New Tool for the Study of StructureâActivity Relationships in Three

Chapter 6

New Tool for the Study of Structure—Activity Relationships in Three Dimensions

Probing Bioactive Mechanisms Downloaded from pubs.acs.org by UNIV OF TEXAS AT DALLAS on 07/12/16. For personal use only.

The Hypothetical Active-Site Lattice 1

Arthur M . Doweyko

Uniroyal Chemical Company, Inc., World Headquarters, Middlebury, CT 06749

A three-dimensional computer-based approach has been developed which predictively models receptor or enzyme binding for molecules of widely different structural types. The method is based upon the intermediate conversion of molecules to points in space which embody both atomic character and partial binding values. The merging of data for a series of known inhibitors results in the construction of a HASL (Hypothetical Active Site Lattice) which serves to quantitatively and predictively model enzyme-inhibitor interaction. Details of the HASL methodology are discussed and the approach illustrated using E. coli dihydrofolate reductase inhibitors. The creative use of computers has led to a variety of ways to generate structure-activity relationships for sets of molecules which bind to receptors or active sites (1-12). These techniques often involve s t a t i s t i c a l treatment of data in a largely retrospective manner which i s further limited by the arbitrary choice of common substructures, pharmacophores, binding points, and molecular overlays. In classical QSAR the limitations can be quite severe i n that regressions are confined to a series of closely related structures often differing in relatively minor ways. More recent innovations involve molecular shape analysis (13) and distance geometry methods (14). These techniques represent significant steps toward a true three-dimensional SAR with some predictive Current address: Ciba-Geigy Corporation, Environmental Health Center, 400 Farmington Avenue, Farmington, CT 06032 0097-6156/89/0413-0082S06.75/0 © 1989 American Chemical Society


6.

DOWEYKO

Tool for SAR Study in Three Dimensions

modelling capabilities. The p r e s e n t i n v e s t i g a t i o n r e p r e s e n t s an e x t e n s i o n o f b o t h m o l e c u l a r shape and d i s t a n c e geometry approaches i n handling molecule-to-molecule comparisons which p e r m i t s the c o n s t r u c t i o n o f an a c t i v e s i t e model capable o f p r e d i c t i n g m o l e c u l a r b i n d i n g based on i n h i b i t i o n d a t a . S t r u c t u r a l comparisons between m o l e c u l e s , w i t h o u t a r b i t r a r y m o l e c u l a r s u p e r p o s i t i o n s , i s made p o s s i b l e t h r o u g h t h e u s e o f a three-dimensional molecular l a t t i c e of points. In a d d i t i o n , a w o r k i n g m u l t i - d i m e n s i o n a l model o f a b i n d i n g s i t e , a h y p o t h e t i c a l a c t i v e s i t e l a t t i c e ( H A S L ) , c a n be b u i l t from b i n d i n g d a t a , e . g . Ki, and used to t e s t m o l e c u l e s w i t h novel structures (15). U n l i k e o t h e r 3D QSAR a p p r o a c h e s , the m o l e c u l e s u n d e r c o n s i d e r a t i o n n e e d n o t b e o f t h e same structural class. Creation of a Molecular

Lattice

I n o r d e r t o m i n i m i z e t h e number o f c a l c u l a t i o n s needed f o r three dimensional molecular manipulations a computationally s i m p l e m e t h o d f o r m o l e c u l a r r e p r e s e n t a t i o n was s o u g h t . This c o n c e r n i s p a r t i c u l a r l y s i g n i f i c a n t when u s i n g d e s k - t o p m i c r o c o m p u t e r s h a v i n g l i m i t e d s p e e d , e v e n when e q u i p p e d w i t h numeric coprocessors. The c o n s t r u c t i o n o f a c o m p u t a t i o n a l l y f a c i l e m o l e c u l a r l a t t i c e i s i l l u s t r a t e d i n F i g u r e 1. The C a r t e s i a n c o o r d i n a t e s o f a m o l e c u l e a r e c o n v e r t e d t o a set o f e q u i d i s t a n t p o i n t s arranged o r t h o g o n a l l y to each other i n three dimensions ( x , y , z d i r e c t i o n s ) . These p o i n t s a r e s e p a r a t e d by a d i s t a n c e r e f e r r e d t o as the r e s o l u t i o n and a r e a l l l o c a t e d w i t h i n the van der W a a l ' s r a d i i o f the atoms c o n s t i t u t i n g the molecule ( s t e p s A - C , F i g u r e 1 ) . The r e s u l t i n g f r a m e w o r k o f p o i n t s w i l l be r e f e r r e d t o a s t h e m o l e c u l a r l a t t i c e . The number o f s u c h p o i n t s i s d e p e n d e n t upon the s i z e o f the m o l e c u l e , the r e s o l u t i o n chosen, and the n a t u r e o f the atoms. In order f o r the m o l e c u l a r l a t t i c e to a c c u r a t e l y r e p r e s e n t the m o l e c u l e , i t i s n e c e s s a r y to add i n f o r m a t i o n to each l a t t i c e p o i n t r e f l e c t i n g the atom w i t h i n w h i c h i t i s found. This process i s i l l u s t r a t e d i n Figure 1 (steps D-E) w h e r e i n a p o r t i o n o f the m o l e c u l e i s shaded to r e p r e s e n t d i f f e r e n t t y p e s o f atoms ( e . g . e l e c t r o n - r i c h , electron-poor). The c o r r e s p o n d i n g l y shaded l a t t i c e p o i n t s r e f l e c t the atom t y p e a n d t h u s c a n be c o n s i d e r e d a f o u r t h d i m e n s i o n a l e x t e n s i o n of the three d i m e n s i o n a l m o l e c u l a r l a t t i c e . A s i m p l e i n d i c a t o r v a r i a b l e was a d o p t e d t o s e r v e a s a p h y s i o c h e m i c a l d e s c r i p t o r and i s r e f e r r e d t o as H , t h e HASL type. L o o s e l y based on the q u a n t i t a t i v e a s s e s s m e n t o f h y d r o p h o b i c ! t y d e r i v e d from a v a r i e t y o f atom t y p e s r e p o r t e d for d i h y d r o f o l a t e r e d u c t a s e i n h i b i t o r s ( 1 6 ) , the v a l u e s f o r H a r e i n t e g e r s e q u a l t o - 1 , 0 , and +1, r o u g h l y c o r r e s p o n d i n g t o a t o m s h a v i n g l o w , medium o r h i g h e l e c t r o n d e n s i t y , respectively. T h e H v a l u e s a r e d e f i n e d b y MM2 a t o m t y p e i n Table I . T h u s , most a l i p h a t i c c a r b o n s , s i l a n e and h y d r o g e n s a r e c o n s i d e r e d e q u i v a l e n t n e u t r a l atoms (H=0), w h i l e h a l o g e n s , o x y g e n , and n i t r o g e n (H=+l) a r e e l e c t r o n - r i c h and


PROBING BIOACTIVE MECHANISMS

'mm..

•+.

>

RESOLUTION

o

o

o

o

o

o o

Figure 1. A schematic representation of 4D HASL construction: [A] molecular structure i n 3D space, containing d i f f e r e n t atoms (black and white), [B] superposition of van der Waal's molecular volume, [C] i d e n t i f i c a t i o n of molecular l a t t i c e points imbedded within the molecular volume, [D] l a t t i c e points shown i n two dimensions, [E] a three- and four-dimensional view of these l a t t i c e points.

6.

Toolfor SAR Study in Three Dimensions

DOWEYKO


c a r b o n y l c a r b o n s , s u l f o n i u m and p h o s p h i n e atoms ( H = - l ) a r e electron-poor. T h i s d i s t i l l a t i o n o f the atom t y p e s to t h r e e c l a s s e s i s l i k e l y an o v e r - s i m p l i f i c a t i o n , but appears to s e r v e w e l l i n HASL c o n s t r u c t i o n i n t h a t i t i s t h e k e y t o a c o n s i s t e n t a l i g n m e n t o f m o l e c u l e s by v i r t u e o f t h e i r a t o m i c makeup. M o l e c u l a r l a t t i c e s c a l c u l a t e d f o r _p_-aminobenzoic a c i d at s e v e r a l r e s o l u t i o n values are i l l u s t r a t e d i n Figure 2.

Table I .

MM2

H

Atom

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 0 -1 0 0 +1 4-1 +1 +1 +1 +1 +1 +1 +1

C C C C H 0 0 N N N F CI Br I

HASL T y p e ( H ) D e f i n i t i o n s

Type

MM2

sp alkane sp alkene sp carbonyl sp acetylene hydrogen C(0)H, C(0)C

15 16

C-(0) sp sp sp fluoride chloride bromide iodide

17 18 19 21 22 23 24 25 26 27 28 37

H

+1 -1 -1 -1 -1 -1 -1 +1 -1 -1 +1

Atom

S S+ S S Si H C H H P B B H N

Type

sulfide sulfonium sulfoxide sulfone silane 0(H) cyclopropyl N(H) C00(H) phosphine >B>B< C=C(H) C=(N)

Comparing M o l e c u l a r L a t t i c e s M o l e c u l e s c a n be q u a n t i t a t i v e l y compared t o one a n o t h e r through the use o f m o l e c u l a r l a t t i c e s . Since each l a t t i c e r e p r e s e n t s a m o l e c u l e as a f i n i t e number o f p o i n t s i n s p a c e , and each p o i n t a l s o c o n t a i n s a t o m i c c h a r a c t e r i n f o r m a t i o n ( s u c h as H ) , i t becomes a s i m p l e m a t t e r t o o v e r l a y t h e l a t t i c e d e s c r i p t i o n o f one m o l e c u l e o v e r t h a t o f a n o t h e r , and c o m p u t e t h e n u m b e r o f common p o i n t s f o u n d b e t w e e n t h e t w o . F i r s t , one m o l e c u l e and i t s l a t t i c e can a c t as a s t a t i o n a r y reference. A s e c o n d m o l e c u l e i s then c e n t e r e d on the f i r s t a n d i t s l a t t i c e i s g e n e r a t e d ( u s i n g t h e same r e s o l u t i o n ) . A f t e r the l a t t i c e s are checked f o r commonalties, the second m o l e c u l e i s s t e p p e d t h r o u g h a s e r i e s o f t r a n s l a t i o n a l and r o t a t i o n a l movements w i t h a l a t t i c e g e n e r a t e d a t e a c h s t e p . T h e d e g r e e o f m a t c h i n g , o r F I T , c a n be c o m p u t e d i n a number of ways. A p r e f e r r e d d e f i n i t i o n o f F I T i s shown i n e q u a t i o n 1. The c o o r d i n a t e s o f the second m o l e c u l e t h a t generated the best o v e r a l l FIT are then taken to r e p r e s e n t the optimum o v e r l a p on the s t a t i o n a r y m o l e c u l e . Since each

Figure 2. An i l l u s t r a t i o n o f l a t t i c e s at s e v e r a l d i f f e r e n t r e s o l u t i o n s u s i n g j>.-aminobenzoic a c i d as an example m o l e c u l e .


6.


DOWEYKO

l a t t i c e point i s four-dimensional, a necessary condition c o m m o n a l i t y i s t h a t two l a t t i c e p o i n t s h a v e i d e n t i c a l H v a l u e s as w e l l as t h r e e - d i m e n s i o n a l coordinates. L PIT

(common)


where

L (common)

=

+ L

(ref)

L (common) L

(ref)

L

(molecule)

for

(1) L

= number between = number to the = number to the

(molecule) o f l a t t i c e p o i n t s i n common two m o l e c u l e s of l a t t i c e points belonging stationary molecule of l a t t i c e points belonging moving molecule

The c o m p a r i s o n o f m o l e c u l e s t o one a n o t h e r u s i n g l a t t i c e s f o r q u a n t i t a t i o n i s i l l u s t r a t e d f o r two s i m p l e c a s e s i n Figure 3. Benzene o v e r l a i d upon i t s e l f and r o t a t e d about i t s c e n t r a l a x i s produces a u n d u l a t i n g l i n e r e f l e c t i n g FIT v a l u e s w h i c h peak e v e r y 60 d e g r e e s c o r r e s p o n d i n g t o o v e r l a p p i n g carbon-hydrogen nodes. I n the case o f toluene on toluene, a s i m i l a r r o t a t i o n a l pattern i s observed w i t h a maximum F I T a c h i e v e d a s t h e s t a g g e r e d m e t h y l g r o u p s a l i g n a t the 300 d e g r e e mark. The f i t t i n g r o u t i n e c o n d u c t e d a t s m a l l e r r e s o l u t i o n v a l u e s , as shown i n t h e b e n z e n e / b e n z e n e e x a m p l e , r e s u l t s i n a more s e n s i t i v e a s s e s s m e n t o f o v e r l a p , r e f l e c t e d by t h e r e s p o n s e / d e g r e e i n t h e v a l u e o f F I T . A f t e r f i t t i n g one m o l e c u l a r l a t t i c e t o a n o t h e r , i t i s p o s s i b l e to merge the i n f o r m a t i o n c o n t a i n e d i n b o t h t o form a composite l a t t i c e . T h i s l a t t i c e would then r e f l e c t the s p a t i a l and a t o m i c r e q u i r e m e n t s o f both m o l e c u l e s simultaneously. The f i t t i n g and m e r g i n g c y c l e c a n be repeated for each a d d i t i o n a l molecule, c o n t i n u a l l y b u i l d i n g up t h e i n f o r m a t i o n c o n t e n t o f t h e r e s u l t i n g c o m p o s i t e lattice. Thus, the composite l a t t i c e o f p o i n t s r e p r e s e n t s the s p a t i a l and a t o m i c c h a r a c t e r requirements o f a l l molecules used i n i t s c o n s t r u c t i o n . The P a r t i a l p K i D i s t r i b u t i o n Enzyme i n h i b i t i o n d a t a i s commonly e x p r e s s e d as 1 ( 5 0 ) o r K i . T h i s d a t a c a n b e made a p a r t o f t h e c o m p o s i t e l a t t i c e . In t h i s way, not o n l y can the l a t t i c e a c t to a s s e s s FIT o f n o v e l structures, but i t can a l s o p r o v i d e an e s t i m a t e o f K i f o r the novel structures. I n o r d e r to c l e a r l y f o c u s on a c t i v e s i t e b i n d i n g , the p r e s e n t i n v e s t i g a t i o n i s l i m i t e d to the c o n s i d e r a t i o n o f c o m p e t i t i v e enzyme i n h i b i t o r s . However, i n p r i n c i p l e , t h e HASL m e t h o d o l o g y w o u l d l e n d i t s e l f to a p p l i c a t i o n s i n v o l v i n g l e s s d e f i n i t i v e b i n d i n g as i s o f t e n e n c o u n t e r e d i n s t u d i e s where o n l y 1(50) v a l u e s a r e a v a i l a b l e , i n c a s e s o f u n s p e c i f i e d b i n d i n g to a r e c e p t o r , o r where i n v i v o data, e . g . percent growth i n h i b i t i o n , are considered.


88


0

90

180

270

Degree of Rotation Q,A

x-rot

+,x

y-rot

v

z-rot

F i g u r e 3. The q u a n t i t a t i o n o f m o l e c u l a r o v e r l a p t h r o u g h the intermediacy of molecular l a t t i c e s . Examples i l l u s t r a t e d a r e the r o t a t i o n a l s u p e r p o s i t i o n i n g o f benzene on benzene and t o l u e n e on t o l u e n e . 01 * L ( c o m m o n ) / L ( r e f ) and 02 * L ( c o m m o n ) / L ( m o l e c u l e ) .

360


6.

DOWEYKO


Enzyme i n h i b i t i o n d a t a i s most c o n v e n i e n t l y e x p r e s s e d a s - l o g K i o r p K i . I n t h i s form, the b i n d i n g v a l u e s are d i r e c t l y p r o p o r t i o n a l to the free energy o f b i n d i n g and, therefore, c a n be d i s s e c t e d i n t o s m a l l e r , a d d i t i v e components. F o r example, as a f i r s t a p p r o x i m a t i o n , the t o t a l p K i o f a n i n h i b i t o r c a n b e d i v i d e d e v e n l y among i t s l a t t i c e points. These l a t t i c e p o i n t s a r e presumed to a c c o u n t f o r the b i n d i n g o f every p a r t of the m o l e c u l e . Such an e q u a l d i s t r i b u t i o n of p a r t i a l pKi values i s c l e a r l y s i m p l i s t i c , since i t i s l i k e l y that a molecule contains portions ( t y p i c a l l y f u n c t i o n a l g r o u p s ) t h a t b i n d more s t r o n g l y t h a n other portions. The key to s o l v i n g the p a r t i a l p K i d i s t r i b u t i o n p r o b l e m i s found i n the body o f i n h i b i t i o n d a t a . The p K i o f e a c h m o l e c u l e ( o r m o l e c u l a r l a t t i c e ) t h a t was u s e d t o c o n s t r u c t t h e c o m p o s i t e l a t t i c e n e e d s t o be i n c o r p o r a t e d i n t o t h e l a t t i c e i n s u c h a way t h a t r e f i t t i n g a n i n h i b i t o r m o l e c u l e t o t h i s l a t t i c e and a d d i n g the p a r t i a l p K i terms at each l a t t i c e point representing that molecule would r e s u l t i n a p r e d i c t e d p K i i d e n t i c a l to the o r i g i n a l v a l u e f o r the f i t t e d molecule. I n t h i s way, a s e l f - c o n s i s t e n t m a t h e m a t i c a l model of a c t i v e s i t e b i n d i n g i s produced. A m e t h o d was f o u n d t h a t d i s t r i b u t e s t h e p a r t i a l p K i v a l u e s i n the r e q u i r e d p r e d i c t i v e manner. T h i s method i s i l l u s t r a t e d i n Figure 4. I n the example g i v e n , molecules A and B , h a v i n g p K i ' s o f 3 . 0 0 and 6 . 0 0 , r e s p e c t i v e l y , a r e used i n an a t t e m p t t o g a i n i n f o r m a t i o n about an a c t i v e s i t e whose l a t t i c e (HASL) c o n s i s t s o f f o u r p o i n t s w i t h p a r t i a l p K i v a l u e s o f 3 . 0 0 , 2 . 0 0 , 1.00, and 0 . 0 0 . This partial pKi d i s t r i b u t i o n i s t o be c o n s i d e r e d a s t h e t a r g e t o f t h e A / B analysis. I n i t i a l l y , both m o l e c u l a r l a t t i c e s r e f l e c t an even d i s t r i b u t i o n o f p K i . The f i t t i n g and m e r g i n g o f m o l e c u l e s A a n d B r e s u l t s i n a HASL w i t h p a r t i a l p K i v a l u e s a v e r a g e d a t each p o i n t . I t i s apparent that r e f i t t i n g e i t h e r molecule o n t o t h e p r e s e n t HASL w o u l d r e s u l t i n p o o r p K i p r e d i c t i v i t y . F i t t i n g m o l e c u l e A o n t o t h e " a v e r a g e d " HASL p r o v i d e s a p r e d i c t i o n of 4.00 (actual pKi = 3.00), while molecule B i s p r e d i c t e d to have a p K i o f 5.00 ( a c t u a l p K i = 6 . 0 0 ) . It is through a subsequent r e i t e r a t i v e technique, reminiscent of the s o l u t i o n o f simultaneous e q u a t i o n s , that a t r u l y p r e d i c t i v e HASL i s o b t a i n e d . U s i n g t h e " a v e r a g e d " HASL a s a s t a r t i n g p o i n t , the f i t t i n g o f molecule A g i v e s r i s e to a set o f c o r r e c t i o n s r e f e r r e d t o a s I N and OUT, whose v a l u e s a r e dependent upon the o v e r a l l e r r o r i n p r e d i c t e d p K i (ERROR). I N c o r r e c t i o n s a r e a p p l i e d o n l y t o t h o s e H A S L p o i n t s common t o b o t h m o l e c u l e A a n d t h e H A S L , w h i l e OUT c o r r e c t i o n s a r e made t o HASL p o i n t s n o t u s e d . Step _ i . i l l u s t r a t e s this p r o c e s s w h e r e i n p r e d i c t e d p K i ERROR = - 1 . 0 0 , I N = - 0 . 3 3 a n d OUT = 1 . 0 0 , g i v i n g r i s e t o a c o r r e c t e d H A S L ( 3 . 0 0 , 1.17, 1.17, 0 . 6 7 ) . The p r o c e d u r e i s r e p e a t e d w i t h e v e r y m o l e c u l e t h a t was u s e d t o c r e a t e t h e H A S L . I n the A / B case a s i n g l e i t e r a t i v e c y c l e w o u l d be c o n s i d e r e d a s t h e f i t t i n g o f m o l e c u l e s A and B , each w i t h c o r r e c t i o n s a p p l i e d . The

PROBING BIOACTIVE MECHANISMS Actual pKi

(2%\

3.00

Molecule A

(3^o)


Molecule B

"Averaged"

^OO)

(lTo)

Predicted pKi

HASL

^ 5 0 J

ERROR

-

IN

-

OUT

=

11

F i t t i n g Molecule B

-1.00 -0.33 1.00

ii.

ERROR IN OUT

»

(^3)

(°^°)

0.66

- 0.22 - -0.66

I t e r a t e d " HASL (Step v i . )

(^^)

4.00 5.00

Molecule A Molecule B

^Too)

F i t t i n g Molecule A i.

Initial Assumption

A c t u a l Molecular Lattice

Predicted pKi

^

^

Molecule A Molecule B

3.00 6.01

Figure 4 . P a r t i a l p K i e s t i m a t e s made by c a r r y i n g out an i t e r a t i v e method on the d e g r e e o f f i t t i n g f o r m o l e c u l e s A and B. ERROR = a c t u a l p K i - p r e d i c t e d p K i . IN i s the c o r r e c t i o n a p p l i e d t o each common l a t t i c e p o i n t , IN = ERROR/NI, where NI * number o f l a t t i c e p o i n t s i n common. OUT i s the c o r r e c t i o n a p p l i e d to e a c h p o i n t o u t s i d e the o v e r l a p , OUT « -ERROR/NO, where NO « number o f l a t t i c e p o i n t s o u t s i d e the o v e r l a p .

6.

DOWEYKO


i t e r a t i v e c y c l e c a n be r e p e a t e d u n t i l e i t h e r the e r r o r i n p r e d i c t i o n i s removed o r m i n i m i z e d . I n the present A / B example, s i x such c y c l e s r e s u l t e d i n near perfect predictivity.


Effect

of

Resolution

R e s o l u t i o n , or the o r t h o g o n a l l a t t i c e p o i n t s p a c i n g , can p l a y a n i m p o r t a n t r o l e i n t h e c a p a b i l i t y o f a HASL t o e f f e c t i v e l y predict binding. T h e r e e x i s t two l o g i c a l e x t r e m e s : (1) very s m a l l s p a c i n g w h i c h r e s u l t s i n a l a r g e number o f l a t t i c e p o i n t s , o r ( 2 ) v e r y w i d e s p a c i n g w h i c h r e s u l t s i n v e r y few lattice points. There are disadvantages at e i t h e r extreme. As t h e r e s o l u t i o n becomes s m a l l e r , t h e number o f l a t t i c e points increases. This effect i s i l l u s t r a t e d for 2,4d i a m i n o - 5 - m e t h y l p h e n y l p y r i m i d i n e ( D 0 1 ) i n F i g u r e 5 A . When the r e s o l u t i o n i s l e s s than the average atomic van der W a a l ' s radius (ca. 1 . 8 - 2 . 0 X ) , t h e number o f r e s u l t i n g p o i n t s i n c r e a s e s w i t h the cube o f the s p a c i n g . This s i t u a t i o n leads to an o v e r - d e s c r i p t i o n o f the m o l e c u l e . I n a d d i t i o n to an o b v i o u s i n c r e a s e i n c o m p u t a t i o n a l time f o r the assessment o f f i t t i n g , a s u b t l e but important drawback a r i s e s : the o v e r d e s c r i p t i o n o f a m o l e c u l e w i l l r e s u l t i n more p o i n t s f o r partial pKi distribution. E s s e n t i a l l y , these points r e p r e s e n t degrees o f freedom to the i t e r a t i v e s o l u t i o n f o r the p a r t i a l p K i d i s t r i b u t i o n p r o b l e m , and t h e r e f o r e , increase the l i k e l i h o o d o f o b t a i n i n g m i s l e a d i n g s o l u t i o n s w h i c h are not unique. T h i s e f f e c t w o u l d be e x p e c t e d t o c o m p r o m i s e HASL predictivity. The second extreme o f w i d e s p a c i n g r e s u l t i n g from a l a r g e r e s o l u t i o n v a l u e would r e p r e s e n t an u n d e r - d e s c r i p t i o n of a molecule. T h e p r e s e n c e o f d i f f e r e n t a t o m t y p e s may n o t b e a c c u r a t e l y a s s e s s e d when u s i n g a l a r g e r e s o l u t i o n . This e f f e c t i s i l l u s t r a t e d i n F i g u r e 5 B f o r t h e same p y r i m i d i n e discussed above. As the r e s o l u t i o n i s i n c r e a s e d beyond 3 a n g s t r o m s , t h e o b s e r v e d p e r c e n t c o m p o s i t i o n o f t h e t h r e e HASL types ( - 1 , 0 , + l ) i s found to d e v i a t e s i g n i f i c a n t l y from the t h e o r e t i c a l v a l u e s c a l c u l a t e d from van der W a a l ' s volumes. In a d d i t i o n , the s o l u t i o n o f the p a r t i a l p K i d i s t r i b u t i o n problem i s a f f e c t e d once a g a i n . Without s u f f i c i e n t points to load with p a r t i a l pKi estimates, p r e d i c t i v i t y is neccesarily l i m i t e d t o some m i n i m a l e r r o r r e g a r d l e s s o f t h e n u m b e r o f i t e r a t i v e cycles performed. From the above c o n s i d e r a t i o n s , i t w o u l d a p p e a r t h a t a r e s o l u t i o n c h o i c e o f 2 - 3 a n g s t r o m s w o u l d be o p t i m a l . This i n t u i t i v e a s s e s s m e n t was t e s t e d u s i n g s e v e r a l m o d e l s y s t e m s . F i v e s u b s t i t u t e d b e n z e n e s w e r e c h o s e n t o c r e a t e a QSAR. T h e s e compounds a r e l i s t e d i n T a b l e I I a l o n g w i t h t h e i r corresponding substituent physiochemical parameters p i (logP) a n d MR ( m o l a r r e f r a c t i v i t y ) . A QSAR s e t w i t h r e a l p a r a m e t e r v a l u e s was u s e d i n t h i s s t u d y i n o r d e r t o o b t a i n a corresponding set of r e a l i s t i c " a c t u a l " pKi values.

92



Table I I . The F i v e Compound QSAR Set Used to T e s t HASL P r e d i c t i v i t y as a F u n c t i o n o f R e s o l u t i o n

pi

MR

0.00

1.03

3.48

1.12

13.94

2.68

-1.23

5.42

1.05

-0.32

6.93

2.52

-0.47

10.33

1.97

A r b i t r a r y r e g r e s s i o n e q u a t i o n ( 2 ) p r o v i d e d the v a l u e s f o r t h i s compound s e t :

pKi

"actual" pKi

2 pKi

-

pi

-

pi 2

-

0 . 1 MR +

3.58

(2)

E a c h compound i n the s e t was f i t t e d to a HASL c o n s t r u c t e d o f the o t h e r f o u r . T h u s , a t each r e s o l u t i o n s t u d i e d , i t was p o s s i b l e to o b t a i n f i v e p r e d i c t e d p K i v a l u e s and compare them to " a c t u a l " v a l u e s . Resolution values r a n g i n g from 1 . 5 to 4 . 0 angstroms ( i n i n c r e m e n t s o f 0 . 1 2 5 I ) were each used to c o n s t r u c t a four-compound HASL which y i e l d e d f i v e tests of p r e d i c t i v i t y . The a v e r a g e e r r o r ( a c t u a l - p r e d i c t e d p K i ) was d e t e r m i n e d a t each r e s o l u t i o n value. The r e s u l t s o f t h i s a n a l y s i s a r e p l o t t e d i n F i g u r e 6 ,

6.

DOWEYKO


Resolution and HASL Size

iOOi


360

1.5

1.0

93

2.0 2.6 3.0 RESOLUTION (I) O H -1-1 A H 0 O H - !

2.0 2.6 3.0 Resolution (X)

F i g u r e 5. The e f f e c t s o f r e s o l u t i o n c h o i c e on m o l e c u l a r l a t t i c e c o n s t r u c t i o n u s i n g D01 as an example. [A] A p l o t o f the t o t a l number o f l a t t i c e p o i n t s as a f u n c t i o n o f r e s o l u t i o n , and [B] a p l o t o f the H d i s t r i b u t i o n as a f u n c t i o n o f r e s o l u t i o n , i n d i c a t i n g that H - d i s t r i b u t i o n values b e g i n to a p p r o a c h t h e o r e t i c a l l e v e l s a t r e s o l u t i o n s l e s s than o r e q u a l to 2 . 8 a n g s t r o m s . (Reproduced from Ref. 15. C o p y r i g h t 1988 A m e r i c a n C h e m i c a l S o c i e t y . )

4

1.4

1.8

2.2

2.6

3

3.4

3.8

Resolution (1) F i g u r e 6. The e f f e c t o f r e s o l u t i o n c h o i c e on p r e d i c t i v i t y . E a c h p o i n t r e p r e s e n t s an e r r o r i n the p r e d i c t e d p K i o f one o f f i v e s u b s t i t u t e d benzenes ( t a k e n from T a b l e I I ) u s i n g a HASL made from the o t h e r f o u r compounds.


94


a n d i n d i c a t e t h a t t h e b e s t p r e d i c t i v i t y was o b s e r v e d when t h e r e s o l u t i o n was i n t h e r a n g e o f 2 - 3 a n g s t r o m s . A s e c o n d t e s t was d e v e l o p e d t o e x a m i n e t h e e f f e c t o f HASL r e s o l u t i o n on t h e e s t i m a t e s o f p a r t i a l p K i w i t h i n t h a t HASL. F i g u r e 7 i l l u s t r a t e s t h e f o u r compounds and p K i v a l u e s comprising this test. _p_-Aminobenzoie a c i d i s shown t o have a p K i o f 7 . 0 0 and i s f u r t h e r d e t a i l e d to i n d i c a t e t h a t the c a r b o x y l g r o u p , amino g r o u p , and p h e n y l r i n g b i n d i n g o c c u r s w i t h p a r t i a l p K i ' s o f 4 . 0 0 , 2 . 0 0 , and 1.00, r e s p e c t i v e l y . S i m i l a r d e t a i l i n g o f p a r t i a l p K i v a l u e s i s shown f o r the o t h e r t h r e e compounds c o n s i s t e n t w i t h t h e _p_-aminobenzoic a c i d structure. C o n s t r u c t i o n o f a HASL f r o m t h e f o u r c o m p o u n d s i s t h e n f o l l o w e d by the f i t t i n g o f j>_-aminobenzoic a c i d . From the f i t t i n g r e s u l t s i t i s p o s s i b l e t o compute the p a r t i a l p K i e s t i m a t e s made b y t h e H A S L f o r e a c h o f t h e t h r e e m o i e t i e s under c o n s i d e r a t i o n , i . e . , the c a r b o x y l , amino, and p h e n y l g r o u p s and compare t h e s e e s t i m a t e s w i t h the a c t u a l o n e s . T h i s i s d o n e b y e x a m i n i n g w h i c h HASL p o i n t s c o r r e s p o n d t o each o f t h e s e m o i e t i e s and a d d i n g t h e i r p a r t i a l p K i t e r m s . T h i s p r o c e d u r e was c a r r i e d o u t o v e r a r e s o l u t i o n r a n g e o f 1.7 t o 3 . 4 a n g s t r o m s ( i n i n c r e m e n t s o f 0 . 1 S). The r e s u l t s a r e l i s t e d i n T a b l e I I I and i l l u s t r a t e d i n F i g u r e 8. The a b s o l u t e a v e r a g e e r r o r i n HASL p r e d i c t i v i t y o f p a r t i a l p K i among t h e t h r e e f u n c t i o n a l i t i e s i s f o u n d t o u n d e r g o a m i n i m u m r o u g h l y i n t h e r a n g e o f 1.9 t o 2 . 5 a n g s t r o m s . Two i n d e p e n d e n t t e s t s d e s i g n e d t o e x a m i n e r e s o l u t i o n e f f e c t s o n HASL p r e d i c t i v i t y h a v e c o n f i r m e d t h a t t h e b e s t r e s u l t s a r e a c h i e v e d w h e n HASL r e s o l u t i o n l i e s w i t h i n a 2 - 3 angstrom range. A m o r e d e m a n d i n g t e s t o f HASL p r e d i c t i v i t y i s i n i t s a p p l i c a t i o n to an a c t u a l i n h i b i t o r s e t u s i n g an enzyme whose a c t i v e s i t e i s w e l l known. Dihydrofolate

Reductase

E . C o l i d i h y d r o f o l a t e r e d u c t a s e (DHFR) i n h i b i t o r s w e r e c h o s e n t o a s s e s s t h e HASL m e t h o d o l o g y s i n c e a l a r g e number o f c o m p e t i t i v e i n h i b i t o r s a r e known w h i c h encompass a v a r i e t y o f structures. I n a d d i t i o n , t h e c r y s t a l s t r u c t u r e o f t h e enzyme and the a c t i v e s i t e o r i e n t a t i o n o f a s t r o n g i n h i b i t o r , m e t h o t r e x a t e ( M T X ) , a r e a l s o k n o w n (17). The s e t o f 72 i n h i b i t o r s t r u c t u r e s (18-22) used f o r t h i s a n a l y s i s i s l i s t e d i n Table 4. A l l s t r u c t u r e s were energy m i n i m i z e d u s i n g MM2 ( Q C P E MM2 was a d a p t e d f o r u s e o n t h e I B M - P C b y K e v i n E . G i l b e r t and J o s e p h J . G a j e w s k i ) . A s d o n e i n c l a s s i c a l QSAR m e t h o d o l o g y , t h e DHFR i n h i b i t o r s e t was d i v i d e d i n t o two g r o u p s : a l e a r n i n g s e t and a t e s t s e t . The l e a r n i n g s e t was s e l e c t e d by u s i n g p a r a m e t e r s s u c h a s t h e number o f d i f f e r e n t a t o m s , number o f r i n g s , and m o l e c u l a r w e i g h t s i n a r e p e t i t i v e v e r s i o n o f t h e a l g o r i t h m o f W o o t o n ( 2 3 - 2 4 ) , w h i c h y i e l d e d 37 c o m p o u n d s t h a t d i f f e r f r o m o n e a n o t h e r a s much a s p o s s i b l e i n terms o f these t h r e e parameters. T h e s e compounds a r e indicated with asterisks i n Table IV. at

T h e l e a r n i n g s e t was u s e d t o g e n e r a t e HASL d e s c r i p t i o n s r e s o l u t i o n s o f 2 . 8 , 3 . 2 , 3 . 5 , and 4 . 0 a n g s t r o m s . Partial


DOWEYKO


4 ..

— COOH

pKi

COOH

7.00

5.00

3.00

1.00

Figure 7. The p a r t i a l p K i v a l u e s a r b i t r a r i l y s e t f o r j ^ a m i n o b e n z o i c a c i d and t h r e e r e l a t e d m o l e c u l e s used to t e s t the H A S L c a p a b i l i t y to e s t i m a t e p a r t i a l p K i v a l u e s a t different resolutions.

Table I I I .

P a r t i a l pKi (Actual)

j^-Aminobenzoic

Acid P a r t i a l

pKi Estimations

COOH

NH2

Phenyl

Total

4.00

2.00

1.00

7.00

Estimated

P a r t i a l pKi

Resolution (Angstroms)

COOH

NH2

Phenyl

Total

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3

2.72 2.42 3.30 3.94 4.37 4.50 2.88 3.19 3.30 3.08 2.86 2.48 2.69 1.91 1.91 1.21 1.65

2.48 2.33 2.28 2.10 1.85 1.66 2.47 2.10 2.04 2.05 2.05 2.65 2.70 3.94 3.94 3.94 3.79

1.95 2.18 1.46 1.05 0.93 1.03 1.63 1.71 1.70 1.91 2.12 2.03 1.79 1.25 1.25 1.99 1.73

7.15 6.93 7.05 7.09 7.15 7.19 6.98 7.00 7.04 7.04 7.03 7.16 7.18 7.10 7.10 7.14 7.17

Abs. Ave. Error 0.90 1.03 0.48 0.07 0.20 0.29 0.74 0.54 0.48 0.63 0.77 1.07 0.93 1.09 1.09 1.91 1.62

4

U

3

M

U h

Ν 0

J

I

Ai

Ο


G0

S3

S

i

Ρ

Ο W

*ϋ 73 Ο m

so as

H 3- F 4- NH2 4-F 4-C1 3,4-(OH)2 4-CH3 3-C1 3- CH3 4- Br 4-0CH3 4-NHC0CH3 3-OCH3 3-Br 3-CF3 3-1 3- CF3 3.4- (OCH3)2 3.5- (0CH3)2 3,4,5-(0CH3)3 3.4- (0H)2 4- 0(CH2)6CH3 4-0(CH2)5CH3 3-0(CH2)7CH3 3-CH20H 3.5- (CH20H)2 3-0(CH2)6CH3

D01-O53

D01* D02 D03 D04 DOS D06 D07* D08 D09 D10 Dll D12* D13 D14 D15 D16* D17* D18* D19 D20* D21* D22* D23 D24 D25 D26 D27*

H

2

3

CH3

N ^ N ^ C H D54-D65

JL Jc

6.18 6.23 6.30 6.35 6.45 6.46 6.48 6.65 6.70 6.82 6.82 6.89 6.93 6.96 7.02 7.23 7.69 7.72 8.38 8.87 3.04 5.60 6.07 6.25 6.28 6.31 6.39

pKi D28 D29 D30* D31 D32 D33 D34 D35 D36* D37 D38* D39* D40* D41* D42* D43* D44* D45* D46* D47 D48* D49* D50* D51 D52 D53 D54*

2

H N'

4-0CH2CH20CH3 3-0H 3-0CH2CH20CH3 3-CH20(CH2)3CH3 3-0CH2C0NH2 3- CH20CH3 4- N(CH3)2 3-0(CH2)3CH3 3- 0(CH2)5CH3 4- 0(CH2)3CH3 3-0CH2C6H5 3.4- (0CH2CH20CH3)2 3.5- (0CH3)2-4-0(CH2)20CH3 3,5-(0CH3)2-4-Br 3,4-(0CH3)2-5-0CH2C00H 3-0CH3-4-Br-5-0CH2C00H 3,4-(0CH3)2-5-0(CH2)2C00H 3-0CH3-4-Br-5-0(CH2)2C00H 3,4-(0CH3)2-5-0(CH2)3C00H 3-0CH3-4-Br-5-0(CH2)3C00H 3,4-(0CH3)2-5-0(CH2)4C00H 3-0CH3-4-Br-5-0(CH2)4C00H 3,4-(0CH3)2-5-0(CH2)5C00H 3-0CH3-4-Br-5-0(CH2)5C00H 3,4-(OCH3)2-5-0(CH2)6COOH 3-0CH3-4-Br-5-0(CH2)6C00H 3-C0NH2 .40 ,47 53 ,55 57 59 78 82 82 89 99 22 35 22 59 80 23 46 46 49 18 40 62 92

pKi

3,5-(0CH3)2 4-0CH3 3,5-(0CH3)2 4-0CH3

3-CF3 3-F H 3-C1 3-1 3-CN 3-CH3 3-(CH2)5CH3 3-C(CH3)3 3-0(CH2)3CH3 3-0CH2C6H5 5.69 5.85 4.51 5.87 5.58 5.51 5.42 5.75 4.72 6.02 5.31 8.36 7.17 6.55 9.31 8.30 5.95 6.89

pKi

Inhibition constants obtained from: Ref. 18 (D01-D40), Ref. 19 (D41-D53), Ref. 20 (D54-D65), Ref. 21 (D68-D72). Asterisk (*) denotes learning set member.

D55* D56* D57* D58 D59* D60* D61* D62 D63* D64 D65* D66* D67* D68 D69* D70 D71* D72

Table IV. Dihydrofolate Reductase Inhibitor Set


V© --4


98


p K i d i s t r i b u t i o n among the HASL p o i n t s was s o l v e d to w i t h i n a p r e d i c t i v i t y ( a c t u a l p K i - p r e d i c t e d p K i ) o f 0.1 p K i u n i t s , w i t h the e x c e p t i o n o f the 4 . 0 X HASL, which was m i n i m i z e d to a p r e d i c t i v i t y o f 1.14 p K i u n i t s . B i n d i n g p r e d i c t i o n s were o b t a i n e d f o r the e n t i r e i n h i b i t o r s e t a t each r e s o l u t i o n and the r e s u l t s p l o t t e d s e p a r a t e l y f o r l e a r n i n g and t e s t s e t members i n F i g u r e 9. As e x p e c t e d , good p r e d i c t i v i t y was o b s e r v e d f o r the members o f the l e a r n i n g s e t , w i t h some p e r c e p t i b l e s c a t t e r i n evidence at 4 angstroms. F o r members o f the t e s t s e t , s c a t t e r was o b s e r v e d to i n c r e a s e w i t h i n c r e a s i n g r e s o l u t i o n , a r e s u l t e s s e n t i a l l y m i r r o r e d i n the c o r r e l a t i o n c o e f f i c i e n t (r). S i n c e the l e a r n i n g s e t does not c o n t a i n a l l the t e s t s e t s t r u c t u r a l i n f o r m a t i o n , the o b s e r v e d s c a t t e r i s e x p e c t e d . The r e s u l t s o b t a i n e d a t 2.8 angstroms a r e e n c o u r a g i n g s i n c e a r e a s o n a b l e HASL was o b t a i n e d ( r = 0 . 7 5 3 ) . Test Set at 2.8 A

Learning Set at 2 8 A

O

a

/

r =0.753

r =0.999 8 9 Actual pKi Learning Sat at 3.2 k

12

8 9 Actual pKi Teat Set at 3.2 A

Figure 9. The effects of resolution choice on H A S L predictivity using comparisons between learning set and test set D H F R inhibitor data. Plots compare predictivities for both sets at 2.8- and 3.2-angstrom resolutions. Correlation coefficients (r) are shown for each plot. (Continued on next page.)


6. DOWEYKO

99


T h e e n t i r e 72 c o m p o u n d s e t was u s e d t o c o n s t r u c t a HASL at 2.8 angstroms i n o r d e r to c h a r a c t e r i z e the a c t i v e s i t e and make c o m p a r i s o n s w i t h c r y s t a l d a t a . T h e r e s u l t i n g HASL w a s f o u n d t o c o n s i s t o f 160 p o i n t s . Although i t is d i f f i c u l t to draw i n s i g h t from the g e o m e t r i c r e p r e s e n t a t i o n o f a HASL, an a t t e m p t i s made i n F i g u r e s 10A a n d 1 0 B . T h e HASL p o i n t s w h i c h r e p r e s e n t H = - l a r e d e p i c t e d a s s m a l l s p h e r e s i n 3D space set apart i n increments of 2.8 angstroms. The c o l o r s g r e e n , y e l l o w , and r e d i n d i c a t e s t r o n g b i n d i n g ( p a r t i a l p K i > 1 . 0 ) , weak b i n d i n g ( 0 . 0 < p a r t i a l p K i < 1 . 0 ) , and p o o r b i n d i n g ( p a r t i a l p K i < 0 . 0 ) , r e s p e c t i v e l y . To h e l p o r i e n t the v i e w e r , p a n e l 10B i n c l u d e s i n h i b i t o r D66 d o c k e d t o t h e H A S L w i t h i t s 2 , 4 - d i a m i n o g r o u p s marked by a r r o w s . In examining the r e l a t i v e o r i e n t a t i o n s o f o t h e r i n h i b i t o r s a f t e r fitting, i t was f o u n d t h a t t h e y t o o h a v e t h e i r 2 , 4 - d i a m i n o g r o u p s o r i e n t e d i n a s i m i l a r manner. Teat Set at 3.5 A

Learning Set at 3.5 A

2

9

Actual pKi Learning Set at 4 0 A

Teat Set at 4.0 A

O O

•

O

• •

• B

n r =0.647

R =0.816

Actual pKi

Actual pKi

Figure 9. Continued. Plots compare predictivities for both sets at 3.5- and 4.0-angstrom resolutions. (Reproduced from ref. 13. Copyright 1980 American Chemical Society.)



100

Figure 10. (Top) A partial representation of the D H F R H A S L showing only those points with H = — 1 . The relative binding energy at each point is indicated by letter: G, pKi > 1.0; A, 0.0 < pKi < 1.0; R, pKi < 0.0. (Bottom) The same view with compound D66 fitted in the HASL.


6.

DOWEYKO


I n o r d e r to t e s t how c l o s e l y t h i s 2.8 X E . c o l i DHFR HASL comes to m i m i c k i n g the a c t u a l a c t i v e s i t e , MTX, i n i t s bound c o n f o r m a t i o n , was used as a p r o b e . The f i t t i n g o f MTX r e s u l t e d i n 65% o f i t s m o l e c u l a r l a t t i c e p o i n t s c o i n c i d i n g w i t h t h o s e o f the HASL w i t h a p r e d i c t e d p K i o f 10.11 ( a c t u a l pKi = 10.89). C o n s i d e r i n g t h a t no M T X - l i k e s t r u c t u r e s were used i n HASL m o d e l , the p r e d i c t e d p K i i s i n q u i t e good agreement w i t h the e x p e r i m e n t a l v a l u e . The o r i e n t a t i o n o f m e t h o t r e x a t e i n the HASL was d i f f e r e n t from the o t h e r 2 , 4 diamino i n h i b i t o r s . This p r e d i c t i o n i s consistent with p u b l i s h e d o b s e r v a t i o n s (25J t h a t the 2 , 4 - d i a m i n o p o r t i o n o f DHFR-bound MTX a p p e a r s i n a d i f f e r e n t o r i e n t a t i o n from t h a t o b s e r v e d f o r the same m o i e t y i n DHFR-bound t r i m e t h o p r i m (D20). The r e l a t i v e o r i e n t a t i o n s adopted a f t e r f i t t i n g t o the DHFR HASL f o r b o t h MTX and t r i m e t h o p r i m (D20) a r e i l l u s t r a t e d i n F i g u r e 11. The p o s i t i o n s o f the 2 , 4 - d i a m i n o g r o u p s i n d i c a t e the r e l a t i v e m o l e c u l a r o r i e n t a t i o n s .

The

HASL Methodology

The l o g i c flow c h a r t i n F i g u r e 12 summarizes the key s t e p s i n the c r e a t i o n and use o f a h y p o t h e t i c a l a c t i v e s i t e l a t t i c e (HASL). The p r o c e s s b e g i n s w i t h s t r u c t u r a l i n p u t , t y p i c a l l y i n the form o f e n e r g y - m i n i m i z e d a t o m i c C a r t e s i a n c o o r d i n a t e s a l o n g w i t h MM2 atom type d e s i g n a t i o n s ( A ) . From t h i s d a t a a m o l e c u l a r l a t t i c e i s c r e a t e d based on a r e s o l u t i o n v a l u e s e l e c t e d by the u s e r ( B ) . T h i s l a t t i c e can e i t h e r be compared w i t h o t h e r m o l e c u l e s , o r c o n s i d e r e d as the i n i t i a l HASL. As new m o l e c u l e s a r e brought i n t o the s y s t e m , each i s put t h r o u g h the f i t t i n g r o u t i n e ( C ) . Predicted binding is immediately a v a i l a b l e (D). The d a t a can then be merged i n t o the e x i s t i n g HASL ( E ) . P a r t i a l p K i d i s t r i b u t i o n can be computed u s i n g HISTORY f i l e s c o n t a i n i n g a l l p r e v i o u s l y f i t t e d molecular coordinates ( F ) . Conclusions A new method f o r q u a n t i t a t i v e s t r u c t u r a l c o m p a r i s o n s , c r e a t i o n o f a h y p o t h e t i c a l a c t i v e s i t e ( H A S L ) , and m o d e l l i n g p o t e n t i a l i n h i b i t o r b i n d i n g has been d e v e l o p e d . The method accommodates a wide v a r i e t y o f s t r u c t u r a l t y p e s and makes no a s s u m p t i o n s about r e l a t i v e o r i e n t a t i o n s between them. The HASL can be used as a p r e d i c t i v e t o o l to a s s e s s p o t e n t i a l l y u s e f u l s t r u c t u r e s and p r o v i d e s the means to c r e a t e and t e s t s t r u c t u r e s c o m p l e t e l y o u t s i d e the l e a r n i n g set. F u r t h e r enhancements to HASL methodology a r e e x p e c t e d to i n c l u d e f a s t e r and more i n t e l l i g e n t f i t t i n g a l g o r i t h m s , the i n c o r p o r a t i o n o f some s t r u c t u r a l f l e x i b i l i t y o p t i o n s to f r e e i n h i b i t o r m o l e c u l e s from the s t a t i c c o n f o r m a t i o n a s s u m p t i o n , and a l g o r i t h m s to e l e c t r o n i c a l l y s y n t h e s i z e p o t e n t i a l i n h i b i t o r s based on the i n f o r m a t i o n c o n t e n t o f a HASL. All programs a r e w r i t t e n i n FORTRAN and BASIC f o r use on IBM-PC c o m p a t i b l e systems and a r e a v a i l a b l e from the a u t h o r .



Figure 11. A comparison o f the f i t t e d o r i e n t a t i o n s on DHFR H A S L f o r t w o i n h i b i t o r s , t r i m e t h o p r i m ( D 2 0 ) a n d methotrexate (MTX). (Reproduced from R e f . 15. C o p y r i g h t 1988 A m e r i c a n C h e m i c a l S o c i e t y . )

the


6.

DOWEYKO

Tod far SAR Study in Three Dimensions

A d d t o

I n f o H A S L ?

Figure 12. HASL l o g i c f l o w c h a r t . [A] i n p u t o f C a r t e s i a n coordinates for structure, [B] g e n e r a t i o n o f l a t t i c e c o n t a i n i n g s p a t i a l and p h y s i o c h e m i c a l i n f o r m a t i o n , [C] f i t t i n g routine i n v o l v i n g superposition of molecular l a t t i c e on HASL, [D] g e n e r a t i o n o f r e s u l t s , which i n c l u d e b i n d i n g p r e d i c t i o n , r e c o r d (HISTORY) f i l e s , and o p t i o n s to merge l a t t i c e s and/or c a l c u l a t e p a r t i a l pKi d i s t r i b u t i o n .

103

104

P R O B I N G BIOACTIVE M E C H A N I S M S

Literature Cited 1. 2.


3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25.

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RECEIVED March 21, 1989

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