A Hierarchal QSAR Molecular Structure Calculator Applied to a

25 A Hierarchal QSAR Molecular Structure Calculator Applied to a Carcinogenic Nitrosamine Data Base B. PETIT, R. POTENZONE, JR., and A. J. HOPFINGER—Department of Macromolecular Science, Case Western Reserve University, Cleveland,OH 44106

Downloaded by UNIV OF ROCHESTER on May 29, 2013 | http://pubs.acs.org Publication Date: November 28, 1979 | doi: 10.1021/bk-1979-0112.ch025

G. KLOPMAN—Department of Chemistry, Case Western Reserve University, Cleveland, OH 44106 M. SHAPIRO—Division of Computer Research and Technology, National Institutes of Health, Bethesda, MD 20014 Lijinsky and coworkers (1) have reported a data base contain ing two quantitative measures of carcinogenic potency for a set of nitrosamines. The first carcinogenic measure, TD50, is the average time, in weeks, for 50% of a set of Sprague-Dawley rats to die relative to a control set of equal population. An upper limit of 100 weeks has been placed on each experiment. The second measure is an overall assessment of relative carcinogen icity, RC, based upon observations made over the course of the experiments. RC is recorded on a discrete scale of 0 to 4 with zero being "noncarcinogenic" and four being "extremely carcino genic". Exposure to the nitrosamine was achieved by placing a fixed dosage in the animal's drinking water. The sites of tumor forma tion were recorded for each compound tested. For specific test ing details see Lijinsky and Taylor reports 2-4. It is to be emphasized that this data base was not constructed from biological experiments designed for quantitative structure activity relation ship, QSAR, studies. The experiments were developed only to a s c e r t a i n whether or not a compound i s " c a r c i n o g e n i c " . Con sequently, r e l a t i v e l y high doses have been used which l e a d t o a narrow range o f responses. Nevertheless, Singer e t a l . CD and Wishnok e t a l . (6) have used b i o l o g i c a l a c t i v i t i e s of the type and q u a l i t y as T D 5 0 to e s t a b l i s h QSAR's f o r some s e t s of nitrosamines. Singer e t a l . (5) found a l i n e a r c o r r e l a t i o n between experimentally measured water/ o c t a n o l p a r t i t i o n c o e f f i c i e n t , P, and the percentage of SpragueDawley r a t s b e a r i n g o l f a c t o r y carcinomas induced by s u b s t i t u t e d N-nitrosopiperidines. In a d d i t i o n , a p a r a b o l i c c o r r e l a t i o n was e s t a b l i s h e d between Ρ and the r e l a t i v e mean l i f e t i m e of the animals b e a r i n g h e p a t o c e l l u l a r carcinomas induced by a s m a l l , but moderately d i v e r s e , set of n i t r o s a m i n e s . Wishnok e t a l . (6) have found the water/hexane p a r t i t i o n c o e f f i c i e n t P and " e l e c t r o n i c f a c t o r s " as measured by T a f t σ* to c o r r e l a t e with c a r c i n o g e n i c a c t i v i t y f o r a s e r i e s of n i t r o s o f

0-8412-0521-3/79/47-112-553$07.25/0 © 1979 A m e r i c a n C h e m i c a l Society

In Computer-Assisted Drug Design; Olson, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


554

COMPUTER-ASSISTED DRUG DESIGN

compounds. However, the a p p l i c a b i l i t y of σ* t o n i t r o s o group s u b s t i t u e n t s i s q u e s t i o n a b l e . Nevertheless, both groups of researchers concluded t h a t t r a n s p o r t o f the carcinogen to the a c t i v e s i t e , as i s assumed modeled through p a r t i t i o n c o e f f i c i e n t , p l a y s a s i g n i f i c a n t r o l e i n s p e c i f y i n g c a r c i n o g e n i c potency. We have c a r r i e d out a s e r i e s of i n v e s t i g a t i o n s i n p u r s u i t of a QSAR f o r a s e t of c y c l i c nitrosamines from the L i j i n s k y data base ( 1 ) . T D 5 0 has been used as the b i o l o g i c a l measure. A l l the c y c l i c nitrosamines considered produced tumors o f the esophagus. In s e v e r a l i n s t a n c e s tumors were found a t a d d i t i o n a l s i t e s i n the animals. I t i s to be emphasized that the occurrence of tumors, and the reduced average l i f e of the animals, due to exposure to nitrosamines, must be assumed i n d i c a t i v e of the c a r c i n o g e n i c potency o f a compound. Our nitrosamine QSAR i n v e s t i g a t i o n s can be c l a s s i f i e d i n terms o f four i n c r e a s i n g l e v e l s of s t r u c t u r a l s o p h i s c a t i o n ; 1. determination of group-additive Q ) molecular d e s c r i p t o r s , 2. c a l c u l a t i o n of d e s c r i p t o r s using molecular mechanics methods (8), 3. c a l c u l a t i o n o f quantum mechanical (molecular o r b i t a l ) (9) d e s c r i p t o r s , and 4. mechanism of a c t i o n computations which employ a l l of the above mentioned d e s c r i p t o r s . In general QSAR models can be constructed from any combina t i o n of the four l e v e l s o f s t r u c t u r e c a l c u l a t i o n . We are c u r r e n t l y developing a software package to compute the d i f f e r e n t c l a s s e s of molecular d e s c r i p t o r s and to c o n s t r u c t a c t i o n models. This software package i s being c a l l e d "A H i e r a r c h a l QSAR Molecular S t r u c t u r e C a l c u l a t o r " . Method 1. Group A d d i t i v e Molecular D e s c r i p t o r s ; Log Ρ values were c a l c u l a t e d u s i n g Rekker fragment constants ( 1 0 ) a p p l y i n g nona d d i t i v e c o r r e c t i o n s according to Leo ( H ) . Fragment constants are not a v a i l a b l e f o r the n i t r o s o group. To estimate t h i s f r a g ment constant, f(NNO), the c y c l i c nitrosamines were grouped according to the types of atoms i n the r i n g . Those compounds c o n t a i n i n g only a l i p h a t i c u n i t s , besides a s i n g l e n i t r o s o group, were grouped together as were the nitrosomorpholines, the n i t r o p i p e r a z i n e s , and d i - N - n i t r o s o - d e r i v a t i v e s . In c o n s t r u c t i n g these c l u s t e r s we assume that the e l e c t r o n i c p r o p e r t i e s of the n i t r o s o group are a l t e r e d by i n - r i n g s u b s t i t u e n t s . In t u r n , changes i n the e l e c t r o n i c p r o p e r t i e s o f the n i t r o s o group a l t e r s i t s o l u t e s o l v e n t behavior and, consequently, l o g P. A l i n e a r l e a s t square f i t of the experimental l o g Ρ versus the c a l c u l a t e d l o g Ρ (not c o n t a i n i n g a c o n t r i b u t i o n from the n i t r o s o group) has been c a r r i e d out f o r each o f these four groups. The negative of the l o g Peal i n t e r c e p t o f the l e a s t - s q u a r e f i t l i n e can be i d e n t i f i e d as f(NNO). The legend o f Table 1 contains the f(NNO) of each


25.

PETIT E T A L .

Q S A R Molecular

Structure

555

Calculator

of the f o u r compound groups. The experimental l o g Ρ are reported by Singer e t a l . (5) and were measured by o p t i c a l d e n s i t y spectroscopy. We have c a r r i e d out a l i n e a r r e g r e s s i o n a n a l y s i s between l o g Pexp and l o g P e a l f o r the complete data base i n Table 1. The c o r r e l a t i o n equation is log P

e x p

= 1.0049 l o g P


Ν = 28

R = .97

c a l

+ .0108

S = ±

(1)

.203

where Ν i s the number of compounds, R i s the c o r r e l a t i o n c o e f f i c i e n t , and S the standard d e v i a t i o n . Log P, at a f i x e d temperature, i s a measure of the f r e e energy d i f f e r e n c e between a s o l u t e i n water and 1-octanol. At room temperature, Ρ =

log

.735

(PH O -

F

2

o c t

).

(2)

Eq. (2) i n d i c a t e s that F H ° and F can both vary, while l o g Ρ remains constant. Consequently, i f the chemical a c t i v i t y ( s o l u t i o n f r e e energy) of a compound i n the aqueous and/or l i p i d medium i s a s i g n i f i c a n t f e a t u r e ( s ) i n c o n t r o l l i n g b i o l o g i c a l a c t i v i t y , l o g Ρ may not be an adequate descriptor. Fortu n a t e l y , a l a r g e number of aqueous a c t i v i t y c o e f f i c i e n t s of organic compounds have been measured (12). Using a group a d d i t i v e formalism and the thermodynamic r e l a t i o n s h i p , 2

aH 0 2

= exp(-F o/RT) H2

o c t

(3)

i t has been p o s s i b l e to construct a s e t of aqueous f r e e energy fragment constants analogous t o Rekker f-constants (10) and Hansch π-constants (13). U20 i s the measured aqueous a c t i v i t y coefficient. The corresponding aqueous f r e e energy fragment constants, w(X), are l i s t e d i n Table 2. No w(NN0) constants were a v a i l a b l e from the a n a l y s i s of the aqueous a c t i v i t y c o e f f i c i e n t . Consequently, we c a r r i e d out computer s i m u l a t i o n c a l c u l a t i o n s to model the i n t e r a c t i o n of water molecules with an NNO group. These s i m u l a t i o n s t u d i e s are i d e n t i c a l to those employed to estimate the aqueous and 1-octanol f r e e energies of some simple o r g a n i c com pounds (14). I n t e r e s t i n g l y , these c a l c u l a t i o n s suggest that the o c t a n o l c o n t r i b u t i o n to l o g Ρ f o r the NNO group i s e s s e n t i a l l y zero. The e l e c t r o s t a t i c i n t e r a c t i o n s between the water molecules and NNO dominate i n the s o l v a t i o n e n e r g e t i c s . The set of molecular aqueous f r e e energies of the c y c l i c n i t r o samines are i n Table 1. Eq. (2) can be s o l v e d f o r F and these d e s c r i p t o r values f o r each of the c y c l i c nitrosamines are a l s o reported i n Table 1. a

o c t

2. Molecular Mechanics D e s c r i p t o r s : A c o n s i s t e n t f o r c e f i e l d (CFF) method, adapted from the MMI program of A l l i n g e r , ( ϋ ) of



556

Table 1 (1 o f 5)

•art l-A

trans

?It
100

4 36

44

4 20

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>100

4 41

1.23

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1.04

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2.59

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25.

557

ÇSAR Molecular Structure Calculator

PETIT E T A L .

2

si

s

S A J

én

^

"

00

*

Ν

U

Ν

«

w

**

22.

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β

< 1

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-1

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en

σ

< Τ OA Ν β

>»

3

00

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!

υ

S

υ

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1

υ

υ

χ

J

-

b.

υ

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r>.

CM

sr

oo

en

m

—

chai

boat

162. ί

-64.7

OH

139.0

OH

ΔΕ(ΙΙ-ΙΙΙ)

(227.5)

(18.4)

OH

OH

-68.0

ΔΕ(ΙΙ-Ι)

137.3

(207.0)

(1.7)

129.5

(224.9)

(38.7)

155.8

(224.7)

(17.2)

158.3

(226.7)

(14.9)

144.0

(226.8)

(18.7)

(224.1)

(36.0)

(224-4)

(13.4)

OH

OH

VJ) -56.7 /

168.2

OH

OH OH

^

-51.7

J

173.0

OH

173.2

-53.5

OH

OH

OH

OH

OH

-44.3

OH

> λ* (

OH

OH

OH

179.8

0H

"(fol"».6


25.

567

ÇSAR Molecular Structure Calculator

PETIT E T A L .

Table 3 I HO y


c

Ε

II

Ε

III

Ε

Δε(ΙΙ-Ι)

Δε(ΙΙ-ΙΙΙ)

-101.8

128.9

81.7

(230.7)

(47.2)

98.4

131.3

111.5

(229.7)

(19.8)

144.8

(231.4)

(16.7)

130.0

(237.1)

(30.9)

142.6

(233.7)

(15.9)

(230.2)

(18.41

(189.2)

(14.8

OH

HO

HO

OH

Cr^-69.9 Cjr

OH

H^~3H

OH

^TL

1615

3>

CA

-ς

160.9

OH

OH

OH

ICJI OH

OH

OH

|^168.

61.6

Φ H3C-CH2CJI

-25,

OH

OH

OH

H C-CH Cil 2

|H C-®C* 3

2 0 0 e 0

2


COMPUTER-ASSISTED DRUG

568

The g e n e r a l i z a t i o n introduced i n t o eq. ( 4 ) i s F i s d e f i n e d as: _F

DESIGN

which

i s the f r a c t i o n of molecules reaching the c r i t i c a l s i t e which have been transformed i n t o an a c t i v e m e t a b o l i t e .


Generally, F has been s e t equal to one, that i s e x p l i c i t metabolic c o n s i d e r a t i o n s have been neglected. In t u r n , K, which accounts f o r drug-target i n t e r a c t i o n s i s d e f i n e d i n our formalism as: Κ i s the a c t i v i t y of the metabolite, i . e . i t s r e a c t i v i t y toward the t a r g e t molecule. We f u r t h e r note that s e v e r a l metabolites are allowed i n the p o s t u l a t e d metabolic pathway of F i g . 2. Therefore, eq. (4) becomes: d(response) dt

_ ACSF.K.

(5)

. 1 1

ι where 1 r e f e r s to the i * * * metabolite and the c o n s t r a i n t ΣΈ± = 1 i s present. Eq. (5) can be solved under three d i f f e r e n t b i o l o g i c a l boundary c o n d i t i o n s : 1

1

1. 2. 3.

Concentration and time are constant, Concentration and response are constant, Response and time are constant.

and

The T D ^ Q and RC measures f a l l i n t o the second c l a s s i f i c a t i o n . Consequently, the f i n a l form of the drug a c t i o n equation becomes

ϊ " Ψ Α

( 6 )

An expression f o r K. was formulated i n terms of a product of s t r u c t u r a l switches:

K

±

=TTs

ui

, where

i n which X . = 1 or 0 depending upon the presence of d e s c r i p t o r u i n metabolite i .

(7)

or absence

V . measures the importance of d e s c r i p t o r u i n metabo l i t e i i n the production of the observed response. The d e s c r i p t o r s employed i n c l u d e those given i n Tables 1 and 3. A i n eq. (6) was s e p a r a t e l y considered as represented by a guassian f u n c t i o n i n l o g Ρ m u l t i p l i e d by the p o p u l a t i o n of the boat conformer. The parent compound was used to determine the values of Log Ρ i n A. Our program MULFIT which i s a form of non-


25.

PETIT E T AL.

ÇSAR

Molecular

Structure

Calculator

569

l i n e a r r e g r e s s i o n a n a l y s i s was used to determine the c o e f f i c i e n t s f o r the A term, the V i and the Έ ± . The values of the F^, i n turn, provide the information to determine which metabolic species are most important i n the a c t i o n model. The V ± i n d i c a t e which molecular d e s c r i p t o r s are most important i n the a c t i o n of a p a r t i c u l a r metabolite. u

U

Results


Two d i s t i n c t types of 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 were c a r r i e d out; one independent of the a c t i o n model, the other based upon the proposed mechanism of a c t i o n . 1.

QSAR-Independent of

an A c t i o n Model:

The T D 5 0 were i n i t i a l l y c o r r e l a t e d against the complete sets of group a d d i t i v e molecular f e a t u r e s , CFF a b s o l u t e conformer energies, and e q u i v a l e n t atom r e s i d u a l charge d e n s i t i e s using l i n e a r r e g r e s s i o n a n a l y s i s . Both l i n e a r and quadratic values were considered f o r each d e s c r i p t o r . The systematic and r e p e t i t i v e d e l e t i o n of a s i n g l e d e s c r i p t o r term from the general c o r r e l a t i o n equation i n d i c a t e d that a l l CFF conformer energies and atomic charge d e n s i t i e s , except f o r those of the C , d i d not c o n t r i b u t e meaningfully to the c o r r e l a t i o n equation. A d d i t i o n a l molecular mechanics d e s c r i p t o r s were constructed by t a k i n g a l l combinations of energy d i f f e r e n c e s between the d i f f e r e n t conformer s t a t e s considered. Several degeneracies arose because of the energy equivalence of some conformers f o r c e r t a i n compounds. Nevertheless some of the sets of energy d i f f e r e n c e s enhanced the c o r r e l a t i o n when both l i n e a r and quad r a t i c values were i n c l u d e d i n the r e g r e s s i o n a n a l y s i s . The d e s c r i p t o r s e t s of energy d i f f e r e n c e s are h i g h l y c o l i n e a r with respect to c o r r e l a t i o n with TD50. Consequently, we sought the one set of energy d i f f e r e n c e s which maximized the s i g n i f i c a n c e of the c o r r e l a t i o n . The energy d i f f e r e n c e between the most s t a b l e boat and most s t a b l e c h a i r form of each compound y i e l d e d the highest c o r r e l a t i o n . These energy d i f f e r e n c e s , ΔΕ, are reported i n Table 1. I t should be noted that these ΔΕ may, i n p a r t at l e a s t , c o r r e l a t e best with TD50 because t h i s data set contains the l e a s t degeneracy ( l a r g e s t number of unique e n t r i e s ) . When the ΔΕ are included i n the c o r r e l a t i o n a n a l y s i s , the atomic charge d e n s i t i e s of the C no longer are s i g n i f i c a n t . This suggests that the c o n t r i b u t i o n of the C charge d e n s i t i e s to the c o r r e l a t i o n are included w i t h i n the ΔΕ. This i s c o n s i s t e n t with the f a c t that the charge d e n s i t i e s are used to determine the CFF energies. If t h i s i s the case, then the C atomic charge d e n s i t i e s do not c o n t r i b u t e to the T D 5 0 c o r r e l a t i o n through chemical r e a c t i v i t y (an i n t e r m o l e c u l a r process), but through conformer s t a b i l i t y (an i n t r a m o l e c u l a r process). a

a

a

a



570

A l l combinations of l i n e a r and q u a d r a t i c values of the r e maining d e s c r i p t o r s were used i n l i n e a r r e g r e s s i o n f i t s to the T TD50. ^[ie roost s i g n i f i c a n t c o r r e l a t i o n equation found i s , TD50 = 97.7

+ 29.7

+ 1.23 Ν - 22

(ΔΕ)

(F

) + 3.8

o c t

(F

) 2 - 6.61

o c t

(ΔΕ)

2

(9)

R = .92

S = ί

8.4

Eq. (9) has been judged s i g n i f i c a n t because the constant term (97.7) i s a t the upper end of the TD50 a c t i v i t y range [0,100]. C o n t r i b u t i o n s of F and ΔΕ from compounds i n the data base to eq. (9) must be to lower TD50. T h i s cannot occur r a n domly as compared to the case where the constant term i s 50, and "random f l u c t u a t i o n " c o n t r i b u t i o n s from F t and ΔΕ to reproduce the range of TD50, [0,100]. The number of d e s c r i p t o r terms i n eq. ( 9 ) , f o u r , two p a i r s of i n t e r f u n c t i o n a l d e s c r i p t o r s , i s small with respect to the number of o b s e r v a t i o n s , 22. There i s a "rule-of-thumb" that the r a t i o of observations to d e s c r i p t o r terms must be f o u r , or more, to y i e l d a s t a t i s t i c a l l y s i g n i f i c a n t r e l a t i o n s h i p . Thus t h i s i s a d d i t i o n a l evidence i n support of the s t a t i s t i c a l v a l i d i t y of eq. (9). Each of the two d e s c r i p t o r s F and ΔΕ appear i n the c o r r e l a t i o n equation (eq. 9) with p a r a b o l i c dependence. This means that each d e s c r i p t o r possesses an optimum value which y i e l d s a maximum, or minimum, c o n t r i b u t i o n to determining Τϋ50· These optimum values can be determined by simple p a r t i a l d i f f e r e n t i a t i o n of eq. ( 9 ) ,


o c t

o c

o c t

8TD D U a F

~ 29.747.6 (Foct) - 0

oct F

3

( oct>opt = ~ -

9

kcal/mole

(10)

Many c y c l i c nitrosamines possess F v a l u e s both l e s s than, and greater than, -3.9 kcal/mole (see Table 1). Thus the com pound data base used to c o n s t r u c t eq. (9) samples a s i g n i f i c a n t range of F - s p a c e with r e s p e c t to TD50. o c t

o c t

Eq. (3) y i e l d s a ( A E ) t of o p

ΔΤΌ D U

8(ΔΕ)

= -6.6 (AE)

+ 2.46 o p t

(ΔΕ) = 0

= 2.69

kcal/mole

(11)

The ( A E ) p t = 2.69 kcal/mole i s a l s o l o c a t e d near the middle of (ΔΕ)-space f o r the range of (ΔΕ) values i n the compound data s e t . Thus the p a r a b o l i c TD50 dependence on (ΔΕ) i s a l s o judged significant. We d i d not s e t a s i d e some compounds to use as " t e s t s " of the QSAR s i n c e the s i z e of the data base i s s m a l l . However, there are 0


25.

PETIT E T

AL.

QSAR Molecular Structure Calculator

571

eleven compounds i n Table 1 which have TD50>100. These com pounds could not be used i n c o n s t r u c t i n g eq. ( 9 ) . However, we can use these compounds to q u a l i t a t i v e l y t e s t (at l e a s t i n terms of extending the range o f ) e q . ( 9 ) by p r e d i c t i n g T D 5 0 . The pre d i c t e d T D 5 0 of the eleven compounds have observed TD50 s>100 are l i s t e d i n Table 4. Only two compounds, 2-carboxy-nitros o p y r r o l i d i n e and 2,3,5,6 t e t r a m e t h y l d i n i t r o s o p i p e r a z i n e , are p r e d i c t e d to have TDso's considerably l e s s than 100. The 2carboxy compound, as w e l l as a l l the c a r b o x y l - c o n t a i n i n g com pounds, w i l l be p r e d i c t e d , from eq. ( 9 ) , to have higher TT^o's i f the charged form of the c a r b o x y l group i s assumed. The poor p r e d i c t i o n of TD50 f o r 2,3,5,6 t e t r a m e t h y l d i n i t r o s o p i p e r a z i n e might be due to the wrong s e l e c t i o n of the molecular c o n f i g u r a t i o n . I f , f o r example, the a l l - e q u a t o r i a l c o n f i g u r a t i o n were s e l e c t e d , ΔΕ i s estimated to be near 10 which would lead to a p r e d i c t e d TD50 of about 110. We r e i t e r a t e that we do not have knowledge of the e x p e r i mental c o n f i g u r a t i o n a l s t a t e s , or the extent of c a r b o x y l i o n i z a t i o n , of the c y c l i c nitrosoamines. The s e l f - c o n s i s t e n c y of the QSAR i s the only i n d i r e c t evidence f o r p r e d i c t i n g con f i g u r a t i o n a l , conformer, and i o n i z a t i o n s t a t e s of the molecules. L i n e a r r e g r e s s i o n a n a l y s i s has p i t f a l l s . There i s always the p o s s i b i l i t y of chance c o r r e l a t i o n s . Hence, we opted to analyze the data using an a l t e r n a t e s t a t i s t i c a l method, namely c l u s t e r a n a l y s i s . The data were s c a l e d so that each of the d e s c r i p t o r s ranged i n value between 0 and 1. Minimal tree spanning methods was employed i n the determination of c l u s t e r s (24). We d i d make use of some g u i d e l i n e s e s t a b l i s h e d i n the l i n e a r r e g r e s s i o n study: Only the four most s i g n i f i c a n t d e s c r i p t o r s ( oct> H20 ΔΕ, and Log P) were used i n the c l u s t e r a n a l y s i s . The r e s u l t s are shown i n F i g . 3. T h i s i s a n o n - l i n e a r map of the d e s c r i p t o r s i n t h e i r four-dimensional space p r o j e c t e d i n t o twodimensions. Nine d i f f e r e n t c l u s t e r s can be i d e n t i f i e d . However, one c l u s t e r plus one member of a nearby c l u s t e r (the enclosed area w i t h i n the map) contains a l l a c t i v e compounds except f o r the 3-hydroxy n i t r o s o - p i p e r i d i n e . That i s , h i g h l y c a r c i n o g e n i c com pounds c l u s t e r together while the "non-carcinogenic" cyclic nitrosamines are s c a t t e r e d about i n the four-dimensional d e s c r i p t o r space. The values of the four d e s c r i p t o r s were a l s o p a i r w i s e c o r r e l a t e d against one another. In a d d i t i o n , the s i n g l e v a r i a b l e (no t e s t i n g f o r the e f f e c t of combinations) p r e d i c t i n g a b i l i t y was measured by p u t t i n g the data i n t o c a t e g o r i e s , based upon t h e i r TD50 value being l e s s than, or greater than, 75. The F i s h e r ranking method was then a p p l i e d to the data base. The r e s u l t s are given i n Table 5. Table 5a i n d i c a t e s that H20 and Log Ρ are h i g h l y c o r r e l a t e d (.76) as w e l l as F and H20 (.88). I n t e r e s t i n g l y , however, F and Log Ρ are much l e s s c o r r e l a t e d (.35). Table 5b i n d i c a t e s that F i s the most


,

F

F

9

F

F

o c t

o c t

o c t


COMPUTER-ASSISTED

572

DRUG DESIGN

Table 4


P r e d i c t e d T D - Q f o r compounds possessing observed TD > 100 u s i n g eq. (9). Compound

P r e d i c t e d TD^^

Nitrosopiperidines 2,6 Dimethyl 2,2,6,6, Tetramethyl 4-t-Butyl 2-Carboxyl 4-Carboxyl -

105.9 99.6 257.2 85.7 98.9

Nitrosopyrrolidines 2,5 Dimethyl 2-Carboxy 2-Carboxy - 4-hydroxy

145.7 37.3 (120.2) 139.2

Nitrosopiperazines Nitrosopiperazine 4-Methyl 2,3,5,6 Tetramethyldinitrosopiperazine

85.0 100.0 35.2

b

D

a)

the c a r b o x y l group i s charged.

b)

the low T D , _ Q i s probably i n d i c a t i v e of s e l e c t i n g the wrong c o n f i g u r a t i o n ( s ) and/or conformer s t a t e s .


a


PETIT E T A L .

QSAR

Molecular

Structure

Calculator

573

90

101 101

101 101

101

Figure 3. 'Nonlinear map of the location (the numbers) of the cyclic nitrosamines in (ΔΕ, Log P, F o, F )-space as determined by cluster analysis. The numbers correspond to the experimental TD in weeks. H2

oct

50



574


Table 5 C o r r e l a t i o n Table of Log P, F H O > oct>

a)

Log Ρ Log Ρ F

F

9

H

F

Foct

H 2 0

a

n

d

Δ Ε β

ΔΕ

1

0

.76

1

.35

.88

1

.12

.24

.26

2 F oct ΔΕ

b)

S i n gle V a r i a b l e P r e d i c t i v e Capacity of Log > H20» oct> · p

Variable

F

1

v

F

F

F

a

n

d

Δ Ε

Unnormalized P r e d i c t i v e Weight 2.24 1.19

oct .07 ΔΕ Log Ρ

.009


25.

PETIT E T A L .

Q S A R Molecular

Structure

Calculator

575

F

important p r e d i c t i v e d e s c r i p t o r followed by H 0 . ^ P, i n d i v i d u a l l y , are of very l i t t l e p r e d i c t i v e v a l u e . This f i n d i n g , i n conjunction with eq. (9), suggests that F t i n eq. (9) i s the dominate p r e d i c t i v e d e s c r i p t o r and ΔΕ only becomes important i n those few cases where F s p r e d i c t i v e capacity fails. 2

o c

f

o c t


2.

QSAR-Using an A c t i o n Model

The set of equations (6-8) employing combinations of molecu l a r d e s c r i p t o r s from Table 1 and the d e s c r i p t o r s from Table 3 were used to d e s c r i b e the a c t i o n model. The optimum a c t i o n model achieved to date f o r the nitrosamines l i s t e d i n Table 6 i s ,

^ 1U

= A C F i P i + F P ) where, 2

(12)

2

50

100 i s an a r b i t r a r y s c a l i n g constant chosen equal to the maximum time d u r a t i o n of the experiments, and A = (8.34

2

expf*05(Log Ρ - 1 . 3 2 ) ] ) ( 1 + exp(-.26

1

ΔΕ))" .

The f r a c t i o n of each metabolite reaching the t a r g e t chosen to be uniform, e.g. Έ ± = (set) = F = (set) =«5. we have assumed a n o n - s e l e c t i v e o x i d i z i n g agent (P-450?) s e t t i n g equal weights to the two metabolic pathways (see P i and P are the switch v a r i a b l e products d e f i n e d as; 2

site is That i s , in F i g . 2).

2

P i -jÏ!

( 1 - V j l X j l ) and,

p

( " " j l j 2 ^ where, l a s t l y ,

x

l l X 2 1

x

31

X X

1

2

4 1

51

o r

x

12 or X

=

2 2

o r

x

v

x

C-C Φ i s formed, e l s e = 0. = 1 i f ( C ) - C - C ® , f o r n_>l, i s formed, e l s e =

1

i f

n

C

C

32 = 1 if c' ~ ^

i s formed

>

e l s e =

°·

or X 4 2 = 1 i f C - C - C ® - C i s formed, e l s e « o r

x

o r

X

52

=

1

i f

=

1

i f

X

0.

0.

> C - C ® (X=halogen) i s formed, e l s e =

0.

*61 62 C = C - C © i s formed, e l s e = 0. The assignment of the Xjj[ were made from an a n a l y s i s of the ΔΕ values given i n Table 3 f o r the model m e t a b o l i t e s . The r e s u l t i n g n o n l i n e a r r e g r e s s i o n f i t of the V j ^ are V - Q = 0.50, V i - .438, V = .484, V = 1.000, V = .021, V = -0.007. Figure 4 i s a p l o t of p r e d i c t e d T D 5 0 , using eq. (12), versus the observed T D 5 0 . The major o u t l y e r i s 4 - k e t o - n i t r o s o p i p e r i d i n e . It i s not p o s s i b l e to compute a c o r r e l a t i o n c o e f f i c i e n t f o r t h i s f i t t i n g procedure since n o n l i n e a r r e g r e s s i o n methods have been employed. 2

3 1

4 1

5 1

6 1



Table 6


Nitrosamines Used i n the Mechanism of A c t i o n Model QSAR. MOLECULE NITROSO-PIPERIDINE 2-METHYL 3-METHYL 4-METHYL 2,6-DIMETHYL 3,5-DIMETHYL 2,2,6,6-TETRAMETHYL 4-T.BUTYL 3-HYDROXY 4-HYDROXY 4-KETO 2-CARBOXY 4-CARBOXY 4-CHL0R0 3,4-DICHLORO 3,4-DIBROMO 1,2,3,6-TETRAHYDROPYRIDINE N-NITR0S0-3-PYRR0LINE N-NITROSO-HEXAMETHYLENEIMINE N-NITROSO-HEPTAMETHYLENEIMINE DIMETHYL-NITROSAMINE DIETHYL-NITROSAMINE BIS-(2-CHL0R0)BIS (2-CYANO) BIS (2-METHOXY) -

TD50 (WEEKS) 38.0 80.0 55.0 40.0 125.0 100.0 125.0 125.0 43.0 44.0 45.0 125.0 125.0 41.0 20.0 36.0 28.0 80.0 28.0 25.0 25.0 30.0 84.0 125.0 63.0


Ε Χ Ρ

·


25.

PETIT E T A L .

ÇSAR

Molecular

Structure

Calculator

577

Figure 4. Plot of experimental ΤΌ- (in weeks) vs. the calculated T D using the mechanism of action QSAR. TD > 100 are assigned a value of 125. >η

5 0

50


COMPUTER-ASSISTED DRUG

578

DESIGN

Discussion 1. QSAR Independent o f Mechanism: The a p p l i c a t i o n o f c l u s t e r a n a l y s i s i s an a t t r a c t i v e method to use because r e l a t i o n s h i p s can be formulated independent of the b i o l o g i c a l data. The c a r c i n o genic nitrosamines have been t r e a t e d i n such a manner. The molecular d e s c r i p t o r s F , H20, Log P, and ΔΕ were c l u s t e r analyzed. The b i o l o g i c a l data was subsequently assigned to the c l u s t e r e d p o i n t s i n the d e s c r i p t o r space. I t was then found that the potent c a r c i n o g e n i c nitrosamines c l u s t e r together, while the l e s s c a r c i n o g e n i c compounds are s c a t t e r e d over d e s c r i p t o r space (see F i g . 2 ) . These f i n d i n g s both complement and support the s i g n i f i c a n c e of eq. (9) which i s the optimuum l i n e a r r e g r e s s i o n equation found u s i n g the data of Table 1. oct dominant d e s c r i p t o r i n the a n a l y s i s , see Table 5b. I t i s n o t p o s s i b l e to g i v e a t r u l y r e l i a b l e b i o c h e m i c a l i n t e r p r e t a t i o n to t h i s f i n d i n g . How ever, one p o s s i b l e e x p l a n a t i o n i s that the carcinogenic- potency depends upon the bioaccumulation o f the nitrosamine i n a p a r t i c u l a r t i s s u e having a s p e c i f i c nonpolar s o l u b i l i t y . F t, the f r e e energy of i n t e r a c t i o n of a compound w i t h a 1-octanol s o l u t i o n , i s assumed to be a measure o f the nonpolar s o l u b i l i t y . oct(°Pt) = -3.9, represents the s o l v a t i o n f r e e energy o f the " t a r g e t " t i s s u e . T h i s conceptual model i n d i r e c t l y p o s t u l a t e s that t r a n s p o r t processes, as modelled through Log P, p l a y only a minor r o l e i n the mechanism o f a c t i o n . The second d e s c r i p t o r i n eqn. ( 9 ) , ΔΕ, i s found to be of minimal s i g n i f i c a n c e according to the s i n g l e v a r i a b l e ranking o f Table 5b. H20 i s ranked as the second most s i g n i f i c a n t s i n g l e v a r i a b l e i n a QSAR. However, the h i g h c o r r e l a t i o n between H20 and F , see Table 5a, e l i m i n a t e s t h i s v a r i a b l e i n m u l t i p l e v a r i a b l e l i n e a r r e g r e s s i o n equations i n v o l v i n g F t . It i s d i f f i c u l t to g i v e a physicochemical meaning to ΔΕ w i t h i n the framework of an a c t i o n mechanism. ΔΕ i s the e q u i l i b rium energy d i f f e r e n c e between the most s t a b l e "boat" and " c h a i r " conformer s t a t e s . However, suppose the production of the u l t i m a t e c a r c i n o g e n i c metabolite depends upon two p a r a l l e l metabolic r e a c t i o n s as depicted i n F i g . 5a. The c o n c e n t r a t i o n , C]_, o f one metabolite i n c r e a s e s with i n c r e a s i n g ΔΕ, while the c o n c e n t r a t i o n o f the second m e t a b o l i t e , C2, decreases with i n c r e a s i n g ΔΕ, F i g . 5b. The c o n c e n t r a t i o n , C3, o f the u l t i m a t e carcinogen i s dependent upon the produce C1C2. In t h i s case the u l t i m a t e dependence o f C3 upon ΔΕ can appear to be p a r a b o l i c over some range o f ΔΕ, see F i g . 5c. T h i s e x p l a n a t i o n i s not c o n s i s t e n t with the a c t i o n mechanism assumed i n our modelling. Nor i s there any experimental support f o r or a g a i n s t a p a i r of p a r a l l e l metabolic r e a c t i o n s . However, p a r a l l e l metabolic r e a c t i o n s can be used to account f o r the r o l e of ΔΕ i n eq. ( 9 ) . F


o c t

F

i

s

t

n

e

o c

F

F

F

o c t

o c

2. QSAR Using an A c t i o n Model: Eq. (12) i n d i c a t e s that Log Ρ i s o f only marginal s i g n i f i c a n c e i n s p e c i f y i n g a c t i v i t y . The


ÇSAR

Molecular

Structure

Calculator

579


PETIT E T A L .

(O

c

Figure 5. (A) Schematic of intermediate metabolite production leading to the production of the ultimate active metabolite; (B) Metabolite 1 concentration increases with increasing ΔΕ, opposite is true for Metabolite 2 concentration; (C) production (concentration) of the ultimate active metabolite exhibits parabolic dependence on ΔΕ.



580


optimum value f o r Log Ρ i s 1.32. This f i n d i n g i s consistent with the c l u s t e r and r e g r e s s i o n QSAR where Log Ρ was not found to be an important d e s c r i p t o r . O v e r a l l , t h i s suggests that transport processes may not be important i n the c a r c i n o g e n i c potency of these c y c l i c nitrosamines. ΔΕ appears i n eq, (12) as a minor d e s c r i p t o r whose i n c r e a s i n g value i n c r e a s e s c a r c i n o g e n i c i t y (TD50 decreases). We have not been able to e x p l a i n the r o l e of ΔΕ i n t h i s QSAR. However, ΔΕ i s even l e s s important i n eq. (12) than i n eq. ( 9 ) . The r o l e of the carbonium i o n metabolites o f the nitrosamines i n s p e c i f y i n g c a r c i n o g e n i c potency can be estimated from an a n a l y s i s of V j ^ . The f o l l o w i n g conclusions have been made; 1. V41 = 1.0 i m p l i e s that secondary carbonium ions are n o t carcinogenic. Z. Vu - V21 - V31 - .5 suggests that the nature o f the s i d e chain o f the carbonium i o n i s not important t o s p e c i f y i n g c a r c i n o g e n i c potency. Further, the common d e f a u l t option to each of these cases (Χχι = X 2 i = 3 i ^ ° , i = 1,2) corresponds to the formation of -CH^©. Thus -CH3® i s estimated to be twice as c a r c i n o g e n i c as each of the three a l t e r n a t e c l a s s e s . 3. V51 - 0 i m p l i e s t h a t halogen s u b s t i t u t i o n or formation of a double bond at an adjacent carbon to the carbonium i o n enhances c a r c i n o g e n i c potency to about the same l e v e l as -CH3 w c a r c i n o g e n i c potency. 4. Q u a l i t a t i v e l y , c a r c i n o g e n i c potency can be ranked as, x

> R-C

»

R_

c - C®— C -

1

3. Summary: The two QSAR s constructed i n t h i s c u r r e n t study of c a r c i n o g e n i c c y c l i c nitrosamines a r e complementary i n that they suggest how to c o n s t r u c t a b e t t e r QSAR. F , formulated i n terms of a bioaccumulation f u n c t i o n a l , along with the carbon ium i o n metabolite model should be coupled together t o form a r e v i s e d QSAR a c t i o n model. Work i s underway on t h i s model p r e s e n t l y i n our l a b o r a t o r y . o c t

Acknowledgements We g r a t e f u l l y acknowledge the f i n a n c i a l support of the N a t i o n a l Cancer I n s t i t u t e ( c o n t r a c t No. NOl-CP-76927), the N a t i o n a l Science Foundation (grant No. ENV 77-74061) and the N a t i o n a l I n s t i t u t e s o f Health ( c o n t r a c t No. 217041).


25.

PETIT ET AL.

QSAR Molecular Structure Calculator

581

References


1.

The data base was provided by W. Lijinsky, Chemical Carcino-Carcinogensis Program, Frederick Cancer Research Canter, Frederick, Md. 21701 (USA). 2. W. Lijinsky and H.W. Taylor, Cancer Lett., 1,359 (1976). 3. W. Lijinsky and H.W. Taylor, Cancer Res., 35, 1270 (1975). 4. W. Lijinsky and H.W. Taylor, Cancer Res., 36, 1988 (1976). 5. G.M. Singer, H.W. Taylor, and W. Lijinsky, Chem.-Biol. Interactions, 19, 133 (1977). 6. J.S. Wishnok, M.C. Archer, A.S. Edelman, and W.M. Rand, Chem. -Biol. Interactions, 20, 43 (1978). 7. See, E.J. Ariens, Drug Design, Academic Press, New York Vols. 1-6 (1971-1976). 8. A.J. Hopfinger, Conformational Properties of Macromolecules, Academic Press, New (1973). 9. L.B. Kier, Molecular Orbital Theory in Drug Research, Academic Press, New York (1971). 10. R. Rekker, The Hydrophobic Fragment Constant, (Elsevier, New York), (1977). 11. A. Leo, Table of Common Fragment Constants, Dept. Chemistry, Pomona College, Claremont, CA (1976). 12. J. Hine and P.D. Mookerjee, J . Org. Chem., 40, 292 (1975). 13. C. Hansch, A. Leo, S.H. Unger, K.H. Kim, D. Nikaitami, and E.J. Lien, J. Med. Chem., 16, 1207 (1973). 14. A.J. Hopfinger and R.D. Battershell, J. Med. Chem., 19, 569 (1976). 15. N.L. Allinger, J.T. Sprague and T. Kiljefors, J . Am. Chem. 96, 5100 (1974). 16. R. Potenzone, Jr., E. Cavicchi, H.J.R. Weintraub, and A.J. Hopfinger, Computers and Chem., 1, 187 (1977). 17. I.D. Blackburne, R.P. Duke, R.A.Y. Jones, A.R. Katritsky, and K.A.F. Record, J. Chem. Soc. Perkins II, 2, 332 (1972). 18. O. Gropen and P.N. Skancke, Acta, Chem. Scand., 25, 1241 (1971). 19. a. R.K. Harris and R.A. Spragg, J. Mol. Spect. 23, 158 (1967). b. Y.L. Chow and C.J. Colon, Canad. J. Chem., 46, 2827 (1968). c. R.K. Harris and R.A. Spragg, J. Mol. Spect., 30, 77 (1969). 20. W. Lijinsky and H.W. Taylor, Int. J. Cancer, 16, 318 (1975). 21. J.A. Pople and D.C. Beveridge, "Approximate Molecular Orbital Theory" (McGraw-Hill, New York) (1970). 22. a. R.C. Bingham, M.J.S. Dewar, and D.H. Lo, J. Am. Chem. Soc., 97, 1285 (1975). b. R.C. Bingham, M.J.S. Dewar, and D.H. Lo, J. Am. Chem. Soc., 97, 1302 (1975). 23. See, M.S. Tute, in Advances in Drug Research (N.J. Harper and A.B. Simmons, eds.) Academic Press, New York, Vol. 6, p. 1, (1971). 24. T.T. Young and T.W. Calvert, Classification, Estimation, and Pattern Recognition, Elsevier, New York (1974). RECEIVED

June 8, 1979.


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