Biological CorrelationsâThe Hansch Approach

1 The Extrathermodynamic Structure-Activity

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Correlations Background of the Hansch Approach

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

The

background

approach proach

supporting

the

versatility

of the

Hansch

is that it is in fact an extrathermodynamic to drug

action.

-activity relationship as equations

which

tive

with

studies

elucidate

the

microscopic

The

information

of various provide simpler

mechanism knowledge

kinds

of drugs is

a convenient and of

similar overall

of complex

on the way for model

drug

expressed compara-

reactions

action

processes

ap-

structure-

to

without in

occurring

vivo.

T n order for a d r u g to e x h i b i t a c e r t a i n b i o l o g i c a l effect, i t m u s t interact w i t h a c e r t a i n c e l l u l a r c o m p o n e n t at the site of action. T h i s c o m p o n e n t is often c a l l e d a receptor.

H o w e v e r , b i o l o g i c a l systems are c o m p o s e d of

a n u m b e r of heterogeneous phases, a n d the site at w h i c h a d r u g is a d m i n i s t e r e d is u s u a l l y separated f r o m the site of a c t i o n . T h u s , the d r u g m u s t b e t r a n s p o r t e d t h r o u g h phase b o u n d a r i e s a n d u n d e r g o

adsorption

a n d d e s o r p t i o n processes w i t h proteins a n d m e m b r a n e s , as w e l l as p a r titioning between

different l i q u i d phases, before it reaches the site of

a c t i o n . M o r e o v e r , the d r u g - r e c e p t o r i n t e r a c t i o n at this site does not o c c u r w i t h o u t p e r t u r b a t i o n b y s u r r o u n d i n g heterogeneous components

s u c h as

w a t e r , s e r u m p r o t e i n , l i p i d p a r t i c l e s , etc. A l t h o u g h the transport processes a n d the d r u g - r e c e p t o r i n t e r a c t i o n are essentially p h y s i c o c h e m i c a l , t h e y are far m o r e c o m p l e x t h a n the h o m o g e n e o u s e q u i l i b r i a a n d rate processes of u s u a l o r g a n i c reactions.

I n this s i t u a t i o n , it w o u l d r a r e l y b e possible

to e l u c i d a t e the m e c h a n i s m of d r u g a c t i o n i f w e w e r e to insist u p o n o n l y d e t e r m i n i s t i c as w e l l as m i c r o s c o p i c models of i n d i v i d u a l stages of the transport a n d i n t e r a c t i o n processes. 1 Van Valkenburg; Biological Correlations—The Hansch Approach Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

2

BIOLOGICAL CORRELATIONS

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

R e c e n t l y , o u r H a n s c h a p p r o a c h has b e e n w i d e l y a c c e p t e d a n d r e c o g n i z e d as a versatile w a y to u n d e r s t a n d d r u g a c t i o n b y a n a l y z i n g the 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 h i p i n v a r i o u s b i o l o g i c a l systems

( I , 2,

3).

T h i s a p p r o a c h assumes that the p h y s i c o c h e m i c a l factors g o v e r n i n g the transport a n d d r u g - r e c e p t o r i n t e r a c t i o n c a n be f a c t o r e d into e l e c t r o n i c , h y d r o p h o b i c , a n d steric components.

I n g e n e r a l , one c a n consider that

the v a r i a t i o n s i n b i o l o g i c a l a c t i v i t y a r i s i n g f r o m s t r u c t u r a l modifications in congeneric drugs depend p h y s i c o c h e m i c a l factors.

u p o n the c o n c o m i t a n t

changes i n

these

T h e a s s u m p t i o n is s u m m a r i z e d as E q u a t i o n 1

w i t h parameters for the f a c t o r e d p h y s i c o c h e m i c a l p r o p e r t i e s , Ε, H, a n d S, respectively.

I n a series of congeners, t h e b i o l o g i c a l a c t i v i t y , B A , for a ΔΒΑ = / ( Δ # , Δ # , Δ δ ) Β Α = f(AE,

reference c o m p o u n d

(1)

AH, AS) + constant

(2)

is a constant . T h u s , E q u a t i o n 2 holds for

m e m b e r of the series.

each

U s u a l l y , the v a l u e of B A is t a k e n to be r e c i p r o

c a l l y p r o p o r t i o n a l to the d r u g c o n c e n t r a t i o n , C , w h i c h causes a s t a n d a r d b i o l o g i c a l response s u c h as E C

5 0

, I50, m i n i m u m i n h i b i t o r y c o n c e n t r a t i o n ,

etc. o n a m o l a r basis. M o r e p r a c t i c a l l y , the free-energy r e l a t e d parameters are u s e d s u c h as l o g 1 / C for Β Α, π or l o g F for AH, σ, σ*, σ', or Δ ^ for AE a n d E

8

or E

8

C

for Δ 5 .

K

A

π is the h y d r o p h o b i c substituent constant

d e r i v e d f r o m the p a r t i t i o n coefficient,

F , w h i c h is u s u a l l y d e t e r m i n e d

w i t h the use of 1 - o c t a n o l / w a t e r system (4, 5 ) , σ is the H a m m e t t constant ( 6 ) , σ' is a n electronic p a r a m e t e r for r a d i c a l reactions ( 7 ) , σ* a n d E

are

s

the Taft's p o l a r a n d steric constants for a l i p h a t i c systems ( 8 ) , a n d E

C

8

the H a n c o c k c o r r e c t e d steric constant ( 9 ) .

is

T h e most w i d e l y u s e d e q u a

t i o n i n this a p p r o a c h is f o r m u l a t e d as E q u a t i o n 3, w h e r e a ( ^ 0 ) , b, ρ, δ, a n d c are constants w h i c h are d e t e r m i n e d b y the regression analysis u s i n g the least-squares m e t h o d . log 1/C — -a

(log P )

2

+ b log Ρ + σ + SE + c Ρ

(3)

8

I n this w a y it is possible to a n a l y z e h o w each of the p h y s i c o c h e m i c a l properties of the m o l e c u l e

is c o n c e r n e d

examples are s h o w n i n E q u a t i o n s 4 - 1 1 .

w i t h the d r u g a c t i o n .

Some

I n these equations, η is the

n u m b e r of points u s e d i n the regression, s is the s t a n d a r d d e v i a t i o n , a n d r is the c o r r e l a t i o n coefficient. NADH

Oxidation,

Inhibition

by Barbiturates

(3)

0 R

X

n

χ K 2

pleo — 1 . 1 1

C-NH

log Ρ +

1.24

6

s 0.261

r 0.921

>=° C-NH

// Ο

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

(4)

1.

Extrathermodynamic

FUJITA

Chymotrypsin, Miscellaneous

Inhibition Neutral

Structure-Activity

by Compounds p2£/ =

3

Correlations

(2)

1.00 log Ρ — 2.60

n s 8 0.139

r 0.995

(5)

0.971

(6)

0.930

(7)

Cat, Inhibition of Salivary Secretion, Benzilic Acid Choline Esters (10,11)

( C H ) C (OH) C O O C H C H — N 5 I 6

5

2

2

2

2

log Β Α — - 3 . 3 1 3 σ * -

0.552π +

2.30

13 0.159 Alfalfa, Growth Inhibition, Benzyl Quaternary Ammonium

Ions (11, 12)

pl HO

CH.,

CH

=

5 0

- 1 . 0 2 σ + 0.64π +

^

:{

/]—Λ/Χ N _ C H CH

2

- ^

1.50

'

9 0.119

^

3

S. Aureus, Bacteriostatic Activity, Kojic Acid Analogs (pH 7) (13) 1 log β-

_

0.97 A l o g K

A

+ 1.49π(Χ) + 9

6

0.511

0.956

(8)

0.938

(9)

0.945

(10)

CH X 2

Carbonic Anhydrase, Benzenesulfonamides, SO NH 2

2

Inhibition, (14) pK

r

=

0.77

Alog K

A

+

0.38π +

0.52

16 0.216

Tobacco Pith, Cytokinin Diphenylureas (15, 16) /

1.71

0

^ ^ - N H C N H C H .

Activity,

l o g 1/C =

Ι.ΙΟσ + 0.36π +

5.68 9

0.178

X


4


Wheat Coleoptile Auxin Activity, I

„

Cylinder, cis-Cinnamic

Acids

(15,

17)

log 1 / C = - 0 . 5 0 (log P)

2

w


+ 2.45 log Ρ 8

0.290 0.815

(11)

I n E q u a t i o n s 10 a n d 11 the σ values are those to the o r t h o p o s i t i o n of the side c h a i n . I n c l a s s i c a l s t r u c t u r e - a c t i v i t y studies, most of the attempts c o n c e n t r a t e d o n c o r r e l a t i n g the a c t i v i t y w i t h one of the m o l e c u l a r p r o p e r t i e s — e.g.,

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

t h e i r e l e c t r o n i c structure (18, 19),

the n a r c o t i c a c t i v i t y w i t h l i p o p h i l i c i t y

the i n s e c t i c i d a l a c t i v i t y of c y c l o d i e n e s w i t h t h e i r t h r e e - d i m e n

(20, 21),

s i o n a l m o l e c u l a r silhouette (22),

etc.

Sometimes the a c t i v i t y c o r r e l a t e d

w e l l w i t h o n l y one of the m o l e c u a r parameters.

I n o u r a p p r o a c h these

are s p e c i a l cases w h e r e other p h y s i c o c h e m i c a l properties d o n o t p l a y c r i t i c a l roles i n d e t e r m i n i n g the v a r i a t i o n i n the a c t i v i t y w i t h i n a set of congeners so that the coefficients d e f i n i n g these other properties are zero. T h e p a r a m e t e r i z a t i o n of the h y d r o p h o b i c most i m p o r t a n t aspects of this a p p r o a c h . stituent or a p a r t of a m o l e c u l e molecules

character is one of

the

T h e π v a l u e of a c e r t a i n sub

is n e a r l y constant i n closely r e l a t e d

a n d m a y b e s u m m e d w i t h other π values to c a l c u l a t e a n d

p r e d i c t u n k n o w n l o g F values of a n u m b e r of m o l e c u l e s (3, 4, 5).

Thus,

the analyses c a n often be p e r f o r m e d w i t h the c a l c u l a t e d l o g F values. O n e e x a m p l e for s u c h a n a d d i t i v e p r i n c i p l e is the l - o c t a n o l / H 0 p a r t i t i o n 2

coefficient of β - B H C ( le, le, 3e, 4e, 5e, 6e-hexachlorocyclohexane ) w h i c h has b e e n d e t e r m i n e d r e c e n t l y b y K u r i h a r a (23).

T h e l o g F v a l u e , 3.78,

is d i v i d e d b y 6 to estimate the π v a l u e of a > C H — C I u n i t . T h e v a l u e , log P ( C H C l ) / 6 = 6

6

e

7r

0.63,

c a l c

.(>CH—CI)

=0.60

0.63, agrees v e r y w e l l w i t h t h a t c a l c u l a t e d as 2π, 0.60, u s i n g 0.41 for a r i n g c a r b o n a t o m , 0.39 for a n a l i p h a t i c c h l o r i n e a t o m , a n d - 0.20 for a b r a n c h i n g structure. S i n c e t h e π v a l u e is c o n s t i t u t i v e , the stereospecific n a t u r e of h y d r o phobic

bonding

for

drug-receptor

interactions c a n b e

delineated

by

regression analyses w i t h the π values of substituents separately f o r e a c h p o s i t i o n of the congeners.

T h u s , the substituent effect o n the e m u l s i n

h y d r o l y s i s of s u b s t i t u t e d p h e n y l g l u c o s i d e s has b e e n n i c e l y d e l i n e a t e d b y a n a l y z i n g k i n e t i c constants separately for m e t a a n d p a r a isomers. m e t a substituents p l a y n o h y d r o p h o b i c complex formation

r o l e i n the

The

enzyme-substrate

(24).


1.

FUJITA

Extrathermodynamic

Structure-Activity

5

Correlations

A n o t h e r e x a m p l e is the case of bacteriostatic a c t i v i t y of k o j i c a c i d analogs w h i c h is a n a l y z e d i n E q u a t i o n 8 ( 1 3 ) .

I n this e q u a t i o n , C

n

the m i n i m u m i n h i b i t o r y c o n c e n t r a t i o n for t h e n e u t r a l m o l e c u l e infra),

a n d π(Χ)

is

(vide

is the p a r a m e t e r for substituents at the 7 p o s i t i o n .

N e i t h e r the use of π ( Χ +

Y ) n o r the a d d i t i o n of ττ(Υ) t e r m i m p r o v e the

c o r r e l a t i o n . T h e substituents, Y , at the 2 p o s i t i o n , s a n d w i c h e d

between

h y d r o x y l a n d ether o x y g e n , m i g h t b e s u r r o u n d e d b y t i g h t l y h y d r a t e d w a t e r molecules so that t h e y are u n a b l e to p a r t i c i p a t e i n the b i n d i n g of the m o l e c u l e w i t h a h y d r o p h o b i c surface of the receptor. T h e a s s u m p t i o n that the n o n l i n e a r d e p e n d e n c e of d r u g a c t i v i t y o n the h y d r o p h o b i c c h a r a c t e r of the m o l e c u l e is expressed b y the q u a d r a t i c terms of l o g F or π has b e e n e x e m p l i f i e d b y a n u m b e r of congeners w h e r e the l o g F values c o v e r a sufficiently large range (2, 3, 2 5 ) .

R e c e n t l y this

has b e e n p r o v e d t h e o r e t i c a l l y w i t h a k i n e t i c m o d e l s i m i l a r to those u s e d i n the m u l t i c o m p a r t m e n t a l analyses (26) b a s e d o n p r o b a b i l i t y concepts (27).

as w e l l as b y a s i m p l e m o d e l

T h e o p t i m u m v a l u e of l o g P, l o g F , 0

o b t a i n e d b y setting the d e r i v a t i v e dlog 1 / C / d l o g F e q u a l to zero, is a u s e f u l p a r a m e t e r for d e s i g n i n g the most potent d r u g i n a set of congeners as w e l l as for i l l u s t r a t i n g the character of b a r r i e r s t h r o u g h w h i c h drugs h a v e to t r a v e l (25,

28).

F r o m E q u a t i o n 11 the l o g F

0

v a l u e for the g r o w t h p r o m o t i o n

of

w h e a t coleoptile segments w i t h c i n n a m i c acids is c a l c u l a t e d as 2.45. T h i s v a l u e is v e r y close to those o b t a i n e d for the g r o w t h p r o m o t i o n of a v e n a coleoptile

segments

with

substituted phenoxyacetic

acids, the l o g P values b e i n g a r o u n d 2 — 2.5 (29, 30). 0

and

phenylacetic

T h u s , the p h y s i c o -

c h e m i c a l c h a r a c t e r of b a r r i e r s to r e a c h the site of a u x i n a c t i o n i n p l a n t tissues w o u l d b e s i m i l a r for different sets of c o m p o u n d s . tions have b e e n o b s e r v e d for the l o g F

0

Similar situa

values of various sets of d r u g s

i n h i b i t i n g g r o w t h of g r a m - n e g a t i v e a n d g r a m - p o s i t i v e b a c t e r i a

(25).

O n e q u e s t i o n sometimes a s k e d b y biologists is w h y the d r u g a c t i o n o n s u c h v a r i o u s levels of b i o l o g i c a l systems as e n z y m e p r e p a r a t i o n s a n d s u b c e l l u l a r organelles as w e l l as w h o l e plants a n d a n i m a l s c a n be a n a lyzed by a common procedure.

F o r instance, the e n z y m e - i n h i b i t o r r e a c

t i o n seems a m u c h s i m p l e r p h e n o m e n o n t h a n the a c t i o n of c y t o k i n i n s o n p l a n t tissues a n d , yet, t h e y are i l l u s t r a t e d i n a s i m i l a r m a n n e r as s h o w n i n E q u a t i o n s 9 a n d 10. I n fact, the e n z y m e - i n h i b i t o r i n t e r a c t i o n i n itself is a c h a i n of c o m p l e x processes for the i n h i b i t o r m o l e c u l e , i n c l u d i n g a n u m b e r of desolvations, collisions w i t h nonspecific sites o n the e n z y m e p r o t e i n , a n d resolvations before r e a c h i n g the specific i n h i b i t i o n site. T h e c o m p l e x i t y is not at a l l less t h a n those c o n s i d e r e d for the transport a n d drug—receptor i n t e r a c t i o n processes of c y t o k i n i n s . T h e s i t u a t i o n is analogous to that a set of every rational number

between

zero

a n d one

corresponds

in a

one-to-one


6



f a s h i o n a n d thus is e q u i v a l e n t to a set of e v e r y integer b e t w e e n zero a n d i n f i n i t y — i . e . , a "set" of b a r r i e r s w h i c h i n h i b i t o r molecules m u s t traverse to r e a c h the i n h i b i t i o n site of the e n z y m e w o u l d be e q u i v a l e n t to a "set" of those for the c y t o k i n i n a c t i v i t y . T h e e n z y m e - i n h i b i t o r i n t e r a c t i o n p r o c esses c o u l d b e a m i n i a t u r e m o d e l of the d r u g a c t i o n i n b i o l o g i c a l systems of the h i g h e r l e v e l . T h u s , w h i c h e v e r m a y be the l e v e l of b i o l o g i c a l sys tems, essentially the same p r o c e d u r e c a n b e a p p l i e d for the d r u g a c t i o n . A n o t h e r q u e s t i o n w h i c h often arises is w h y s u c h diverse b i o l o g i c a l effects of different p h y s i o l o g i c a l significance are r a t i o n a l i z e d b y

essen

t i a l l y the same t y p e of e q u a t i o n w h e r e o n l y p h y s i c o c h e m i c a l properties of drugs are c o n s i d e r e d .

A s a suitable approximation, any biological

effect c a n b e defined b y t w o aspects. c h a r a c t e r s u c h as p h o t o s y n t h e t i c

O n e is its specific p h y s i o l o g i c a l

inhibition, parasympatholytic action,

bacteriostatic a c t i o n , etc., w h i c h is d e t e r m i n e d b y the b i o l o g i c a l test object a n d the specificity of the receptor.

T h e other aspect is t h e m a g n i

t u d e of the effect w h i c h c a n b e m e a s u r e d q u a n t i a t i v e l y . It c a n b e f u r t h e r d i v i d e d into sub-elements s u c h as affinity a n d i n t r i n s i c a c t i v i t y as d i s cussed b y A r i e n s ( 3 1 ) . It is g e n e r a l l y a c c e p t e d t h a t a d r u g initiates a c h a i n of events w h i c h e v e n t u a l l y leads to a specific b i o l o g i c a l effect b u t w h i c h does n o t i n v o l v e the d r u g after it triggers the m e c h a n i s m t h r o u g h a d r u g - r e c e p t o r i n t e r a c t i o n . F o r e x a m p l e , sucrose tastes sweet, b u t the r o l e of sucrose m o l e cules is to s t i m u l a t e the taste b u d s , a n d t h e y d o not p a r t i c i p a t e i n the process of sensory c o n d u c t i o n as s u c h . T h e m a g n i t u d e of the observable b i o l o g i c a l response is a d i r e c t r e flection

of the i n t e n s i t y of the c h a i n of p h y s i o l o g i c a l events w h i c h , i n

t u r n , is d e t e r m i n e d b y the degree of d r u g - r e c e p t o r

interaction.

The

degree of drug—receptor i n t e r a c t i o n is c o n t r o l l e d b y the p h y s i c o c h e m i c a l properties of the partners a n d the d r u g c o n c e n t r a t i o n at the site of a c t i o n , w h i c h , i n t u r n , is g o v e r n e d

b y the p h y s i c o c h e m i c a l transport

process.

T h u s , as far as a specific b i o l o g i c a l effect is c o n c e r n e d , i t is reasonable to consider that the m a g n i t u d e of the response is expressed b y a f u n c t i o n of the p h y s i c o c h e m i c a l properties of the d r u g m o l e c u l e .

It is the m a g n i

t u d e of the b i o l o g i c a l effect w h i c h is u s e d for the s t r u c t u r e - a c t i v i t y analyses. A n i n t e r e s t i n g e x a m p l e w h i c h w o u l d i l l u s t r a t e the a b o v e s i t u a t i o n is the case of D D T a n d its analogs a l t h o u g h t h e i r 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 h i p has not b e e n successfully a n a l y z e d b y E q u a t i o n 3. D D T is w e l l k n o w n as a n i n s e c t i c i d e w h i c h k i l l s b y d i s r u p t i n g nerve c o n d u c t i o n (32).

D D T analogs w h e r e the ρ,ρ'-substituents o n the benzene rings are

c h a n g e d are k n o w n to e x h i b i t v a r i o u s degrees of a c t i v i t y ( 3 3 ) .

DDE,

w h i c h is f o r m e d b y d e h y d r o c h l o r i n a t i o n of D D T , is not i n s e c t i c i d a l . A


1.

Extrathermodynamic

FUJITA

Structure-Activity

7

Correlations

s i m i l a r p a t t e r n of a c t i v i t y for this class of c o m p o u n d s has b e e n o b s e r v e d for the i n h i b i t i o n of the c y c l i c p h o t o p h o s p h o r y l a t i o n of b a r l e y

(34).

T h u s , e v e n i f the o b s e r v e d p h y s i o l o g i c a l effect is d i s t i n c t l y different, the m a g n i t u d e of a c t i v i t y seems to f o l l o w the same p r i n c i p l e . F o r D D T a n d its analogs the m a i n c o n c e r n is to find a w a y to the i n t e r a c t i o n w i t h receptor sites w h i c h is c a p a b l e of m a t c h i n g t h e i r p h y s i c o c h e m i c a l p r o p erties regardless of w h e t h e r the sites are l o c a t e d o n the insect n e r v e o r o n the chloroplasts. E v e n i f the i m p o r t a n t r o l e of p h y s i c o c h e m i c a l factors g o v e r n i n g the m a g n i t u d e of d r u g a c t i v i t y w o u l d b e c o m e clearer, one m i g h t s t i l l

be

r e l u c t a n t to accept this a p p r o a c h since the p r o c e d u r e is e m p i r i c a l r a t h e r t h a n t h e o r e t i c a l . W i t h the use of regression analysis, i t is p o s s i b l e to separate the relative significance of p h y s i c o c h e m i c a l factors i n the o v e r a l l a c t i o n of a d r u g . O f course, one or a f e w of the o v e r a l l processes c o u l d be e x p e c t e d to be c r i t i c a l i n d e t e r m i n i n g the d r u g a c t i v i t y . w e cannot i d e n t i f y these p a r t i c u l a r processes,

However,

e s p e c i a l l y w h e n for

a m p l e the w h o l e a n i m a l b o d y is u s e d to evaluate d r u g a c t i o n .

ex

Thus,

even i f a n e q u a t i o n w h i c h shows a significant role of the electronic factor is o b t a i n e d for c o n g e n e r i c d r u g s , p h y s i c a l o r g a n i c chemists m a y b e d i s t r u s t f u l of u s i n g the H a m m e t t σ or the T a f t σ* constant for a r e a c t i o n w h i c h cannot b e i d e n t i f i e d . E v e n so, the separation of p h y s i c o c h e m i c a l factors p l a y i n g roles i n the o v e r a l l d r u g a c t i v i t y is a n i m p o r t a n t p o i n t f r o m w h i c h to start a search for e l u c i d a t i n g the m e c h a n i s m of the d r u g a c t i o n . Some examples are c o n s i d e r e d i n the f o l l o w i n g sets of c o m p a r a tive correlations. Substituted

Phenyl

Diethyl

Phosphates

R a t e of a l k a l i n e h y d r o l y s i s in vitro log fc . == 1.35σ~ hyd

(35)

5.09

n s r 7 0.238 0.955

(12)

6

0.297 0.985

(13)

8

0.206 0.990

(14)

I n h i b i t i o n against flyhead acetylcholinesterase (35, 36) pl

5 0

= 2.37σ" + 4.38

T o x i c i t y against house fly (1, 35) -logLD

5 0

= 0 . 3 6 1 o g P + 2.65a- + 2.44

T h e p o s i t i v e ρ values of these correlations for reactions of s u b s t i t u t e d p h e n y l phosphates m a y i n d i c a t e a c o m m o n

feature i n these reactions

w h e r e a n u c l e o p h i l i c attack o n p h o s p h o r u s is a c r i t i c a l step. T h e m a g n i tudes of the ρ values of E q u a t i o n s 13 a n d 14 are v e r y close to each other b u t s i g n i f i c a n t l y l a r g e r t h a n that of E q u a t i o n 12. T h u s , the e l e c t r o n i c effect of the substituents o n the insect m o r t a l i t y c a n b e r e l a t e d m o s t l y to an effect o n the e n z y m e i n h i b i t i o n a n d p l a y s o n l y a m i n o r r o l e i n the


8


transport step.


H o w e v e r , besides the u s u a l n u c l e o p h i l i c attack o n p h o s

p h o r u s w h i c h occurs in vitro,

other steroelectronic

factors

should

be

c o n s i d e r e d for the in vivo e n z y m a t i c reactions. Substituted

Phenyl

N-Methyl

Carbamates

R a t e of a l k a l i n e h y d r o l y s i s in vitro log fc H-] = 2.48σ" +

(37)

3.03

[0

F l y h e a d acetylcholinesterase i n h i b i t i o n (38, pl

5 0

_

ο.69π -

0.95σ' + 1.19X +

n 6

s 0.156

r 0.977

(15)

53

0.415

0.913

(16)

39)

3.50

A m o r e c o m p l e x s i t u a t i o n is o b s e r v e d w i t h carbamate

insecticides.

H e r e , the s i g n of the ρ v a l u e o n E q u a t i o n 16 for the e n z y m e i n h i b i t i o n is opposite that i n E q u a t i o n 15 for the in vitro

alkaline hydrolysis.

In

E q u a t i o n 16, X is a p o s i t i o n p a r a m e t e r w h i c h takes a v a l u e of 1 for m e t a substituents a n d 0 for p a r a substituents. T h e e n z y m e i n h i b i t i o n has b e e n c o n s i d e r e d to o c c u r b y c a r b a m y l a t i o n at the serine O H i n the a c t i v e site of acetylcholinesterase, a n d thus the m e c h a n i s m s h o u l d i n c l u d e a step for the n u c l e o p h i l i c attack of the serine O H o n the c a r b a m y l g r o u p .

The

negative s i g n of ρ a n d the significance of the X t e r m i n E q u a t i o n 16 s h o u l d i n d i c a t e that, at least, the c a r b a m y l a t i o n of the e n z y m e is not the c r i t i c a l step, a n d q u i t e different stereoelectronic

conditions are r e q u i r e d

for this series of c o m p o u n d s f r o m those for the in vitro

nucleophilic

h y d r o l y s i s a n d also f r o m those for the enzyme—inhibitor i n t e r a c t i o n of the p h o s p h a t e

insecticides.

A l t h o u g h the difference

i n the

electronic

effect of substituents o n the e n z y m e i n h i b i t i o n has b e e n r e c o g n i z e d exist b e t w e e n

to

carbamates a n d phosphates, o n l y b y s e p a r a t i n g p h y s i c o -

c h e m i c a l effects w o u l d w e k n o w to w h a t degree t h e y are different a n d w h e t h e r or not other effects m a y p l a y roles. 2-Bromoethylthiobenzenes H y d r o l y s i s in vitro

(40)

log k ( 3 0 ° ) — - 1 . 2 3 σ R a t e of a l k y l a t i o n in vitro Û

n 8

6.59

(17)

(41) S—CH2CH2R

^V-S—CH CH Br 2

s r 0.048 0.984

2

X

logk(30°)

1.98σ

-4.10

12

0.073 0.994


(18)

1.

Extrathermodynamic

FUJITA

T o x i c i t y against eggs of Tetranychus telanus ( L . )

-log LC As

5 0

Structure-Activity

9

Corrections

(42)

— - 2 . 1 8 π + 1.69ττ -

1.45σ + 4.38

2

n

s

r

8

0.164

0.968

(19)

s h o w n i n E q u a t i o n 19, the s u b s t i t u e n t effects o n the o v i c i d a l

a c t i v i t y c a n be s e p a r a t e d i n t o h y d r o p h o b i c a n d e l e c t r o n i c factors.

There

is a n o p t i m a l v a l u e for h y d r o p h o b i c i t y f o r the o v i c i d a l a c t i o n of this set of c o m p o u n d s .

T h a t the σ v a l u e i n E q u a t i o n 19 is s i m i l a r to those o b

t a i n e d for in vitro reactions w o u l d suggest t h a t a c o m m o n step is c r i t i c a l i n b i o l o g i c a l as w e l l as in vitro reactions.

F o r the in vitro reactions, the

r a t e - d e t e r m i n i n g step is c o n s i d e r e d to b e the f o r m a t i o n of c y c l i c s u f o n i u m ions (40,

41).

Fenamic

Acids

COOH

Uncoupling activity with rat h e a r t m i t o c h o n d r i a

(43)

log l / C i = 0.78π + 0.36 A\ogK

+ 4.32

A

n 11

s 0.200

r 0.939

(20)

12

0.106

0.867

(21)

A n t i - i n f l a m m a t o r y a c t i v i t y against a n t i s e r u m i n d u c e d r a t edema (43) log B A , = 0.39TT + 0.37 A l o g K

A

+

1.55

A s s h o w n i n E q u a t i o n s 20 a n d 2 1 , the u n c o u p l i n g a c t i v i t y a n d a n t i i n f l a m m a t o r y a c t i v i t y of f e n a m i c a c i d analogs, i n c l u d i n g mefenamic

flufenamic

acids, are v e r y s i m i l a r i n t h e i r d e p e n d e n c e o n b o t h

and

hydro

p h o b i c a n d e l e c t r o n i c effects of substituents. I n these equations, the s u b s c r i p t , i, means t h a t the d r u g a c t i v i t i e s are c a l c u l a t e d o n the basis c o n c e n t r a t i o n of the i o n i z e d f o r m .

b i o l o g i c a l effects, w h i c h are also o b s e r v e d inflammatory drugs, have i n t e r a c t i o n w i t h receptors Alkyl

i n m a n y other a c i d i c a n t i

similar physicochemical

mechanisms

x^^^X^sOzNHz

Mouse, antistrychnine activity

8

i n the

(44).

2-Sulfamoylbenzoates

l o g 1/C = 0.21 E (R)

of

I t has b e e n suggested t h a t these t w o

(45)

COOR

— 0.24 log Ρ — 3.87 σ* (R)

+3.05 n 9

s 0.058

r 0.959


(22)

10


M o u s e , antielectroshock a c t i v i t y


(45)

log 1 / C = 0.40 E (R) - 0.92 log F - 6.34 σ* (R) - 0 . 5 3 Χσ(Χ,Υ) +2.91

n 12

8

s r 0.224 0.860

(23)

H a m o r a n d L i e n h a v e a n a l y z e d a n t i c o n v u l s a n t activities of s u l f a m o y l benzoates.

F o r the test of a n t i s t r y c h n i n e a c t i v i t y , c o m p o u n d s h a v i n g the

same a r o m a t i c substituents are u s e d so that no 2 σ ( Χ , Υ ) t e r m appears i n E q u a t i o n 22.

T h e y h a v e suggested that the s i m i l a r i t y of equations i n

terms of steric, h y d r o p h o b i c , indicates a common

a n d e l e c t r o n i c p r o p e r t i e s of

substituents

a n t i c o n v u l s a n t m e c h a n i s m for t h e t w o

effects of this set of c o m p o u n d s .

biological

T h e y h a v e also suggested

that the

m e c h a n i s m of a c t i o n of these drugs was q u i t e different f r o m those

of

b a r b i t u r a t e s a n d other h y p n o t i c s w h e r e q u i t e different s t r u c t u r e - a c t i v i t y correlations of p h y s i c o c h e m i c a l significance h a v e b e e n o b t a i n e d . MAO

Inhibitors

R a t liver M A O , phenoxyethylcyclo p r o p y l a m i n e s (46)

pl

5 0

= 0.70 E

mm

8

+

1.64σ + 0.20ττ +

4.15

n 18

s r 0.330 0.945

(24)

Beef liver M A O , substituted β-carbolines (47, 48)

pl

5 0

= 0.61 Ε >* + 0 . 7 2 a 6

8

4b

+ 0.52ττ + 3.03

8 0.124

0.985

(25)

0.273 0.942

(26)

R a t l i v e r Μ Α Ο , p a r g y l i n e d e r i v a t i v e s (47, 49) f y—

pl

5 0

= 0.79 E

4

8

CH

CH —Ν—CH2—C=CH

+ 1.02σ + 0.44ττ + 2

3

2

5.49

10


1.

FUJITA

Extrathermodynamic

Structure-Activity

11

Correlations

K u t t e r a n d H a n s c h h a v e a n a l y z e d the m o n o a m i n e oxidase i n h i b i t i o n of p h e n o x y e t h y l c y c l o p r o p y l a m i n e s (46).

E q u a t i o n 24 shows that specific

steric effects as w e l l as e l e c t r o n - a t t r a c t i n g a n d h y d r o p h o b i c p r o p e r t i e s of substituents are responsible to the a c t i v i t y . R e c e n t l y , i t has b e e n s h o w n that the E v a l u e c a n b e u s e d as a n i n d e x for i n t e r m o l e c u l a r steric effects 8

(46).

I n E q u a t i o n 24, E

mm

8

is the s u m of E values of substituents at the 8

t w o m e t a positions. T h e p o s i t i v e s i g n of the coefficient of this t e r m means that the c o r r e s p o n d i n g positions o n the r e c e p t o r site cannot a c c o m m o d a t e l a r g e r substituents because of steric restraint. S i m i l a r substituent effects are o b s e r v e d for t h e a n t i - M A O a c t i v i t y of β-carbolines a n d p a r g y l i n e d e r i v a t i v e s (47).

I n E q u a t i o n 25, E

s

6

'

8

is the

s u m of values of the 6 a n d 8 substituents, a n d a b is the σ v a l u e of s u b 4

stituents to the 4 b p o s i t i o n . I n E q u a t i o n 26, E

e

4

corresponds to the p a r a

substituent a n d σ to the ortho p o s i t i o n of the side c h a i n . T h e c o i n c i d e n c e 2

i n the stereoelectronic effects of substituents o n the M A O i n h i b i t i o n is s u r p r i s i n g l y g o o d f o r these three classes of i n h i b i t o r s . O n the s t r u c t u r a l f o r m u l a s s h o w n a b o v e , the arrows i n d i c a t e positions w h e r e the σ values are d i r e c t e d , a n d the s h a d e d circles s h o w s t e r i c a l l y l i m i t e d positions. T h u s , the i n d i v i d u a l correlations are s u b s t a n t i a t e d , a n d p h y s i c o c h e m i c a l significance is p r o v e d b y s i m i l a r b i o l o g i c a l correlations. T h e examples a b o v e are o n l y a f e w of n u m e r o u s instances w h i c h h a v e b e e n f o u n d so far.

I n m a n y cases i t is possible to find clues to

d e v e l o p the studies o n the m e c h a n i s m of d r u g a c t i o n b y e x a m i n i n g d i f ferences or c o m m o n

features a m o n g s t r u c t u r e - a c t i v i t y a n d s t r u c t u r e -

r e a c t i v i t y r e l a t i o n s h i p s . E v e n i f d e t a i l e d m i c r o s c o p i c m e c h a n i s m s o n the o v e r a l l processes of d r u g a c t i o n are not i d e n t i f i e d e x p l i c i t l y , explanations of substituent effects a n d sometimes i n f o r m a t i o n a b o u t c r i t i c a l process ( es ) d e t e r m i n i n g the a c t i v i t y c a n b e o b t a i n e d b y c o m p a r i s o n w i t h those of s i m p l e r a n d s i m i l a r m o d e l reactions a n d / o r d r u g actions w i t h the use of free-energy r e l a t e d parameters.

T h u s , our procedure can be called an

e x t r a t h e r m o d y n a m i c a p p r o a c h (50)

to d r u g a c t i o n .

E v e n m o r e i m p o r t a n t , the equations are a c o n v e n i e n t w a y to store a n d r e t r i e v e i n f o r m a t i o n o n s t r u c t u r e - a c t i v i t y relationships w h e n b i n e d w i t h the use of a l a r g e c o m p u t e r .

I f the enormous

com

a m o u n t of

i n f o r m a t i o n a c c u m u l a t e d so far is stored i n the c o m p u t e r , one c a n sort out a set of equations a c c o r d i n g to t h e i r c h a r a c t e r i s t i c features s u c h as the m a g n i t u d e a n d s i g n of the coefficient of e a c h terms a n d intercept. I n this w a y the s t r u c t u r e - a c t i v i t y correlations o b t a i n e d for a c e r t a i n series of c o n g e n e r i c d r u g s o n v a r i o u s b i o l o g i c a l systems a n d for v a r i o u s series of drugs o n a c e r t a i n b i o l o g i c a l system or for v a r i o u s series of drugs o n v a r i o u s b i o l o g i c a l systems c a n b e classified a n d c o m p a r e d i n terms of t h e i r p h y s i c o c h e m i c a l significance. A s i l l u s t r a t e d e l e g a n t l y b y C o r w i n


12



H a n s c h ( C h a p . 2 ) , the c o m p u t e r i z e d a p p r o a c h s h o u l d b e a serious step toward quantitative comparative

pharmacodynamics.

W h i l e the v e r s a t i l i t y is w e l l a c c e p t e d , p r a c t i c i n g this a p p r o a c h .

one s h o u l d b e cautious i n

T h e l a c k of a d d i t i v i t y of ττ a n d l o g Ρ values

has b e e n f o u n d i n molecules w h e r e i n t r a m o l e c u l a r interactions are n o t n e g l i g i b l e (51, 52, 53).

T h e l o g Ρ values of ^ - p y r i d y l m e t h y l d i a l k y l a m i n e s

h a v e b e e n d e t e r m i n e d as s h o w n i n T a b l e I ( 5 2 ) . T h e values c a l c u l a t e d o n the basis of STT, π ( p y r i d i n e ) = =

0.65, ir(-CH^)

=

0.5 a n d 7 r [ N ( C H ) ] 3

2

—0.35, are q u i t e different f r o m the c o r r e s p o n d i n g e x p e r i m e n t a l values.

T h e l a c k of a d d i t i v i t y s h o u l d i n d i c a t e p e c u l i a r i n t r a m o l e c u l a r interactions d e p e n d i n g u p o n the side c h a i n structure. I n s u c h cases, i t is essential to use t h e e x p e r i m e n t a l l o g Ρ values f o r s t r u c t u r e - a c t i v i t y correlations. Log Ρ Values of β-Pyridylmethyldialkylamines

Table I.

r ^ N - C H r - Ν

-CH

R log Ρ

-C2H5

S

obsd. calcd.

-iso-C H

-C H 3

3

7

7

0.49 0.80

1.01 1.80

1.46 2.30

2.27 1.90

1.47 2.80

0.31

0.79

0.84

0.37

1.33

A l t h o u g h the l a c k of a d d i t i v i t y is, i n a w a y , a d r a w b a c k to the s i m p l i c i t y a n d v e r s a t i l i t y of this a p p r o a c h , the difference b e t w e e n c a l c u l a t e d a n d e x p e r i m e n t a l l o g Ρ values c a n sometimes give i m p o r t a n t i n f o r m a t i o n o n t h e c o n f o r m a t i o n of the m o l e c u l e i n the aqueous phase ( 5 1 , 54).

The

ττ values of p o l a r substituents o b t a i n e d i n the a l k y l d e r i v a t i v e s are h i g h e r t h a n c o r r e s p o n d i n g values c a l c u l a t e d f r o m the a r y l a l k y l d e r i v a t i v e s . T h e differences

( n e a r l y constant a r o u n d 0.6) are t h o u g h t to arise f r o m i n t r a

m o l e c u l a r h y d r o p h o b i c b o n d i n g of the side c h a i n w i t h the a r o m a t i c r i n g i n a r y l a l k y l c o m p o u n d s w h i c h causes a b e n d i n g c o n f o r m a t i o n i n the a q u e ous phase. D e t a i l e d studies o n the n a t u r e of l o g Ρ a n d π parameters are discussed b y several authors i n subsequent chapters. It is i m p o r t a n t to d e t e r m i n e w h e t h e r or not e a c h substituent p a r a m e ter is a n i n d e p e n d e n t v a r i a b l e . If a c o n s i d e r a b l e c o r r e l a t i o n exists b e t w e e n t w o parameters i n a set of c o m p o u n d s , evaluate

the

q u a l i t y of

i t is often difficult to

s t r u c t u r e - a c t i v i t y correlations.

T a b l e I I are for the m u s c a r i n e - l i k e a c t i v i t y of m e a s u r e d b y the b l o o d pressure descent of cats

The

acetylcholine (55).

data i n analogs

T h e effect of

c a t i o n i c h e a d structure has b e e n a n a l y z e d u s i n g p h y s i c o c h e m i c a l p a r a m e ters of the Ν substituents

(11).


1.

Extrathermodynamic

FUJITA

Structure-Activity

13

Correlations n s r 7 0.490 0.954 7 0.490 0.954 7 0.490 0.954

log Β Α = - 5 . 1 8 Χσ* + 4.22 %Ε° - 0.063 log Β Α = 26.62 2ττ + 37.89 XE - 0.063 log Β Α = - 5 . 8 3 2σ* - 3.34 2π - 0.063 C

8

(27) (28) (29)

E q u a t i o n s 2 7 - 2 9 w i t h t w o parameters seem to s h o w reasonable c o r r e l a t i o n . A l t h o u g h E q u a t i o n 28 w o u l d b e u n a c c e p t a b l e because of u n u s u a l l y large p a r a m e t e r coefficients, the correlations are c o m p l e t e l y

equivalent

statistically. A s far as c o m p o u n d s

concerned,

u s e d for the analyses are

it is i m p o s s i b l e to choose the t w o significant parameters.

I n this case,

besides a significant c o r r e l a t i o n b e t w e e n parameters π a n d E

8y

m u t u a l relationships a m o n g three parameters.

there are

E a c h p a r a m e t e r is ex

pressed as a l i n e a r c o m b i n a t i o n of the other t w o a n d is not separated f r o m others. T o o b t a i n m e a n i n g f u l correlations, substituents m u s t be selected so that the substituent parameters i n c l u d e d i n a set of congeners are as separated as possible.

I n this e x a m p l e , not o n l y the h y d r o g e n , m e t h y l ,

a n d e t h y l , w h o s e parameters v a r y i n p a r a l l e l , b u t groups s u c h as i s o p r o p y l ( *

=

σ

-0.19, π =

1.60, E

C

8

=

1.20, E ° = 8

-0.47),

teri-butyl

- 1 . 5 4 ) , or t r i f l u o r o e t h y l ( σ * =

(σ* =

- 0 . 3 0 , ττ

0.92, π — 1.48, E ° =

c o u l d b e u s e d as the Ν substituents. T h e s i t u a t i o n has b e e n recently b y C r a i g

reviewed

(56).

Sometimes the use of q u a n t u m c h e m i c a l l y d e t e r m i n e d i n d i c e s (1, or o x i d a t i o n - r e d u c t i o n potentials (58)

57)

=

-0.79)

8

24,

i n s t e a d of the H a m m e t t - T a f t

constants, the use of c h r o m a t o g r a p h i c a l l y o b t a i n e d h y d r o p h o b i c i t y p a rameter, AR , m

(5, 59)

i n s t e a d of π or l o g P , or the a d d i t i o n of

variables s u c h as those for h y d r o g e n b o n d i n g (60), Table II.

I

+

CH COOCH CH N—R 3

Substituents

Me Me Me Η Me Me Et α

(61),

Muscarine-like A c t i v i t y of Acetylcholine Analogs Ri 2

2

2

Parameters

R

R

Me Me H H Me Et Et

Me H H H Et Et Et

2

other

d i p o l e moments

3

2σ*

2ττ

0.00 0.49 0.98 1.47 -0.10 -0.20 -0.30

0.00 -0.50 -1.00 -1.50 0.50 1.00 1.50

log ΒΑ 0.00 0.32 0.64 0.96 -0.38 -0.76 -1.14

0.00 -1.70 -2.70 -3.30 -0.48 -2.60 -3.30

Β Α is the activity relative to acetylcholine.


14


b o n d polarizations

(62),


a n d p o s i t i o n parameters

(39)

in Equation 3

c a n b e justified for the i m p r o v e d c o r r e l a t i o n . I n a n y case, it is a d v i s a b l e not to use too m a n y parameters i n E q u a t i o n 3.

U n l e s s the n u m b e r of c o m p o u n d s u s e d i n the regression is l a r g e

so that the degrees of f r e e d o m are sufficient, a statistically significant c o r r e l a t i o n w o u l d not be o b t a i n e d . F o r e x a m p l e , the d e p o l a r i z i n g a c t i v i t y of five q u a t e r n a r y a m m o n i u m ions against e l e c t r i c eel electroplax

(63)

is expressed b y E q u a t i o n 30 w i t h the s u m of the substituent constants of four N-substituents

(11).

log A = The

correlation

- 4 . 5 1 2 σ * + 4.212ΤΓ + 6.56 XE ° + 3.14 η = 5 s = 0.162 r = 0.992 a

coefficient

seems r a t h e r l o w .

is v e r y

high, and

the

(30)

standard

deviation

H o w e v e r , a n F test reveals that the c o r r e l a t i o n is not

justified at the 0.90 l e v e l of p r o b a b i l i t y .

I n E q u a t i o n 30, the n u m b e r

of

degrees of f r e e d o m , e q u a l to one, is so l o w that the F v a l u e , w h i c h is a f u n c t i o n of the n u m b e r , b e c o m e s r a t h e r s m a l l . 53.6 )

(F

3 t

i =

26.6, F , i , i o 3

0 l

=

I n g e n e r a l , the l a r g e r the n u m b e r of degrees of f r e e d o m , the m o r e

s i g n i f i c a n t l y r e d u c e d is the v a r i a n c e i n the a c t i v i t y d a t a . W h e n a statisti c a l l y s i g n i f i c a n t c o r r e l a t i o n is o b t a i n e d w i t h f e w e r parameters a n d

yet

a n i m p r o v e d c o r r e l a t i o n is e x p l o r e d b y a d d i n g another p a r a m e t e r ,

the

l e v e l of confidence at w h i c h the a d d i t i o n a l p a r a m e t e r is justified s h o u l d be e x a m i n e d w i t h F tests. It is not e n o u g h for a m u l t i p l e p a r a m e t e r e q u a t i o n just to

"work"

a n d to g i v e a n i m p r o v e d c o r r e l a t i o n as H i g u c h i a n d D a v i s h a v e

empha

sized recently nificance.

(64).

T h e correlation must have a physicochemical

sig

R e c e n t l y , E q u a t i o n 31 has b e e n p r e s e n t e d b y B u c h e l a n d his

co-workers herbicides

for the i n h i b i t i o n of the H i l l r e a c t i o n w i t h

1,2,4-triazinone

(65). ο

2 pl

5 0

=

5.23 -

16.57 δ + 45.04 δ + 2.11 AR (3) - 3.36 AR (3) + 2.22AR (6) -0.50Δ/Μ6) η = 28 s = 0.418 r = 0.938 (31) 2

M

M

2

2

M

I n this e q u a t i o n , δ is a d i f f e r e n t i a l p a r a m e t e r d e v e l o p e d f r o m a n d p o l y a m i d e t h i n - l a y e r c h r o m a t o g r a p h y , a n d AR (3) M

Sephadex

a n d AR (6) M

the values for the substituents at the 3 a n d 6 positions, r e s p e c t i v e l y . n u m b e r of c o m p o u n d s is sufficiently l a r g e so t h a t the c o r r e l a t i o n

are The could

b e a c c e p t e d statistically. A l t h o u g h E q u a t i o n 31 c a n b e u s e d to p r e d i c t


1.

Extrathermodynamic

FUJITA

Structure-Activity

activities of untested c o m p o u n d s

15

Corrections

i n this p a r t i c u l a r set of c o m p o u n d s , i t

is difficult to accept its p h y s i c o c h e m i c a l significance o n a g e n e r a l m o d e of a c t i o n of H i l l r e a c t i o n i n h i b i t o r s . T h e m o r e parameters u s e d for c o r r e l a t i o n , the m o r e

difficult i t w o u l d b e to d e t e r m i n e

the

comparative

correlations a n d the less attractive w i l l be the p h y s i c o c h e m i c a l e l u c i d a t i o n . F o r a set of i o n i z a b l e drugs w h e r e large changes i n the degrees of i o n i z a t i o n are o b s e r v e d , the a p p a r e n t a c t i v i t y e x h i b i t e d b y a d r u g is not a s u i t a b l e i n d e x to b e a n a l y z e d . U n l e s s the effect of i o n i z a t i o n is sepa r a t e d f r o m other p h y s i c o c h e m i c a l effects, the c o r r e l a t i o n w o u l d not have a p h y s i c o c h e m i c a l significance. fact, l o g l / ( C

i o n

+

T h e apparent activity, log 1 / C

is, i n

e n t r a i ) , w h i c h is not a free-energy r e l a t e d i n d e x for

the m a g n i t u d e of a c t i v i t y either of the n e u t r a l or i o n i z e d m o l e c u l e both.

W i t h a r e l a t i v i s t i c a p p r o a c h to this p r o b l e m , w e

E q u a t i o n 32 a n d 33 for the i o n i z a b l e drugs (66,

p l a n to

67).

log 1/C + log (K + [ H ] ) / [ H ] = -a (log P) + b log Ρ + σ + SE s + c +

A

+

2

log

1/C

+

Ρ

-\- [ H ] ) / K = —a (log Ρ ) + b log Ρ + 'σ + SE + c'

log (KA

or use

+

(32)

A

2

Ρ

8

(33)

F r o m the bacteriostatic a c t i v i t y d a t a of k o j i c a c i d d e r i v a t i v e s deter m i n e d at p H 6, 7, a n d 8 w i t h s. aureus, equations

w e have d e r i v e d the f o l l o w i n g

(13).

F o r the a p p a r e n t a c t i v i t y : p H 6:

log 1/C — 0.863 A l o g K + 1.587 π(Χ) η = 9 s = 0.585

+ 1.571 r = 0.946

(34)

log 1/C = 0.568 A l o g K + 1.456 π(Χ) n = 9 s = 0.516

+ 1.632 r = 0.944

(35)

log 1/C = 0.358 A l o g K + 1.205 *(X) n = 9 s = 0.476

+ 1.600 r = 0.930

(36)

A

p H 7:

A

p H 8:

A

F o r the n e u t r a l molecule : pH 6:

1/C

+ [H+] ) / [ H ] = 0.959 A l o g K + 1.601 π(Χ) + 1.580 n = 9 s = 0.586 r = 0.949

(37)

+ [H ] ) / [H ] = 0.970 A l o g # + 1.487 π ( Χ ) + 1.708 η = 9 s = 0.511 r = 0.956

(8)

log 1/C + log (K + [ H ] ) / [ H ] = 1.132 A\ogK + 1.235 π(Χ) + 1.974 n = 9 s = 0.460 r = 0.960

(38)

log

+

log (KA

+

A

pH 7:

log

1/C

+

log (KA

+

+

A

p H 8:

A

+

+

A

F o r the i o n i z e d f o r m : p H 6:

log

1/C

+

log (KA

+ [ H ] )/K = 1.606 *(X) + 3.517 η = 9 s = 0.544 r = 0.938 +

A


(39)

16


p H 7:

log 1 / C + log (K

p H 8:

+ [ H ] )/K = 1.491 π(Χ) + 2.651 η = 9 s = 0.474 r = 0.944

(40)

+ [ H ] )/K = 1.215 *{X) + 2.009 n = 9 s = 0.449 r = 0.927

(41)

+

A

l o g 1/C + log (K

A

+

A


A

C o m b i n e d equations, p H 6, 7, a n d 8: l o g 1 / C + l o g (K

A

+

[H ] ) / [H ] = n = 27 +

log 1 / C + log {K

+

A

1.020 A l o g K + 1.439π + s = 0.509 r = 0.943

1.754 (42)

A

+ [ H ] ) /K = 1.437π + 2.726 n = 27 s = 0.832 r = 0.823 +

A

(43)

I n these equations, the 7 r ( X ) is that of the substituents, s u c h as h y d r o g e n , h a l o g e n , a n d h y d r o x y l , at the 7-position.

N e i t h e r the use of

TT(X + Y ) n o r the a d d i t i o n of ? r ( Y ) t e r m i m p r o v e the correlations as d e s c r i b e d before for E q u a t i o n 8. T h e correlations are almost e q u i v a l e n t , q u a l i t a t i v e l y s p e a k i n g , a l t h o u g h those for the a c t i v i t y of i o n i z e d f o r m are s l i g h t l y better t h a n the others as far as t h e y are c o n s i d e r e d separately. T h u s , it m i g h t seem of n o great v a l u e to consider the effect of i o n i z a t i o n . H o w e v e r , i f w e c o m b i n e E q u a t i o n s 8, 37, a n d 38, E q u a t i o n 42 is o b t a i n e d for the a c t i v i t y of the n e u t r a l m o l e c u l e at three different p H ' s w i t h the use of 27 d a t a points. E q u a t i o n 42 shows m u c h better c o r r e l a t i o n t h a n E q u a t i o n 43, w h i c h is d e r i v e d i n a s i m i l a r m a n n e r for the a c t i v i t y of the ionized form.

Since the b a c t e r i a l g r o w t h is not affected m u c h b y p H

changes f r o m 6 to 8, the f o r m of the k o j i c a c i d d e r i v a t i v e s responsible for the bacteriostatic a c t i v i t y is l i k e l y to be the n e u t r a l m o l e c u l e , a n d the i o n i z e d f o r m seems to p l a y o n l y a m i n o r role i n the a c t i v i t y , i f any. E q u a t i o n s s u c h as 34, 35, a n d 36, w h i c h m i g h t be o n l y of use to i n d i c a t e a g e n e r a l t r e n d , are, i n effect, u n a b l e to e l u c i d a t e t h e p H d e p e n d e n c e of a c t i v i t y a n d to g i v e a n y i n f o r m a t i o n a b o u t the a c t i v e f o r m . It s h o u l d be n o t i c e d that f r o m the a c t i v i t y d a t a m e a s u r e d at a c e r t a i n fixed

p H , the correlations of e q u i v a l e n t q u a l i t y are o b t a i n e d b o t h

the n e u t r a l a n d i o n i z e d forms.

T h e r e are interrelations a priori

E q u a t i o n s 32 a n d 33 s u c h as ρ — ρ = where p

p

and c — & =

A

for

between

p H — pKA > std

is the H a m m e t t r e a c t i o n constant for the i o n i z a t i o n e q u i l i b r i u m

A

and p K A

s t d

is the v a l u e of a s t a n d a r d c o m p o u n d .

T h u s , it is o n l y possible

to p r e d i c t the m o l e c u l a r f o r m responsible for the a c t i v i t y b y c o m p a r i n g E q u a t i o n s 32 a n d 33 d e r i v e d f r o m data o b t a i n e d at various p H . over, the o p t i m u m v a l u e of l o g K , A

l o g K °, A

More

for the a p p a r e n t a c t i v i t y of

i o n i z a b l e congeners c a n b e d e r i v e d b y setting the d e r i v a t i v e of either E q u a t i o n 32 or 33 e q u a l to zero as s h o w n i n E q u a t i o n s 44 a n d 45. a w 1/C

K

A

,

[H ] +


1.

FUJITA

Extrathermodynamic

Structure-Activity

Correlations

l o g i ^ ° = l o g ( - i ^ - p H

17

(45)

S i m i l a r situations h a v e b e e n discussed f o r s u b s t i t u t e d p h e n o l s (66) a n d sulfa d r u g s (67) i n d e t a i l . W h e n s t r u c t u r a l modifications are m a d e at v a r i o u s positions i n a set of

complex

d r u g molecules,

this a p p r o a c h

combined

with

the Free-

W i l s o n m a t h e m a t i c a l m o d e l w o u l d b e a s u i t a b l e t o o l (68). I f the m a t h e m a t i c a l c o n t r i b u t i o n s of substituents a n d parts of molecules are a d d i t i v e for a c e r t a i n b i o l o g i c a l effect o f a series of d r u g s , the c o n t r i b u t i o n values of substituents a t e a c h p o s i t i o n c a n b e a n a l y z e d f u r t h e r w i t h o u r a p p r o a c h . E x a m p l e s are discussed b y P a u l C r a i g i n C h a p t e r 8. W h e n d r u g biotransformations a n d excretions o c c u r before r e a c h i n g the site o f action a n d c o m m o n m e c h a n i s m s are c o n s i d e r e d f o r a set o f drugs, the rate constants d e t e r m i n e d b y the m u l t i c o m p a r t m e n t a l analysis or its counterparts c o u l d b e a n a l y z e d so t h a t the m o d e s o f m e t a b o l i s m , d i s t r i b u t i o n , a n d excretion are e l u c i d a t e d p h y s i c o c h e m i c a l l y ( 69, 70, 71 ). H o w e v e r , f o r t h e cases w h e r e specific

biotransformations

for certain

m e m b e r s o r each m e m b e r of c o n g e n e r i c drugs are involved—e.g., for the plant-growth

r e g u l a t i n g a c t i v i t y of g i b b e r e l l i n s

(72)—the

structure-

a c t i v i t y r e l a t i o n s h i p c o u l d n o t b e successfully a n a l y z e d b y E q u a t i o n 3 o r its modifications. F r o m the l i n e o f r e a s o n i n g that a n y b i o l o g i c a l effect o f drugs s h o u l d be a result o f c h e m i c a l a n d / o r p h y s i c o c h e m i c a l p e r t u r b a t i o n o n the b i o l o g i c a l system, the r e l a t i o n s h i p b e t w e e n s t r u c t u r e a n d a c t i v i t y o b s e r v e d for a n y k i n d of d r u g s h o u l d b e a n a l y z a b l e o n the basis o f p h y s i c o c h e m i c a l parameters. A l t h o u g h there are examples w h e r e E q u a t i o n 3 o r its m o d i fication

fails i n a n a l y z i n g the c o r r e l a t i o n , this does not o b v i a t e the p h y s i -

c o c h e m i c a l m e c h a n i s m b e h i n d the d r u g a c t i o n . W e h o p e that this a p p r o a c h , w h i c h is s t i l l i n a n e a r l y stage, w i l l achieve f u r t h e r d e v e l o p m e n t s a n d s t i m u l a t e other r e l a t e d fields o f science so that the m e c h a n i s m s of the d r u g a c t i o n c a n b e u n d e r s t o o d

comprehensively.

Acknowledgment T h e a u t h o r thanks C o r w i n H a n s c h f o r i n v a l u a b l e discussions since our first project o n this a p p r o a c h b e g a n i n 1961.

Literature Cited 1. Hansch, C., Fujita, T., J. Amer. Chem. Soc. (1964) 86, 1616. 2. Hansch, C., Accounts Chem. Res. (1969) 2, 232. 3. Hansch, "Drug Design," E. J. Ariëns, Ε., Vol. 1, p. 271, Academic, New York, 1971.


18



4. Fujita, T., Iwasa, J., Hansch,C.,J. Amer. Chem. Soc. (1964) 86, 5175. 5. Iwasa, J., Fujita, T., Hansch,C.,J. Med. Chem. (1965) 8, 150. 6. Hammett, L. P., "Physical Organic Chemistry," 2nd ed., p. 347, McGraw Hill, New York, 1970. 7. Hansch,C.,J. Med. Chem. (1968) 11, 920. 8. Taft, R. W., Jr., "Steric Effects in Organic Chemistry," p. 556, M. S. New man, Ed., Wiley, New York, 1956. 9. Hancock, C. K., Meyers, Ε. Α., Yager, B. J., J. Amer. Chem. Soc. (1961) 83, 4211. 10. Ford-Moore, A. H., Ing, H. R., J. Chem. Soc. 1947, 55. 11. Fujita, T., Nishioka, T., Takayama,C.,Nakajima, M., unpublished data. 12. Newhall, F. W., J. Agr. Food Chem. (1971) 19, 294. 13. Ichimoto, I., Kotani, T., Tatsumi, C., Fujita, T., "Abstracts of Papers," Annual National Meeting, Agricultural Chemical Society of Japan, Fukuoka, 1970, p. 110. 14. Kakeya, N., Yata, N., Kamada, Α., Aoki, M., Chem. Pharm. Bull. (1969) 17, 2558. 15. Fujita, T., Chem. Regulation Plants (Tokyo) (1970) 5, 124. 16. Bruce, M. I., Zwar, J. Α., Proc. Roy. Soc. (1966) B165, 245. 17. Ugochukwu, Ε. N., Wain, R. L., Ann. Appl. Biol. (1968) 61, 121. 18. Nagata,C.,Yonezawa, T., Fukui, K., Tgashira, Y., Cancer Res. (1955) 15, 233. 19. Pullman, Α., Pullman, B., Adv. Cancer Res. (1955) 3, 117. 20. Meyer, K. H., Hemmi, H., Biochem. Z. (1935) 277, 39. 21. Overton, Ε., Z. Physiol. Chem. (1897) 22, 189. 22. Soloway, S. B., Adv. Pest Control Res. (1965) 6, 85. 23. Kurihara, N., private communication (1971). 24. Hansch,C.,Deutsch, E. W., Smith, R. N., J. Amer. Chem. Soc. (1965) 87, 2738. 25. Lien, E. J., Hansch,C.,Anderson, S. M., J. Med. Chem. (1968) 11, 430. 26. Penniston, J. T., Beckett, L., Bentley, D. L., Hansch,C.,Mol. Pharmacol. (1969) 5, 333. 27. McFarland, J.M.,J. Med. Chem. (1970) 13, 1192. 28. Hansch,C.,IlFarmaco (1968) 23, 293. 29. Hansch,C.,Muir, R. M., Fujita, T., Maloney, P. P., Geiger, F., Streich, M., J. Amer. Chem. Soc. (1963) 85, 2817. 30. Muir, R. M., Fujita, T., Hansch,C.,Plant Physiol. (1967) 42, 1519. 31. Ariens, Ε. J., "Molecular Pharmacology," Vol. 1, p. 176, Academic, New York, 1964. 32. Yamasaki, T., Narahashi, T., Botyu-Kagaku (1957) 22, 296. 33. Metcalf, R. L., "Organic Insecticides," p. 135, Wiley, New York, 1955. 34. Upshall, D. G., Goodwin, T. W., J. Sci. Food Agr. (1964) 15, 846. 35. Fukuto, T. R., Metcalf, R. L., J. Agr. Food Chem. (1956) 4, 930. 36. Hansch, C., Deutsch, E. W., Biochim. Biophys. Acta (1966) 112, 381. 37. O'Brien, R. D., Hilton, B. D., Gilmour, L., Mol. Pharmacol. (1966) 2, 593. 38. Metcalf, R. L., Fukuto, T. R., J. Agr. Food Chem. (1965) 13, 220. 39. Hansch, C., "Biochemical Toxicology of Insecticides," R. D. O'Brien and I. Yamamoto, Eds., p. 33, Academic, New York, 1970. 40. Ishida, S., Ida, M., Agr. Biol. Chem. (Tokyo) (1967) 31, 410. 41. Ishida, S., Yamada, O., Agr. Biol. Chem. (Tokyo) (1967) 31, 417. 42. Ishida, S., Agr. Biol. Chem. (Tokyo) (1966) 30, 800. 43. Muraoka, S., Terada, H., Fujita, T., "Abstracts of Papers," 91st National Meeting, Pharmaceutical Society of Japan, Fukuoka, 1971, p. 412. 44. Whitehouse, M. W., "Pharmaceutical Chemistry—2," p. 39, Butterworth, London, 1969. 45. Hamor, G. H., Lien, E. J., Il Farmaco (1969) 24, 704. 46. Kutter, E., Hansch, C., J. Med. Chem. (1969) 12, 647.


1.

FUJITA

Extrathermodynamic

Structure-Activity

Correlations

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47. Fujita, T., Ban, T., unpublished data. 48. Ho, B. T., Li, Ko-Chin, Walker, K. E., Tansey, L. W., Kralik, P. M., McIsaac, W. M., J. Pharm. Sci. (1970) 59, 1445. 49. Swett, L. R., Martin, W. B., Taylor, J. D., Everett, G. M., Wykes, Α. Α., Gladish, Y. G., Ann. N.Y. Acad. Sci. (1963) 107, 891. 50. Leffler, J. E., Grunwald, E., "Rates and Equilibria of Organic Reactions," p. 128, Wiley, New York, 1963. 51. Hansch, C., Anderson, S. M., J. Org. Chem. (1967) 32, 2583. 52. Fujita, T., Nakajima, M., Soeda, Y., Yamamoto, I., Pesticide Biochem. Physiol. (1971) 1, 151. 53. Currie, D. J., Lough, C. E., Silver, R. F., Holmes, H. L., Can. J. Chem. (1966) 44, 1035. 54. Leo, Α., Hansch, C., J. Org. Chem. (1971) 36, 1539. 55. Holton, P., Ing, H. R., Brit. J. Pharmacol. (1949) 4, 190. 56. Craig, P. N., J. Med. Chem. (1971) 14, 680. 57. Neely, W. B., White, H. C., Rudzik, Α., J. Pharm. Sci. (1968) 57, 1176. 58. Kutter, E., Machleidt, H., Reuter, W., Wildfeuer, Α., 161st National Meet ing, ACS, Los Angeles, Calif., 1971. 59. Boyce, C. B. C., Milborrow, Β. V., Nature (1967) 208, 2275. 60. Hansch, C., Lien, E. J., Biochem. Pharmacol. (1968) 17, 709. 61. Clayton, J. M., Purcell, W. P., J. Med. Chem. (1969) 12, 1087. 62. Hansch, C., Coats, E., J. Pharm. Sci. (1970) 59, 731. 63. Podleski, T. R., Biochem. Pharmacol. (1969) 18, 211. 64. Higuchi, T., Davis, S. S., J. Pharm. Sci. (1970) 59, 1376. 65. Draber, W., Buchel, K. H., Dickore, K., 2nd International Congress of Pesticide Chemistry, Israel, 1971. 66. Fujita, T., J. Med. Chem. (1966) 9, 797. 67. Fujita, T., Hansch, C., J. Med. Chem. (1967) 10, 991. 68. Fujita, T., Ban, T., J. Med. Chem. (1971) 14, 148. 69. Lien, E. J., Hansch, C., J. Pharm. Sci. (1968) 57, 1027. 70. Lien, E. J., Drug Intelligence Clin. Pharm. (1970) 4, 7. 71. Lien, E. J., Koda, R. T., Tong, G. L., Drug Intelligence Clin. Pharm. (1971) 5, 38. 72. Crozier, Α., Kuo, C. C., Durley, R. C., Pharis, R. P., Can. J. Bot. (1970) 48, 867. RECEIVED

June 17, 1971.


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