m c o n s t a n t € o r t h e enzyme s u b s t r a t e complex. Comparison of eq 10 and 11 f o r t h e p a r a d e r i v a t i v e s i n d i c a t e s t h a t complex formation depends on both e l e c t r o n i c and hydrophobic f a c t o r s . The c o r r e l a t i o n c o e f f i c i e n t i s much b e t t e r and s t a t i s t i c a l l y q u i t e s i g n i f i c a n t f o r eq 11. The p o s i t i v e s i g n s of t h e c o e f f i c i e n t s f o r IT and a i n d i c a t e t h a t l i p o p h i l i c and e l e c t r o n - a t t r a c t i n g groups promote complex formation. Comp a r i n g eq 12 and 13, one f i n d s t h a t f o r meta isomers hydrophobic bonding i s a p p a r e n t l y n o t p o s s i b l e . N o s i g n i f i c a n t improvement i n c o r r e l a t i o n res u l t s on t h e i n t r o d u c t i o n of t h e v term. A s i m i l a r set of e q u a t i o n s was d e r i v e d 5 6 t o show t h e s u b s t i t u e n t e f f e c t on t h e h y d r o l y s i s rate c o n s t a n t k3. Equally good c o r r e l a t i o n s were obtained except i n t h i s s t e p ; as one might e x p e c t , t h e c o e f f i c i e n t w i t h IT h a s a n e g a t i v e s i g n . T h i s i n d i c a t e s t h a t hydrophobic bonding slows down d e s o r p t i o n of t h e cleaved p r o d u c t s . S i n c e good c o r r e l a t i o n s w e r e o b t a i n e d i n eq 11 and 13 w i t h o u t t h e u s e of s t e r i c c o n s t a n t s , i t is assumed t h a t t h e s e are unimportant, a t least f o r f u n c t i o n s as l a r g e as t h o s e s t u d i e d . The meaning of t h e words s t e r i c and e l e c t r o n i c i n t h e s e d i s c u s s i o n s is somewhat ambiguous. For example, t h e l i n e a r r e l a t i o n s between parachor and t o x i c i t y found by McGowan o r t h e u s e of t h e s o l u b i l i t y parameter 6 by Mullins could b e viewed as i n d i c a t i n g a d i r e c t r e l a t i o n between t h e s i z e of t h e s u b s t i t u e n t and i t s a b i l i t y t o produce a g i v e n b i o l o g i c a l response. The a f f i n i t y of a n a p o l a r group f o r a l i p i d phase w i l l a l s o b e a f u n c t i o n
3 52
Sect. VI
-
Smi s sman, Ed.
T o p i c s in C h e m i s t r y
of i t s s i z e and, t o a lesser e x t e n t , i t s shape. Thus i t i s n o t always e a s y , even i n t h e a b s t r a c t , t o s e p a r a t e t h e b i n d i n g r o l e of hydrophobic bonding by an a p o l a r f u n c t i o n from i t s r o l e of d i s t o r t i n g a hydrophobic r e g i o n by i t s s i z e . We are a t t e m p t i n g t o u s e hydrophobic bonding as &f i n e d by p a r t i t i o n c o e f f i c i e n t s as s i m p l e h o l d i n g of t h e drug t o t h e act i v e s i t e , r e a l i z i n g t h a t o f t e n t h i s r o l e cannot be s e p a r a t e d from t h e c o n f o r m a t i o n a l change t h e a p o l a r group w i l l , i n t h e b i n d i n g p r o c e s s , produce i n an enzyme o r membrane.’ S t e r i c e f f e c t s , t h e n , a r e t h o s e due t o s i z e o r arrangement i n s p a c e of s u b s t i t u e n t s which cannot b e accounted f o r by t h e hydrophobic c o n s t a n t s l o g P and TI. These w i l l b e b o t h i n t r a - and i n t e r m o l e c u l a r i n n a t u r e . I n t h e same way, e l e c t r o n i c e f f e c t s w i l l overl a p w i t h hydrophobic bonding s i n c e t h e p o s i t i o n of e q u i l i b r i u m i n t h e d i s t r i b u t i o n of a drug between phases w i l l b e a f u n c t i o n of i t s e l e c t r o n i c s t r u c t u r e . Indeed, i t h a s been shown27 t h a t TI v a r i e s w i t h O . However, t h i s v a r i a n c e i s n o t g r e a t i f t h e s u b s t i t u e n t s a r e s e p a r a t e d by one o r more atoms. The term e l e c t r o n i c e f f e c t s means h i g h l y s p e c i f i c e f f e c t s i n g e n e r a l n o t a s s o c i a t e d w i t h t h e p a r t i t i o n i n g p r o c e s s . These would b e e f f e c t s involved i n a chemical r e a c t i o n o r charge t r a n s f e r p r o c e s s where a change i n e l e c t r o n d e n s i t y t o o small t o make a s i g n i f i c a n t d i f f e r e n c e i n l o g P could c a u s e a l a r g e change i n a r a t e o r e q u i l i b r i u m c o n s t a n t . Using t h e s e somewhat a r b i t r a r y d i v i s i o n s of s u b s t i t u e n t e f f e c t s and r e g r e s s i o n a n a l y s i s , a s t a r t can b e made i n s e p a r a t i n g t h e e f f e c t s of groups of atoms on t h e b i o l o g i c a l a c t i v i t y of a s e t of congeners. Hansch and co-workers have n o t , f o r example, a t t e m p t e d t o f a c t o r o u t hydrogen bonding. I n gene r a l t h e y have worked w i t h systems where t h i s could b e accounted f o r i n terms of o and IT. P u r c e l l e t a l . have s u g g e s t e d a way of d e a l i n g s p e c i f i c a l l y with t h i s t e r m 3 6 . I n a d d i t i o n t o many e a r l y examples1 , b i o l o g i c a l r e s p o n s e has been found t o be q u a n t i t a t i v e l y l i n e a r l y dependent on l o g P o r IT i n t h e i n h i b i t i o n of t h e H i l l r e a c t i o n 5 7 9 5 8 a c t i v i t y of p e n i c i l l i n s s 9 , t o x i c i t y of benz o i c a c i d s t o mosquito larvae28, phenol c o e f f i c i e n t s 2 8 , c h o l i n e s t e r a s e i n h i b i t o r, ~ and ~ ~ catechol-amine a c t i v i t y 6 0 .
Hernker61 w a s one of t h e f i r s t to a t t e m p t t h e q u a n t i t a t i v e c o r r e l a t i o n of b i o c h e m i c a l r e s p o n s e u s i n g b o t h p a r t i t i o n c o e f f i c i e n t s and i o n i z a t i o n c o n s t a n t s t o account f o r t h e uncoupling a c t i o n of p h e n o l s . The l i n e a r combination of TI and 0 h a s been found t o h o l d f o r s e v e r a l enzymic reaction^^^^^^ as w e l l as t h e b i n d i n g of phenols by p r o t e i n 5 5 , t h e t o x i c i t y of p h e n o l s 6 2 , t h e uncoupling a c t i o n of p h e n o l s 6 2 , and t h e r e l a t i v e sweetness of n i t r ~ a n i l i n e s ~ An ~ . i n t e r e s t i n g a p p l i c a t i o n i s t h a t of McMahon63. Equation 14 w a s formulated f o r t h e enzymic r e d u c t i o n of aromatic ketones t o alcohols. logVm,,
+
+
n = 10
r = 0.89
(14) O f c o u r s e t h e most i n t e r e s t i n g and d i f f i c u l t drug s t u d i e s a r e t h o s e i n which whole organisms a r e i n v o l v e d . It h a s been p o s t u l a t e d 6 4 t h a t i n g e n e r a l , f o r t h e s e s t u d i e s one would e x p e c t a p a r a b o l i c r e l a t i o n between ~ ~ 1~5 .~ l o g 1/C and l o g P. T h i s h a s l e d t o t h e d e ~ e l o p m e n tof~ eq =
0.334~
1.2390
0.824
l o g 1/C = - k ( l o g P ) 2
+
k‘logP
+
pa
+
k”
(15)
Chap. 34
Drug D e s i g n
Hansch
3 53
I n t h e development of t h i s model a p r o b a b i l i s t i c view i s t a k e n f o r movement of drug from t h e exobiophase o r p o i n t of i n j e c t i o n t o t h e s i t e s of a c t i o n . It i s assumed t h a t as P-to d r u g s become more and more i s o l a t e d i n t h e water phase and e v e n t u a l l y become u n a b l e t o c r o s s l i p i d b a r r i e r s . A s Pthe reverse is true. Somewhere between P=O and P=m t h e r e w i l l b e an i d e a l v a l u e (Po) f o r a g i v e n s e t of congeners i n a g i v e n b i o l o g i c a l systein s u c h t h a t t h o s e members having t h i s v a l u e w i l l f i n d t h e s i t e s of a c t i o n v i a a random walk p r o c e s s i n t h e minimum time. T h i s assumes s t e r i c and e l e c t r o n i c (pKa, e t c . ) f a c t o r s are c o n s t a n t . I n o t h e r words, a g r e a t e r number of molecules of drug w i t h Po would r e a c h t h e s i t e s of a c t i o n i n t h e t e s t i n t e r v a l t h a n d r u g s having o t h e r P v a l u e s . I n e f f e c t , one e x p e c t s a change i n t h e mechanism of movement i n a s e t of d r u g s h a v i n g a s u f f i c i e n t s p r e a d i n P v a l u e s . The movements of t h e lower members of t h e series w i l l b e mostly determined by i n t e r a c t i o n s w i t h water, w h i l e t h o s e of t h e h i g h e r members w i l l b e determined by hydrophobic i n t e r a c t i o n s w i t h l i p i d s . Such p a r a b o l i c r e l a t i o n s may even b e found i n c l o s e d systems of t h e t y p e used i n n a r c o s i s s t u d i e s . Ferguson66 h a s s t a t e d t h a t probably i n most e x p e r i ments on n a r c o s i s a complete e q u i l i b r i u m i s n e v e r r e a c h e d i n t h e p e r i o d of exposure and t h e r e s u l t s a r e t i m e dependent. R e s u l t s w i l l b e even more t i m e dependent i n open systems such as whole animals where e l i m i n a t i o n and b i o t r a n s f o r m a t i o n are c o n t i n u o u s p r o c e s s e s . Such r e s u l t s can even b e exp e c t e d i n t i s s u e experiments o r work w i t h p a r t i a l l y p u r i f i e d enzymes. S i n c e a c t i v i t y i s u s u a l l y e x p r e s s e d a s l o g 1 / C , t h e most a c t i v e compounds t e s t e d a r e o f t e n i n v e r y low c o n c e n t r a t i o n , sometimes less t h a n M. While l o g 1/C may b e l i n e a r w i t h r e s p e c t t o l o g P a t h i g h e r c o n c e n t r a t i o n s eq 6-8 i n d i c a t e t h a t h i g h l y l i p o p h i l i c m o l e c u l e s w i l l b e v e r y t i g h t l y bound t o p r o t e i n s s o t h a t t r u e e q u i l i b r i u m i s n o t reached i n t e s t t i m e . The lower t h e t e s t c o n c e n t r a t i o n s become, t h e more l i k e l y t h e d e p a r t u r e from l i n e a r i t y through l o c a l i z a t i o n of m o l e c u l e s i n p a r t i c u l a r l y l i p o p h i l i c material. Of c o u r s e t h e r e are r e a s o n s o t h e r t h a n b i n d i n g by l i p i d s o r p r o t e i n s which might c a u s e a d e p a r t u r e from l i n e a r i t y i n t h e r e l a t i o n s h i p of l o g 1 / C and l o g P o r TI. M e t a b o l i c o r e l i m i n a t i o n r e a c t i o n s n o t s i g n i f i c a n t a t low v a l u e s of l o g P c o u l d , w i t h i n c r e a s i n g l o g P , become v e r y i m p o r t a n t . A good example of t h i s i s i n t h e metabolism of a l k y l a r y l e t h e r i n r a b b i t s 67. I n (111) when R i s e t h y l o r m e t h y l , d e a l k y l a t i o n i s t h e main r e a c t i o n . When R i s p r o p y l o r b u t y l , w - 1 hydroxy l a t i o n becomes more i m p o r t a n t . S i n c e t h e r a t e of m e t a o/ bolism of drugs may b e l i n e a r l y r e l a t e d 6 8 t o l o g P , (111) t h i s may b e a n i m p o r t a n t c o n t r i b u t i n g f a c t o r f o r t h e bCH, p a r a b o l i c dependence of a c t i v i t y on l i p o p h i l i c charOR acter. Another unknown i s t h e l i p o p h i l i c s p a c e a t t h e s i t e of a c t i o n a v a i l a b l e f o r t h e hydrophobic moiety of t h e d r u g . I f t h i s i s q u i t e l i m i t e d , t h e n a p o i n t i s soon reached where l o g 1/C and l o g P a r e no l o n g e r l i n e a r l y a s s o c i a t e d . The p r o b a b i l i s t i c n a t u r e of t h e l o g P terms i n eq 15 does a good d e a l t o i n s u r e a r e a s o n a b l e f i t of a set of d a t a as long as i n d i v i d u a l congeners i n t h e set do n o t d e p a r t r a d i c a l l y from t h e b e h a v i o r of t h o s e having similar l i p o p h i l i c c h a r a c t e r . I n p r i n c i p l e , l o s s through metabolism o r e l i m i n a t i o n i s n o t d i f f e r e n t t h a n l o s s through b i n d i n g i f t h e s e l o s s e s depend o n l y on l o g P. Good r e s u l t s have
Po.
u c ‘7’
Sect. V I - T o p i c s i n C h e m i s t r y
3 54 -
Smi s sman, Ed.
been o b t a i n e d w i t h eq 15 f o r plant-growth regulator^^^ , chloromycetin anal o g (Garrett69 ~ ~ ~ and c o l l e a g u e s have found a more l i n e a r dependence of c h l o r o m y c e t i n a c t i v i t y under d i f f e r e n t test c o n d i t i o n s ) , t h y r o x i n e anal o g s 2 8 , phenol coef f i c i e n t s 2 8 , c a r c i n o g e n i c i t y of a r o m a t i c compounds2* , and t h e l o c a l i z a t i o n of benzeneboronic a c i d s i n b r a i n and tumor t i s s u e 7 ( ] .
A c o n s t a n t which may prove t o b e v e r y u s e f u l i n drug d e s i g n i s l o g Po ( o r no). T h i s f i g u r e can b e found by t a k i n g t h e p a r t i a l d e r i v a t i v e of eq 1 5 and s e t t i n g t h i s e q u a l t o z e r o . Once t h i s h a s been e s t a b l i s h e d f o r a set of d r u g s , i t becomes a u s e f u l bench mark from which t o s t a r t t h e des i g n of a completely new drug t o a c t on t h e same sites. For example, i t w a s found t h a t l o g Po f o r phenoxyacetic a c i d s a c t i n g as plant-growth regul a t o r s i s 2.03. Log Po f o r p h e n y l a c e t i c a c i d s a c t i n g i n t h e same system i s 2.47. I f one wished t o d e s i g n a new a c i d t o a c t i n t h i s system, one of t h e f e a t u r e s which one would d e s i g n i n t o t h e f i r s t test m o l e c u l e would b e l o g P of about 2.2. By means of t h e a d d i t i v e - c o n s t i t u t i v e c h a r a c t e r of l o g P one could d e s i g n s u c h compounds on p a p e r w i t h o u t c a r r y i n g o u t extensive partition coefficient studies. While s u i t a b l e t e c h n i q u e s t o h a n d l e s t e r i c e f /@\/OTzEt f e c t s between s u b s t r a t e and t h e material comprising (IV) t h e s i t e s of a c t i o n are a t p r e s e n t o u t of r e a c h , intramolecular s t e r i c i n t e r a c t i o n s can be handled q u a n t i t a t i v e l y , a t least i n some i n s t a n c e s u s i n g T a f t ' s E, parameter22,56. Equations 16 and 1 7 , f o r m u l a t e d from t h e work of Metcalf and Fukuto c o r r e l a t e 2 2 s u b s t i t u e n t e f f e c t s of R i n (IV) on t h e i n h i b i t i o n of c h o l i n e s t e r a s e by a l k y l p h o s p h o n i c a c i d esters.
'./
0 1
ozd
l o g K = 3.74 E, l o g K = -1.680*
+ 7.54 + 0.1511 + 4.05
E,
+
7.21
n = 13
r = 0.901
(16)
n = 13
r = 0.907
(17)
Comparison of eq 1 6 and 1 7 i n d i c a t e s t h a t n e i t h e r e l e c t r o n i c nor hydrophobic f a c t o r s p l a y a n i m p o r t a n t p a r t i n t h e i n h i b i t i o n . Thus i t a p p e a r s t h a t t h e phosphonates i n t e r a c t w i t h t h e enzyme i n such a way t h a t t h e y cannot come i n c o n t a c t w i t h a hydrophobic r e g i o n of t h e p r o t e i n . The .k r a n g e of e l e c t r o n i c f o r c e s covered by t h e R groups w a s s m a l l so t h a t u may b e more i m p o r t a n t t h a n eq 17 would i n d i c a t e . Some o v e r l a p between E, The f a c t t h a t Es, a and o* c o n s t a n t s t e n d s t o o b s c u r e t h e r o l e of u*. c o n s t a n t d e r i v e d from h y d r o l y s i s s t u d i e s under homogeneous c o n d i t i o n s , should a p p l y t o heterogeneous c a t a l y s i s i s s u r p r i s i n g and i n d i c a t e s much more u s e f o r t h i s parameter t h a n one would have had r e a s o n t o e x p e c t . Another method f o r o b t a i n i n g biochemical s u b s t i t u e n t c o n s t a n t s i s Considerable e f f o r t 7 ' a v a i l a b l e i n t h e v a r i o u s forms of chromatography. 7 3 h a s been made t o g a t h e r and A% v a l u e s f o r t h e e f f e c t of s u b s t i t u e n t s on
RF .
%
A%=%$-\
%
I n eq 18, R M ~i s c a l c u l a t e d from t h e v a l u e of a p a r e n t compound and Rp from t h a t of a d e r i v a t i v e having s u b s t i t u e n t X. ARM i s a c o n s t a n t a n a l o gous t o II and i n f a c t a c l o s e c o r r e l a t i o n e x i s t s between t h e two as i s
Hansch
Drug Design
Chap. 34 shown1 i n eq 19.
= -l.l03AR,
+
0.647
r = 0.970
n = 12
355 -
(19)
I n measuring t h e A R M v a l u e s i n eq 1 9 , Green and M a r c i n k i e w i ~ z ~used l trig o 1 and d i i s o p r o p y l e t h e r i n reversed-phased, t a n k l e s s f l a t - b e d chroma~ ~ shown t h a t % v a l u e s c o r r e l a t e t h e tography. Boyce and M i l b ~ r r o whave m o l l u s c i c i d a l a c t i v i t y of a series of N - n - a l k y l t r i t y l a m i n e s assuming a p a r a b o l i c r e a c t i o n e x i s t s between l o g LD50 and %. Thus RM o r ARM v a l u e s can b e used i n eq 1 5 i n p l a c e of l o g P o r 1 ~ . C o n s i d e r a b l e e f f o r t 3 5 s75-*O h a s been made t o understand biochemic a l and pharmacological problems u s i n g quantum mechanical c a l c u l a t i o n s of e l e c t r o n d e n s i t i e s w i t h molecules. While t h i s h a s been u s e f u l i n exp l a i n i n g how a p a r t i c u l a r bond i s broken o r made75, l i n e a r r e l a t i o n s between c a l c u l a t e d e l e c t r o n d e n s i t i e s and b i o l o g i c a l a c t i v i t y are n o t a b l y l a c k i n g . An e x c e p t i o n coming from t h e work of Fukui i s i l l u s t r a t e d i n eq 20 and 2 1 which cprrelate t h e n i c o t i n e - l i k e a c t i v i t y of m e t a d e r i v a t i v e s of C6H50CH2CH2N(CH3)3 w i t h t h e s u p e r d e l o c a l i z a b i l i t y ( S o ( N 3 ) of e l e c t r o n s a t t h e o r t h o p o s i t i o n and t h e f r o n t i e r e l e c t r o n d e n s i t y (f6:;) on t h e e t h e r oxygen. logA = 13.742 So(4 logA = 30.392 f ( E ) OXY
- 10.465 - 20.924
n = 6
r = 0.994
(20)
n = 6
r = 0.949
(21)
The combination of such e l e c t r o n i c d e n s i t i e s w i t h a hydrophobic bonding c o n s t a n t does y i e l d good r e s u l t s 2 8 , 5 6 as i l l ~ s t r a t e dby~ ~eq 22 and 23. log% = 2 2 . 9 1 ~ - 42.49
log% = 0 . 2 9 ~+ 18.166.
-
33.82
n = 6
r
0.685
(22)
n = 6
r = 0.995
(23)
=
I n t h e above e q u a t i o n s Ax, from t h e work of Jacobson, r e p r e s e n t s t h e relat i v e rates of a c y l a t i o n of a r o m a t i c amines having s u b s t i t u e n t s X by means of pigeon l i v e r a c e t y l t r a n s f e r a s e . E r e p r e s e n t s t h e c a l c u l a t e d e l e c t r o n d e n s i t i e s on t h e n i t r o g e n atom made by P e r a u l t and Pullman. Equation 22 a c c o u n t s f o r o n l y 47% of t h e v a r i a n c e i n t h e d a t a w h i l e eq 23 a c c o u n t s f o r 99%. Thus i t a p p e a r s t h a t quantum m e c h a n i c a l l y o b t a i n e d e l e c t r o n d e n s i t i e s can b e e x t r e m e l y u s e f u l t o t h e m e d i c i n a l c h e m i s t . I n t h i s way t h e r e l a t i v e e l e c t r o n d e n s i t y on each atom i n t h e m o l e c u l e can b e found and through r e g r e s s i o n a n a l y s i s t h e r e l a t i v e importance of t h i s d e n s i t y a t one o r p o i n t s i n t h e m o l e c u l e c a n b e e v a l u a t e d . T h i s approach o f f e r s , i n p r i n c i p l e , a g r e a t advantage o v e r t h e u s e of u . What a r e t h e g u i d e l i n e s t h a t s u b s t i t u e n t o f f e r t h e d e s i g n e r of d r u g s ? The g r e a t s u c c e s s geneous o r g a n i c r e a c t i o n s 1 * and t h e more modest method w i t h heterogeneous b i o c h e m i c a l r e a c t i o n s t h e u s e of eq 24 and 25 as a r e a s o n a b l e working
constant analysis has t o of t h i s method i n homoachievements of t h i s would s e e m t o v a l i d a t e hypothesis.
I n eq 24 w e are assuming5' t h a t t h e u l t i m a t e l y measured b i o l o g i c a l response ( t o x i c i t y , r e s i s t a n c e t o a m e t a b o l i c p r o c e s s , E D 5 0 , e l i m i n a t i o n ,
356
Sect. VI
-
T o p i c s in C h e m i s t r y
Smi s sman, Ed.
e t c . ) i s governed by one r a t e - l i m i t i n g p r o c e s s f o r which kgR i s a r a t e o r equilibrium constant. i n eq 2 4 , mt/H r e p r e s e n t s t h a t p o r t i o n of t h e f r e e energy change which can be a t t r i b u t e d t o hydrophobic bonding, AFglect Tepr e s e n t s a n e l e c t r o n i c component, and AFzteric r e p r e s e n t s h i g h l y s p e c i f i c s p a t i a l demands of r e a c t a n t s and p r o d u c t s on t h e f r e e energy change. Of c o u r s e , were s u f f i c i e n t d a t a a v a i l a b l e , one might p r o f i t a b l y f a c t o r each of t h e terms i n eq 2 4 and 25 i n t o s e v e r a l t o r e p r e s e n t s u s p e c t e d c r i t i c a l p a r t s of a molecule. S u b s t i t u e n t e f f e c t s on l o g kgR of eq 24 are r e p r e s e n t e d i n eq 2 5 .
E q u a t i o n s 24 and 25 w e r e formulated f o r t h e c a s e where t h e drug is a t t h e s i t e of a c t i o n o r t h e s i t u a t i o n where t r u e e q u i l i b r i u m w i t h t h e exobiophase i s e s t a b l i s h e d a s envisaged by Ferguson. From t h e p r e s e n t l i m i t e d work i t would appear t h a t 'XXFi/H might be r e p r e s e n t e d by l o g P , T I ,%, ARM, B (Zahradnik15) and, under c e r t a i n cond i t i o n s p a r a c h o r . The 6xF~1ec term may be r e p r e s e n t e d u s i n g t h e v a r i o u s forms "'of (5, quantum m e c h a n i c a i l y c a l c u l a t e d e l e c t r o n d e n s i t i e s o r chemic a l s h i f t s ' ' o b t a i n e d v i a NMR. I t should a l s o b e p o s s i b l e t o f o r m u l a t e s u i t a b l e c o n s t a n t s from I R and UV s p e c t r a . Attempts t o u s e polarographi c a l l - o b t a i n e d c o n s t a n t s do n o t seem t o b e as u s e f u l as one might expect' 5 , 8 3
.
The c a s e where s u b s t i t u e n t changes r e s u l t i n l a r g e d i f f e r e n c e s i n i o n i z a t i o n i s one of g r e a t importance s i n c e s o many d r u g s are e i t h e r weak a c i d s o r weak b a s e s . The d e g r e e of i o n i z a t i o n h a s long been r e c o n i z e d as has p l a y i n g a p a r t i n drug a c t i v i t y 8 4 . I n a c a r e f u l a n a l y s i s , F u j i t a " shown how s u b s t i t u e n t e f f e c t s on i o n i z a t i o n should be s e p a r a t e d from o t h e r e l e c t r o n i c e f f e c t s of s u b s t i t u e n t s .
It does n o t seem p o s s i b l e t o make any g e n e r a l o b s e r v a t i o n s about s u i t a b l e ways of r e p r e s e n t i n g 6XF&eric f o r t h e i n t e r a c t i o n s between a drug and i t s r e c e p t o r s . By c o n s i d e r i n g se ts of congeners i n which g r o s s s t e r i c changes a r e avoided ( e . g . , c o n s i d e r i n g D isomers s e p a r a t e l y from L i s o m e r s , e t c . ) u s e f u l c o r r e l a t i o n s can b e made. I n f a c t , where t h e twoparameter e q u a t i o n c a n be shown t o h o l d o v e r a r e a s o n a b l e r a n g e of subs t i t u e n t s , one c a n make d e d u c t i o n s about GXFEteric by c o n t i n u i n g t o i n crease t h e s i z e of X u n t i l t h e two-parameter e q u a t i o n f a i l s . I n t h i s way one c a n , t o a l i m i t e d e x t e n t , map t h e f r e e s p a c e around a r e c e p t o r s i t e . P ~ r t o g h e s e ~ ~i n- ~a n~ e, x t e n s i o n of t h e approach of Zahradnik, h a s shown t h a t l i n e a r r e l a t i o n s h i p s between d i f f e r e n t c o n g e n e r i c s e t s of a n a l g e s i c s can b e used t o make more f i r m d e c i s i o n s about whether t h e sets are a c t i n g i n t h e same three-dimensional way on t h e s a m e receptors. The t h r e e sets of congeners i n which R of V w a s h e l d c o n s t a n t ( i . e . , 1. R' = C O z E t , 2 . R' = O C O E t and 3. R' = OCOCH3) were v a r i e d by changes i n R. Least s q u a r e f i t s of sets 1 v s . 2 , 1 v s . 3 , and 3 v s . 2 gave
/\. 1
( V>
I
4.
\
t P' i
/t t
'w' A
Chap. 3 4
Hansch
Drug Design
3 57 -
s l o p e s c l o s e t o 1 w i t h good c o r r e l a t i o n c o e f f i c i e n t s . Such tests can be used t o h e l p e s t a b l i s h t h e f a c t t h a t , f o r example, R i n each series is i n t h e same p h y s i c o t h e m i c a l environment on t h e r e c e p t o r s . By e x p l o r i n g a l a r g e enough number of sets of s y s t e m a t i c a l l y v a r i e d congeners one could o b t a i n c o n s i d e r a b l e i n f o r m a t i o n about t h e geometry of t h e r e c e p t o r s i t e s . The f a c t t h a t simply changing t h e l e n g t h of R can l e a d t o a complete change i n t h e mechanism of a c t i o n ( e . g . , a g o n i s t t o a n t a g o n i s t ) h a s been thoroughly documented by AriEnsB8. A c a r e f u l case s t u d y i n which t h e ent h a l p i c and e n t r o p i c r o l e s of t h e s u b s t i t u e n t s i n t r a n s i t i o n from a g o n i s t t o a n t a g o n i s t have been c o n s i d e r e d h a s been made by B e l l e a u , T a n i and L i e B 9 . Miller and HanschZ5 have p r e s e n t e d e v i d e n c e t o show t h a t when two hydrophobic areas are p r e s e n t i n a drug and o n l y a l i m i t e d s p a c e f o r hydrophobic bonding e x i s t s i n an enzyme, t h e more hydrophobic of t h e two groups may determine t h e c o n f i g u r a t i o n of b i n d i n g . Thus s t e r i c i n t e r a c t i o n s of r e c e p t o r s i t e and s u b s t r a t e are extremely d i f f i c u l t t o e v a l u a t e . The c o n f o r m a t i o n a l p e r t u r b a t i o n s of drug on r e c e p t o r r e c e p t o r on drug w i l l t a x t o t h e l i m i t o u r a b i l i t y t o unt a n g l e t h e mechanism of drug a c t i o n f o r many y e a r s t o come. However, t h e u s e of s u b s t i t u e n t c o n s t a n t s and l a r g e computers f o r r e g r e s s i o n a n a l y s i s o f f e r s u s new hope denied workers a few y e a r s ago. References
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
J . I w a s a , T. F u j i t a and C. Hansch, J . Med. Chem., 8, 1 5 0 ( 1 9 6 5 ) . J . Ferguson, P r o c . Roy. S O C . , 387 ( 1 9 3 9 ) . J . Ferguson, "Mecanisme D e L a Narcose," C e n t r e N a t i o n a l d e l a Recherche S c i e n t i f i q u e , P a r i s , 1 9 5 0 , p 25. F. Brink and J . M. P o s t e r n a k , J . C e l l . Comp. P h y s i o l . , 32, 2 1 1 ( 1 9 4 8 ) . J . C. McGowan, J . Appl. Chem., 1,1 2 0 5 ( 1 9 5 1 ) . J. C. McGowan, J . Appl. Chem., 4, 4 1 ( 1 9 5 4 ) . J . C. McGowan, N a t u r e , 200, 1 3 1 7 ( 1 9 6 3 ) . J . C. McGowan, J . Appl. Chem., l6, 103 ( 1 9 6 6 ) . L. J . M u l l i n s , Chem. Rev., 54, 289 ( 1 9 5 4 ) . L. P a u l i n g , S c i e n c e , 15 ( 1 9 6 1 ) . S . L. Miller, P r o c . NatLAcad. S c i . , 1515 ( 1 9 6 1 ) . K. W. Miller, W. D. M. Paton and E. G . Smith, N a t u r e , 206, 574 ( 1 9 6 5 ) . I . R. F e n i c h e l and S . B. Horowitz, S c i e n c e , 152, 1110 ( 1 9 6 6 ) . D. Agin, L . Hersh and D. Holtzman, P r o c . N a t l . Acad. S c i . , 53, 952
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Sect. VI - T o p i c s i n C h e m i s t r y
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E. W. Deutsch and C. Hansch, N a t u r e , 2,7 5 ( 1 9 6 6 ) . C. Hansch, P r o c . I n t . Cong. Pharmacol., Sao P a u l o , 1 9 6 6 . E. M i l l e r and C. Hansch, J . Pharm. S c i . , 56, 92 ( 1 9 6 7 ) . C. C i l e n t o and M. Berenholc, Biochim. Biophys. Acta, 94, 2 7 1 ( 1 9 6 5 ) . T. F u j i t a , J . I w a s a and C. Hansch, J . Am. Chem. Soc., 86, 5175 ( 1 9 6 4 ) . C. Hansch and T. F u j i t a , J . Am. Chem. Soc., 86, 1 6 1 6 ( 1 9 6 4 ) . E . C. J o r g e n s e n and J . W. Reid, J . Med. Chem., 8, 533 ( 1 9 6 5 ) . J . Kopeck? and K. Bozek, E x p e r i e n t i a , 23, 1 2 5 ( 1 9 6 7 ) . K. BoEek, J. Kopeck?, M. Krivucova and V . Vlachova, Experimentia, 20, 667 ( 1 9 6 4 ) . J . Kopeck?, K. Bogek and D. Vlachova, Nature, 207, 9 8 1 ( 1 9 6 5 ) . S . I . M i l l e r , J . Am. Chem. SOC., 8l, 101 ( 1 9 5 9 ) . W. P . P u r c e l l , Biochim. Biophys. Acta, 105,2 0 1 ( 1 9 6 5 ) . W . P. P u r c e l l , J . Med. Chem., 9, 294 ( 1 9 6 6 ) . W . P. P u r c e l l , J . G. Beasley, R . P. Quintana and J . A. S i n g e r , J . Med. Chem. , 9, 297 ( 1 9 6 6 ) . L. P. Hamett, " P h y s i c a l Organic Chemistry,'' McGraw-Hill, New York, N.Y. , 1 9 4 0 . Y. Yukawa, Y . Tsuno and M. Sawada, B u l l . Chem. SOC. J a p . , 39, 2274 (1966). K. S . Dodgson, B. Spencer and K. W i l l i a m s , Biochem. J . , 64, 216 (1956). T. Ingami, S . S. York and A . P a t c h o r n i k , J . Am. Chem. SOC., 87, 126 (1965). M. Caplow and W. P. J e n c k s , Biochemistry, L, 883 ( 1 9 6 2 ) . R. A. D e i t r i c h , L. Hellerman and J . Wein, J . B i o l . Chem., 237, 560 (1961). R. L. Nath and H. N. Rydon, Biochem. J . , 57, 1 ( 1 9 5 4 ) . 0 . Gawron, C. J . G r e l e c k i and M. Duggan, Arch. Biochim. Biophys., 44, 455 ( 1 9 5 3 ) . R. Hanson, Acta Chem. Scand., l6, 1 5 9 3 ( 1 9 6 2 ) . R. L. Metcalf and T. R. Fukuto, J . Econ. Entomol., 55, 340 ( 1 9 6 2 ) . P . Hey, B r i t . J . Pharmacol., 1,117 ( 1 9 5 2 ) . T. C. B r u i c e and S . J . Benkovic, "Bioorganic Mechanisms," Vol. I , W.A. Benjamin Co., New York, N . Y . , 1 9 6 6 , p 1 9 . D. E. Koshland, Cold S p r i n g Harbor Symposia on Q u a n t i t a t i v e Biology, 2 7 , 473 ( 1 9 6 3 ) . J . Monod, J . Wyman and J . Changeux, J . Mol. B i o l . , l2, 8 8 ( 1 9 6 5 ) . B. B e l l e a u , J . Med. Chem. , 7 , 7 7 6 ( 1 9 6 4 ) . W. Kauzmann, Advan. P r o t e i n Chem., l 4 . , 37 ( 1 9 5 9 ) . D. J . C u r r i e , C. E. Lough, R. F. S i l v e r and H. L . Holmes, Can. J . Chem., 44, 1 0 3 5 ( 1 9 6 6 ) . P . Bracha and R. D. O'Brien, J . Econ. Entomol., 2,1255 ( 1 9 6 6 ) . C. Hansch, K. Kiehs and G . L. Lawrence, J . Am. Chem. S O C . , 87, 5770 (1965). C. Hansch, E . W . Deutsch and R. N . Smith, 3 . Am. Chem. Soc., 87, 2738 (1965) C. Hansch and E . W. Deutsch, Biochim. Biophys. Acta, 112, 3 8 1 ( 1 9 6 6 ) . K. H. Biichel, W. Draber, A . T r e b s t and E . P i s t o r i u s , Z e i t . Naturf o r s c h . , 21, 243 ( 1 9 6 6 ) . C . Hansch and E . W. Deutsch, J . Med. Chem., 8, 705 ( 1 9 6 5 ) . P . P r a t e s i , P r o c . I n t . Congress Pharmacol., Sao P a u l o , 1 9 6 6 .
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H. C. Hemker, Biochim. Biophys. A c t a , 63, 46 ( 1 9 6 2 ) . T . F u j i t a , J . Med. Chem., 2, 797 (1966). R. E . McMahon, H. W. Culp and M. M. Marsh, 149th N a t i o n a l Meeting of t h e American Chemical S o c i e t y , A t l a n t i c C i t y , N . J . , September, 1965. C. Hansch, A. R . S t e w a r d , J . Iwasa and E . W. Deutsch, Mol. Pharmacol., -1, 205 (1965). C. Hansch, R. M. Muir, T. F u j i t a , P. P. Maloney, F. G e i g e r and M. S t r e i c h , J . Am. Chem. S o c . , 85, 2817 (1963). J . Ferguson, Chem. I n c . , 1964,818. H . Yoshimura, H. T s u j i and H. Tsukamoto, Chem. Pharm. B u l l . , l4, 939 (1966). C. Hansch, A. R. Steward and J . I w a s a , J . Med. Chem., 8, 868 (1965). E . R. Garrett, 0. K. Wright, G. H. Miller and K. L . Smith, J . Med. Chem., 2, 203 (1966). C. Hansch, A. R. Steward and J . Iwasa, Mol. Pharmacol., 1,8 7 (1965). J. Green and S. Marcinkiewicz, J . Chromatog., 10,389 (1963). L. S. Bark and R. J . T. Graham, T a l a n t a , 13,1281 (1966). L. S. Bark and R. J . T. Graham, J . Chromatog., 23, 417 (1966). C. B. C. Boyce and B. V. Milborrow, N a t u r e , 208, 537 (1965). B. Pullman and A. Pullman, "Quantum B i o c h e m i s t r y , " I n t e r s c i e n c e P u b l i s h e r s , New York, N . Y . , 1963. B. Pullman, " E l e c t r o n i c A s p e c t s of B i o c h e m i s t r y ,I' Academic P r e s s , 1964, p 559. K. Fukui, K. Morokuma, C. Nagata and A. Imamura, B u l l . Chem. SOC. J a p a n , 34, 1224 (1961). K. Fukui, C. Nagata and A. Imamura, S c i e n c e , 132, 87 (1960). A. Szent-Gyorgyi, " I n t r o d u c t i o n t o a Submolecular B i o l o g y , " Academic P r e s s , New York, N.Y., 1960. F. Yoneda and Y . N i t t a , Chem. Pharm. B u l l . , l3, 574 ( 1 9 6 5 ) . R. W. T a f t , E . P r i c e , I. R. Fox, I. C. Lewis, K. K. Anderson and G. T. Davis, J . Am. Chem. S o c . , 85, 3146 (1963). E. R. Garrett and A. G . Cosimano, J . Pharm. S c i . , 55, 702 (1966). L. G . P a l e g and R. Muir, P l a n t P h y s i o l . , 27, 285 (1952). A. A l b e r t , "Selective T o x i c i t y , " J o h n Wiley & Sons, New York, N.Y., 3 r d Ed., 1965, p 178. P. S. P o r t o g h e s e , J . Pharm. S c i . , 54, 1079 ( 1 9 6 5 ) . P. S. P o r t o g h e s e and T. N . R i l e y , J . Pharm. S c i . , 54, 1 8 3 1 (1965). P. S . P o r t o g h e s e , J . Med. Chem., 8, 609 (1965). E. J . AriEns, "Molecular Pharmacology," Vol. 1, Sec. 11, Academic P r e s s , N e w York, N . Y . , 1964. B. B e l l e a u , H. T a n i and F. L i e , J . Am. Chem. Soc., 87, 2283 ( 1 9 6 5 ) .
Chapter 34. The U s e of S u b s t i t u e n t C o n s t a n t s i n Drug Design Corwin Hansch, Pomona C o l l e g e , Claremont, C a l i f o r n i a The s u b j e c t of s t r u c t u r e - a c t i v i t y r e l a t i o n s i n m e d i c i n a l chemistry is almost boundless. Few p a p e r s a r e now published without some d i s c u s s i o n of t h i s problem. The work considered i n t h i s review i s l i m i t e d t o t h a t concerned w i t h mathematical c o r r e l a t i o n s between s t r u c t u r e and activity. The u s e of physical-chemical r e f e r e n c e systems t o s e r v e a s scales w i t h which one could d i s c u s s i n q u a n t i t a t i v e t e r m s t h e r e l a t i o n between b i o l o g i c a l a c t i v i t y and chemical s t r u c t u r e e x c i t e d g r e a t i n t e r e s t a t t h e t u r n of t h e c e n t u r y . C. R i c h e t , J . Traube, H . Fiihner and e s p e c i a l l y H . Meyer and E. Overton gave t h r u s t t o t h i s movement. It was observed, almost e n t i r e l y i n a l i p h a t i c systems, t h a t as one i n c r e a s e d t h e c h a i n l e n g t h i n a homologous series a r e g u l a r i n c r e a s e i n a s t a n d a r d b i o l o g i c a l response o c c u r r e d . L i n e a r r e l a t i o n s between a s t a n d a r d r e s p o n s e and t h e number of carbon atoms i n t h e c h a i n , w a t e r s o l u b i l i t y , s u r f a c e t e n s i o n lowering a b i l i t y , vapor p r e s s u r e and o i l - w a t e r p a r t i t i o n c o e f f i c i e n t s were o f t e n found i n many d i f f e r e n t tests. An example of t h i s t y p e of c o r r e l a t i o n u s i n g p a r t i t i o n c o e f f i c i e n t s coming from t h e work of Overton is : l o g 1 / C = 0.858 logP
+
0.837
n = 28
r = 0.978
(1)
I n eq 1, C r e p r e s e n t s t h e molar c o n c e n t r a t i o n of v a r i o u s a l c o h o l s , k e t o n e s and esters producing i s o n a r c o s i s i n t a d p o l e s , P i s t h e octanol-water part i t i o n c o e f f i c i e n t , n i s t h e number of d a t a used i n f i n d i n g t h e c o n s t a n t s v i a t h e method of least s q u a r e s , and r i s t h e c o r r e l a t i o n c o e f f i c i e n t . The c o n s t a n t s i n eq 1 are s l i g h t l y d i f f e r e n t from t h o s e published' and t h e c o r r e l a t i o n is a l i t t l e b e t t e r because of t h e u s e of imprpved P v a l u e s . An important advance w a s made by Ferguson2y3 who showed t h a t t h e following generalization holds. ci = kAi l / n
I n eq 2 , Ci is t h e c o n c e n t r a t i o n of t h e ithmember of a series producing a n e q u i v a l e n t response, k and n are t h e c o n s t a n t s , and A. i s a p h y s i c a l 1 chemical d i s t r i b u t i o n c o n s t a n t of t h e above mentioned k i n d . Ferguson p o i n t e d o u t t h a t f o r n o n s p e c i f i c n a r c o t i c s i n s t a t e s of e q u i l i b r i u m , biol o g i c a l a c t i v i t y i s r e l a t e d t o thermodynamic a c t i v i t y . Ferguson's approach was extended by Brink and Post-._-nak4 and i t i s now e v i d e n t t h a t t h e r e a r e many i n s t a n c e s where e q u a l d e g r e e s of n a r c o s i s a r e caused by molecules having e q u a l thermodynamic a c t i v i t i e s . Other approaches t o e x p l a i n i n g t h e e f f e c t of n a r c o t i c a c t i v i t y i n terms of physical-chemical - ~ Mullinsg McGowan u s i n g parachor parameters are t h o s e of M c G ~ w a n ~and and Mullins u s i n g H i l d e b r a n d ' s s o l u b i l i t y parameter and m o l a l volume, have
.
3 48 -
Sect. VI
-
Topics in C h e m i s t r y
S m i s sman, Ed.
assembled e v i d e n c e t o s u p p o r t t h e view t h a t t h e m o l e c u l a r volume of t h e n a r c o t i c is of c r i t i c a l importance i n d e t e r m i n i n g n a r c o s i s . PaulinglO and Miller'' have s u g g e s t e d t h a t a n e s t h e t i c potency i s r e l a t e d t o t h e a b i l i t y of a n e s t h e t i c s t o form h y d r a t e s . M i l l e r , Paton and Smith' and o t h e r s have c r i t i c i z e d t h e Pauling-Miller view. Agin, Hersh and Holtzman14 have shown t h a t eq 3 g i v e s an e x c e l l e n t c o r r e l a t i o n f o r t h e r e l a t i o n between minimum b l o c k i n g c o n c e n t r a t i o n (MBC) of 3 9 l o c a l a n e s t h e t i c s i n f r o g s a r t o r i u s muscle w i t h p o l a r i z a b i l i t y (a) and t h e i o n i z a t i o n p o t e n t i a l (I) of t h e d r u g s . Zahradnik15, i n a s y s t e m a t i c s t u d y u s i n g mice and c a r e f u l l y cont r o l l e d c o n d i t i o n s , developed a set of c o n s t a n t s f o r a l k y l groups from t h e l i n e a r Hammett-like p o s t u l a t e thattftog (T./T,,) = aB where T r e p r e 1 s e n t s t h e molar c o n c e n t r a t i o n of t h e i member of a set of a l i p k a t i c cong e n e r s producing a s t a n d a r d b i o l o g i c a l r e s p o n s e and T~~ i s t h e concentrat i o n of t h e e t h y l d e r i v a t i v e . 6 i s a c o n s t a n t c h a r a c t e r i s t i c of t h e subs t i t u e n t ( R of RX) and a i s a c o n s t a n t c h a r a c t e r i s t i c of t h e system. The c o n s t a n t B w a s determined f o r 25 R groups and a w a s e v a l u a t e d f o r 39 d i f f e r e n t b i o l o g i c a l systems. While t h i s s i n g l e parameter approach works w e l l f o r i n h i b i t o r y s t u d i e s of homologous groups of a l i p h a t i c compounds where h i g h l y s p e c i f i c e l e c t r o n i c and s t e r i c e f f e c t s are n o t c r i t i c a l , i t h a s n o t been extended t o more complex systems. The above i d e a s have provided i n s i g h t i n t o n o n s p e c i f i c b i o l o g i c a l i n h i b i t i o n s ; however, t h i s knowledge h a s n o t been of g r e a t h e l p i n t h e des i g n and m o d i f i c a t i o n of d r u g s of h i g h s p e c i f i c i t y . Two approaches have been emerging i n r e c e n t y e a r s t o supplement t h e m e d i c i n a l c h e m i s t s ' i n t u i t i o n on t h e e f f e c t of s u b s t i t u e n t v a r i a t i o n on drug a c t i v i t y . I n one aproach de novo s u b s t i t u e n t c o n s t a n t s have been d e r i v e d by simply f i n d i n g t h e " b e s t numbers'' t o go w i t h g i v e n s u b s t i t u e n t s on a p a r t i c u l a r drug a c t i n g i n a s t a n d a r d t e s t . The o t h e r approach h a s used s u b s t i t u e n t cons t a n t s d e r i v e d from model n o n b i o l o g i c a l systems. The f i r s t work on t h e former of t h e s e two t r a c k s a p p e a r s t o b e t h a t of B r u i c e , Kharasch and Winzlerl working w i t h t h y r o x i n e d e r i v a t i v e s . T h e i r ,approach has been s t a t e d i n more g e n e r a l terms by F r e e and Wilson17. The method can b e ill u s t r a t e d w i t h t h e i r example f o r a s e t of t e t r a c y c l i n e (I) a n a l o g s . The r e l a t i v e b i o l o g i c a l a c t i v i t y f o r each d e r i v a t i v e c a n be formulated a s t h e l i n e a r combination of t h e c o n t r i b u t i o n of each of t h e groups r e p r e s e n t e d by X , Y and R: Biological a c t i v i t y = p
+
a[X.] 1
+ c[Ril
+
bEY.1 1
(1)
One can w r i t e a set of s i m u l t a n e o u s e q u a t i o n s , one f o r each compound t e s t e d , t h e s o l u t i o n of which g i v e s t h e c o n t r i b u t i o n t o t h e a c t i v i t y f o r each a [ X i ] , e t c . T a b l e I l i s t s t h e r e s u l t s f o r t h e t e t r a c y c l i n e s .
Table I X
R
a[Hl a[CH3]
75
b[C11
84
-112
b[Brl
-16
349 -
Hansch
Drug Design
Chap. 3 4
Y
c “Hz
I
123 18
c [ CH3CONHI
!J =
161
-218 Of t h e t o t a l of 1 8 p o s s i b l e d e r i v a t i v e s r e s u l t i n g from d i f f e r e n t combinat i o n s of R, X and Y , 10 had been t e s t e d . Presumably, a c t i v i t i e s f o r t h e o t h e r e i g h t can b e c a l c u l a t e d from t h e s u b s t i t u e n t c o n s t a n t s i n T a b l e I . The method i s of g r e a t e s t v a l u e when a l a r g e group of d e r i v a t i v e s and f u n c t i o n s i s i n v o l v e d . There a r e of c o u r s e many o b j e c t i o n s t h a t come t o mind i n c o n s i d e r i n g t h e above t e c h n i q u e . Modern c h e m i s t r y h a s l o n g recognized t h e g r e a t importance of s t e r i c and e l e c t r o n i c e f f e c t s of s u b s t i t u e n t s on r a t e and e q u i l i b r i u m p r o c e s s e s 1 8 . From t h e Meyer-Overton work and from more r e c e n t t h e hydrophobic bonding power of funct i o n a l groups i s s e e n t o b e a v e r y i m p o r t a n t s u b s t i t u e n t e f f e c t . These t h r e e e f f e c t s a r e lumped i n t o each of t h e c o n s t a n t s under R, X and Y of T a b l e I . Hence i t would seem t h a t i n g e n e r a l , c o n s t a n t s d e r i v e d f o r one s e t of congeners w i l l n o t b e u s e f u l f o r a n o t h e r set c a u s i n g a d i f f e r e n t b i o l o g i c a l r e s p o n s e . N e v e r t h e l e s s , t h i s e m p i r i c a l method of d e r i v i n g cons t a n t s f o r t h e r e l a t i v e e f f e c t s of chemical groups on b i o l o g i c a l a c t i v i t y i s bound t o b e more h e l p f u l i n t h e long run t h a n unguided i n t u i t i o n . Purc e l l 3 4 has been s t u d y i n g t h e Free-Wilson method. Some i n f o r m a t i o n i s a l r e a d y i n hand t o show t h a t such e m p i r i c a l cons t a n t s are r e l a t e d t o more fundamental p a r a m e t e r s . C i l e n t o and Berenholc have shownz6 t h a t t h e r e i s a good l i n e a r c o r r e l a t i o n between f(X) o b t a i n e d f o r 1 6 t h y r o x i n e a n a l o g s (11) and t h e n e g a t i v e l o g a r i t h m of t h e l i f e t i m e of t h e phosphorescent s t a t e ( e q u i v a l e n t t o t h e t r i p l e t t o s i n g l e t t r a n s i t i o n i n n a p h t h a l e n e a n a l o g s ) f o r t h e f i v e f u n c t i o n s where X = H , CH3, C l , B r , I. They conclude t h a t t h e s t r o n g T+S t r a n s i t i o n i n d i i o d o t y r o s i n e and t h y r o x i n e d e r i v a t i v e s makes t h e s e compounds v e r y e f f i c i e n t i n t h e t r a n s f e r of t r i p l e t - s t a t e energy. Using t h e subx s t i t u e n t o f o r t h e e l e c t r o n i c e f f e c t and / \ H \ n f o r t h e hydrophobic e f f e c t z 7 of /WH,CHNH,COOH .-.\-R /-.\s u b s t i t u e n t s , i t i s s e e n from eq 4 t h a t f(X’) d e r i v e d by B r u i c e e t a l . x’/ X/ (11) i s i n f a c t r e l a t e d t o t h e s e more fundamental c o n s t a n t s .
\.-.
<-
f(X’)
It h a s of t h y r o x i n e t h e u s e of B been shown30
-
= 0.3081~
0.5640
- 1.672
n = 7
r
=
0.934
(4)
been shown28 t h a t IT and o c a n b e used t o r a t i o n a l i z e t h e SAR a n a l o g s and J ~ r g e n s e n *h~a s t e s t e d t h e p r e d i c t i v e v a l u e of and IT w i t h a t e r t - b u t y l a n a l o g of t h y r o x i n e . It h a s a l s o t h a t Zahradnik‘s $ c o n s t a n t s a r e l i n e a r l y r e l a t e d t o IT.
Kopeck; and Bozek31,32 have a l s o been s t u d y i n g t h e u t i l i t y of emp i r i c a l s u b s t i t u e n t c o n s t a n t s i n an i n v e s t i g a t i o n of t h e t o x i c i t y of d i s u b s t i t u t e d benzenes. I n t h e i r e q u a t i o n (5) t h e y have used a n i n t e r a c t i o n
3 50 -
Sect. VI
-
Topics i n Chemistry
Smi s sman, Ed.
term of t h e t y p e d i s c u s s e d by Miller33 f o r t h e l i n e a r combination of terms i n t h e f o r m u l a t i o n of m a t h e m a t i c a l m o d e l s .
I n eq. 5 , HH r e p r e s e n t s benzene and XY a d i s u b s t i t u t e d d e r i v a t i v e . Quite good c o r r e l a t i o n s w e r e o b t a i n e d u s i n g eq 5 f o r n o n s p e c i f i c t o x i c i t y . The c o n s t a n t bX i s s t a t e d t o b e l i n e a r l y r e l a t e d t o f(X’) of Bruice e t a l . Puree1136 , following t h i s g e n e r a l approach, h a s s t u d i e d amides which are i n h i b i t o r s of c h o l i n e s t e r a s e . P u r ~ e 1 Y 136~ and ~ co-workers have a l s o i n v e s t i g a t e d a v a r i e t y of p h y s i c a l chemical parameters t o r a t i o n a l i z e t h e SAR f o r these inhibitors. A f t e r t h e r a t h e r i n t e n s e work on t h e c o r r e l a t i o n of b i o l o g i c a l act i v i t y w i t h p a r t i t i o n c o e f f i c i e n t s of t h e e a r l y y e a r s of t h i s c e n t u r y had reached a s t a n d s t i l l , new hope f o r r a t i o n a l i z i n g t h e b i o l o g i c a l a c t i v i t y of o r g a n i c compounds appeared i n t h e work of H a m m e t t 3 7 . The H a m m e t t equat i o n and o t h e r v a r i a t i o n s of i t 1 a ~ 3 a have proved t o be v e r y s u c c e s s f u l i n c o r r e l a t i n g chemical r e a c t i v i t y w i t h t h e e l e c t r o n i c o r s t e r i c e f f e c t s of s u b s t i t u e n t s f o r t h e r e a c t i o n s of o r g a n i c compounds i n homogeneous solut i o n s . Although a good many a t t e m p t s have been made39’47 t o apply t h e H a m m e t t e q u a t i o n t o biochemical systems, t h e r e s u l t s have, w i t h few except i o n s , been d i s a p p o i n t i n g . Such a n e x c e p t i o n i s seen i n t h e enzymatic hyd r o l y s i s of phenyl s u l f a t e s 3 9 from which eq 6 r e s u l t s 2 4 . l o g l / K m = 0.9300
+
2.522
n = 10
r = 0.931
(6)
I n eq 6, K i s t h e Michaelis c o n s t a n t . Good c o r r e l a t i o n w i t h o w a s a l s o The b e s t l i n e a r r e l a t i o n s w i t h o have been found uso b t a i n e d wyth Vmax. i n g more o r less pure enzymes. The l a c k of s u c c e s s w i t h o i n biochemical s t e r i c i n t e r a c t i o n s of s u b s t i t systems h a s g e n e r a l l y been a t t r i b ~ t e dt o~ ~ u e n t s w i t h t h e enzyme o r l i p o p r o t e i n membranes. Recent work21-25 would i n d i c a t e t h a t w h i l e s t e r i c i n t e r a c t i o n s are extremely i m p o r t a n t , t h e conc e p t of lock-and-key f i t of enzyme and s u b s t r a t e h a s been over-emphasized a t t h e expense of hydrophobic bonding. The importance t o t h e m e d i c i n a l chemist of t h e more f l e x i b l e c h a r a c t e r of enzymes which is emerging from t h e work of Koshlandlt9 and others5O h a s been analyzed by Belleau51. A most important new concept f o r t h e d e s i g n e r of drugs is t h a t of t h e hydrophobic bond19 y 2 0 ,s2. The view of Hansch and co-workers is t h a t i f a s u i t a b l e parameter can be formulated f o r t h i s , t h e n by means of t h e w e l l known c o n s t a n t s 1 8 o , a+, O-, o*, and E,, many of t h e powerful t o o l s of p h y s i c a l o r g a n i c chemistry might b e brought t o b e a r on m e d i c i n a l chemic a l problems. To t h i s end octanol-water p a r t i t i o n c o e f f i c i e n t s (P) have Y ~ a d~ d i t. i v e - c o n s t i t u t i v e been s t u d i e d as a r e f e r e n c e standard1 Y ~ ~ The n a t u r e of l o g P and IT (IT = logP - logP where P r e f e r s t o a p a r e n t moleX H H c u l e and P t o a d e r i v a t i v e ) means t h a t from a r e l a t i v e l y few v a l u e s Of X l o g P, many o t h e r s can b e calculated1,24,27,53,54. The u s e f u l n e s s of t h e s e parameters f o r measuring binding of n e u t r a l molecules w i t h p r o t e i n s i s i l l u s t r a t e d i n eq 7 - 2 .
Drug Design
Chap. 34 l o g 1 / C = 0.71 logP l o g 1 / C = 0.58 logP
+
+ +
Hansch
351 -
1.51
n = 17
r = 0.950
(7)
2.40
n = 4
r = 0.961
(8)
n = 19
r
(9)
l o g 1 / C = 0 . 6 8 1 ~ 3.48
= 0.962
I n eq 7-9, C is t h e molar c o n c e n t r a t i o n of compound n e c e s s a r y t o produce a 1-to-1 complex w i t h bovine hemog1obin2l (eq 7 ) and bovine serum albumin (eq 8 and 9 ) . Equation 7 c o r r e l a t e s t h e binding of 1 7 m i s c e l l a n e o u s compounds ( e . g . , phenols, a n i l i n e s , naphthalene) and eq 8 c o r r e l a t e s t h e binding of 4 barbiturate^^^. I n eq 9 , t h e comparative c o n s t a n t IT i s used55 t o c o r r e l a t e t h e binding of phenols by serum albumin. The s l o p e s of t h e t h r e e e q u a t i o n s a r e s u r p r i s i n g l y c l o s e , i n d i c a t i n g t h a t t h e binding of n e u t r a l molecules t o two d i f f e r e n t p r o t e i n s can be q u a n t i t a t i v e l y def i n e d u s i n g l o g P o r IT as hydrophobic bonding c o n s t a n t s . For t h e s e s i t u a t i o n s no h i g h l y s p e c i f i c s t e r i c o r e l e c t r o n i c parameters a r e n e c e s s a r y t o rationalize the results. Going t o t h e n e x t more complex s i t u a t i o n , t h a t of enzymic r e a c t i o n s , i t can be shown t h a t t h e l i n e a r combination of IT and 0 can account f o r t h e s u b s t i t u e n t e f f e c t s i n t h e h y d r o l y s i s of phenyl g l u c o s i d e s by e m ~ l s i n ~ ~ . Using r e g r e s s i o n a n a l y s i s , eq 10-13 are d e r i v e d t o i l l u s t r a t e how one can f a c t o r s u b s t i t u e n t e f f e c t s on a biochemical r e a c t i o n . P a r a Groups
Meta Groups
+ 0.331~+
l o g Ke = 0.52a
2.03
l o g Ke =
0.620
+
+ 1.63 0 . 1 2 ~+ 0.96 +
1.80
l o g Ke = 0.95a l o g Ke =
1.59
n = 8
r = 0.753
(10)
n = 8
r = 0.921
(11)
n = 6
r = 0.949
(12)
n = 6
r = 0.963
(13)
Ke r e p r e s e n t s t h e e q u i l i b r i u m c o n s t a n t € o r t h e enzyme s u b s t r a t e complex. Comparison of eq 10 and 11 f o r t h e p a r a d e r i v a t i v e s i n d i c a t e s t h a t complex formation depends on both e l e c t r o n i c and hydrophobic f a c t o r s . The c o r r e l a t i o n c o e f f i c i e n t i s much b e t t e r and s t a t i s t i c a l l y q u i t e s i g n i f i c a n t f o r eq 11. The p o s i t i v e s i g n s of t h e c o e f f i c i e n t s f o r IT and a i n d i c a t e t h a t l i p o p h i l i c and e l e c t r o n - a t t r a c t i n g groups promote complex formation. Comp a r i n g eq 12 and 13, one f i n d s t h a t f o r meta isomers hydrophobic bonding i s a p p a r e n t l y n o t p o s s i b l e . N o s i g n i f i c a n t improvement i n c o r r e l a t i o n res u l t s on t h e i n t r o d u c t i o n of t h e v term. A s i m i l a r set of e q u a t i o n s was d e r i v e d 5 6 t o show t h e s u b s t i t u e n t e f f e c t on t h e h y d r o l y s i s rate c o n s t a n t k3. Equally good c o r r e l a t i o n s were obtained except i n t h i s s t e p ; as one might e x p e c t , t h e c o e f f i c i e n t w i t h IT h a s a n e g a t i v e s i g n . T h i s i n d i c a t e s t h a t hydrophobic bonding slows down d e s o r p t i o n of t h e cleaved p r o d u c t s . S i n c e good c o r r e l a t i o n s w e r e o b t a i n e d i n eq 11 and 13 w i t h o u t t h e u s e of s t e r i c c o n s t a n t s , i t is assumed t h a t t h e s e are unimportant, a t least f o r f u n c t i o n s as l a r g e as t h o s e s t u d i e d . The meaning of t h e words s t e r i c and e l e c t r o n i c i n t h e s e d i s c u s s i o n s is somewhat ambiguous. For example, t h e l i n e a r r e l a t i o n s between parachor and t o x i c i t y found by McGowan o r t h e u s e of t h e s o l u b i l i t y parameter 6 by Mullins could b e viewed as i n d i c a t i n g a d i r e c t r e l a t i o n between t h e s i z e of t h e s u b s t i t u e n t and i t s a b i l i t y t o produce a g i v e n b i o l o g i c a l response. The a f f i n i t y of a n a p o l a r group f o r a l i p i d phase w i l l a l s o b e a f u n c t i o n
3 52
Sect. VI
-
Smi s sman, Ed.
T o p i c s in C h e m i s t r y
of i t s s i z e and, t o a lesser e x t e n t , i t s shape. Thus i t i s n o t always e a s y , even i n t h e a b s t r a c t , t o s e p a r a t e t h e b i n d i n g r o l e of hydrophobic bonding by an a p o l a r f u n c t i o n from i t s r o l e of d i s t o r t i n g a hydrophobic r e g i o n by i t s s i z e . We are a t t e m p t i n g t o u s e hydrophobic bonding as &f i n e d by p a r t i t i o n c o e f f i c i e n t s as s i m p l e h o l d i n g of t h e drug t o t h e act i v e s i t e , r e a l i z i n g t h a t o f t e n t h i s r o l e cannot be s e p a r a t e d from t h e c o n f o r m a t i o n a l change t h e a p o l a r group w i l l , i n t h e b i n d i n g p r o c e s s , produce i n an enzyme o r membrane.’ S t e r i c e f f e c t s , t h e n , a r e t h o s e due t o s i z e o r arrangement i n s p a c e of s u b s t i t u e n t s which cannot b e accounted f o r by t h e hydrophobic c o n s t a n t s l o g P and TI. These w i l l b e b o t h i n t r a - and i n t e r m o l e c u l a r i n n a t u r e . I n t h e same way, e l e c t r o n i c e f f e c t s w i l l overl a p w i t h hydrophobic bonding s i n c e t h e p o s i t i o n of e q u i l i b r i u m i n t h e d i s t r i b u t i o n of a drug between phases w i l l b e a f u n c t i o n of i t s e l e c t r o n i c s t r u c t u r e . Indeed, i t h a s been shown27 t h a t TI v a r i e s w i t h O . However, t h i s v a r i a n c e i s n o t g r e a t i f t h e s u b s t i t u e n t s a r e s e p a r a t e d by one o r more atoms. The term e l e c t r o n i c e f f e c t s means h i g h l y s p e c i f i c e f f e c t s i n g e n e r a l n o t a s s o c i a t e d w i t h t h e p a r t i t i o n i n g p r o c e s s . These would b e e f f e c t s involved i n a chemical r e a c t i o n o r charge t r a n s f e r p r o c e s s where a change i n e l e c t r o n d e n s i t y t o o small t o make a s i g n i f i c a n t d i f f e r e n c e i n l o g P could c a u s e a l a r g e change i n a r a t e o r e q u i l i b r i u m c o n s t a n t . Using t h e s e somewhat a r b i t r a r y d i v i s i o n s of s u b s t i t u e n t e f f e c t s and r e g r e s s i o n a n a l y s i s , a s t a r t can b e made i n s e p a r a t i n g t h e e f f e c t s of groups of atoms on t h e b i o l o g i c a l a c t i v i t y of a s e t of congeners. Hansch and co-workers have n o t , f o r example, a t t e m p t e d t o f a c t o r o u t hydrogen bonding. I n gene r a l t h e y have worked w i t h systems where t h i s could b e accounted f o r i n terms of o and IT. P u r c e l l e t a l . have s u g g e s t e d a way of d e a l i n g s p e c i f i c a l l y with t h i s t e r m 3 6 . I n a d d i t i o n t o many e a r l y examples1 , b i o l o g i c a l r e s p o n s e has been found t o be q u a n t i t a t i v e l y l i n e a r l y dependent on l o g P o r IT i n t h e i n h i b i t i o n of t h e H i l l r e a c t i o n 5 7 9 5 8 a c t i v i t y of p e n i c i l l i n s s 9 , t o x i c i t y of benz o i c a c i d s t o mosquito larvae28, phenol c o e f f i c i e n t s 2 8 , c h o l i n e s t e r a s e i n h i b i t o r, ~ and ~ ~ catechol-amine a c t i v i t y 6 0 .
Hernker61 w a s one of t h e f i r s t to a t t e m p t t h e q u a n t i t a t i v e c o r r e l a t i o n of b i o c h e m i c a l r e s p o n s e u s i n g b o t h p a r t i t i o n c o e f f i c i e n t s and i o n i z a t i o n c o n s t a n t s t o account f o r t h e uncoupling a c t i o n of p h e n o l s . The l i n e a r combination of TI and 0 h a s been found t o h o l d f o r s e v e r a l enzymic reaction^^^^^^ as w e l l as t h e b i n d i n g of phenols by p r o t e i n 5 5 , t h e t o x i c i t y of p h e n o l s 6 2 , t h e uncoupling a c t i o n of p h e n o l s 6 2 , and t h e r e l a t i v e sweetness of n i t r ~ a n i l i n e s ~ An ~ . i n t e r e s t i n g a p p l i c a t i o n i s t h a t of McMahon63. Equation 14 w a s formulated f o r t h e enzymic r e d u c t i o n of aromatic ketones t o alcohols. logVm,,
+
+
n = 10
r = 0.89
(14) O f c o u r s e t h e most i n t e r e s t i n g and d i f f i c u l t drug s t u d i e s a r e t h o s e i n which whole organisms a r e i n v o l v e d . It h a s been p o s t u l a t e d 6 4 t h a t i n g e n e r a l , f o r t h e s e s t u d i e s one would e x p e c t a p a r a b o l i c r e l a t i o n between ~ ~ 1~5 .~ l o g 1/C and l o g P. T h i s h a s l e d t o t h e d e ~ e l o p m e n tof~ eq =
0.334~
1.2390
0.824
l o g 1/C = - k ( l o g P ) 2
+
k‘logP
+
pa
+
k”
(15)
Chap. 34
Drug D e s i g n
Hansch
3 53
I n t h e development of t h i s model a p r o b a b i l i s t i c view i s t a k e n f o r movement of drug from t h e exobiophase o r p o i n t of i n j e c t i o n t o t h e s i t e s of a c t i o n . It i s assumed t h a t as P-to d r u g s become more and more i s o l a t e d i n t h e water phase and e v e n t u a l l y become u n a b l e t o c r o s s l i p i d b a r r i e r s . A s Pthe reverse is true. Somewhere between P=O and P=m t h e r e w i l l b e an i d e a l v a l u e (Po) f o r a g i v e n s e t of congeners i n a g i v e n b i o l o g i c a l systein s u c h t h a t t h o s e members having t h i s v a l u e w i l l f i n d t h e s i t e s of a c t i o n v i a a random walk p r o c e s s i n t h e minimum time. T h i s assumes s t e r i c and e l e c t r o n i c (pKa, e t c . ) f a c t o r s are c o n s t a n t . I n o t h e r words, a g r e a t e r number of molecules of drug w i t h Po would r e a c h t h e s i t e s of a c t i o n i n t h e t e s t i n t e r v a l t h a n d r u g s having o t h e r P v a l u e s . I n e f f e c t , one e x p e c t s a change i n t h e mechanism of movement i n a s e t of d r u g s h a v i n g a s u f f i c i e n t s p r e a d i n P v a l u e s . The movements of t h e lower members of t h e series w i l l b e mostly determined by i n t e r a c t i o n s w i t h water, w h i l e t h o s e of t h e h i g h e r members w i l l b e determined by hydrophobic i n t e r a c t i o n s w i t h l i p i d s . Such p a r a b o l i c r e l a t i o n s may even b e found i n c l o s e d systems of t h e t y p e used i n n a r c o s i s s t u d i e s . Ferguson66 h a s s t a t e d t h a t probably i n most e x p e r i ments on n a r c o s i s a complete e q u i l i b r i u m i s n e v e r r e a c h e d i n t h e p e r i o d of exposure and t h e r e s u l t s a r e t i m e dependent. R e s u l t s w i l l b e even more t i m e dependent i n open systems such as whole animals where e l i m i n a t i o n and b i o t r a n s f o r m a t i o n are c o n t i n u o u s p r o c e s s e s . Such r e s u l t s can even b e exp e c t e d i n t i s s u e experiments o r work w i t h p a r t i a l l y p u r i f i e d enzymes. S i n c e a c t i v i t y i s u s u a l l y e x p r e s s e d a s l o g 1 / C , t h e most a c t i v e compounds t e s t e d a r e o f t e n i n v e r y low c o n c e n t r a t i o n , sometimes less t h a n M. While l o g 1/C may b e l i n e a r w i t h r e s p e c t t o l o g P a t h i g h e r c o n c e n t r a t i o n s eq 6-8 i n d i c a t e t h a t h i g h l y l i p o p h i l i c m o l e c u l e s w i l l b e v e r y t i g h t l y bound t o p r o t e i n s s o t h a t t r u e e q u i l i b r i u m i s n o t reached i n t e s t t i m e . The lower t h e t e s t c o n c e n t r a t i o n s become, t h e more l i k e l y t h e d e p a r t u r e from l i n e a r i t y through l o c a l i z a t i o n of m o l e c u l e s i n p a r t i c u l a r l y l i p o p h i l i c material. Of c o u r s e t h e r e are r e a s o n s o t h e r t h a n b i n d i n g by l i p i d s o r p r o t e i n s which might c a u s e a d e p a r t u r e from l i n e a r i t y i n t h e r e l a t i o n s h i p of l o g 1 / C and l o g P o r TI. M e t a b o l i c o r e l i m i n a t i o n r e a c t i o n s n o t s i g n i f i c a n t a t low v a l u e s of l o g P c o u l d , w i t h i n c r e a s i n g l o g P , become v e r y i m p o r t a n t . A good example of t h i s i s i n t h e metabolism of a l k y l a r y l e t h e r i n r a b b i t s 67. I n (111) when R i s e t h y l o r m e t h y l , d e a l k y l a t i o n i s t h e main r e a c t i o n . When R i s p r o p y l o r b u t y l , w - 1 hydroxy l a t i o n becomes more i m p o r t a n t . S i n c e t h e r a t e of m e t a o/ bolism of drugs may b e l i n e a r l y r e l a t e d 6 8 t o l o g P , (111) t h i s may b e a n i m p o r t a n t c o n t r i b u t i n g f a c t o r f o r t h e bCH, p a r a b o l i c dependence of a c t i v i t y on l i p o p h i l i c charOR acter. Another unknown i s t h e l i p o p h i l i c s p a c e a t t h e s i t e of a c t i o n a v a i l a b l e f o r t h e hydrophobic moiety of t h e d r u g . I f t h i s i s q u i t e l i m i t e d , t h e n a p o i n t i s soon reached where l o g 1/C and l o g P a r e no l o n g e r l i n e a r l y a s s o c i a t e d . The p r o b a b i l i s t i c n a t u r e of t h e l o g P terms i n eq 15 does a good d e a l t o i n s u r e a r e a s o n a b l e f i t of a set of d a t a as long as i n d i v i d u a l congeners i n t h e set do n o t d e p a r t r a d i c a l l y from t h e b e h a v i o r of t h o s e having similar l i p o p h i l i c c h a r a c t e r . I n p r i n c i p l e , l o s s through metabolism o r e l i m i n a t i o n i s n o t d i f f e r e n t t h a n l o s s through b i n d i n g i f t h e s e l o s s e s depend o n l y on l o g P. Good r e s u l t s have
Po.
u c ‘7’
Sect. V I - T o p i c s i n C h e m i s t r y
3 54 -
Smi s sman, Ed.
been o b t a i n e d w i t h eq 15 f o r plant-growth regulator^^^ , chloromycetin anal o g (Garrett69 ~ ~ ~ and c o l l e a g u e s have found a more l i n e a r dependence of c h l o r o m y c e t i n a c t i v i t y under d i f f e r e n t test c o n d i t i o n s ) , t h y r o x i n e anal o g s 2 8 , phenol coef f i c i e n t s 2 8 , c a r c i n o g e n i c i t y of a r o m a t i c compounds2* , and t h e l o c a l i z a t i o n of benzeneboronic a c i d s i n b r a i n and tumor t i s s u e 7 ( ] .
A c o n s t a n t which may prove t o b e v e r y u s e f u l i n drug d e s i g n i s l o g Po ( o r no). T h i s f i g u r e can b e found by t a k i n g t h e p a r t i a l d e r i v a t i v e of eq 1 5 and s e t t i n g t h i s e q u a l t o z e r o . Once t h i s h a s been e s t a b l i s h e d f o r a set of d r u g s , i t becomes a u s e f u l bench mark from which t o s t a r t t h e des i g n of a completely new drug t o a c t on t h e same sites. For example, i t w a s found t h a t l o g Po f o r phenoxyacetic a c i d s a c t i n g as plant-growth regul a t o r s i s 2.03. Log Po f o r p h e n y l a c e t i c a c i d s a c t i n g i n t h e same system i s 2.47. I f one wished t o d e s i g n a new a c i d t o a c t i n t h i s system, one of t h e f e a t u r e s which one would d e s i g n i n t o t h e f i r s t test m o l e c u l e would b e l o g P of about 2.2. By means of t h e a d d i t i v e - c o n s t i t u t i v e c h a r a c t e r of l o g P one could d e s i g n s u c h compounds on p a p e r w i t h o u t c a r r y i n g o u t extensive partition coefficient studies. While s u i t a b l e t e c h n i q u e s t o h a n d l e s t e r i c e f /@\/OTzEt f e c t s between s u b s t r a t e and t h e material comprising (IV) t h e s i t e s of a c t i o n are a t p r e s e n t o u t of r e a c h , intramolecular s t e r i c i n t e r a c t i o n s can be handled q u a n t i t a t i v e l y , a t least i n some i n s t a n c e s u s i n g T a f t ' s E, parameter22,56. Equations 16 and 1 7 , f o r m u l a t e d from t h e work of Metcalf and Fukuto c o r r e l a t e 2 2 s u b s t i t u e n t e f f e c t s of R i n (IV) on t h e i n h i b i t i o n of c h o l i n e s t e r a s e by a l k y l p h o s p h o n i c a c i d esters.
'./
0 1
ozd
l o g K = 3.74 E, l o g K = -1.680*
+ 7.54 + 0.1511 + 4.05
E,
+
7.21
n = 13
r = 0.901
(16)
n = 13
r = 0.907
(17)
Comparison of eq 1 6 and 1 7 i n d i c a t e s t h a t n e i t h e r e l e c t r o n i c nor hydrophobic f a c t o r s p l a y a n i m p o r t a n t p a r t i n t h e i n h i b i t i o n . Thus i t a p p e a r s t h a t t h e phosphonates i n t e r a c t w i t h t h e enzyme i n such a way t h a t t h e y cannot come i n c o n t a c t w i t h a hydrophobic r e g i o n of t h e p r o t e i n . The .k r a n g e of e l e c t r o n i c f o r c e s covered by t h e R groups w a s s m a l l so t h a t u may b e more i m p o r t a n t t h a n eq 17 would i n d i c a t e . Some o v e r l a p between E, The f a c t t h a t Es, a and o* c o n s t a n t s t e n d s t o o b s c u r e t h e r o l e of u*. c o n s t a n t d e r i v e d from h y d r o l y s i s s t u d i e s under homogeneous c o n d i t i o n s , should a p p l y t o heterogeneous c a t a l y s i s i s s u r p r i s i n g and i n d i c a t e s much more u s e f o r t h i s parameter t h a n one would have had r e a s o n t o e x p e c t . Another method f o r o b t a i n i n g biochemical s u b s t i t u e n t c o n s t a n t s i s Considerable e f f o r t 7 ' a v a i l a b l e i n t h e v a r i o u s forms of chromatography. 7 3 h a s been made t o g a t h e r and A% v a l u e s f o r t h e e f f e c t of s u b s t i t u e n t s on
RF .
%
A%=%$-\
%
I n eq 18, R M ~i s c a l c u l a t e d from t h e v a l u e of a p a r e n t compound and Rp from t h a t of a d e r i v a t i v e having s u b s t i t u e n t X. ARM i s a c o n s t a n t a n a l o gous t o II and i n f a c t a c l o s e c o r r e l a t i o n e x i s t s between t h e two as i s
Hansch
Drug Design
Chap. 34 shown1 i n eq 19.
= -l.l03AR,
+
0.647
r = 0.970
n = 12
355 -
(19)
I n measuring t h e A R M v a l u e s i n eq 1 9 , Green and M a r c i n k i e w i ~ z ~used l trig o 1 and d i i s o p r o p y l e t h e r i n reversed-phased, t a n k l e s s f l a t - b e d chroma~ ~ shown t h a t % v a l u e s c o r r e l a t e t h e tography. Boyce and M i l b ~ r r o whave m o l l u s c i c i d a l a c t i v i t y of a series of N - n - a l k y l t r i t y l a m i n e s assuming a p a r a b o l i c r e a c t i o n e x i s t s between l o g LD50 and %. Thus RM o r ARM v a l u e s can b e used i n eq 1 5 i n p l a c e of l o g P o r 1 ~ . C o n s i d e r a b l e e f f o r t 3 5 s75-*O h a s been made t o understand biochemic a l and pharmacological problems u s i n g quantum mechanical c a l c u l a t i o n s of e l e c t r o n d e n s i t i e s w i t h molecules. While t h i s h a s been u s e f u l i n exp l a i n i n g how a p a r t i c u l a r bond i s broken o r made75, l i n e a r r e l a t i o n s between c a l c u l a t e d e l e c t r o n d e n s i t i e s and b i o l o g i c a l a c t i v i t y are n o t a b l y l a c k i n g . An e x c e p t i o n coming from t h e work of Fukui i s i l l u s t r a t e d i n eq 20 and 2 1 which cprrelate t h e n i c o t i n e - l i k e a c t i v i t y of m e t a d e r i v a t i v e s of C6H50CH2CH2N(CH3)3 w i t h t h e s u p e r d e l o c a l i z a b i l i t y ( S o ( N 3 ) of e l e c t r o n s a t t h e o r t h o p o s i t i o n and t h e f r o n t i e r e l e c t r o n d e n s i t y (f6:;) on t h e e t h e r oxygen. logA = 13.742 So(4 logA = 30.392 f ( E ) OXY
- 10.465 - 20.924
n = 6
r = 0.994
(20)
n = 6
r = 0.949
(21)
The combination of such e l e c t r o n i c d e n s i t i e s w i t h a hydrophobic bonding c o n s t a n t does y i e l d good r e s u l t s 2 8 , 5 6 as i l l ~ s t r a t e dby~ ~eq 22 and 23. log% = 2 2 . 9 1 ~ - 42.49
log% = 0 . 2 9 ~+ 18.166.
-
33.82
n = 6
r
0.685
(22)
n = 6
r = 0.995
(23)
=
I n t h e above e q u a t i o n s Ax, from t h e work of Jacobson, r e p r e s e n t s t h e relat i v e rates of a c y l a t i o n of a r o m a t i c amines having s u b s t i t u e n t s X by means of pigeon l i v e r a c e t y l t r a n s f e r a s e . E r e p r e s e n t s t h e c a l c u l a t e d e l e c t r o n d e n s i t i e s on t h e n i t r o g e n atom made by P e r a u l t and Pullman. Equation 22 a c c o u n t s f o r o n l y 47% of t h e v a r i a n c e i n t h e d a t a w h i l e eq 23 a c c o u n t s f o r 99%. Thus i t a p p e a r s t h a t quantum m e c h a n i c a l l y o b t a i n e d e l e c t r o n d e n s i t i e s can b e e x t r e m e l y u s e f u l t o t h e m e d i c i n a l c h e m i s t . I n t h i s way t h e r e l a t i v e e l e c t r o n d e n s i t y on each atom i n t h e m o l e c u l e can b e found and through r e g r e s s i o n a n a l y s i s t h e r e l a t i v e importance of t h i s d e n s i t y a t one o r p o i n t s i n t h e m o l e c u l e c a n b e e v a l u a t e d . T h i s approach o f f e r s , i n p r i n c i p l e , a g r e a t advantage o v e r t h e u s e of u . What a r e t h e g u i d e l i n e s t h a t s u b s t i t u e n t o f f e r t h e d e s i g n e r of d r u g s ? The g r e a t s u c c e s s geneous o r g a n i c r e a c t i o n s 1 * and t h e more modest method w i t h heterogeneous b i o c h e m i c a l r e a c t i o n s t h e u s e of eq 24 and 25 as a r e a s o n a b l e working
constant analysis has t o of t h i s method i n homoachievements of t h i s would s e e m t o v a l i d a t e hypothesis.
I n eq 24 w e are assuming5' t h a t t h e u l t i m a t e l y measured b i o l o g i c a l response ( t o x i c i t y , r e s i s t a n c e t o a m e t a b o l i c p r o c e s s , E D 5 0 , e l i m i n a t i o n ,
356
Sect. VI
-
T o p i c s in C h e m i s t r y
Smi s sman, Ed.
e t c . ) i s governed by one r a t e - l i m i t i n g p r o c e s s f o r which kgR i s a r a t e o r equilibrium constant. i n eq 2 4 , mt/H r e p r e s e n t s t h a t p o r t i o n of t h e f r e e energy change which can be a t t r i b u t e d t o hydrophobic bonding, AFglect Tepr e s e n t s a n e l e c t r o n i c component, and AFzteric r e p r e s e n t s h i g h l y s p e c i f i c s p a t i a l demands of r e a c t a n t s and p r o d u c t s on t h e f r e e energy change. Of c o u r s e , were s u f f i c i e n t d a t a a v a i l a b l e , one might p r o f i t a b l y f a c t o r each of t h e terms i n eq 2 4 and 25 i n t o s e v e r a l t o r e p r e s e n t s u s p e c t e d c r i t i c a l p a r t s of a molecule. S u b s t i t u e n t e f f e c t s on l o g kgR of eq 24 are r e p r e s e n t e d i n eq 2 5 .
E q u a t i o n s 24 and 25 w e r e formulated f o r t h e c a s e where t h e drug is a t t h e s i t e of a c t i o n o r t h e s i t u a t i o n where t r u e e q u i l i b r i u m w i t h t h e exobiophase i s e s t a b l i s h e d a s envisaged by Ferguson. From t h e p r e s e n t l i m i t e d work i t would appear t h a t 'XXFi/H might be r e p r e s e n t e d by l o g P , T I ,%, ARM, B (Zahradnik15) and, under c e r t a i n cond i t i o n s p a r a c h o r . The 6xF~1ec term may be r e p r e s e n t e d u s i n g t h e v a r i o u s forms "'of (5, quantum m e c h a n i c a i l y c a l c u l a t e d e l e c t r o n d e n s i t i e s o r chemic a l s h i f t s ' ' o b t a i n e d v i a NMR. I t should a l s o b e p o s s i b l e t o f o r m u l a t e s u i t a b l e c o n s t a n t s from I R and UV s p e c t r a . Attempts t o u s e polarographi c a l l - o b t a i n e d c o n s t a n t s do n o t seem t o b e as u s e f u l as one might expect' 5 , 8 3
.
The c a s e where s u b s t i t u e n t changes r e s u l t i n l a r g e d i f f e r e n c e s i n i o n i z a t i o n i s one of g r e a t importance s i n c e s o many d r u g s are e i t h e r weak a c i d s o r weak b a s e s . The d e g r e e of i o n i z a t i o n h a s long been r e c o n i z e d as has p l a y i n g a p a r t i n drug a c t i v i t y 8 4 . I n a c a r e f u l a n a l y s i s , F u j i t a " shown how s u b s t i t u e n t e f f e c t s on i o n i z a t i o n should be s e p a r a t e d from o t h e r e l e c t r o n i c e f f e c t s of s u b s t i t u e n t s .
It does n o t seem p o s s i b l e t o make any g e n e r a l o b s e r v a t i o n s about s u i t a b l e ways of r e p r e s e n t i n g 6XF&eric f o r t h e i n t e r a c t i o n s between a drug and i t s r e c e p t o r s . By c o n s i d e r i n g se ts of congeners i n which g r o s s s t e r i c changes a r e avoided ( e . g . , c o n s i d e r i n g D isomers s e p a r a t e l y from L i s o m e r s , e t c . ) u s e f u l c o r r e l a t i o n s can b e made. I n f a c t , where t h e twoparameter e q u a t i o n c a n be shown t o h o l d o v e r a r e a s o n a b l e r a n g e of subs t i t u e n t s , one c a n make d e d u c t i o n s about GXFEteric by c o n t i n u i n g t o i n crease t h e s i z e of X u n t i l t h e two-parameter e q u a t i o n f a i l s . I n t h i s way one c a n , t o a l i m i t e d e x t e n t , map t h e f r e e s p a c e around a r e c e p t o r s i t e . P ~ r t o g h e s e ~ ~i n- ~a n~ e, x t e n s i o n of t h e approach of Zahradnik, h a s shown t h a t l i n e a r r e l a t i o n s h i p s between d i f f e r e n t c o n g e n e r i c s e t s of a n a l g e s i c s can b e used t o make more f i r m d e c i s i o n s about whether t h e sets are a c t i n g i n t h e same three-dimensional way on t h e s a m e receptors. The t h r e e sets of congeners i n which R of V w a s h e l d c o n s t a n t ( i . e . , 1. R' = C O z E t , 2 . R' = O C O E t and 3. R' = OCOCH3) were v a r i e d by changes i n R. Least s q u a r e f i t s of sets 1 v s . 2 , 1 v s . 3 , and 3 v s . 2 gave
/\. 1
( V>
I
4.
\
t P' i
/t t
'w' A
Chap. 3 4
Hansch
Drug Design
3 57 -
s l o p e s c l o s e t o 1 w i t h good c o r r e l a t i o n c o e f f i c i e n t s . Such tests can be used t o h e l p e s t a b l i s h t h e f a c t t h a t , f o r example, R i n each series is i n t h e same p h y s i c o t h e m i c a l environment on t h e r e c e p t o r s . By e x p l o r i n g a l a r g e enough number of sets of s y s t e m a t i c a l l y v a r i e d congeners one could o b t a i n c o n s i d e r a b l e i n f o r m a t i o n about t h e geometry of t h e r e c e p t o r s i t e s . The f a c t t h a t simply changing t h e l e n g t h of R can l e a d t o a complete change i n t h e mechanism of a c t i o n ( e . g . , a g o n i s t t o a n t a g o n i s t ) h a s been thoroughly documented by AriEnsB8. A c a r e f u l case s t u d y i n which t h e ent h a l p i c and e n t r o p i c r o l e s of t h e s u b s t i t u e n t s i n t r a n s i t i o n from a g o n i s t t o a n t a g o n i s t have been c o n s i d e r e d h a s been made by B e l l e a u , T a n i and L i e B 9 . Miller and HanschZ5 have p r e s e n t e d e v i d e n c e t o show t h a t when two hydrophobic areas are p r e s e n t i n a drug and o n l y a l i m i t e d s p a c e f o r hydrophobic bonding e x i s t s i n an enzyme, t h e more hydrophobic of t h e two groups may determine t h e c o n f i g u r a t i o n of b i n d i n g . Thus s t e r i c i n t e r a c t i o n s of r e c e p t o r s i t e and s u b s t r a t e are extremely d i f f i c u l t t o e v a l u a t e . The c o n f o r m a t i o n a l p e r t u r b a t i o n s of drug on r e c e p t o r r e c e p t o r on drug w i l l t a x t o t h e l i m i t o u r a b i l i t y t o unt a n g l e t h e mechanism of drug a c t i o n f o r many y e a r s t o come. However, t h e u s e of s u b s t i t u e n t c o n s t a n t s and l a r g e computers f o r r e g r e s s i o n a n a l y s i s o f f e r s u s new hope denied workers a few y e a r s ago. References
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