Pesticide Synthesis Through Rational Approaches

15 Bulk and Steric Parameters in Binding and Reactivity of Bioactive Compounds MARVIN CHARTON

Downloaded by TUFTS UNIV on October 24, 2016 | http://pubs.acs.org Publication Date: June 26, 1984 | doi: 10.1021/bk-1984-0255.ch015

Pratt Institute, Brooklyn, NY 11205 The use of s t e r i c parameters such as and of methods such as the branching equ ations to represent s t e r i c effects on b i o a c t i v i t y i s j u s t i f i e d . Transport para meters are composite; they are a function of differences in intermolecular forces. The function of bulk and area parameters i s to provide the proper mix of intermol ecular forces required by a p a r t i c u l a r mode of b i o a c t i v i t y . In the absence of parabolic or b i l i n e a r behavior b i o a c t i v i t y can be modeled by an equation based on intermolecular forces and s t e r i c effects. Correlation analysis i s the most e f f e c t i v e , simple, generally applicable method f o r the q u a n t i f i c a t i o n of s t r u c t u r a l e f f e c t s on chemical, p h y s i c a l , or b i o l o g i cal properties. It was f i r s t successfully applied to b i o l o g i c a l a c t i v i t i e s by Hansch and h i s coworkers(X) i n an equation of the form BA

= τ

x

rr

+

x

PO^ +

h

(1

where ΒΑχ represents the b l o a c t l c i t y of the substrate bearing the substituent X ; p T, and h are c o e f f i c i ents; a i s the Hammett e l e c t r i c a l e f f e c t parameter. " i s a transport parameter defined by the equation $

ΤΓ s log χ

Ρ

Χ

- log

P

H

(2)

i n which P and PJJ are n-octanol-water p a r t i t i o n c o e f f i c i e n t s f o r X-substltuted and unsubstltuted subX

0097-6156/ 8 4 / 0 2 5 5 - 0 2 4 7 S 0 9 . 0 0 / 0

© 1984 American ChfimicalJSocietv

Magee et al.; Pesticide Synthesis Through Rational Approaches ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

)

248

PESTICIDE SYNTHESIS THROUGH RATIONAL APPROACHES

s t r a t e s r e s p e c t i v e l y . I t was soon apparent that suc c e s s f u l q u a n t i f i c a t i o n of b i o a c t i v i t y frequently r e quired more than e l e c t r i c a l and transport parameters. S t e r i c e f f e c t parameters that had been developed f o r the q u a n t i f i c a t i o n of chemical r e a c t i v i t i e s and p h y s i c a l p r o p e r t i e s were then incorporated i n the c o r r e l a t i o n equation. The Hansoh equation then takes the form BA

X

= pcr

%

* T r x

x

+ T T « • s ζ/χ • h 8

X

(3)

where T i s a transport parameter such as l o g P o r ΤΓ C i s a composite e l e c t r i c a l e f f e c t parameter, U a s t e r i c parameter. The f e term i s introduced to aocoint. for the p a r a b o l i c dependence on the transport para meter which i s f r e q u e n t l y observed f o r b l o a c t l v i t i e s . Separation of the e l e c t r i c a l e f f e c t i n t o l o c a l i z e d ( f i e l d and/or i n d u c t i v e ) and delocallzed(resonance) e f f e c t s gives


9

ΒΑχ = Ufa

•

*

4 Γ χ • Τ Γχ· • h Τι

8

(4)

In Equations 3 and 4 ; / ° , L, D, S, T , T and h are co efficients. I t i s convenient i n c o r r e l a t i o n a n a l y s i s to des c r i b e a data s e t as having the general s t r u c t u r e X-a-Y i n which X i s a v a r i a b l e s u b s t i t u e n t , Y the a c t i v e site at which some measurable phenomenon occur& and α i s a s k e l e t a l group to which X and Y are bonded. As the search f o r improved 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 relationehip8(QSAR)went on, new parameters were o o n t l n u a l l y Introduced, g e n e r a l l y on a t r i a l and e r r o r b a s i s . Among these were a group of parameters which represent a measure of s u b s t i t u e n t volume and are c a l l e d bulk parameters. Although thousands of ex amples of QSAR i n v o l v i n g s t e r i c and/or bulk parameters are now extant i n the l i t e r a t u r e , t h e i r i n t e r p r e t a t i o n has remained open to question. Thus, i t has been pointed out that s t e r i c parameters such as and £5 are at l e a s t i n p a r t derived from i n t r a m o l e c u l a r i n t e r a c t i o n s whereas those i n b i o l o g i c a l systems are gener a l l y i n t e r m o l e c u l a r . Much disagreement as to the mean ing of c o r r e l a t i o n s w i t h bulk parameters has appeared i n the literature(£) · Some authors have argued that they are a measure of s t e r i c e f f e c t s . A number of oases have now been reported i n which a receptor s i t e on a biopolymer undergoes conformational changes t o b e t t e r accomodate a s u b s t r a t e . Thus, i n place of the f i x e d shape lock of the "lock-and-key* theory, i n whioh the l o c k i s the receptor s i t e and the key the substrate that binds to i t , we now have a f l e x i b l e lock and f l e x i b l e key. x

8



15.

CHARTON

Binding and Reactivity of Bioactive Compounds

249

I t I s argued that volume i s a better measure of s t e r i c e f f e o t s f o r a f l e x i b l e lock receptor than are V o r Es» A l t e r n a t i v e l y , i t has been suggested that bulk parameters are a c t u a l l y a measure of p o l a r i z a b l l i ty and represent London(dispersion)forces i n s u b s t r a t e receptor s i t e binding. QSAR are u s e f u l i n the design of p e s t i c i d e s and m e d i c i n a l drugs, and i n environmental problems such as the p r e d i c t i o n of t o x i c i t y and b i o d e g r a d a b l l i t y . An e m p i r i c a l r e l a t i o n s h i p can be properly used only f o r i n t e r p o l a t i o n whereas one based s o l i d l y on w e l l - e s t a b l i s h e d theory can be used a t l e a s t to some extent f o r e x t r a p o l a t i o n as w e l l . I t seems of r e a l importance, then, to determine the nature and s i g n i f i c a n c e of s t e r i c and bulk parameters i n QSAR. S t e r i c Parameters The Nature of S t e r i c E f f e c t s , s t e r i c e f f e o t s r e s u l t from e l e c t r o s t a t i c r e p u l s i o n s between electrons i n o r b i t a l e on non-bonded atoms. Such r e p u l s i o n s always r e s u l t i n an Increase i n the energy of a system. We define s t e r l o ; e f f e c t s which r e s u l t i n an increase i n some measurable p h y s i c a l , chemical, or b i o l o g i c a l property as s t e r i c augmentation, those which r e s u l t In a decrease i n the property as s t e r i c d i m i n u t i o n ^ ) · There are several categories of s t e r i c e f f e c t s . They include : 1. S t e r i c e f f e c t s due to change i n coordination number and h y b r i d i z a t i o n of a r e a c t i n g atom. 2. S t e r i c i n h i b i t i o n of resonance. 3· S t e r i c i n h i b i t i o n of s o l v a t i o n . 4. S t e r i c determination of conformation. 5· S t e r i c s h i e l d i n g of the a c t i v e s i t e . The

Minimal S t e r i c

TnteraQtlon(MSl)

Principle.

As

all

s t e r i c i n t e r a c t i o n s r e s u l t i n an increase i n the energy of a system, the observed s t e r i c e f f e c t i n the system w i l l be the smallest p o s s i b l e . Thus, when the s t e r i c e f f e c t of a group X depends on i t s conformation, the group w i l l prefer that conformation which r e s u l t s i n the smallest possible s t e r i c i n t e r a c t i o n . This i s

the MSI principle(1,4). Conformational dependence of the s t e r i c e f f e c t . Some groups show l i t t l e o r no conformational dependence of t h e i r s t e r i c e f f e c t s ( 3 K Non-oonformationally dependent groups are monatomlo (halogen or hydrogen). M2 symmetric top (M i s hybridized sps), :MH o r :JIH, MZ , 3

8


4

250


and MZ s u b s t i t u e n t s are minimally conformationally dependent* Problems i n c h a r a c t e r i z i n g s t e r i c e f f e c t s are g e n e r a l l y due to s u b s t i t u e n t s which show a c o n s i d erable dependence of t h e i r s t e r i c e f f e c t on conformat i o n . Among groups o f t h i s type are M Z i Z ( C H B r ) , MZiZeZ (CHMeCl) and planar ifbonded (Xp/r ) s u b s t i t u e n t s such as a r y l , v i n y l , n i t r o , and carbonyl. Most a l k y l and s u b s t i t u t e d alkyl.groups f a l l i n t h i s category. Xp groups when attached to planarVbonded s k e l e t a l groups, Gp*r , w i l l e x h i b i t a v a r i a b l e d e l o c a l i z e d e l e c t r i c a l e f f e c t r e l a t e d to t h e i r v a r i a b l e s t e r i c e f f e o t 6

8

8

8

3


d

e

r

Vag Waals R a d i i And Related S t e r i c Parameters. Van der Waals r a d i i have long been considered a v a l i d measure of atomic s i z e . Taft proposed the f i r s t v a l i d s e t of s t e r i c parameters f o r c o r r e l a t i o n a n a l y s i s defined from acid h y d r o l y s i s of e s t e r s . Charton derived equa t i o n s f o r the c a l c u l a t i o n of Van der Waals r a d i i , r y , of symmetric top MZ groups(6). These values of the Van der Waals r a d i i were used, together with that f o r H, to show that Es i s a l i n e a r f u n c t i o n of r y . 8

ES>X = a i r

v > x

+ *o

(5)

Thus, Es i s an r y based s t e r i c parameter. The r y v a l ues themselves have been used as s t e r i c parameters. F i n a l l y , Charton has defined the V s t e r i c parameteras ( J )

V*

ryx - ryH - 1.20

•

(6)

Groups which exert conformationally dependent(CD) s t e r i c e f f e c t s oannot have s t e r i c parameters defined f o r them i n t h i s way. S t e r i c parameters f o r these groups are g e n e r a l l y obtained i n d i r e c t l y from chemical r e a c t i v i t i e s . The s t e r i c demands o f a r e a c t i o n vary from one r e a c t i o n to another and no s l g n l e s e t of s t e r i c parameters w i l l s u f f i c e f o r a l l r e a c t i o n types. For almost a l l group types, three d i f f e r e n t Van der Waals r a d i i are of importance, l e a d i n g to three d i f f e r e n t V values(3^6,J)· These r y values a r e : I. r ; the minimum Van der Waals r a d i u s perpendic u l a r to the group a x i s . · V.mx* maximum Van der Waals r a d i u s perpendic u l a r to the group a x i s . 3 · v.ax» Waals r a d i u s p a r a l l e l to the grpup a x l e . The group a x i s i s c o l l i n e a r with the bond J o i n i n g s u b s t i t u e n t X and s k e l e t a l group G. For monatomic vm l n

2

r

r

tee

t h e

V a l î

â

e

r


15.

CHARTON


251

groups the minimum, maximum and p a r a l l e l Van der Waals r a d i i are equal to each other. For c y l i n d r l c a l l y symmetric groups such as CN or C=CH the maximum and minimum r a d i i are equal. From Equation 6 we obtain ifox, Z4n and l>àx parameters. The Vef constants, determined from chemical r e a c t i v i t i e s f o r groups with conformat i o n a l l y dependent s t e r i c e f f e c t s , are probably close to Vmn values.


Topological Parameterization of Steric

Effects*

We h a -

ve noted that d i f f e r e n t r y based s t e r i c parameters w i l l be required f o r conformationally dependent groups in order to account f o r phenomena with d i f f e r e n t s t e r i c requirements. This must r e s u l t i n a m u l t i p l i c i t y of s t e r i c parameters f o r d i f f e r e n t types of phenomena. The d i f f i c u l t y can be avoided by the use of t o p o l o g i c a l methods which represent s t e r i c e f f e c t s as the r e s u l t of contributions of a l l atoms other than H in the group. Various t o p o l o g i c a l methods have been proposed. The discussion here w i l l be r e s t r i c t e d to the branching equations (iUUjJl). simple branohlng (SB) equation i s defined by 1 1 x 6

m Ak - 1=1

(7)

l

where QAk i s the quantity to be correlated f o r the substrate bearing the a l k y l substituent Ak. The v a r i a ble n Is equal to the number of branches (C-C bonds) at the 1th C atoms tt the Ak group. The numbering i s begun at the substituent C atom bonded to the s k e l e t a l group (Figure 1 ) . a and a are c o e f f i c i e n t s . The SB equation can be extended to substituents other than Ak groups. It has a great advantage over ^ Es and r e l a t ed parameters. When i t i s r e s t r i c t e d to a c y c l i c groups MZfZfZf thè n i are exact and free of e r r o r . The SB equation suffers from a serious disadvantage i n i t s assumption that the e f f e c t of branohlng i s independent of the order of attachment of the branohes. This Is equivalent to averaging the e f f e c t of the branches at some 1th atom. We may account f o r the e f f e c t of the order of branching by means of the expanded branching (XB) equation, x

x

0

(8) Q

Ak

5

ill

jS

a

U

n

i

J

i n which n i j represents the number of Jth branohes on atoms designated 1. a i j and a are again c o e f f i c i e n t s . 0 0


252


As in the SB equation groups are numbered s t a r t i n g w i * th the atom bonded to the s k e l e t a l group (Figure 2). The XB equation i s a very good model of s t e r i c e f f e c t s and i s Indeed generally more e f f e c t i v e than the SB equation. This i s to be expected from the operation of the MSI p r i n c i p l e . Thus, f o r example, an n-amyl group can choose a conformation which leads to a small s t e r i c e f f e c t . A 3-amyl group can do so to a much smaller extent. A t-amyl group cannot choose a conformation which w i l l minimize the s t e r i c e f f e c t of the branches at C . The XB equation has two disadvantages r e l a t i v e to the SB equation. The f i r s t i s that the much l a r g e r number of variables requires a much l a r g e r data set f o r good r e s u l t s . The second i s that f o r a l l a l k y l groups other than methyl n must equal 1. Direct determination of a i s therefore impossible as n is e s s e n t i a l l y constant throughout the data set and cannot be used as a v a r i a b l e . Then from Equation 8,


1

x x

x x

^Ak

=

0

1

1

*

a

x x

*

8 Î Î

a

n

** * ie i»

\^ j ^ i j i j a

+

n

*

(9)

a o 0

or ft

a

n

a

Ak ~ i « x « • isi>i3 +

The Nature o f S t e r i c E f f e c t s

%

a

a

â i i » i i • oo

(10)

on B l o a o t l v l t y

The Mac F a r l a n d Model o f R l o a c t l Y i t y *

in order to

dis-

cuss the nature of the s t e r i c effeots that are l i k e l y to be encountered i n b l o a c t i v l t y studies i t i s neoessary to have a model of substrate b l o a c t i v l t y . The mode l presented here i s based on that proposed by MaoFarland (1Q). Consider a bioactive substrate (bas) whloh has been introduced into some organism or component thereof. Its b l o a c t i v l t y r e s u l t s from some combination of the following s t e p s : 1· Transport - The bas moves from the point of entry to some receptor s i t e . In the course of i t s t r a v e l s i t may cross one or more biomembranes (Figure 3 ) · The bas may d i f f u s e through the f i r s t aqueous phase (Φ ) to the anterior membrane surface (ams) or i t may bind to plasma protein (pip) whloh transports i t to the ams. It may then d i f f u s e through the membrane or a l t e r n a t i v e l y form a com plex with a l i p i d soluble membrane c a r r i e r mole cule (mom) which c a r r i e s i t to the p o s t e r i o r memχ


CHARTON


C

253

3

/

2

3

5


c - c 1

2

c —

\c

c 3

c — 2

4

c —

c —

3

—

c —

c

c

5

4

4

\

F i g u r e 1. V a l u e s o f n. f o r use w i t h t h e SB e q u a t i o n and r e l a t i o n s h i p s d e r i v e d f r o m i t . n^ = n^ = 3, n^ = 4 , n^ = 2. n = 4 b

Z c G —

/ -

2 1

1

C

\ 2 3 _

c 2

2

3 2

/

C

C

3 1 _

3

1

c

C

4

1

-

x

C

5 2

41

V F i g u r e 2. V a l u e s o f n.. f o r use w i t h t h e XB e q u a t i o n and r e l a t i o n s h i p s d e r i v e d f r o m i t . n^^ = 32 42 51 n = 1, n = 3, n =2. n = 4. =

5 2

3 1

4 1

n

=

n

=

Π

fa


=

Magee et al.; Pesticide Synthesis Through Rational Approaches ACS Symposium Series; American Chemical Society: Washington, DC, 1984. pms

Figure 3. Step 1 i n the modified MacFarland b i o a c t i v i t y model: D i f f u s i o n c a r r i a g e by plasma p r o t e i n from the entry point to the a n t e r i o r membrane su face (ams); t r a n s f e r from the f i r s t aqueous phase (0^) to the ams; passage through the membrane by d i f f u s i o n or by l i p i d soluble membrane c a r r i e r mole cule; bound to the p o s t e r i o r membrane surface (pms) t r a n s f e r from the pms t the second aqueous phase ( 0 « ) .

ams


15.


CHARTON

255


brane surface (pms). The bas i s then transferred to the second aqueous phase (ζΑι). 2. Receptor-bas binding - a. R e c o g n i t i o n . The bas and the receptor (rep) form a weak complex*(Fig ure 4)(bas * · r e p ) , b. B i n d i n g , Conformational changes may occur in e i t h e r or both the bas and the rep. The bas w i l l a l i g n i t s e l f to form a strongly bound complex (Figure 5)(bas · r e p ) . 3· Chemical reaction - The receptor reacts with and/or catalyzes reactions of the bas forming product (prd). The model i s summed up in Scheme 1 · Scheme 1. The MaoFarland Model of 1*

1a

bas(^)^

Id bas.. ν ams ««un

2a

^=

e bas

bas 2,3· ι

Bloactivlty

bas

VPras;

lis

bas(j^ | 8

4

mem*

x

b a s i ^ ) ^ ^ bas

rep ν rop • prd

rop

bas, bioactive substrate; rep, receptor; ams, a n t e r i o r membrane surface; pms, posterior membrane surface; p i p , plasma p r o t e i n ; mem, l i p i d soluble membrane c a r r i e r molecule; p r d , product; φι, 1th aqueous phase; bas · rep, weak oomplex; b a s » r e p , strong complex; bas · r e p * , t r a n s i t i o n s t a t e . 9

In the transport step s t e r i c e f f e c t s oan r e s u l t from s t e r i c I n h i b i t i o n of binding or s t e r i c i n h i b i t i o n of solvation while in the binding step s t e r i c h i n d r ance can decrease the strength of binding to the r e ceptor. The s t e r i c e f f e c t s encountered in the chemical reaction step are of the same types as those found in any a b i o t i c chemical r e a c t i o n . We have noted above that i t has been suggested that s t e r i c e f f e c t s in the binding step may not be well represented by parameters such as if and Es as they are i n t r a - , not intermolecu l a r . We can test the v a l i d i t y of this argument by ex amining the c o r r e l a t i o n of data f o r a b i o t i c systems involving Intermolecular i n t e r a c t i o n s with if or Es* As the argument i s presented as j u s t i f i c a t i o n for a s t e r i c i n t e r p r e t a t i o n of the r e s u l t s of c o r r e l a t i o n s with bulk parameters i t also r u l e s out any topological par-




Figure 4. Step 2a i n the modified MacFarland b i o a c t i v i t y model. Recognition i n v o l v i n g t r a n s f e r from 0^ to the r e ceptor surface with formation of a weak complex.



CHARTON


substrate in f i n a l conformation

Figure 5. Step 2b i n the modified MacFarland b i o a c t i v i t y model. Binding, i n v o l v i n g the change from a weak to a strong complex. Conformational changes i n both substrate and receptor s i t e may take place.



258

ameters whloh do not represent both s t e r l o e f f e c t s and polarlzabllity. A b i o t i c Modal Syateme. Possible a b i o t i c model systems are l i s t e d i n Table I. We have reoently studied s t e r i c en charge transfer (ct) complex formation ( 1 1 ) · Both V a n d Δ ι / w e r e considered as s t e r i c parameters. Δΐίίβ defined by the expression

when!/χ i s greater than or equal to Z/mn Gp · When^Gc i s l e s s than T/mn (jp f


f

ΔΙ/

50

(12)

A Vis intended for use when X i s bonded to a planar bonded s k e l e t a l group (Gp ) as If i s l e s s than or equal to the h a l f thickness of GpTr (#mn,Gp7r) should exert no s t e r i c e f f e c t on ct complex formation* Gener a l l y , best r e s u l t s were indeed obtained with AVa.B the s t e r i c parameter. Table I.

A b i o t i c Model Systems

System

Data

Models s t e r i c e f f e c t s on

ot oomplex formation

log

Ke

Β

moleoular a s s o c i a t i o n

log

Ke

B, S

intermolecular hydrogen bonding

log

Ke

B, S

r e a c t i v i t y in heterogen eous c a t a l y s i s

log

kr

Β

chromatographic data

log log

Va» Rf»

binding to abiopolymers

log

Ke

Β

a r t i f i c i a l enzyme models

log

kr

R

I, log

Β, S t

R

Ke, equilibrium constant; k r , rate constant; Rf, rate of f l o w , ; tR, retention time; V Q , s p e o i f i o retention volume; I, retention index,; B, binding; S, s o l v a t i o n ; R, r e a c t i v i t y ; o t , charge t r a n s f e r .


15.


CHARTON

259

We have studied data f o r one molecular a s s o c i a tion s e t , the s e l f a s s o c i a t i o n of d l a l k y l ketones, u s ing the XB equation with the addition of a term In the number of C atoms (n ) as a measure of p o l a r l z a b l l i t y . Thus, c

s

Pesticide Synthesis Through Rational Approaches

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