Bioregulators for Pest Control - American Chemical Society

9 Use of Transition-State Theory in the Development of Bioactive Molecules

Downloaded by PENNSYLVANIA STATE UNIV on March 16, 2013 | http://pubs.acs.org Publication Date: April 26, 1985 | doi: 10.1021/bk-1985-0276.ch009

YEHIA A. I. ABDEL-AAL1 and BRUCE D. HAMMOCK Departments of Entomology and Environmental Toxicology, University of California, Davis, CA 95616

The application o f transition s t a t e t h e o r y t o enzyme catalysis is p r e s e n t e d in terms o f m e c h a n i s t i c and e n e r g e t i c approaches. These t r e a t m e n t s emphasize t h e rationale o f u s i n g transition s t a t e a n a l o g s as bio active m o l e c u l e s . I n c l u d e d in this c h a p t e r a r e some criteria f o r d e t e r m i n i n g if a compound is a transition s t a t e a n a l o g . A h y p o t h e s i s is t h e n p r e s e n t e d t h a t t h e initial b i n d i n g o f some insecticidal carbamates and organophosphates t o acetylcholinesterase is dependent in p a r t upon their m i m i c k i n g t h e transition s t a t e c o n figuration o f acetylcholine. As an indication o f how transition s t a t e t h e o r y c o u l d be a p p l i e d t o problems in agricultural c h e m i s t r y , we p r e s e n t d a t a from t h i s l a b o r a t o r y t h a t some t r i f l u o r o m e t h y l k e t o n e inhibitors o f i n s e c t j u v e n i l e hormone e s t e r a s e ( s ) a r e transition s t a t e mimics and e x t e n d t h i s argument by a p p l y i n g a q u a n t i t a t i v e structure-activity relationship approach to these analogs. There has been a n o b v i o u s d e c l i n e i n t h e number o f commercial a g r i c u l t u r a l and p h a r m a c e u t i c a l c h e m i c a l s d u r i n g t h e l a s t decade. There a r e two major r e a s o n s f o r t h i s d e c l i n e . F i r s t , there are i n c r e a s i n g l y t i g h t e r r e q u i r e m e n t s f o r market development. To u s e a g r i c u l t u r a l c h e m i c a l s as a n example, we s e e an i n c r e a s i n g l y narrow m a r g i n o f p r o f i t f o r f a r m e r s and i n c r e a s i n g c o n c e r n o v e r e n v i r o n mental h e a l t h e f f e c t s . The c o s t o f r e g i s t r a t i o n , p r o d u c t i o n and marketing a l s o continues t o i n c r e a s e . Secondly, the cost of d i s c o v e r y has i n c r e a s e d d r a m a t i c a l l y . There a r e numerous components t o t h i s o b s e r v a t i o n as w e l l , b u t s i m p l i s t i c a l l y one c a n s e e t h a t t o meet t h e t i g h t r e q u i r e m e n t s f o r market development, more complex and e x p e n s i v e s y n t h e s e s and b i o a s s a y s a r e r e q u i r e d . Random s c r e e n i n g w i t h t h e a i d o f some s e r e n d i p i t y s e r v e d e f f e c t i v e l y i n t h e p a s t f o r the d i s c o v e r y o f new b i o l o g i c a l a c t i v i t i e s , y e t we have reached t h e

1

O n leave from the Department of Plant Protection, College of Agriculture, Assiut University, Assiut, A . R . Egypt.

0097-6156/85/0276-0135$07.50/0 © 1985 American Chemical Society

In Bioregulators for Pest Control; Hedin, P., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

BIOREGULATORS FOR PEST CONTROL


136

p o i n t of d i m i n i s h i n g r e t u r n s w i t h r e g a r d t o i t s a p p l i c a t i o n t o f u t u r e problems. T h e r e f o r e , a theme of s e v e r a l of the m a n u s c r i p t s from t h i s m e e t i n g r e l a t e s t o the development of new paradigms f o r the d i s c o v e r y of b i o l o g i c a l a c t i v i t y . M o l e c u l e s can r e a c t w i t h a b i o l o g i c a l m a t r i x i n many ways. At l e a s t some b i o l o g i c a l a c t i v i t y i s common among c h e m i c a l l y r e a c t i v e species. F o r i n s t a n c e , M i c h a e l a c c e p t o r s and a c e t y l a t i n g a g e n t s a r e commonly i r r i t a t i n g agents or g e n e r a l c y t o t o x i n s . M o l e c u l e s may r e v e r s i b l y r e a c t w i t h b i o l o g i c a l systems based upon o n l y s o l u b i l i t y o r weak m o l e c u l a r i n t e r a c t i o n s w i t h b i o l o g i c a l d e p r e s s a n t s as prime examples. However, t h e s e m o l e c u l e s l a c k the s p e c i f i c i t y d e s i r e d f o r f i e l d a p p l i c a t i o n and the p o t e n c y needed f o r economic f e a s i b i l i t y . However, i f an a l k y l a t i n g agent has a h i g h a f f i n i t y f o r n u c l e i c a c i d s , i f an a c e t y l a t i n g agent b i n d s w e l l t o an enzyme a c t i v e s i t e , or i f an i n e r t m o l e c u l e can form s e v e r a l weak m o l e c u l a r i n t e r a c t i o n s w i t h a r e c e p t o r s i t e , t h e s e m o l e c u l e s may d i s p l a y v e r y h i g h b i o l o g i c a l a c t i v i t y indeed. D u r i n g the l a s t s e v e r a l y e a r s we have become impressed w i t h the u t i l i t y of t r a n s i t i o n s t a t e t h e o r y i n the o p t i m i z a t i o n as w e l l as the d i s c o v e r y of b i o l o g i c a l l y a c t i v e s t r u c t u r e s . Empirical approaches i n d i c a t e t h a t a mimic of an e n z y m e - s u b s t r a t e t r a n s i t i o n s t a t e c o u l d have a K j below 1 0 ^ M (± 2) · A l t h o u g h one i s not l i k e l y t o p r e c i s e l y mimic a t r a n s i t i o n s t a t e , even a vague mimic c o u l d s t i l l be a v e r y p o t e n t i n h i b i t o r . T h e r e f o r e , we f e e l t h a t t r a n s i t i o n s t a t e t h e o r y i s l i k e l y t o be one of s e v e r a l approaches u s e f u l i n a g r i c u l t u r a l c h e m i s t r y . Thus i n the f o l l o w i n g pages we p r e s e n t a b r i e f r e v i e w of the a p p l i c a t i o n of t r a n s i t i o n s t a t e t h e o r y i n enzyme c a t a l y s i s i n terms of b o t h m e c h a n i s t i c and e n e r g e t i c treatments. These t r e a t m e n t s i n t r o d u c e the r a t i o n a l e of u s i n g t r a n s i t i o n s t a t e a n a l o g s as b i o a c t i v e m o l e c u l e s . Data from t h i s l a b o r a t o r y were p r e s e n t e d as an example of the use of t r a n s i t i o n s t a t e t h e o r y i n the development o f p o t e n t i n h i b i t o r s of i n s e c t j u v e n i l e hormone e s t e r a s e ( s ) . - 1

9

T r a n s i t i o n State

Theory

I t i s w e l l known from s t r u c t u r a l and k i n e t i c s t u d i e s t h a t enzymes have w e l l - d e f i n e d b i n d i n g s i t e s f o r t h e i r s u b s t r a t e s 03), sometimes form c o v a l e n t i n t e r m e d i a t e s , and g e n e r a l l y i n v o l v e a c i d i c , b a s i c and n u c l e o p h i l i c g r o u p s . Many of the c o n c e p t s i n c a t a l y s i s a r e based on t r a n s i t i o n s t a t e (TS) t h e o r y . The f i r s t q u a n t i t a t i v e f o r m u l a t i o n of t h a t t h e o r y was e x t e n s i v e l y used i n the work o f H. E y r i n g ( 4 , _ 5 ) · Noteworthy c o n t r i b u t i o n s t o the b a s i c t h e o r y were made by o t h e r s (see (6) f o r review). As an e l e m e n t a r y i n t r o d u c t i o n , we w i l l a p p l y the fundamental assumptions of the TS t h e o r y i n s i m p l e enzyme c a t a l y s i s as f o l l o w s . (a) In e v e r y c h e m i c a l r e a c t i o n the r e a c t a n t s a r e i n e q u i l i b r i u m w i t h an u n s t a b l e a c t i v a t e d complex, the t r a n s i t i o n s t a t e complex, which decomposes t o g i v e p r o d u c t s . In t h i s complex c h e m i c a l bonds a r e i n the p r o c e s s of b e i n g formed or b r o k e n . T h e r e f o r e , i t o c c u r s a t the peak of the r e a c t i o n c o o r d i n a t e diagram, i . e . a t the s a d d l e p o i n t s o f p o t e n t i a l energy s u r f a c e s (_7). In c o n t r a s t , i n t e r m e d i a t e s , whose bonds a r e f u l l y e s t a b l i s h e d , occupy the t r o u g h s i n the diagram ( F i g u r e 1 ) . These i n t e r m e d i a t e s can e i t h e r be t r a n s i e n t


9.

ABDEL-AAL AND

137

Development of Bioactive Molecules

HAMMOCK

or a c t u a l i s o l a t a b l e i n t e r m e d i a t e s such as an a c y l enzyme, (b) I t i s p o s t u l a t e d t h a t the s t a r t i n g m a t e r i a l s ( i n case of enzyme c a t a l y s i s the enzyme (E) and i t s s u b s t r a t e ( S ) ) a r e i n e q u i l i b r i u m w i t h a l l complexes which o c c u r b e f o r e the a c t i v a t e d complex (ES ) and a l s o w i t h the a c t i v a t e d complex i t s e l f " E q u a t i o n 1".

Ε + S

Km ^ES

kcat >ES*

kT/h >E

ι

+ Products

(1)

t


*2 (c) The i m p o r t a n t p o s t u l a t e i s made t h a t i n t h i s t h e o r y a l l t h e a c t i v a t e d complexes decompose t o p r o d u c t s a t e x a c t l y the same r a t e f o r a g i v e n temperature. T h i s means t h a t the r a t e i s p r o p o r t i o n a l to the c o n c e n t r a t i o n o f ES* w i t h a u n i v e r s a l p r o p o r t i o n a l i t y con s t a n t (kT/h) where k i s the Boltzmann's c o n s t a n t , Τ i s the a b s o l u t e temperature and h i s the P l a n k ' s c o n s t a n t . A t 25° (kT/h) e q u a l s 6.212xl0 sec" . 1 2

1

r a t e - kT

[ES*]

However ES* i s i n e q u i l i b r i u m w i t h Ε and e q u i l i b r i u m constant K as f o l l o w s :

(2)

S and

i s governed by

the

t

[ES*]

= Κ*

(3)

[EUS] S u b s t i t u t i o n f o r the v a l u e of [ES*] i n " E q u a t i o n 2" " E q u a t i o n 3" r e s u l t s i n the f o l l o w i n g e q u a t i o n :

from

r a t e = [E] [ S J K ^ k T j h

(4)

However, from " E q u a t i o n 1" the r a t e a l s o s h o u l d be p r o p o r t i o n a l t o [E] and [S] and a second o r d e r r a t e c o n s t a n t ( k 2 ) : rate - k [E][S]

(5)

2

Comparing " E q u a t i o n 5" w i t h k

2

" E q u a t i o n 4"

indicates that:

- kT K £

(6)

( d ) A s p e c i a l p r o p e r t y of the a c t i v a t e d TS complex i s t h a t i t has a u n i q u e , v e r y l o o s e i n t e r n a l mode o f v i b r a t i o n , which i s u n s t a b l e with respect to d i s s o c i a t i o n i n t o products. This " v i b r a t i o n " occurs a l o n g the r e a c t i o n c o o r d i n a t e ( F i g u r e 1 ) . T h e r e f o r e we w i l l c o n s i d e r the TS complex as the end p o i n t on the energy p r o f i l e f o r simplicity. F r e e Energy Change and TS T h e o r y . We w i l l now e x p r e s s the mechanism of enzyme c a t a l y s i s " E q u a t i o n 1" i n terms o f the change i n the f r e e energy as f o l l o w s :


138

BIOREGULATORS F O R PEST C O N T R O L

AG„ E+S

AG

4-

-7

ES

ES*

(7)

• AG*. By a p p l y i n g t h e well-known r e l a t i o n s h i p between t h e G i b b s - e n e r g y change and t h e e q u i l i b r i u m c o n s t a n t ( 8 ) t o t h e above scheme, one finds:


AG* = -RT I n K*

(8)

where K* i s t h e e q u i l i b r i u m c o n s t a n t between t h e r e a c t a n t s and t h e TS. Analogous e q u a t i o n s r e l a t e t h e e q u i l i b r i u m c o n s t a n t o f any s t e p and t h e c o r r e s p o n d i n g f r e e energy change. JJpon rearrangement o f " E q u a t i o n 8" and i n t r o d u c i n g t h e v a l u e o f K i n terms o f AG i n t o " E q u a t i o n 6", t h e f o l l o w i n g e q u a t i o n r e s u l t s : t

k

2

t

-AG*/RT = kT . e h

(9)

U s i g g t h e f a m i l i a r r e l a t i o n s h i p between g i b b s f r e e energy change ( A G ) and t h e change i n t h e e n t h a l p y (AH ) and e n t r o p y ( A S ) , t

fc

AG*

t

=ΔΗ* -TAS*

(10) *

" E q u a t i o n 9" c a n be e x p r e s s e d i n terms o f AH follows: -AH /RT AS /R k - kT . e e h t

ic t

and AS as t

t

(11)

2

" E q u a t i o n 11" i n d i c a t e s , from t h e t h e o r e t i c a l p o i n t o f view, t h a t k f o r a p a r t i c u l a r enzyme c a n be a c c e l e r a t e d by e i t h e r a d e c r e a s e i n the e n t h a l p y and^or an i n c r e a s e i n t h e e n t r o p y o f t h e ^ o v e r a l l r e a c t i o n E+S — * ES so t h a t t& w i l l be n e g a t i v e and ^ will be p o s i t i v e i n t h e above e q u a t i o n . The r o l e o f e n t r o p y change i n terms o f d i f f e r e n t e n t r o p y v e c t o r s , t r a n s l a t i o n a l , r o t a t i o n a l and i n t e r n a l e n t r o p i e s i n enzyme c a t a l y s i s i s n o t an easy t a s k and t h e r e a d e r s h o u l d r e f e r t o s p e c i a l t e x t b o o k s i n p h y s i c a l o r g a n i c chemis t r y ( s e e ( 8 ^ and r e f e r e n c e s t h e r e i n ) . T h e o r e t i c a l l y f o r m i n g a TS complex (ES ) from an enzyme and s u b s t r a t e (2 + 1 r e a c t i o n ) would l e a d t o a l o s s o f t h e e n t r o p y o f t h r e e degrees o f t r a n s l a t i o n a l freedom. However, a l o o s e t r a n s i t i o n s t a t e w i t h a h i g h p o t e n t i a l energy may, perhaps, be c o n s i d e r e d as two m o l e c u l e s i n c l o s e j u x t a p o s i t i o n b u t r e t a i n i n g c o n s i d e r a b l e e n t r o p y freedom. Furthermore, enzymic r e a c t i o n s a r e d i f f e r e n t from pure o r g a n i c c h e m i c a l r e a c t i o n s s i n c e t h e former r e a c t i o n t a k e s p l a c e i n t h e c o n f i n e s o f t h e enzyme s u b s t r a t e complex. T h e r e f o r e , t h e remarkably h i g h c a t a l y t i c a c t i v i t y o f enzymes c o u l d be a t t r i b u t e d t o l o c a l i z a t i o n o f S o r S w i t h i n t h e a c t i v e s i t e w i t h s u s c e p t i b l e bonds o f t h e s u b s t r a t e o r i t s TS c o n f i g u r a t i o n o p t i m a l l y o r i e n t e d t o t h e a p p r o p r i a t e c a t a l y t i c 2

t

t



9.

ABDEL-AAL AND

139


HAMMOCK

m o i e t i e s of the enzyme ( 3 ) . Due t o t h i s l o c a l i z a t i o n and o r i e n t a t i o n , t h e s u b s t r a t e would be r o u g h l y c o n s i d e r e d as p a r t o f the same m o l e c u l e as the c a t a l y t i c group so t h e r e i s no e x t e n s i v e l o s s i n e n t r o p y as the r e a c t i o n would be assumed t o be i n t r a m o l e c u l a r . I f t h e r e i s a g r e ^ t l o s s of e n t r o p y , i t would be on f o r m i n g the ES r a t h e r t h a n ES complex which r e s u l t s i n i n c r e a s i n g 1^ ( 8 ) . The e n t r o p y change i n terms o f t r a n s l a t i o n a l , r o t a t i o n a l and i n t e r n a l r o t a t i o n a l e n t r o p y has been d i s c u s s e d i n more d e t a i l (9,10) i n f a v o r of c o n t r i b u t i o n t o the b i n d i n g o f Ε and S* r a t h e r than S. However, the Van der Waals a t t r a c t i o n ( h y d r o p h o b i c bonding) i n enzyme-sub s t r a t e i n t e r a c t i o n s might i n c r e a s e the e n t r o p y o f e i t h e r ES o r ES as compared t o t h a t o f the r e a c t a n t s by e j e c t i n g water m o l e c u l e s f o r m e r l y bound t o the c a t a l y t i c s i t e ( s ) ( 1 1 ) . As i l l u s t r a t e d i n the above d i s c u s s i o n , S* b i n d s more t i g h t l y t o the enzyme than S. Thus more m o l e c u l e s of s o l v a t i n g water would be r e l e a s e d upon the f o r m a t i o n o f ES* r e s u l t i n g i n an a d d i t i o n a l e n t r o p i e advantage f o r i t s formation. Such h y d r o p h o b i c bonding and e n t r o p y change i n t h e r e a c t i o n o f enzyme w i t h s u b s t r a t e o r i n h i b i t o r s w i l l be f u l l y ex p l a i n e d i n t h e next s e c t i o n . T r a n s i t i o n S t a t e and B i n d i n g Energy. There a r e a t l e a s t two major f a c t o r s which a c c o u n t f o r enzyme c a t a l y s i s . The f i r s t one i s a c o m b i n a t i o n o f e n t r o p i e , a c i d base c a t a l y s i s and e l e c t r o s t a t i c effects. The second one depends m o s t l y on the enzyme s u b s t r a t e c o m p l e m e n t a r i t y which r e s u l t s i n a l a r g e amount o f b i n d i n g energy which may be used to d i s t o r t the s u b s t r a t e t o the s t r u c t u r e o f the p r o d u c t s ( 1 2 ) . The l a t t e r f a c t o r seems t o be o f h i g h importance i n l o w e r i n g the a c t i v a t i o n energy o f the o v e r a l l r e a c t i o n and s u b s e q u e n t l y i n c r e a s i n g t h e magnitude of k which i s d e f i n e d as k /K i n the s i m p l e M i c h a e l i s - M e n t e n mechanism where K = K . L e t us now put the s i m p l e scheme f o r enzyme c a t a l y s i s i n terms of b o t h mecha n i s t i c and e n e r g e t i c e n t i t i e s . 2

c a t

s

K

E+S

ν

m ^ ES

kcat

m

m

. >ES*

w

N

— AG

(12)

^cat AG

t

The above scheme can be seen c l e a r l y from F i g u r e 2 i n which A G i s a l g e b r a i c a l l y n e g a t i v e , i . e . f a v o r a b l e r e a c t i o n due t o the r e a l i z a t i o n o f b i n d i n g energy. However, A G * i s p o s i t i v e ( u n f a v o r a b l e r e a c t i o n ) due t o the a c t i v a t i o n energy o f bond rearrangement i n the a c t i v a t e d TS complex. J h a t i s the a c t i v a t i o n e n e r g y A G f o r t h e whole p r o c e s s (E+S * ES ) would be S

t

AC

AG

+

AG,

(13)

s

S u b s t i t u t i o n f o r the v a l u e of A G * i n " E q u a t i o n 9" by " E q u a t i o n 13" r e s u l t s i n the f o l l o w i n g e q u a t i o n :

AG* +

AG


g

140



ES*

Reaction coordinate F i g u r e 1. Schematic r e p r e s e n t a t i o n i n an e n z y m e - c a t a l y z e d r e a c t i o n .

*G*=ûG + A(f =ûG +Ad+AG ( s

s

REACTION

b

o f the f r e e energy

changes

(—) )

COORDINATE

F i g u r e 2. Schematic r e p r e s e n t a t i o n o f the f r e e e n e r g y changes i n an e n z y m e - c a t a l y z e d r e a c t i o n where t h e enzyme i s comple mentary t o e i t h e r t h e s u b s t r a t e ( b r o k e n l i n e s ) o r t o i t s t r a n s i t i o n state configuration ( s o l i d l i n e s ) .


9.


ABDEL-AAL AND HAMMOCK

k

2

=

kcat/Km " kT h

e

-AG*/RT e

-AG /RT e

141

(14)

From t h e above e q u a t i o n i t c a n be shown t h a t t h e b i n d i n g energy o f ES complex and/or o f E S * complex c a n p l a y a c r u c i a l r o l e i n l o w e r i n g AG o r AG r e s p e c t i v e l y and e v e n t u a l l y i n c r e a s i n g t h e c a t a l y t i c activity (k /K ). However, s i n c e t h e s t r u c t u r e o f t h e s u b s t r a t e (based on TS t h e o r y ) changes throughout t h e r e a c t i o n , i t i s l i k e l y t h a t t h e u n d i s t o r t e d enzyme c a n have maximum complementariness t o o n l y one s p e c i e s (S o r S ) o f t h e s u b s t r a t e ( 8 ) . A t t h i s p o i n t an important q u e s t i o n a r i s e s r e g a r d i n g which form o f s u b s t r a t e would have t h e h i g h e s t c o m p l e m e n t a r i t y and t h e h i g h e s t b i n d i n g energy i n i t s r e a c t i o n w i t h t h e enzyme. The importance o f t h e above q u e s t i o n comes from t h e f a c t t h a t i t s answer i s c o n s i d e r e d t o be t h e main r a t i o n a l e f o r t h e development o f TS-analogues (TSA) as enzyme i n hibitors. The q u a l i t a t i v e answer t o t h i s q u e s t i o n was i n t r o d u c e d by Haldane (12) and P a u l i n g (1,2) as t h e f a v o r e d c o m p l e m e n t a r i t y would be between t h e enzyme and t h e t r a n s i t i o n s t a t e p o r t i o n (S ) o f the s u b s t r a t e r a t h e r than between t h e enzyme and t h e s u b s t r a t e itself. I n s u p p o r t i n g t h e g r e a t i n s i g h t o f Haldane and P a u l i n g , F e r s h t ( 8 ) proved c o l l e c t i v e l y t h a t t h e i n t r i n s i c b i n d i n g energy i n driving k / K would be i n f a v o r o f t h e t r a n s i t i o n s t a t e . I n t h e f o l l o w i n g p a r a g r a p h s we w i l l s l i g h t l y modify F e r s h t ' s approach t o show t h a t i t i s e n e r g e t i c a l l y e x p e n s i v e f o r enzyme c a t a l y z e d r e a c t i o n s t o have maximum b i n d i n g i n t e r a c t i o n s w i t h t h e s u b s t r a t e r a t h e r than i t s TS c o n f i g u r a t i o n . g


c a t

c a t

m

m

Assume t h a t t h e e x t r a b i n d i n g energy r e s u l t i n g from complemen t a r i t y t o t h e s u b s t r a t e o r t o i t s TS e q u a l s AGfc. I f t h i s e x t r a b i n d i n g energy i s i n t h e enzyme s u b s t r a t e complex, i t w i l l d e c r e a s e the v a l u e o f K and reduce i t s f r e e energy change t o become uGq-uG^. However, s i n c e t h e f o r m a t i o n o f TS complex w i l l l e a d t o a r e d u c t i o n i n b i n d i n g energy as t h e s u b s t r a t e geometry changes t o g i v e p o o r e r f i j and e v e n t u a l l y t h i s w i l l i n c r e a s e AG f o r k t o be AG + 2 A G « A G ç f o r t h e o v e r a l l r e a c t i o n ( k / K ) can be c a l c u l a t e d (see F i g u r e 2) t o be t h e sum o f AG v a l u e s f o r t h e p r e c e d i n g s t e p s as f o l l o w s : m

c a t

b

c a t

m

(15) AG +AG +AG S u b s t i t u t i o n f o r t h e components of AG?! ("Equation 15") i n t o " E q u a t i o n 9": -AG*/RT k

2

38

kcat/Km = kT . e h

-AG /RT e 8

-AG /RT e b

(16)

Comparing " E q u a t i o n 16" w i t h " E q u a t i o n 14" where i n t h e l a t t e r t h e maximum i n t r i n s i c b i n d i n g energy was assumed t o be i n t h e a c t i v a t e d TS complex and t a k i n g i n t o c o n s i d e r a t i o n AG t o be o r i g i n a l l y b


142

BO IREGULATORS FOR PEST CONTROL

p o s i t i v e i n " E q u a t i o n 16" one f i n d s t h a t the f a v o r a b l e maximum f i t i s l i k e l y t o be w i t h the t r a n s i t i o n s t a t e c o n f i g u r a t i o n r a t h e r t h a n the s u b s t r a t e i t s e l f . In f a c t the enzyme can have an e x t r a AGfc/RT c a t a l y t i c a c t i v i t y by a f a c t o r o f e (by d i v i d i n g " E q u a t i o n 14" o v e r " E q u a t i o n 16") j u s t by u s i n g the same amount of b i n d i n g e n e r g y i n i n t e r a c t i o n w i t h S* r a t h e r t h a n w i t h S. I t i s not h a r d t o r e a l i z e the above arguments s i n c e ^cat/^m * independent of the i n t e r a c t i o n s i n the i n i t i a l e n z y m e - s u b s t r a t e complex ( F i g u r e 2 ) . A l t h o u g h the o v e r a l l c a t a l y t i c a c t i v i t y of an enzyme c a t a l y z e d r e a c t i o n can be a c c o u n t e d f o r b o t h by the a f f i n i t y o f the s u b s t r a t e t o the enzyme ( 1 ^ or more a c c u r a t e l y l/î^) and the s u b s t r a t e r e activity ( k ) , the l a t t e r v a l u e seems t o be more i m p o r t a n t i n r e f l e c t i n g the e x t r a b i n d i n g e n e r g y i n t h e ES* complex. This b i n d i n g energy, as mentioned b e f o r e , w i l l d e c r e a s e the energy of a c t i v a t i o n f o r the r e a c t i v i t y p r o c e s s (k ). T h i s h y p o t h e s i s has been s u p p o r t e d w i t h some s e r i n e p r o t e a s e s where i n c r e a s i n g the l e n g t h o f the l e a v i n g group i n c r e a s e d k for c h y m o t r y p s i n (13,14) o r i n c r e a s i n g the l e n g t h of the p o l y p e p t i d e c h a i n o f the s u b s t r a t e i n c r e a s e d k t f o r e l a s t a s e ( 1 5 ) . The c a t a l y t i c rate constant ( k ) f o r j u v e n i l e hormone e s t e r a s e from the l a r v a l hemolymph o f T r i c h o p l u s i a n i u s i n g J H j , J H u i (16) and JHJI (17) as s u b s t r a t e s was k i n e t i c a l l y measured t o be r e s p e c t i v e l y 37.1, 19.4 and 31.8 m i n " . Mumby and Hammock (18) r e p o r t e d the p a r t i t i o n c o e f f i c i e n t ( l o g Ρ v a l u e s ) f o r 3 s e r i e s o f g e r a n y l de r i v a t i v e s and J H j . The l o g Ρ v a l u e f o r the l a t t e r compound was 3.71. Log Ρ v a l u e s f o r the 2 , 3 - u n s a t u r a t e d - 6 , 7 - e p o x i d e s , as the c l o s e s t s e r i e s t o the s t r u c t u r e o f JH homologs, were s u b j e c t e d t o Hansen's approach (19,20) t o measure the s u b s t i t u e n t h y d r o p h o b i c i t y (π). The % v a l u e f o r CH3 was c a l c u l a t e d from d i f f e r e n t com p a r i s o n s t o be 0.47, 0.49, 0.54 w i t h an a v e r a g e v a l u e o f 0.5 i n an e x c e l l e n t agreement w i t h the r e p o r t e d v a l u e s f o r CH3 (0.49-0.56) c a l c u l a t e d from the o c t a n o 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 of f o u r d i f f e r e n t systems ( 2 1 ) . Therefore i t i s reasonably accepted to c a l c u l a t e the e x p e c t e d l o g Ρ v a l u e s f o r J H u and J H m from t h a t o f J H j u s i n g the π v a l u e f o r CH3 group. I n t e r e s t i n g l y a good c o r r e l a t i o n between l o g Ρ and k f o r the t h r e e homologs was o b t a i n e d ( F i g u r e 3 ) . T h i s c o r r e l a t i o n might i n d i c a t e t h a t the b i n d i n g energy t h r o u g h h y d r o p h o b i c i n t e r a c t i o n s i s l i k e l y t o be i n v o l v e d i n the TS complex (ES ) . S i n c e v a l u e s o f were o b t a i n e d from d i f f e r e n t hemolymph p o o l s , the a c t i v i t y o f the enzyme from one s i n g l e hemolymph p o o l was measured towards the t h r e e homologs a t a f i n a l molar c o n c e n t r a t i o n o f 5x10"^ and the d a t a were p l o t t e d a g a i n s t l o g P. The same r e l a t i o n was o b t a i n e d as w i t h k which i s e x p e c t e d s i n c e a t the s u b s t r a t e c o n c e n t r a t i o n used (~two o r d e r s o f magnitude g r e a t e r than the v a l u e s o f K f o r the t h r e e homologs), the v e l o c i t y would a p p r o x i m a t e Vmax and the l a t t e r equals k a t [ t ] ' An e x c e l l e n t l i n e a r f u n c t i o n r e l a t i o n s h i p ( r » 0 . 9 9 9 ) between the v e l o c i t y and k ( F i g u r e 3, i n s e t ) was o b t a i n e d and s u p p o r t s the above d i s c u s s i o n . One o f the advantages o f the above a p p r o a c h i s t h a t one can e s t i m a t e the m o l a r e q u i v a l e n c y o f a s p e c i f i c enzyme i n crude p r e p a r a t i o n s . S i n c e a t enzymes u b s t r a t e s a t u r a t i o n c o n d i t i o n s v ^ V ^ ^ k Q ^ t E ^ ] , the above r e l a t i o n ( F i g u r e 3, i n s e t ) e n a b l e s the c a l c u l a t i o n o f [ E ] from the


s

c a t

c a t

c a t

c a

c a t

1

c

a

t

k

c

a

t

c a t

m

E

C

2

c

a

t

t


9.

ABDEL-AAL A N D H A M M O C K

143


s l o p e o f t h e I n s e t (1.22 nmoles/ml plasma) which i s e q u i v a l e n t t o 1.22xlO"" M o f j u v e n i l e hormone e s t e r a s e i n t h e hemolymph o f T. n i . I n f a c t t h i s average number i s i n c l o s e agreement w i t h t h a t c a l c u l a t e d from u s i n g each s u b s t r a t e s e p a r a t e l y u s i n g d i f f e r e n t hemolymph p o o l s ( 1 6 ) . The a b i l i t y t o d e t e r m i n e t h e m o l a r i t y o f a c a t a l y t i c s i t e i n s i t u i s o f tremendous b e n e f i t i n t h e e l u c i d a t i o n o f p h y s i o l o g i c a l or pharmacokinetic parameters. 6


T r a n s i t i o n S t a t e A n a l o g s (TSA) The q u a l i t a t i v e d e s c r i p t i o n o f enzyme c a t a l y s i s i n terms o f t h e TS t h e o r y ( P a u l i n g , 1_,2) t h a t the enzyme i s complementary t o an un s t a b l e m o l e c u l e w i t h o n l y t r a n s i e n t e x i s t e n c e ; namely, t h e a c t i v a t e d complex (ES*) f o r which t h e power o f a t t r a c t i o n by the enzyme i s much g r e a t e r t h a n t h a t o f t h e s u b s t r a t e i t s e l f has been d i s c u s s e d e n e r g e t i c a l l y ( 8 ) and m e c h a n i s t i c a l l y (10,22-25). P a u l i n g ' s a s s e r t i o n has opened a new e r a i n enzymology, and r e l e v a n t t o o u r d i s c u s s i o n i s t h e s t a b i l i z a t i o n o f t h e a c t i v a t e d complex and TSA as p o w e r f u l enzyme i n h i b i t o r s . As the t r a n s i t i o n s t a t e i s a mathe m a t i c a l construction (with a t y p i c a l h a l f - l i f e of l O " ^ m s e c , ( 2 2 ) ) , i t s s t r u c t u r e cannot be d e f i n e d i n common c h e m i c a l s i g n language. I n f a c t d i f f i c u l t y i n i s o l a t i n g and d e f i n i n g t r a n s i t i o n s t a t e complexes was the major r e a s o n b e h i n d the r e c r e a t i o n o f P a u l i n g ' s concept t o d e s i g n s t a b l e a n a l o g s a p p r o a c h i n g t h e s t r u c t u r e of t h e a l t e r e d s u b s t r a t e i n the t r a n s i t i o n s t a t e w i t h o u t u n d e r g o i n g c a t a l y t i c conversion. E v e n t u a l l y t h e s e TSA a r e e x p e c t e d t o be s t a b i l i z e d upon the r e a c t i o n w i t h t h e enzyme t o such a degree t h a t t h e y approach ground s t a t e energy minima ( F i g u r e 4 ) . T h i s s t a b i l i z a t i o n would i n f a c t e n a b l e i n d i r e c t o b s e r v a t i o n o f the s t r u c t u r e o f t h e enzyme-TS by u s i n g t h e a v a i l a b l e t e c h n i q u e s . Furthermore, i f a TSA t a k e s advantage o f t h e a d d i t i o n a l , f a v o r a b l e b i n d i n g i n t e r a c t i o n s t h a t a r e i n h e r e n t i n ES* i n t e r a c t i o n s , i t c o u l d be an e x t r e m e l y p o w e r f u l i n h i b i t o r t o the l i m i t o f s t o i c h i o m e t r i c r e action. T h e o r e t i c a l l y a p e r f e c t TSA would have t h e same a f f i n i t y f o r t h e enzyme as the t r a n s i t i o n s t a t e o f the s u b s t r a t e ( F i g u r e 4 ) . The q u e s t i o n a t i s s u e now i s : what i s t h e magnitude o f enzyme-TS a f f i n i t y as compared t o enzyme s u b s t r a t e a f f i n i t y ? This question has been f u l l y d e c l a r e d by s e v e r a l workers (10,22,23,25). In the f o l l o w i n g p a r a g r a p h s we w i l l summarize t h e i r m a t h e m a t i c a l approach i n a s i m p l e way. Note t h a t i n t h i s s e c t i o n a l l e q u i l i b r i a a r e d e f i n e d as a s s o c i a t i o n c o n s t a n t s . The two r e a c t i o n s t o be compared a r e : K

E+S ^

ES ^ — ^ E S

(17)

where K^s i s t h e e q u i l i b r i u m a s s o c i a t i o n c o n s t a n t the enzyme and s u b s t r a t e .

E+S* ν However, t h e r e s h o u l d 18" as f o l l o w s :

(= 1/K ) m

between

ES*

be a h y p o t h e t i c a l

(18) step

that precedes

"Equation




8 E ^> R Ç ^ E ^ RÇ-OE ^ 3

CF

F

3

CF

3

C£

F i g u r e 7. Proposed scheme f o r the r e a c t i o n s o f J H - e s t e r a s e w i t h JH homologs (A) and w i t h t r i f l u o r o m e t h y l k e t o n e s ( B ) .

PI

5 0

(Calc'd)

F i g u r e 8 . R e l a t i o n s h i p between the observed P I 5 0 v a l u e s the P I 5 0 v a l u e s c a l c u l a t e d from " E q u a t i o n 3 5 " .


and

156


From the s l o p e of the p h y s i c o c h e m i c a l parameters i n " E q u a t i o n 36" i t appeared t h a t π, MR and σ have about the same weight i n m o d e l i n g the a c t i v i t y of the 13 meta and p a r a s u b s t i t u t e d compounds. The im portance of Ε and cT seems t o be l e s s a l t h o u g h h i g h c o v a r i a n c e between E and b o t h π and MR i s a s e r i o u s o b s t a c l e p r e v e n t i n g the true d e l i n e a t i o n of E effects. Meanwhile the e q u a t i o n r e v e a l s t h a t h y d r o p h o b i c s u b s t i t u e n t s ( p o s i t i v e π term) w i t h l a r g e MR and el e c t r o n d o n a t i n g p r o p e r t i e s ( n e g a t i v e σ term) would enhance the i n h i b i t o r y potency o f the t r i f l u o r o m e r c a p t o p h e n y l a c e t o n e as a p a r e n t compound. I n f a c t t h i s was the r a t i o n a l e b e h i n d s y n t h e s i z i n g the p a r a t - b u t y l a n a l o g , and i t came out t o be the most a c t i v e congener among the t e s t e d compounds. S i n c e c o v a r i a n c e between MR and π i s low ( r ^ « 0.46), they a r e c o n s i d e r e d t o be o r t h o g o n a l and have different substituent effects. As d i s c u s s e d e a r l i e r f o r the a l k y l compounds, t h e s e s u b s t i t u e n t e f f e c t s might e s t a b l i s h d i f f e r e n t type of i n t e r a c t i o n s , i . e . p o l a r and a p o l a r i n t e r a c t i o n s . Since these compounds a r e s u b s t i t u t e d i n the same p o s i t i o n s , i t i s not c l e a r whether those t y p e s o f i n t e r a c t i o n s a r e i n two d i f f e r e n t t y p e s of enzymic spaces o r one space which i s open t o s u r r o u n d i n g s o l u t i o n . I n any case t h i s l e a d s t o f u r t h e r r e s e a r c h i n which c r y s t a l l o g r a p h i c s t r u c t u r e of JHE might shed some l i g h t on the b i n d i n g s p a c e ( s ) and the r o l e o f d e s o l v a t i o n i n t h e i r i n t e r a c t i o n w i t h t h e s e n o v e l i n hibitors. A t t h i s moment, the c o e f f i c i e n t of n e a r 1 w i t h % i n " E q u a t i o n 36" s h o u l d not be i g n o r e d and as has been d i s c u s s e d b e f o r e (70) f o r p a p a i n l i g a n d i n t e r a c t i o n s , b r i n g s out the c l o s e p a r a l l e l between b i n d i n g t o JHE and p a r t i t i o n i n g i n t o o c t a n o l . T h i s i n d i c a t e s t h a t t h e r e might be a t r u e h y d r o p h o b i c pocket on the enzyme a c t i v e s u r f a c e where i n t e r a c t i o n i s d r i v e n by d e s o l v a t i o n and the i n t e r a c t i o n i s l i k e l y to be e n t r o p i e i n n a t u r e . This conclusion s h o u l d not be o v e r s i m p l i f i e d s i n c e e x t e n s i v e thermodynamic s t u d i e s c e r t a i n l y a r e r e q u i r e d t o shed some l i g h t on the r o l e of b o t h e n t r o p y and e n t h a l p y changes f o r the i n h i b i t i o n p r o c e s s by t h e s e compounds. s


s

The s e l e c t i v e i n h i b i t i o n o f JHE and o r n a p h t h y l a c e t a t e e s t e r a s e ( s ) by o r t h o , meta and p a r a s u b s t i t u t e d compounds showed t h a t meta and p a r a s u b s t i t u t i o n o f f e r e d s e l e c t i v i t y towards JHE, however, the o r t h o s u b s t i t u t e d compounds f a v o r e d i n h i b i t i o n o f ce-naphthyl a c e t a t e e s t e r a s e s ( 5 4 ) . I t was thought t h a t s u b s t i t u t i o n i n the o r t h o p o s i t i o n might be d e t r i m e n t a l f o r i n h i b i t i o n of JHE. T h e r e f o r e we d e c i d e d t o add E v a l u e f o r the o r t h o s u b s t i t u e n t s i n the r e g r e s s i o n a n a l y s i s t o merge the o r t h o compounds w i t h t h e i r meta and p a r a a n a l o g s i n the same r e g r e s s i o n , " E q u a t i o n 37". s

P I = 5 . 0 5 + 0.74 50

Σπ + 1.14

Σ l o g MR

- 0.61

Σσ-0.11

( Σσ)

2

+ 0.61

E

g

(ortho) η 18

r 0.92

s 0.45

(37)

By comparing " E q u a t i o n s 36 and 37" one can see t h a t the c o e f f i c i e n t s o f π and MR a r e more s t a b l e t o the a d d i t i o n of the o r t h o compounds to the r e g r e s s i o n a n a l y s i s . However, the c o e f f i c i e n t s o f σ terms became s m a l l upon the a d d i t i o n of E ortho. The s t a b i l i t y of the s



9.

ABDEL-AAL AND

HAMMOCK

157


c o e f f i c i e n t s o f π and MR i n a d d i t i o n t o t h e f a c t t h a t the i n t e r c e p t s i n b o t h e q u a t i o n s a r e so s i m i l a r t o t h e o b s e r v e d P I 5 0 v a l u e (5.08) f o r the p a r e n t u n s u b s t i t u t e d compound might suggest the v a l i d i t y o f these e q u a t i o n s and s u p p o r t the above d i s c u s s i o n i n m o d e l i n g t h e i n t e r a c t i o n of t h e s e compounds w i t h JHE i n terms of t h e i r h y d r o p h o b i c i t y and molar r e f r a c t i v i t y . F i g u r e 9 shows the r e l a t i o n be tween the o b s e r v e d P I 5 0 v a l u e s f o r the members of the a r o m a t i c s e r i e s and the P I 5 0 v a l u e s c a l c u l a t e d from " E q u a t i o n 37". I n c o n c l u s i o n , a l t h o u g h our QSAR f o r the i n h i b i t i o n o f JHE w i t h t r i f l u o r o m e t h y l k e t o n e s does not o f f e r an e x c e l l e n t and sharp f i t of the d a t a t o t h e r e g r e s s i o n ("Equations 33-37"), i t might p r o v i d e the c h e m i s t w i t h a model and rough base l i n e f o r t e s t i n g new com pounds. I n g e n e r a l the i n t e r a c t i o n s of t h e s e compounds w i t h JHE a r e l i k e l y t o be h y d r o p h o b i c and nonhydrophobic. Whether the l a t t e r type i s s e p a r a b l e from the former o r i n f a c t i t i s h y d r o p h o b i c w i t h out b e i n g dependent on d e s o l v a t i o n i s not c l e a r . N e v e r t h e l e s s , as t h e s e compounds a r e c o n s i d e r e d to be s t a b l e TSA, t h e y o f f e r a v a l u a b l e t o o l i n s t u d y i n g the x - r a y c r y s t a l l o g r a p h y of JHE and i t s TS complex from which v a l u a b l e i n f o r m a t i o n can be c o u p l e d w i t h the QSAR s t u d y and would g r e a t l y i n c r e a s e our u n d e r s t a n d i n g o f JH-JHE interaction. I t i s worth r e p o r t i n g t h a t one of t h e s e a n a l o g s was a t t a c h e d t o i n s o l u b l e s u p p o r t and proved t o be an e x c e l l e n t l i g a n d f o r the p u r i f i c a t i o n o f JHE by a f f i n i t y chromatography ( 5 1 ) . T h i s i s the f i r s t s t e p i n a p p r o a c h i n g the t h r e e d i m e n s i o n a l s t r u c t u r e of JHE and J H E - i n h i b i t o r complex.

9h

PIso (Calc'd)

F i g u r e 9. R e l a t i o n s h i p between the o b s e r v e d P I 5 0 v a l u e s the P I 5 0 v a l u e s c a l c u l a t e d from " E q u a t i o n 37".


and


158 Acknowledgments

This work was supported, in part, by NIEHS Grant ROI ES02710-03 and and award in Agricultural Chemistry from the Herman Frasch Foun dation. B. D. Hammock by NIEHS Research Career Development Award 5K04 ES00107-05. The illuminating discussion and technical assis tance of Terry Hanzlik and Jim Ottea, and the patience of Ms. Peggy Kaplan and Kathleen Dooley in typing and revising the manuscript are gratefully appreciated.


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