5 Physicochemical Approaches to Drug Design
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WILLIAM P. PURCELL and JOHN M. CLAYTON Department of Molecular and Quantum Biology, College of Pharmacy, University of Tennessee Medical Units, Memphis, Tenn. 38103
One of the most potentially design
is the attempt
in molecular
structure
a quantitative
successful
approaches
to place correlations
with changes in biological
and predictive
level. While
have been made in this area by chemists of regression
analyses,
tions, and parameterization measurements.
molecular
It is concluded
therapeutic
agents without
pharmacological
pharmacoloillustrates
orbital
and
for the future in
exhaustive
the
calcula-
physicochemical
that quantitative
-activity studies hold some promise
on
efforts
and linear free-energy
lated models along with their modifications are reviewed.
activity
and
using various
The mathematical
drug
changes
qualitative
gists for over 100 years, more recent progress potential
to
between
synthetic
re-
applications structuredesigning work
and
screening.
" C o r over 100 years chemists a n d p h a r m a c o l o g i s t s h a v e b e e n i n t r i g u e d b y o b s e r v e d changes i n b i o l o g i c a l effects of c h e m i c a l congeners p a r a l l e l i n g s o m e w h a t m i n o r alterations i n m o l e c u l a r structure.
Following
m a n y successes a n d failures since the i n i t i a l w o r k , this interest continues to increase a m o n g m e d i c i n a l chemists as the l e v e l of s o p h i s t i c a t i o n of t h e m e t h o d s f o r s t u d y i n g a n d " i s o l a t i n g " these substituent effects i n d r u g d e s i g n i m p r o v e s . O f u l t i m a t e interest is the u t i l i z a t i o n of these t e c h n i q u e s to a c h i e v e a r a t i o n a l , c u s t o m d e s i g n of t h e r a p e u t i c agents a l o n g w i t h t h e e l u c i d a t i o n of a c t i v i t y m e c h a n i s m s at the s u b m o l e c u l a r l e v e l ( 1 ). It is necessary to p o i n t o u t i n i t i a l l y that i n a r e p o r t of this t y p e i t w o u l d b e v i r t u a l l y i m p o s s i b l e to i n c l u d e e v e r y w o r k that has b e e n significant to the d e v e l o p m e n t of the m e t h o d s p r e s e n t e d here.
W h i l e the
authors h a v e a t t e m p t e d to g i v e a representative s a m p l e of these c o n t r i b u t i o n s , t h e y h a v e n o t a t t e m p t e d a n exhaustive r e v i e w . I n v i e w of the n u m e r o u s literature examples of the a p p l i c a t i o n of p h y s i c o c h e m i c a l m e t h 123
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
124
DRUG DISCOVERY
ods to d r u g d e s i g n , the interested r e a d e r is r e f e r r e d to m o r e t h o r o u g h treatments of the m e t h o d o l o g y ( 1-3 ) a n d r e v i e w s of t h e r e c e n t l i t e r a t u r e (^8). I n the late 1860s C r u m - B r o w n a n d F r a s e r d e m o n s t r a t e d that g r a d u a l alterations i n m o l e c u l a r s t r u c t u r e of c e r t a i n d r u g s c o i n c i d e d w i t h changes i n t h e i r e l i c i t e d b i o l o g i c a l responses
(9).
T h e s e observations l e d to the
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p o s t u l a t e that the a c t i v i t y of a d r u g (φ) features ( C )
w a s a f u n c t i o n of its s t r u c t u r a l
(Equation 1). Φ = /(C)
(1)
Further, experimental w o r k on narcotic
agents i n 1893
led Richet
to
p o s t u l a t e that the degree of a c t i v i t y of the c o m p o u n d s w a s i n v e r s e l y r e l a t e d to t h e i r w a t e r s o l u b i l i t i e s (10).
Meyer and Overton expanded
this w o r k just at the t u r n of the t w e n t i e t h c e n t u r y to s h o w that the nar c o t i c activities of c e r t a i n congeners p a r a l l e l e d t h e i r o i l / w a t e r p a r t i t i o n i n g p r o p e r t i e s (11-15).
O f course, this p a r a m e t e r w a s d e s i g n e d to s i m u l a t e
the in vivo c o n d i t i o n of the drug's p a r t i t i o n i n g b e t w e e n a n aqueous b i o p h a s e a n d a l i p o p h i l i c site of a c t i o n .
I n 1907,
Fuhner
quantitatively
a p p r o x i m a t e d the b i o l o g i c a l responses of a h o m o l o g o u s series of narcotics (16,
17).
H e d e m o n s t r a t e d t h a t the decrease i n equiresponse
tions of these c o m p o u n d s f o l l o w e d a g e o m e t r i c ( 1 / 3 ) , ( 1 / 3 ) , etc.] 2
3
concentra
progression
[1,
1/3,
as the n u m b e r of c a r b o n atoms i n c r e a s e d i n the
series. I n f u r t h e r investigations o f the r e l a t i o n s h i p b e t w e e n other 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 of m o l e c u l e s a n d t h e i r b i o l o g i c a l responses, in
1904
observed
a c t i o n (18).
a correlation between
surface
tension a n d
Traube narcotic
T h e s e d a t a l e d W a r b u r g to postulate a m e c h a n i s m of nar
c o t i c a c t i o n f o r these agents i n 1921 (19).
S i m i l a r l y , i n 1917 M o o r e n o t e d
that the b o i l i n g p o i n t s of a series of i n s e c t i c i d e f u m i g a n t s p a r a l l e l e d t h e i r toxicities (20,
21).
A n i m p o r t a n t o b s e r v a t i o n i n s t r u c t u r e - a c t i v i t y studies was m a d e b y F e r g u s o n i n 1939 w h e n h e d e m o n s t r a t e d a n i n t e r r e l a t i o n s h i p a m o n g m u c h of the earlier w o r k (22).
E q u a t i o n 2 w a s p o s t u l a t e d to d e s c r i b e
b i o l o g i c a l responses of several c o n g e n e r i c series, w h e r e C
{
d
=
the
is the c o n c e n -
kA™i
(2)
t r a t i o n of c o n g e n e r i necessary to e l i c i t a d e f i n e d response, A i is a p h y s i c o c h e m i c a l or d e s c r i p t i v e p a r a m e t e r
f o r the c o m p o u n d (e.g., p a r t i t i o n
coefficient o r n u m b e r of c a r b o n atoms i n a side c h a i n ), a n d k a n d m are constants f o r the series.
S i n c e Ci is u s u a l l y less t h a n 1, the negative l o g a
r i t h m of E q u a t i o n 2 leads to E q u a t i o n 3, w h i c h is m o r e u s e f u l i n q u a n t i tative s t r u c t u r e - a c t i v i t y studies a n d is a basis f o r s i m i l a r w o r k t o d a y (23,
24,
25).
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
PURCELL AND CLAYTON
log
Physicochemical
=
q
-
log k -
125
Approaches
m l o g Ai
(3)
F u r t h e r a p p l i c a t i o n s of p h y s i c o c h e m i c a l parameters to b i o l o g i c a l a c t i v i ties w e r e m a d e b y M c G o w a n (26, 27, 28).
H e has successfully c o r r e l a t e d
the b i o l o g i c a l activities of selected series of m o l e c u l e s w i t h t h e i r m o l e c u l a r v o l u m e s or p a r a c h o r s .
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F u r t h e r major c o n t r i b u t i o n s to, d e v e l o p m e n t of, a n d a p p l i c a t i o n s of q u a n t i t a t i v e s t r u c t u r e - a c t i v i t y correlations b e g a n i n 1956 w i t h t h e w o r k of B r u i c e a n d c o - w o r k e r s (29).
Their empirical, mathematical
method
w a s a p p l i e d to t h e c o r r e l a t i o n of t h y r o x i n e - l i k e activities of a series of congeners w i t h t h e s u m of constants a s s i g n e d to different substituents of the m o l e c u l e s .
U s i n g E q u a t i o n 4 t h e y o b t a i n e d excellent
correlations
log % t h y r o x i n e - l i k e a c t i v i t y = &Σ/ + c
(4)
b e t w e e n c a l c u l a t e d a n d o b s e r v e d activities. I n E q u a t i o n 4, 2/ = fx' + foR') w h e r e f , f >, a n d f ' x
x
(fx
+
a r e e n t i r e l y e m p i r i c a l a n d w e r e selected
0R
s i m i l a r to t h e m e t h o d of H a m m e t t f o r the e v a l u a t i o n of s i g m a constants. S u b s c r i p t s X , X ' , a n d OK structures of interest
represent substituent positions of t h e m o l e c u l a r
(29).
F r e e a n d W i l s o n gave a m o r e g e n e r a l d e s c r i p t i o n of this m a t h e m a t i c a l ( e m p i r i c a l ) m o d e l i n 1964 ( 30). b i o l o g i c a l response
A c c o r d i n g to t h e i r m e t h o d , t h e d e f i n e d
( B R ) of a congener i n a h o m o l o g o u s series is e q u a l
to t h e s u m of the substituent g r o u p c o n t r i b u t i o n s to t h e a c t i v i t y p l u s that of t h e p a r e n t structure ( μ ) , E q u a t i o n 5. F o r e x a m p l e , P u r c e l l has u s e d BR
= Σ (group c o n t r i b u t i o n s ) + μ
(5)
this m e t h o d i n s t u d y i n g the anticholinesterase potencies of a h o m o l o g o u s series of 3 - c a r b a m o y l p i p e r i d i n e s ( I )
(31).
If a m e t h y l g r o u p w e r e s u b -
R
R
2
3
I s t i t u t e d at p o s i t i o n R
t
a n d e t h y l groups w e r e s u b s t i t u t e d at positions R
a n d R , E q u a t i o n 5 w o u l d b e c o m e E q u a t i o n 6, w h e r e 3
BR
= [CH ] 3
R l
+ [C H ] 2
5
R 2
+ [C H ] 2
5
R 3
[CH ] 3
R l
+ μ
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
2
is t h e (6)
126
DRUG DISCOVERY
activity
c o n t r i b u t i o n of
[C H ,]R 2
R
represents
2
a
methyl
group
substituted
at
position
Ri,
the a c t i v i t y c o n t r i b u t e d b y a n e t h y l g r o u p substi
t u t e d at p o s i t i o n R , a n d [ C H ] R stands f o r the e t h y l g r o u p at R 2
2
3
5
I n v i e w of the a s s u m e d e q u i v a l e n c y of R
3
(31).
a n d R , the l i n e a r e q u a t i o n
2
3
c a n be s i m p l i f i e d b y r e d u c i n g the n u m b e r of u n k n o w n s , a n d E q u a t i o n 6 b e c o m e s E q u a t i o n 7.
A c c o r d i n g l y , a n e q u a t i o n is g e n e r a t e d
for
each
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compound. B R
=
[CH,]
R L
+
w i t h a m e a s u r e d b i o l o g i c a l response. equations)
2[C H ] 2
5
R 2
+
μ
(7)
I n a d d i t i o n , restrictions ( s y m m e t r y
are p l a c e d o n e a c h n o n e q u i v a l e n t substituent p o s i t i o n .
That
is, the s u m m a t i o n of the g r o u p c o n t r i b u t i o n s at e a c h n o n e q u i v a l e n t p o s i t i o n m u s t e q u a l zero over the entire set of equations (30).
T h u s , f o r this
e x a m p l e , there w o u l d be t w o s y m m e t r y equations i n a d d i t i o n to the other equations.
T h e s i m u l t a n e o u s equations
b y the m e t h o d of least squares.
are t h e n s o l v e d i n d e p e n d e n t l y
S o l u t i o n of the equations y i e l d s the c a l
c u l a t e d a c t i v i t y c o n t r i b u t i o n of e a c h substituent g r o u p as w e l l as of the p a r e n t structure.
that
F o r c o m p a r i s o n w i t h the o b s e r v e d b i o l o g i c a l
activities, the c a l c u l a t e d t o t a l a c t i v i t y of each m o l e c u l e c a n b e o b t a i n e d b y s u m m a t i o n of these g r o u p c o n t r i b u t i o n s a n d μ (30).
The main pur
pose of s u c h a treatment is to r a n k the b i o l o g i c a l activities of the sub stituent groups w h i l e n o t i n g possible 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 s a n d to p r e d i c t the c o m p o u n d s of the series not tested, a n d p o s s i b l y n o t s y n t h e s i z e d , w h i c h w o u l d h a v e the greatest p o t e n t i a l f o r f u r t h e r i n v e s t i g a tion
(32). F o r a m e a n i n g f u l a p p l i c a t i o n of this m e t h o d , the b i o l o g i c a l d a t a
s h o u l d meet three basic prerequisites : ( 1 ) m o l e c u l e s i n the series s h o u l d be closely s i m i l a r to increase the p r o b a b i l i t y of t h e i r h a v i n g the
same
m e c h a n i s m of a c t i o n , ( 2 ) b i o l o g i c a l a c t i v i t y d a t a selected s h o u l d be a c c u rate, q u a n t i t a t i v e , a n d m e a s u r e d u n d e r u n i f o r m c o n d i t i o n s f o r the series, and (3)
the g r o u p c o n t r i b u t i o n s m u s t b e i n t r i n s i c a l l y a d d i t i v e f o r the
c h o s e n a c t i v i t y parameters (32).
It is also d e s i r a b l e to h a v e a h i g h n u m b e r
of degrees of f r e e d o m since the greater the ratio of the n u m b e r of o b s e r v a tions to the n u m b e r of u n k n o w n s , the m o r e r e l i a b l e are the results
(32).
R e c e n t l y , the p r o b l e m of i l l - c o n d i t i o n i n g has b e e n n o t e d w h e n this m e t h o d is a p p l i e d to c e r t a i n series of d a t a (33).
E x p l i c i t conditions for a p p l y i n g
the m e t h o d as w e l l as the statistical i n t e r p r e t a t i o n of the results
were
also d e f i n e d . T h e major l i m i t a t i o n of the m e t h o d lies i n the f a c t that the a c t i v i t y c o n t r i b u t i o n s of the substituents must be a d d i t i v e . T o date, most l i t e r a t u r e examples of a p p l i c a t i o n s of this m e t h o d u n f o r t u n a t e l y h a v e
been
m a d e b y laboratories different f r o m the one w h i c h generated the d a t a .
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
PURCELL AND CLAYTON
Physicochemical
127
Approaches
A m u c h m o r e d e s i r a b l e s i t u a t i o n exists w h e n d a t a g e n e r a t i o n a n d analysis are m a d e b y t h e same l a b o r a t o r y f o r o n l y t h e n are t h e n a t u r e , l i m i t a t i o n s , and quantitative reliability of the data fully realized a n d appreciated. A t a b o u t t h e t i m e of F r e e a n d W i l s o n ' s w o r k , K o p e c k y a n d c o - w o r k e r s introduced a similar mathematical T h e y tested f o u r equations
structure-activity model
(34,
35).
( E q u a t i o n s 8 - 1 1 ) f o r t h e expression o f t h e
q u a n t i t a t i v e difference b e t w e e n t h e l o g L D
values o f p- (34) a n d m-
5 0
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( 3 5 ) d i s u b s t i t u t e d benzenes a n d b e n z e n e . BA
= a
BA
= bjby
x
y
(9)
ΒA = c + c
dd
(10)
= c + c + dd
(11)
x
BA
(8)
+ a
x
y
-
x
y
x
y
y
I n E q u a t i o n s 8 - 1 1 a, b, c, a n d d represent the substituent c o n t r i b u t i o n to the t o t a l a c t i v i t y o f t h e c o m p o u n d s w h i l e t h e subscripts χ a n d y denote the substituent positions o n t h e p a r e n t m o l e c u l e .
Neither the additive
m o d e l ( n o t i c e a b l y s i m i l a r t o the F r e e - W i l s o n m o d e l )
(Equation 8), the
multiplicative model ( E q u a t i o n 9 ) , nor the combined model ( E q u a t i o n 10)
described the biological activity significantly.
T h e c o m b i n e d ex
p r e s s i o n ( E q u a t i o n 1 1 ) , h o w e v e r , gave a statistically significant
corre
l a t i o n b e t w e e n substituent a c t i v i t y a n d b i o l o g i c a l response f o r b o t h t h e m- (35) a n d p- (34) d i s u b s t i t u t e d series. A t t h e t i m e that t h e basic f o r m u l a t i o n a n d testing of t h e m a t h e m a t i c a l m o d e l s o f q u a n t i t a t i v e s t r u c t u r e - a c t i v i t y correlations w e r e b e i n g m a d e , another t y p e o f a p p r o a c h , t h e l i n e a r free-energy r e l a t e d m o d e l , w a s i n t r o d u c e d (2).
U s i n g t h e basic H a m m e t t e q u a t i o n (22, 36) f o r the c h e m i c a l
reactions o f b e n z o i c a c i d d e r i v a t i v e s ( E q u a t i o n 12 ), several investigators a t t e m p t e d q u a n t i t a t i v e correlations b e t w e e n 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 log (/CXAH) =
ρσ
(12)
a n d b i o l o g i c a l response (1,37).
I n E q u a t i o n 12, k
l i b r i u m constants f o r reactions
of substituted a n d unsubstituted
x
a n d fc are t h e e q u i H
com
p o u n d s , r e s p e c t i v e l y , σ is a constant w h i c h d e p e n d s e n t i r e l y o n t h e n a t u r e a n d p o s i t i o n o f t h e substituent, a n d ρ is a constant w h i c h d e p e n d s o n t h e t y p e a n d c o n d i t i o n s o f r e a c t i o n as w e l l as t h e n a t u r e o f t h e c o m p o u n d (22).
R e w r i t t e n as E q u a t i o n 13, t h e H a m m e t t e q u a t i o n c l e a r l y illustrates log k
x
= ρσ + l o g
fc
H
(13)
the l i n e a r r e l a t i o n s h i p b e t w e e n t h e substituent constant σ a n d t h e l o g a r i t h m of the r e a c t i v i t y of t h e c o m p o u n d ( f c ) (1,38). x
Since the logarithm
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
128
DRUG
DISCOVERY
of a n e q u i l i b r i u m constant is p r o p o r t i o n a l to the change i n G i b b s free energy
( E q u a t i o n 14)
energy r e l a t e d " (38).
E q u a t i o n 13 a n d others l i k e it are
(39),
"free-
I n E q u a t i o n 14, R is the i d e a l gas constant, AF° AF°
=
-
is (14)
RT In k
the G i b b s free energy change, Τ is absolute temperature, a n d k is the Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 27, 2015 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0108.ch005
e q u i l i b r i u m constant for the r e a c t i o n . A p p l i c a t i o n s of this H a m m e t t l i n e a r free-energy r e l a t e d e q u a t i o n to several b i o l o g i c a l systems b y v a r i o u s i n vestigators, h o w e v e r , y i e l d e d o n l y l i m i t e d success f r o m about 1952 1966 (37, 40-A7).
to
S u c h a p p l i c a t i o n s l e d H a n s e n to p r o p o s e a " b i o l o g i c a l "
H a m m e t t e q u a t i o n w i t h a restrictive set of c o n d i t i o n s f o r a p p l i c a t i o n (48).
E v e n w i t h these restrictions, h o w e v e r , i t has met w i t h o n l y l i m i t e d
success. T h e use of the H a m m e t t e q u a t i o n was e x t e n d e d b y Z a h r a d n i k a n d c o - w o r k e r s to relate other p h y s i c o c h e m i c a l parameters
of
homologous
series of c o m p o u n d s to t h e i r b i o l o g i c a l activities ( E q u a t i o n 15)
(49).
I n E q u a t i o n 15, τ is the m o l a r c o n c e n t r a t i o n of the i t h congener of a n {
log (τ,·/τ *) β
= αφ
(15)
a l i p h a t i c h o m o l o g o u s series necessary to e l i c i t a d e f i n e d b i o l o g i c a l re sponse, τ
is the m o l a r c o n c e n t r a t i o n of the e t h y l d e r i v a t i v e of the series
et
r e q u i r e d to p r o d u c e a s i m i l a r response, α is a constant w h i c h d e p e n d s u p o n the nature of the series of c o m p o u n d s a n d the b i o l o g i c a l system, a n d β is a p h y s i c o c h e m i c a l p a r a m e t e r stituent.
w h i c h d e p e n d s u p o n the
sub
V a r i o u s types of β h a v e b e e n u s e d , i n c l u d i n g the H a m m e t t a n d
T a f t constants, o n several h o m o l o g o u s series i n v a r i o u s b i o l o g i c a l systems A g a i n the use of a single parameter, h o w e v e r , to define a b i o
(49-52).
l o g i c a l response has g i v e n correlations of l i m i t e d significance. R e c o g n i z i n g the p h y s i c o c h e m i c a l n a t u r e of b i o l o g i c a l reactions
and
r e a l i z i n g the i m p o r t a n c e of p a r t i t i o n i n g i n a drug's r e a c h i n g its site of a c t i o n (53,
54),
H a n s c h a n d c o - w o r k e r s e x p a n d e d the l i n e a r free-energy
r e l a t e d expression i n 1964 to i n c l u d e a d d i t i o n a l p h y s i c o c h e m i c a l p a r a m eters (55, 56, 57).
F o l l o w i n g the a p p r o a c h of T a f t ( 5 8 )
i n the l i n e a r
c o m b i n a t i o n of t w o constants, t h e y d e r i v e d a n e w expression
(Equation
16) f o r the c o r r e l a t i o n of b i o l o g i c a l a c t i v i t y w i t h m o l e c u l a r structure i n l o g (1/C)
= *rx +
w h a t is c a l l e d the "ρ-σ-π e q u a t i o n " ( 5 5 ) .
ρσ + k
(16)
2
C represents the m o l a r c o n c e n
t r a t i o n of a congener necessary to elicit a d e f i n e d b i o l o g i c a l response, ΤΓ is the substituent p a r t i t i o n i n g p a r a m e t e r d e f i n e d as the difference b e t w e e n the l o g a r i t h m s of the o c t a n o l / w a t e r
p a r t i t i o n coefficients
of the
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
sub-
5.
PURCELL AND CLAYTON
Physicochemical
129
Approaches
stituted a n d u n s u b s t i t u t e d p a r e n t c o m p o u n d i n the series the H a m m e t t substituent constant, a n d k
p, a n d k
l9
2
erated b y regression analysis of the series.
( 5 9 ) , σ is
are constants
gen
A l t h o u g h a l l t h e terms are
free-energy r e l a t e d a n d a p p r o x i m a t e true t h e r m o d y n a m i c constants, t h e e q u a t i o n is t e r m e d " e x t r a t h e r m o d y n a m i c " since these parameters
are
u s e d i n systems other t h a n those s i m i l a r to the systems i n w h i c h they
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w e r e d e t e r m i n e d (55,
60).
A f t e r m e e t i n g w i t h m u c h success i n c o r r e l a t i n g the s t r u c t u r e - r e sponse d a t a i n a w i d e v a r i e t y o f systems (7, 61), this basic e q u a t i o n w a s m o d i f i e d b y a d d i n g or s u b s t i t u t i n g a v a r i e t y of parameters i n attempts to d e s c r i b e better the activities of n u m e r o u s c o m p o u n d s .
O n e of t h e
foremost m o d i f i c a t i o n s of this basic e q u a t i o n has b e e n the postulate that the b i o l o g i c a l response to a d r u g is p a r a b o l i c a l l y a n d n o t l i n e a r l y r e l a t e d to its p a r t i t i o n i n g properties r e s u l t i n g i n the i n c l u s i o n of a π t e r m (56, 2
57, 62).
A l t h o u g h i t m a y seem that the parameters i n E q u a t i o n 16 are
s o m e w h a t a r b i t r a r y a n d h i g h l y e m p i r i c a l , it c a n be s h o w n that these variables c a n b e d e r i v e d f r o m first p r i n c i p l e s . Justification f o r t h e m m a y b e a p p a r e n t w h e n o n e considers the r a n d o m w a l k process b y w h i c h a d r u g reaches its site of a c t i o n . Since the m o l e c u l e must cross a series of l i p o i d a l m e m b r a n e s o r barriers, the e l i c i t e d response d e p e n d s m o r e o n its c o n c e n t r a t i o n at the receptor site t h a n o n the q u a n t i t y of d r u g a d m i n istered ( 5 6 ) . T h e r e f o r e , the rate of b i o l o g i c a l response m a y b e g i v e n b y : d(response)/ift =
ACkx
(17)
w h e r e A is the p r o b a b i l i t y of a molecule's r e a c h i n g its receptor site, C is the c o n c e n t r a t i o n of d r u g a d m i n i s t e r e d , a n d k
x
is the e q u i l i b r i u m or rate
constant i n v o l v e d at the active site. AC w o u l d t h e n represent the effec tive i n t r a c e l l u l a r c o n c e n t r a t i o n of d r u g .
T o a p p l y this e q u a t i o n p r a c
t i c a l l y , i t is necessary to d e t e r m i n e e x p e r i m e n t a l l y the values of A a n d kx (56).
It w a s f o r this a p p r o x i m a t e e v a l u a t i o n of A that t h e -π t e r m w a s
derived while k
x
w a s a p p r o x i m a t e d b y the H a m m e t t σ p a r a m e t e r
(22).
If one assumes a n o p t i m u m π v a l u e of ττ f o r a m a x i m u m e l i c i t e d re 0
sponse a n d assumes the b i o l o g i c a l response f o l l o w s a n o r m a l G a u s s i a n d i s t r i b u t i o n w i t h respect to π w h i l e other factors are h e l d constant, E q u a t i o n 18 i n w h i c h a a n d b are constants is o b t a i n e d A = /(*) = a e x p [ -
(z -
(56).
r. y/b]
(18)
o
E x p a n s i o n of E q u a t i o n 18 y i e l d s E q u a t i o n 19. A s s u m i n g that ττ is c o n 0
A = a exp [(— π + 2ττ 2
0
— π )/6] 0
2
(19)
stant f o r a p a r t i c u l a r series of congeners i n the g i v e n b i o l o g i c a l system, one obtains E q u a t i o n 20, w h e r e c a n d d are constants r e p l a c i n g the terms
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
130
DRUG DISCOVERY
= a exp [ ( -
A i n 7τ . 0
x
+
2
cx +
(20)
d)/b]
S u b s t i t u t i n g E q u a t i o n 20 i n t o E q u a t i o n 17 y i e l d s E q u a t i o n 21,
w h e r e the rate of b i o l o g i c a l response is r e p l a c e d b y a constant, k', a exp [ ( -
k' =
x
+
2
cx +
since (21)
d ) / b ] Ck
x
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one is interested i n the response l e v e l d u r i n g a specific t i m e i n t e r v a l rather t h a n its rate.
T a k i n g the l o g a r i t h m of E q u a t i o n 21 a n d r e a r r a n g i n g the
terms gives E q u a t i o n 22, i n w h i c h the constants f r o m E q u a t i o n 21 h a v e log (1/C) =
-
&x + 2
/dx +
k
log k
+
2
b e e n c o m b i n e d to y i e l d s i m p l i f i e d constants, k, k
a n d k>.
u
of E q u a t i o n 12 f o r l o g k
(22)
x
and incorporating —log k ,
x
h o m o l o g o u s series, i n t o constant e q u a t i o n ( E q u a t i o n 23)
Substitution
constant
u
for a
results i n the w i d e l y u s e d H a n s c h
k
2
(56).
l o g (1/C) =
-
/cx + /cix +
ρσ +
2
(23)
k
2
A p p l i c a t i o n of this e q u a t i o n to series of b i o l o g i c a l d a t a i n v o l v e s the s u m m a t i o n of the p h y s i c o c h e m i c a l parameters f o r a l l of the
substituents
a l o n g w i t h the g e n e r a t i o n of a n e q u a t i o n of the f o r m of E q u a t i o n for e a c h o b s e r v a t i o n . log
24
F o r example, H a n s c h a n d D e u t s c h have a p p l i e d
(l/C)
=
&Σχ
2
+
ΑαΣχ +
ρΣσ
+
(24)
k
2
this m e t h o d to s t u d y the s t r u c t u r e - a c t i v i t y correlations of 2 , 6 - d i a l k o x y phenylpenicillins (II) OR
i n the presence of s e r u m
(63).
2
CO—NH—CH—CH
OR
I
I
OC
Ν
C—(CH ) 3
2
1 CH—COOH
2
II W h e n a m e t h y l g r o u p is s u b s t i t u t e d at R i w i t h h y d r o g e n s at e q u i v a l e n t positions R , the r e s u l t i n g ρ-σ-π e q u a t i o n is E q u a t i o n 25. 2
l o g (1/C)
=
-
Â;(* CH + 2
3
P(*CH + 3
2x
2
H
) + Αα(ποΗ + 3
Simultaneous
2*H)
+
2 σ ) + kz Η
(25)
s o l u t i o n of t h e e q u a t i o n s g e n e r a t e d f o r e a c h of the e i g h t m e m b e r s of this series gives E q u a t i o n 26.
S i n c e the c o r r e l a t i o n coefficient, r, is a m e a s u r e
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
Physicochemical
PURCELL AND CLAYTON
l o g (1/C) = O . O l x of t h e goodness
2
-
0.316z +
o f fit b e t w e e n
131
Approaches
1.76σ +
1.853
r = 0.930
(26)
the calculated a n d observed data, the
e q u a t i o n appears to d e s c r i b e a d e q u a t e l y t h e b i o l o g i c a l response p a r a m eters
(63). T h e r e a l v a l u e of this 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 to d r u g d e s i g n
lies i n its flexibility to m o d i f i c a t i o n b y i n c o r p o r a t i n g or d e l e t i n g a v a r i e t y
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of p h y s i c o c h e m i c a l parameters.
F o r e x a m p l e , i t m a y b e u s e d to e l u c i d a t e
the m e c h a n i s m o f d r u g a c t i o n at t h e s u b m o l e c u l a r l e v e l b y d e t e r m i n a t i o n of t h e r e l a t i v e i m p o r t a n c e of e a c h p a r a m e t e r i n d e s c r i b i n g t h e b i o l o g i c a l response.
I n the above example, H a n s c h a n d D e u t s c h used modifications
of E q u a t i o n 24 i n attempts to isolate substituent effects ( E q u a t i o n s 27 a n d 28) (63).
A n a l y s i s of the d a t a u s i n g t h e π p a r a m e t e r alone ( E q u a t i o n
=
log ( I / O log ( I / O 27) y i e l d e d r =
=
*ix +
(27)
k
2
*ιπ + kv + 2
(28)
k,
0.823 w h i l e i n c l u s i o n of σ w i t h π ( E q u a t i o n 28)
gave
r = 0.929. C o m p a r i s o n of t h e c o r r e l a t i o n coefficients of E q u a t i o n s 26 a n d 28 i n d i c a t e s that t h e ?r t e r m does n o t m a k e a significant c o n t r i b u t i o n t o 2
the b i o l o g i c a l response (63).
E x t e n s i o n of this i d e a to a n o t h e r b i o l o g i c a l
system has s h o w n that the e l e c t r o n i c p a r a m e t e r σ m a d e a significant c o n t r i b u t i o n to the a c t i v i t y i n that p a r t i c u l a r system (64).
T h i s illustrates
the p r o b l e m i n v o l v e d i n t h e p r o p e r selection of p a r a m e t e r
combinations
to d e s c r i b e a d e q u a t e l y b i o l o g i c a l response i n different systems. A n o t h e r p o t e n t i a l use of this l i n e a r free-energy c u s t o m t a i l o r i n g a d r u g is p a r a m e t e r
related method i n
optimization. Once a particular
series of d a t a has b e e n a n a l y z e d , o n e m a y e v a l u a t e π f o r t h e series a n d 0
m a k e this t h e starting p o i n t i n s u g g e s t i n g m o l e c u l e s f o r f u r t h e r synthesis a n d testing.
U s e of this a p p r o a c h also m i g h t i n d i c a t e that a different
series of c o m p o u n d s s h o u l d b e c o n s i d e r e d i f o p t i m u m parameters
have
a l r e a d y b e e n a c h i e v e d i n t h e c o m p o u n d s tested ( 1 ). A s w a s true i n the m a t h e m a t i c a l a p p r o a c h , one of t h e foremost l i m i t a tions of this m e t h o d is its d e p e n d e n c e o n accurate, q u a n t i t a t i v e b i o l o g i c a l data.
I n a d d i t i o n , t h e q u a n t i t a t i v e n a t u r e of t h e l i n e a r free-energy r e
l a t e d m o d e l is l i m i t e d b y t h e a c c u r a c y of t h e e x p e r i m e n t a l p h y s i c o c h e m i c a l parameters as w e l l as t h e i r a p p l i c a b i l i t y i n systems s o m e w h a t distant to those i n w h i c h t h e y w e r e d e t e r m i n e d . A l t h o u g h t h e p l o t of H a m m e t t σ values gives a d i s t i n c t b r e a k i n l i n e a r r e l a t i o n s h i p p a r a l l e l i n g a s u d d e n c h a n g e i n m e c h a n i s m of a c t i o n
(38,
65),
such a change
i n biological
m e c h a n i s m of a c t i o n m a y n o t b e r e a d i l y d e t e c t e d i n t h e H a n s c h analysis. A l s o , at t h e present t i m e , there is n o a p p a r e n t means to d e t e r m i n e w h e t h e r a n a d m i n i s t e r e d d r u g o r some m e t a b o l i t e of this d r u g is r e s p o n s i b l e f o r a n
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
132
DRUG DISCOVERY
e l i c i t e d response f r o m c o n g e n e r to c o n g e n e r i n this a p p r o a c h .
Despite
these l i m i t a t i o n s , h o w e v e r , this m e t h o d does offer a basis o r s t a r t i n g p o i n t f o r i n c r e a s i n g t h e l e v e l o f s o p h i s t i c a t i o n a n d a c c u r a c y to d e s c r i b e m o r e a d e q u a t e l y t h e c o m p l e x i t y o f events s u r r o u n d i n g d r u g
response.
I n a d d i t i o n to these attempts at q u a n t i t a t i v e s t r u c t u r e - a c t i v i t y m o d e l b u i l d i n g , a t h e o r e t i c a l a p p r o a c h , q u a n t u m c h e m i s t r y , has b e e n u s e d to s t u d y c h e m i c a l c o m p o u n d s of b i o l o g i c a l interest ( I , 3 , 66).
I n this c o n -
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n e c t i o n , o n e s h o u l d m e n t i o n t h e major c o n t r i b u t i o n s of t h e P u l l m a n s i n a p p l y i n g q u a n t u m c h e m i s t r y to b i o l o g y since 1950 (67-71).
Their work
o n t h e p o s s i b l e m e c h a n i s m of c h e m i c a l carcinogenesis i n terms of q u a n tum
m e c h a n i c a l p r o p e r t i e s as w e l l as c a l c u l a t i o n s o n t h e n u c l e i c a c i d
constituents has p r o v i d e d m u c h of t h e f o u n d a t i o n f o r t h e i n c r e a s i n g i n terest i n q u a n t u m b i o l o g y .
A t a somewhat
more fundamental level,
L o w d i n has also b e e n a p i o n e e r i n t h e a p p l i c a t i o n of q u a n t u m m e c h a n i c s to p r o b l e m s of b i o l o g i c a l interest
H i s t h e o r e t i c a l c a l c u l a t i o n s of
(72).
the p r o p e r t i e s o f t h e n u c l e i c a c i d base p a i r s has l e d to a p r o p o s e d m e c h a nism of D N A replication. In
1965 N e e l y p u b l i s h e d a n e x a m p l e of t h e u t i l i t y of m o l e c u l a r
o r b i t a l t h e o r y i n c o r r e l a t i o n studies (73).
T h i s s t u d y i l l u s t r a t e d t h e use
of q u a n t u m c h e m i c a l c a l c u l a t i o n s as a n a i d i n c o r r e l a t i n g m o l e c u l a r structure of selected o r g a n o p h o s p h a t e s terase i n h i b i t o r y potencies.
a n d carbamates w i t h their cholines-
K i e r has b e e n another p i o n e e r i n u t i l i z i n g
quantum
mechanics
(74-80).
F r o m several types of c a l c u l a t i o n s h e has p r e d i c t e d t h e p r e -
to p o s t u l a t e
ferred conformations
the nature
of isolated molecules
of biological
receptors
of b i o l o g i c a l interest a n d
r e l a t e d t h e i r l o w e s t e n e r g y c o n f o r m a t i o n s to t h e n a t u r e of t h e i r receptors (80). M o r e r e c e n t l y n u m e r o u s investigators h a v e m a d e w i d e use of these b a s i c m e t h o d s i n t h e p h y s i c o c h e m i c a l a p p r o a c h to d r u g d e s i g n .
Using
the m a t h e m a t i c a l m o d e l of F r e e a n d W i l s o n ( 3 0 ) , B e a s l e y a n d P u r c e l l h a v e g i v e n t h e first e x a m p l e of the successful p r e d i c t i o n of t h e a c t i v i t y of a c o m p o u n d b e f o r e its synthesis (81).
I n 1965 P u r c e l l r e p o r t e d t h e p r e -
d i c t e d b u t y r y l c h o l i n e s t e r a s e i n h i b i t o r y p o t e n c y of l - d e c y l - 3 - ( N - e t h y l - N methylcarbamoyl)piperidine hydrobromide, C H , R = C H ) (31). 2
5
3
3
(I, R i =
Ci H i, 0
2
R2
=
T h r e e years later this c o m p o u n d w a s s y n t h e s i z e d
a n d e v a l u a t e d b i o c h e m i c a l l y . T h e o b s e r v e d a n d p r e d i c t e d response values a g r e e d w i t h i n e x p e r i m e n t a l error (81).
B a n a n d F u j i t a h a v e also a p p l i e d
this m e t h o d to t h e n o r e p i n e p h r i n e u p t a k e i n h i b i t i o n o f selected p a t h o m i m e t i c amines (82).
sym-
A g a i n , excellent correlations w e r e o b t a i n e d
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 response
values.
M o r e r e c e n t efforts h a v e b e e n c o n c e r n e d w i t h attempts to correlate structure w i t h a c t i v i t y , u t i l i z i n g m i n o r m o d i f i c a t i o n s of the l i n e a r freee n e r g y r e l a t e d m o d e l s (4, 5, 6, 8, 83).
A l t h o u g h the basic transport a n d
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
PURCELL AND CLAYTON
Physicochemical
133
Approaches
e l e c t r o n i c parameters a r e u s u a l l y r e t a i n e d , several parameters other t h a n π a n d σ have been studied. H a n s c h a n d co-workers obtained
excellent
c o r r e l a t i o n s i n a w i d e v a r i e t y o f studies u s i n g l o g Ρ i n s t e a d of t h e s u b stituent
7Γ p a r a m e t e r
where
of t h e c o m p o u n d (84, 85).
Ρ is d e f i n e d as t h e p a r t i t i o n
coefficient
T h e in vitro p a r t i t i o n i n g system o f interest
f o r t h e in vivo s i m u l a t i o n c o n t i n u e s to b e that of o c t a n o l a n d w a t e r
(86).
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A l t h o u g h other p a r t i t i o n i n g systems w e r e s t u d i e d [ s u c h as o l e y l a l c o h o l / water
(87)1,
v e r y l i t t l e i m p r o v e m e n t , i f a n y , has b e e n s h o w n i n t h e
correlations u s i n g other p a r t i t i o n i n g systems (86).
Others have obtained
excellent s t r u c t u r e - a c t i v i t y correlations b y a p p r o x i m a t i n g t h e t r a n s p o r t phenomenon w i t h the chromatographic parameter R
(88S3).
m
M o r e extensive p a r a m e t e r v a r i a t i o n s h a v e b e e n r e p o r t e d i n t h e a p proximation of electronic
substituent
parameters.
I n a d d i t i o n to t h e
w i d e l y used σ value, numerous workers have applied the Taft σ * param eter (58, 60) to a l i p h a t i c systems w i t h v a r y i n g degrees o f success (2, 4, 8, 94, 95). (μ)
M c F a r l a n d has suggested t h e use of g r o u p d i p o l e m o m e n t s
a n d e l e c t r o n i c p o l a r i z a b i l i t y parameters ( a ) i n a d d i t i o n t o H a m m e t t
σ values t o e x p l a i n better t h e e l e c t r o n i c interactions b e t w e e n d r u g s a n d receptors (96, 97).
H e o b t a i n e d excellent results i n c o r r e l a t i n g i n h i b i t o r y
rate constants of E. colt b y c h l o r a m p h e n i c o l analogs ( E q u a t i o n 2 9 ) l o g (1/C) = β χ ζ
2
+
kK + 2
kG + Z
& μ + hoc +
(96). (29)
h
4
M o r e r e c e n t l y h e has g i v e n a n extensive d e r i v a t i o n o f t h e t h e o r e t i c a l basis f o r i n c l u d i n g b o t h t h e μ a n d a parameters 2
(97).
C l a y t o n a n d P u r c e l l h a v e i l l u s t r a t e d t h e p r e d i c t i v e u t i l i t y o f this m e t h o d w h e n a p p l i e d t o selected b u t y r y l c h o l i n e s t e r a s e i n h i b i t o r s
(94).
T h e y o b t a i n e d q u a n t i t a t i v e correlations u s i n g σ * values, a m i d e g r o u p d i p o l e m o m e n t s , a n d μ i n a d d i t i o n to h y d r o p h o b i c parameters.
In addi
t i o n , H a n s c h a n d c o - w o r k e r s h a v e u s e d T a f t steric parameters (E )
(60)
a n d ρ Κ values to o b t a i n excellent correlations i n v a r i o u s systems
(84).
s
α
E has r e c e n t l y b e e n s h o w n t o b e q u a n t i t a t i v e l y r e l a t e d to v a n d e r W a a l ' s s
r a d i i f o r s y m m e t r i c a l t o p - l i k e substituents
(98)
w h i l e pK
a
values h a v e
b e e n u s e d as a m e a s u r e of e l e c t r o n d e n s i t y d i s t r i b u t i o n s (99).
Fukuto
a n d c o - w o r k e r s c o m b i n e d Taft's E a n d σ * parameters i n a p h y s i c o c h e m 8
i c a l a p p r o a c h to t h e m o d e of a c t i o n of o r g a n o p h o s p h o r u s insecticides (95 ). M o d i f i e d H a m m e t t substituent constants (100) w e r e u s e d b y G a r r e t t et al. t o d e s c r i b e t h e b a c t e r o s t a t i c a c t i v i t i e s of a series of s u l f a n i l a m i d e s (101).
H a n s c h also u s e d t h e h o m o l y t i c s u b s t i t u e n t constants (E ) R
Y a m a m o t o a n d O t s u (102)
of
i n a n a l y z i n g t h e a c t i v i t y o f selected c h l o r
a m p h e n i c o l d e r i v a t i v e s (103).
T h e r e s u l t i n g correlations l e d to t h e h y
pothesis o f a f r e e - r a d i c a l m e c h a n i s m of c h l o r a m p h e n i c o l a c t i o n .
Sub
stituent measures o f π e l e c t r o n c h a r g e d e n s i t y d i s t r i b u t i o n s (σι a n d σ ) π
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
134
DRUG DISCOVERY
w e r e u s e d b y S a s a k i a n d S u z u k i to i l l u s t r a t e t h e d e p e n d e n c e of
(104)
p a r t i t i o n coefficients a n d b i o l o g i c a l a c t i v i t y o n m o l e c u l a r e l e c t r o n i c c o n ditions (105). I n a d d i t i o n to these, t h e use of several other t h e r m o d y n a m i c s u b stituent constants has b e e n i n v e s t i g a t e d (1, 4, 106). t r e n g a u s e d m o l a r a t t r a c t i o n constants (107,108),
F o r example, Os-
a n d T u r n e r a n d Batter-
s h e l l h a v e c o r r e l a t e d c h e m i c a l r e a c t i v i t i e s , v a p o r pressures, a n d p a r t i t i o n
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coefficients o f a series o f i s o p h t h a l o n i t r i l e s w i t h t h e i r f u n g i c i d a l p r o p erties
(109).
Jones a n d c o - w o r k e r s u s e d regression analyses to s t u d y t h e eifects of field
constants a n d resonance parameters
(110)
o f some c a r b a m a t e d e
r i v a t i v e s o n t h e i r p e n e t r a t i o n a n d d e t o x i c a t i o n w i t h some success
(111).
S i m i l a r studies h a v e also b e e n m a d e b y F u k u t o a n d c o - w o r k e r s u s i n g selected
oximes a n d t h e i r anticholinesterase
activities
(112).
Kakeya
et al. u s e d c h e m i c a l shifts a n d v a l e n c e force constants i n a d d i t i o n t o other t h e r m o d y n a m i c parameters i n t h e s t r u c t u r e - a c t i v i t y s t u d y of a series o f sulfonamide carbonic anhydrase inhibitors
(113).
T h e c o m b i n a t i o n of q u a n t u m m e c h a n i c a l c a l c u l a t i o n s a n d t h e l i n e a r free-energy r e l a t e d m o d e l has b e e n u s e d r e c e n t l y b y several investigators i n d r u g a c t i v i t y studies—i.e., a v a r i e t y of i n d i c e s o b t a i n e d f r o m t h e q u a n t u m c h e m i c a l c a l c u l a t i o n s has b e e n u t i l i z e d i n these correlations (4, 8, F o r e x a m p l e , N e e l y a n d c o - w o r k e r s o b t a i n e d excellent correlations
114).
b e t w e e n t h e energy of t h e highest o c c u p i e d m o l e c u l a r o r b i t a l , a r e l a t i v e m e a s u r e of t h e a b i l i t y of a m o l e c u l e to d o n a t e a n e l e c t r o n to a n a c c e p t o r m o l e c u l e , o f a series of i m i d a z o l i n e s a n d t h e i r a n a l g e t i c potencies
(115).
I n a n analysis o f t h e l i n e a r free-energy r e l a t i o n s h i p s i n d r u g - r e c e p t o r i n t e r a c t i o n s , C a m m a r a t a has s h o w n a t h e o r e t i c a l i n t e r p r e t a t i o n of sub stituent constants i n a b i o l o g i c a l context
(116, 117).
H e has s e p a r a t e d
the free e n e r g y c h a n g e o c c u r r i n g i n a r e a c t i o n i n t o its electronic, d e s o l v a t i o n , a n d steric c o m p o n e n t s , d e f i n e d e a c h i n terms o f its c o n t r i b u t i o n s , a n d a p p r o x i m a t e d these c o n t r i b u t i o n s w i t h q u a n t u m m e c h a n i c a l i n d i c e s (118, 119).
U s i n g a t o m i c o r b i t a l coefficients a n d t o t a l e l e c t r o n i c
charge
o n c e r t a i n p o r t i o n s o f t h e m o l e c u l e , C a m m a r a t a o b t a i n e d excellent
cor
relations b e t w e e n q u a n t u m m e c h a n i c a l i n d i c e s a n d s u l f a n i l a m i d e a c t i v i t y (120) . H e also suggested t h e use o f π net charge, ττ-electrophilic a n d n u c l e o p h i l i c s u p e r d e l o c a l i z a b i l i t i e s , a n d energy l e v e l differences to inter pret drug-receptor selected (121)
interactions.
cholinesterase
W h e n this a p p r o a c h w a s a p p l i e d to
inhibitors, he obtained very good
correlations
.
H e r m a n n et al. o b t a i n e d g o o d correlations b e t w e e n t h e r e l a t i v e sub strate efficiencies of some acetophenones t o w a r d r a b b i t k i d n e y reductase a n d selected
q u a n t u m m e c h a n i c a l parameters
(122).
T h e substituent
indices were derived f r o m electron density calculations a n d energy dif-
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
PURCELL AND CLAYTON
Physicochemical
135
Approaches
ferences b e t w e e n g r o u n d a n d i n c i p i e n t t r a n s i t i o n states (122).
I n the
s t u d y of t h e D N A i n t e r c a l a t i o n b y c h l o r o q u i n e d e r i v a t i v e s , Bass et (123)
ah
c a l c u l a t e d s i g m a - e l e c t r o n c h a r g e d i s t r i b u t i o n s a n d u s e d these i n
a d d i t i o n to other substituent parameters t o investigate a m e c h a n i s m p r o p o s e d b y O ' B r i e n a n d H a h n (124)
for antimalarial activity. T h e deriva-
t i o n of a n d r a t i o n a l e b e h i n d t h e i n c l u s i o n o f this t e r m i n t o t h e H a n s c h e q u a t i o n w e r e also g i v e n
(123).
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It m a y seem t h a t t h e v a r i o u s structure—activity m o d e l s a n d p a r a m eters are n o t t r u l y so i n d e p e n d e n t as t h e y a r e p r e s e n t e d here. this s u s p i c i o n is justified.
Certainly
Recently, Singer a n d P u r c e l l evaluated the
i n t e r r e l a t i o n s h i p s a m o n g t h e q u a n t i t a t i v e structure—activity m o d e l s a n d i l l u s t r a t e d t h e i r s i m i l a r i t i e s (125).
A l s o , t h e parameters
m o d e l s c a n n o t b e t o t a l l y i n d e p e n d e n t of o n e another. tempts
t o find those parameters
u s e d i n these O n e m e r e l y at-
w h i c h alone o r i n c o m b i n a t i o n
best
d e s c r i b e t h e b i o l o g i c a l a c t i v i t y . I n v i e w of this, L e o et al. h a v e r e p o r t e d a c o m p a r i s o n of the parameters c u r r e n t l y u s e d i n studies of this t y p e
(86).
A p a r t f r o m t h e i r use i n l i n e a r free-energy r e l a t e d equations, q u a n t u m m e c h a n i c a l c a l c u l a t i o n s h a v e b e e n u s e d i n other w a y s i n d r u g d e s i g n studies.
N a g y a n d N a d o r f o u n d that t h e c e n t r a l e x c i t i n g effect of a m -
p h e t a m i n e s increases w i t h a decrease of the n e g a t i v e charge, as determ i n e d b y q u a n t u m m e c h a n i c a l m e t h o d s , o n t h e s e c o n d c a r b o n of t h e benzene
ring
(126).
C o r c o d a n o c a l c u l a t e d the r i n g c a r b o n
reactivity
i n d i c e s of some p h e n y l a c e t i c a c i d d e r i v a t i v e s a n d s h o w e d that this p a r a m eter correlates w e l l w i t h t h e i r a u x i n i c activities (127).
U s i n g the H i i c k e l
m o l e c u l a r o r b i t a l m e t h o d , M a i n s t e r a n d M e m o r y p r o p o s e d that
super-
d e l o c a l i z a b i l i t y m a y b e u s e d i n c h a r a c t e r i z i n g c h e m i c a l c a r c i n o g e n s ( 128 ). I n other studies, P u r c e l l a n d S u n d a r a m u s e d the s u m of t h e e n e r g y of t h e h i g h e s t o c c u p i e d m o l e c u l a r o r b i t a l ( H O M O ) a n d that of the l o w e s t e m p t y m o l e c u l a r o r b i t a l ( L E M O ) as a measure of m o l e c u l a r electronegat i v i t y w h e n a p p l i e d to q u i n o l i n e m e t h a n o l a n t i m a l a r i a l s (129).
Sharpless
a n d G r e e n b l a t t f o u n d e l e c t r o n d e n s i t y , L E M O , a n d p K v a l u e s to correa
late w e l l w i t h t h e a c r i d i n e toxicities to v a r i o u s m i c r o o r g a n i s m s
(130).
T h e s e correlations h a v e l e d t o t h e i r p o s t u l a t i o n of a m e c h a n i s m of a c t i o n . I n a final e x a m p l e , A n d r e w s u s e d q u a n t u m c h e m i c a l m e t h o d s to c a l c u l a t e the d i p o l e m o m e n t s of a series of a n t i c o n v u l s a n t d r u g s a n d r e l a t e d c o m pounds
(131).
T h e s e c a l c u l a t i o n s suggest a m e c h a n i s m of a c t i o n f o r
these d r u g s different f r o m that w h i c h h a d b e e n p r o p o s e d p r e v i o u s l y ( 132 ). O n e a d d i t i o n a l area of i n c r e a s i n g interest
i n the physicochemical
a p p r o a c h to d r u g d e s i g n is t h e use of i n s t r u m e n t a l m e t h o d s , p a r t i c u l a r l y n u c l e a r m a g n e t i c resonance ( N M R ) . w o r k e r s (133, 134),
Pioneered b y Jardetzky a n d co-
t h e use of N M R i n studies of drug—receptor inter-
actions at the m o l e c u l a r l e v e l is s h o w i n g great p r o m i s e .
This
technique
is u s e d p r i m a r i l y t o f o l l o w t h e c h a n g e effected i n t h e r e l a x a t i o n rates o f
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
136
DRUG DISCOVERY
t h e p r o t o n s of a s m a l l m o l e c u l e u p o n b i n d i n g to a m a c r o m o l e c u l e
by
o b s e r v i n g d i f f e r e n t i a l p e a k b r o a d e n i n g of its N M R s p e c t r u m . I n a d d i t i o n , changes i n the c h e m i c a l shift of the N M R s p e c t r u m of the s m a l l m o l e c u l e h a v e b e e n u s e d to investigate s u b s t r a t e - r e c e p t o r
interactions.
T h u s far,
N M R has b e e n a p p l i e d su c c e ssf u lly to the s t u d y of e n z y m e - s u b s t r a t e i n teractions
(135,
136),
enzyme-coenzyme
z y m e - i n h i b i t o r interactions
(136,
138).
interactions
and
(137),
en-
A l t h o u g h the l i t e r a t u r e is be-
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g i n n i n g to s h o w n u m e r o u s in vitro examples of the u t i l i t y of N M R i n this area, one r e c e n t a p p l i c a t i o n has u s e d the intact c e l l u l a r system ( 139 ).
In
this s t u d y , F i s c h e r a n d Jost d i r e c t l y o b s e r v e d the i n t e r a c t i o n of e p i n e p h r i n e w i t h its r e c e p t o r site i n the m o u s e l i v e r c e l l a n d w e r e able to postulate the n a t u r e of the i n t e r a c t i o n ( 139 ). A s is the case w i t h the other p h y s i c o c h e m i c a l m e t h o d s , h o w e v e r , the p o t e n t i a l of the a p p l i c a t i o n of N M R to d r u g d e s i g n is great, b u t m u c h d e v e l o p m e n t lies a h e a d f o r its r e a l i z a t i o n . A d v a n c e s h a v e b e e n a n d are b e i n g m a d e i n the p h y s i c o c h e m i c a l a p proaches to d r u g d e s i g n . A l t h o u g h progress has b e e n s l o w i n d e v e l o p i n g q u a n t i t a t i v e 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 s b e c a u s e of the
complexity
of the b i o l o g i c a l systems u n d e r l y i n g a n o b s e r v a b l e response f r o m a d r u g a n d there is n o p r o m i s e that these t e c h n i q u e s offer a p a n a c e a
in drug
d e s i g n , there is great p o t e n t i a l i n " d i s s e c t i n g the r o l e of the i m p o r t a n t m o l e c u l a r forces at w o r k w h i c h y i e l d different b i o l o g i c a l responses i n the series of c o n g e n e r s "
(140)
a n d i n using physicochemical methods
for
selecting p r o m i s i n g m o l e c u l e s f o r synthesis a n d e v a l u a t i o n . A s i n v i r t u a l l y a l l areas of scientific a d v a n c e m e n t , the v a r i o u s areas of e n d e a v o r are at different levels of s o p h i s t i c a t i o n .
F o r example,
one
k n o w s m o r e a b o u t the m o l e c u l a r structure of a n i s o l a t e d m o l e c u l e f r o m i n s t r u m e n t a l analyses t h a n a b o u t the specific i n t e r a c t i o n of this m o l e c u l e w i t h a c o m p l i c a t e d b i o l o g i c a l system.
I l l u s t r a t i n g this c o n d i t i o n i n a n -
other w a y , one c o u l d say that the l e v e l of s o p h i s t i c a t i o n of h a n d l i n g s i m u l t a n e o u s equations is greater t h a n the u n d e r s t a n d i n g of a p a r a m e t e r f r o m p h a r m a c o l o g i c a l testing. It is i m p o r t a n t , h o w e v e r , to r e c o g n i z e that c e r t a i n areas w i l l l a g b e h i n d others as one attempts m o r e rigorous interpretations i n interactions b e t w e e n m o l e c u l e s a n d b i o l o g i c a l systems.
In
the a u t h o r s ' o p i n i o n , this does not m e a n that w o r k s h o u l d stop i n one area i n o r d e r f o r the l e v e l of s o p h i s t i c a t i o n to " c a t c h u p " i n another area. R a t h e r , the entire a c t i v i t y s h o u l d m o v e a l o n g w i t h o u t the
investigators'
b e c o m i n g p r e o c c u p i e d w i t h the i m b a l a n c e of the levels of d e v e l o p m e n t of the areas of a c t i v i t y . F o r e x a m p l e , i t is most f o r t u n a t e that the d e r i v a t i o n of the S c h r o d i n g e r e q u a t i o n (141)
d i d not " w a i t " f o r the d e v e l o p m e n t of
h i g h s p e e d d i g i t a l c o m p u t e r s , w h i c h c o u l d g i v e p r a c t i c a l a p p l i c a t i o n to its solution.
This analogy holds for d r u g design.
T h a t is, one s h o u l d c o n -
t i n u e efforts to p u t structure—activity r e l a t i o n s h i p s o n a q u a n t i t a t i v e l e v e l e v e n t h o u g h there are l i m i t a t i o n s to the significance of c e r t a i n b i o l o g i c a l
In Drug Discovery; Bloom, Barry, et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
5.
PURCELL AND CLAYTON
Physicochemical
137
Approaches
a c t i v i t y d a t a . A s l o n g as t h e investigators are a w a r e of these l i m i t a t i o n s , it is a p p r o p r i a t e to c o n t i n u e to refine the m o d e l s . F e w p e o p l e w o u l d h a v e p r e d i c t e d a successful " m o o n w a l k , " a n d f e w w o u l d t r y to p r e d i c t t h e t i m e at w h i c h n e w d r u g m o l e c u l e s
can be
d e s i g n e d s p e c i f i c a l l y w i t h o u t exhaustive synthetic w o r k a n d p h a r m a c o l o g i c a l s creen in g.
T h e p o t e n t i a l of p r e d i c t i n g a c c u r a t e l y t h e b i o l o g i c a l
a c t i v i t y of a m o l e c u l e b e f o r e its synthesis
does a p p e a r
to exist;
only
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c o n t i n u e d w o r k i n this area a n d t i m e w i l l d e t e r m i n e w h e t h e r or n o t this p o t e n t i a l is r e a l .
Acknowledgment T h e authors g r a t e f u l l y a c k n o w l e d g e s u p p o r t b y the U . S. A r m y M e d i cal Research
a n d Development C o m m a n d (DA-49-193-MD-2779),
the
N a t i o n a l S c i e n c e F o u n d a t i o n ( G B - 7 3 8 3 ) , t h e C o t t o n P r o d u c e r s Institute, a g r a n t f r o m E l i L i l l y C o . , a n d a N a t i o n a l Institutes of H e a l t h F e l l o w s h i p (5FOl-GM43,699-02)
f r o m t h e N a t i o n a l Institute
of G e n e r a l M e d i c a l
Sciences d u r i n g t h e p e r i o d this m a n u s c r i p t w a s w r i t t e n .
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