Bulk and Steric Parameters in Binding and Reactivity of Bioactive

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

Bulk and Steric Parameters in Binding and Reactivity of Bioactive

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