An approach to modeling the mutagenicity of nitroarenes

0895.7177188 $3.00+0.00 Pergamon Pressplc

Math/ Cornput. Mode//&, Vol. II,pp. 837-842,1988 Printedin Great Britain

MODELLING

AN APPROACH

M. Randi!

TO MODELING

(d,e)

(a) Department

of

University,

Iowa Ames,

(b) Department

of

50311,

OF NITROARENES

and

Computer

and

Ames

(c),

D.H.

Science,

Rouvray

Drake

(d)

University,

Laboratory-DOE(*),

Iowa

State

Iowa 50011, U.S.A.

Computer

Science

and

4323 N 37th St., Omaha, Nebraska (c) Institut

II

(b), B. Jerman-Blajif

Mathematics

Moines,

DESIGN

THE MUTAGENICITY

(a), S.C. Grossman

and S. El-Basil

Des

DRUG

"Josef

Stefan",

Chemistry,

68111,

U.S.A.

53,

61000

POB

North

High

Lujbljana,

School,

Slovenia,

Yugoslavia. (d) Department

of

Chemistry,

University

of

Georgia,

Athens,

Georgia

30602, U.S.A. (e) Permanent Egypt,

Using

Abstract.

relationships

by

descriptors

are

best

reproduce

terms

of their

for

Pharmacy,

Kasr

El-Aini

methods

selection weighted

we

of

examine

numbers

Subsequently,

various

analyzed

to

which

the

experimentally

mutagenic

observed

potency.

of a statistical

Mutagenicity,

determine

molecular

ordering

Our findings

now

be

of

nitroarenes,

laws

quantum-mechanical the molecular complexity the

the

may

at some

"lower"

empirical testing

level

then,

currently

the

QSAR

character

be continued

been

accumulated

structural

of

tries

one

regardless

the are models

can

type

constitute

an

evaluate

SAR

"similar"

For

effects.

been

one with

molecular shall

ongoing

that

them

fully.

responsible

can

"distance" been

for

837

this

of

the

often

space.

information

system. by

as

for

as

Experience stating

elicit

that

"similar"

innnediately confronts

of quantifying For a

provisionally

criteria

represented

structure

systems

between

similarity.

view be

of

output,

assertion

the problem

of

doubt.

empirical

relationship

summarized

compounds This

such

corresponding

lack

within be

a

the

the

can

in

well-defined beyond

methodology

find

and

of

we

knowledge

the

to

occurs

implied

that

suggests

with

in

are made of inputs and outputs

input

important

Their

until sufficient

be

events

have

given

to what

neglected

"resolution". this

regularities

and

details

field.

to

Records

a

least

established

parallels

whether

descriptors.

philosophy

theory.

however,

which

in

to previous

at

be

underlying

schemes

at

the enormous

biomolecular

of

The

raised,

Such

viable.

approaches

and of

in

of

events

structures

molecular

might

systems,

interactions

describing

time

part

The

be

as

adopted

be

mode!s

still

a

may

electronic

viewed

has

biological

question

quantitative of

In view

level.

of

dictate

fragments descriptors

are compared

graph theory,

that

doubt

are

atomic

technique.

SAR

little

which

fragment

circumstances, can

Cairo,

Molecules

from

constructed.

INTRODUCTION

There

St.,

structure-activity

nitroarenes.

path

and

by means

KeywordS.

a

suitably

considered

results

of

graph-theoretical

(SAR)

represented

are

Faculty

address:

11562.

the notion the

technical resolved

structures

as points

moment, question by

that

using have

in an n-dimensional

THE BASIS OF THE GRAPH-THEORETICAL

APPROACH

Rosenkranz selected

Although

structures

and

one

cannot

of

structures

variations

represent

speak

in

continuous

their

and

observation

for

changes

to

be able

of

compounds.

the

properties

molecules

can

objects

properties,

many

structurally-related This

of

discrete

be

occur

upgraded

among

gradually.

to

the

level

of a

The

(1984)). here

testing

out

compounds

useful

basis

theoretical

models

that

the

This

is

the

most

activities

of

structures

differ even

some structural

of

a

to predict

magnitude,

group

provides

biological

because

by

relative

least

the

active

orders

several

though

activity

the

and

set claim

compounds

of show

similarity.

POSTULATE: A

molecular

molecular

structure

structures

similarity will

in

display

physical, (Randic

that

their

(1985),

of

overcome

a

studies.

scalar

How given one lies

is

one

property?

to

this

in

the

use

of

characterizing

the

descriptors.

Once

physical,

properties

property)

to

conceptual in attempts

one

of

can

finding

a

in

a

molecular be

mathematical and

done,

biological

considered

for

involves

no

thus

mathematical used

specific

to properties

transformed parameter as

a

OF

on

the

the

in

by

consists

of

calculated the

possible In

Fig.

certain in

1

known

present

molecular

of the nitroarenes

the

most

we

environment.

potent to

bacterial be

found

These mutagens,

genotoxic

(see

diagrams

for

display

to

the

select group

bioactivity), fragments consider

and

evaluate

the

compounds

The

in

(1984),

frequency

both

is

is

and then

responsible It

compound.

comparisons

of

active

probability

each

those

approach,

Rosenkranz the

substructure of

and

alternative and

based

selected

the

structures

An

fragments

make

we

among

molecular

evaulating

activity

Next,

fragments

Klopman

a

the

selected

then

different

that

are

between

compounds.

and

where

We

between

of

for mutagenic

extreme

different

similarity

described

for

CHARACTERIZATION

(those

standards.

molecular

sequences,

bioactivity.

similarity

that

STRUCTURE

that

the

occurrence

GRAPH-THEORETICAL

here.

molecules

latter

molecular

inactive OUTLINE

the

screen

various

fragments

study.

as

descriptors.

their

of

structure-property-

represent

compounds

then

into

molecular

first

of

parameters

and

structures

of the

studied

here in identifying

fragments

mathematical

feasible.

which

We

elements

(a mathematical

becomes

J

diagrams

systems

that may be responsible

standard

of the kind encountered

is

appropriately

descriptor

as

1 The molecular

We are interested

molecular

property,

task

a

parameters

a parameter

to relate The

be

activity

a

to

mathematical

can

I

scalars.

structure

activity.

difficulties

directly.

as

fragments

interest

E

H

nitroarene

chemical

of

structures

One is not relating

FIG.

studies

chemical

of

G

F

difficulty

of selected

3

to from

conceptual

this

r

B

general,

In structure-activity of

A

expressed

whereas

relate

out

with

in are

conceived

way

correlation

essential

particular,

be

their

arising

properties

in

in

properties

structure-activity

and

cannot

then

is

quantities,

structures

properties

(1986)).

dilemma

Molecular

of

considerable

biological

postulate

major

activities

as

display

Randid et al.,

this

aggregate

similarity

and

structure-property

and

an

mathematical

substantial

chemical,

Adoption

or

between

is the

two approaches.

as pollutants

are

among

and

the

are

also

Klopman

and

Both

methods

fragments i.e.

consider

and both

conclusions

various

are aposteriori are

drawn

from

molecular in nature, existing

Proc. 6th Int. Conf. on Mathematical

experimental two

results.

approaches

is

one

of

the

mutagenicity

of

I(2),

I(k)

As

The

path

numbers,

k.

The

weighting

than

diminish

the

Such

weights

for

of

a

specific

for

numbers

so-called

atomic

individual

the

by

atoms

to

atomic

of

standard

(the This

set). for

the

we

the

made

activity.

with most

potent

results

in

structures.

compare on

the

the

a

each

of the fragments

comparison a

selected in

partial the

In

derived

for

to

compound

phase,

with

observed

that

relative From

compound.

we can evaluate

the

ordering

second

ordering

experimentally

latter comparison

Our

respect

this

the relevance

considered.

the

in

@

2.438

the

path

the

of

sums

of

atoms

values)

characterize were

3.174

I

3.164

values

ID

the

3.166

(the

fragments atomic

constituting

2.438

molecule

a

to

3.l49M

numbers

individual

of

for

always

the

structure

fragmental

connectivity

used

set

is

a

graph-

compare

l/sqrt

used

in

and

the

assuming

mutagenicity

are

order

characterization

atoms,

characterized for

ID

structures

we

First,

considered.

been

We

methods.

pertinent

distinctive

two

combine

which

numbers

atoms,

now

theoretical

based

is

bond

Computed

environments.

path

are

We

of length

in

molecular

1975).

graph.

distant

the

already

individual

represent atomic

of

adopted

n

for

the

(Randid, the

all

more

and

have

definition index

m

suitably

paths

introduced of

neighbors

invariant

use

count

weighting

where

n),

.

nearest

where

,

graph

factors,

role

start

in the molecular

were

The

We

. ..I

shall

P(k),

the

with the sequence

I(k),

we

P(k),

one,

neighbors.

here.

the

which

reinvestigate

selected

invariants paths,

(m

. ...

a

weighted

less

we

a structure

I(3),

between

instructive,

nitroarenes

enumerates

I.

thus

reasons

by characterizing II(l),

A comparison

is

839

Modelling

3.167

molecular

3.559

3.561

3.136

3.137

fragments.

Some differentiation

kinds, is

such

both

as the

in

heteroatoms

always

unit,

heteroatoms compelling

reasons

between

- C,

C

the model bond

C

-

N,

other

and

C

-

the

the

are

bonds. to

type

used here in computing

l/sqrt

(m

the weighted

It

simplify

such differences.

the

Thus,

. n)

are

paths.

the It

Fig. 19 is

atomic

2

we

list

nonhydrogen

atoms

sums

of

descriptors.

are

Atoms

seen

in

observe

atomic

from atom to atom. environment

to

path

path

sums

for

structures the

to

the

most to

are

most

their

potent

individual

order

structure,

numbers

differ

of apparently

similar

to have similar

numerical

start

nitroarenes of

Fig.

and

3.

by

letters

is

assigned

to

next

according

Departures

between

FOR ACTIVE

leading

from

of potency our

results

is one and

found by Klopman to be responsible for

FRAGMENTS

substructure

for

to

mutgenicity

considering

This

the

on

findings.

search

our

by

B so

potency.

discrepancies

requirements

A

in our predictions

THE SEARCH

We

letter

structure,

relative

alphabetic

represented The

alphabet.

potent

all

1-nitropyrene. how

path sums for each of atoms of I-nitropyrene.

and the experimental

atomic

interesting

The of

indicate

METHOD

In

the 19 nonhydrogen

of no

explicitly

0

The atomic

FIG. 2.

same

groups

there

justifiable

by ignoring of

in

to differentiate

probably

weights

no

However,

considered

present,

3.105

nitrogen,

and

possible.

grouped

and

are

therefore

and

structures

are

structural

atoms of different

oxygen

carbon,

desirable

because

is

between

of

the the

in

fragment two

Rosenkranz

the F(I)

fragments (1984)

the mutagenicity

to

of the

Proc. 6th Int.

Cotzf: on Mathrmuticul

Modding

TABLE

A listing

1.

of the atomic the seven atoms

F(1)

F(2)

F(5)

F(3)

F(6)

2

Illustration

fragments

of the various

considered

molecular

nitroarenes.

In

fragment

atomic

the

Table

orders are

have

fragments of

the

the

that

the

In

similarity

Table

from

Table

of 7-dimensional A

and

Y

or

is

Euclidean Small

of

in

correspond similarity. large

values

example, matrix

the

2.4388

3.0695

3.4628

3.1264

3.1511

3.5737

2.4388

3.0694

3.4624

3.1265

3.1516

3.5751

C

2.4391

2.4391

3.07

3.4641

3.1277

3.1531

3.5781

D

2.4394

2.4394

3.0706

3.4659

3.1288

3.1544

3.5806

E

2.4393

2.4393

3.0704

3.4653

3.1289

3.1552

3.5829

F

2.4262

2.4262

3.0477

3.3973

3.0924

3.1233

3.5357 3.5698

G

2.4384

2.4384

3.0688

3.4607

3.1249

3.1492

H

2.4432

2.4432

3.0772

3.4857

3.1375

3.1598

3.5855

I

2.4446

2.4446

3.0795

3.4926

3.1417

3.1644

3.5942

J

2.4281

2.4281

3.0508

3.4068

3.0977

3.1286

3.5451

compounds

This

is

in

values

because

A

in

the

(fragment)

indicate

to

that

are

row

deduce

responsible

considerable

Observe, the

0.0015,

most

same

of

for

bottom

the

in

the

similarity

to

orderings

the

sequences

that

is

done

by

indicates

connecting

Each

(structures). a

both

branching

in

in on

B.

QSAR

by

(Randit

extracting In practice

identical of

the

AS the

two complete

rows.

crossing

is

based

on

from

order

partial satisfy

row

F(1)

in

work

1986), one can deduce

et al.

is

F(1)

to

approach

graph-theoretical

to

row

previous

in

Table

top

similarity second

of

letters

the

lines

partial

order

diagram.

bioactive B

TABLE

Part of the similarity

2.

for the molecular

fragment

S(X,Y)

matrix

F(1)

n

I

0

R

r

11015 .0052

DO15

0

D

E

F

G

H

I

J

.ooa7 .0107 .0920 .0051 .0310 .0434 .0766

.0040 .0076 .0095 .0924 .0063 .0306 0429 ,077O

similarity

one

of

the

As a consequence,

that

the

to

respectively.

and

structures

=

relative

this

at

ranking

in

outlined

B

relative

that

relative

and

adjacent

space,

indicate

first

the

the

ordered

A

the

relatively

may

the

by the

hand,

the

we

Y

similarity.

on

vectors.

the

S(X,Y)

the

illustrated

which

and

to

mutagens,

of

vector

to be found.

is

set,

activity

S(X,Y)

other

A

be

can

similarity

nitroarenes

a pair

S(A,B)

smallest

as

in S(X,Y),

potent

and

which

of

of

from

viewed

is measured

X

part

are

between

limited

that

show

the

structures

On

have

in

in

other

associated

to

we

vectors

the

molecules the

atoms 2

most

similarity

distance

corresponding

that

the

of

The

values

points

B,

any

considered.

active,

S(X,Y), 1

components =

as

vary by several

CH

matrix,

where

X

of

These

The atoms of the fragment

overlap.

entries

each

1.

reported

this

7

6

2.4388

2

for

for

Fig.

activities

of magnitude. so

list

sums

in

been

individual

selected

we

path

shown

nitroarenes

nitroarenes

1

5

2.4388

The

in this study.

4

3

B

based

but their

2

A

their

the

shown in Figure

F(4) 1

FIG. 3.

F(1)

for fragment

sums for each of

compound

"owes"

structural

for the activity

its

features of A.

x x i ~i I I I BGCDEHIiF

BACGGEHIJF

841

Proc. 6th Int. Conf. on Mathematical Modelling

resulting

The

graphically

partial

in Fig.

displays

the

structures,

and

for

that

the

the

in

do

so

visible the

meaningful also

Klopman

one

of

its

owes

features The

A

G

to

capture

important

different

the distinction

between

no

of show

In our

scheme

and

logic

testing

for the structural

perhaps

similarity

REMRKS

fragments By

in

A).

however,

that the fragment well We

the

ought

fragments,

or

emphasize

the

By

using

between

in

the

fragments search

may

activity.

be

and there are no structural

been

selected

the

minor

change when

in

approach

an

atom

applied

inactive.

seen

two

to

not

relevant of

be

the

sensitive

fragments

(the

in a fragment)

and,

structurally-related

clarify

from the restricted

do

for

outline

within

several

can

or

approach

search

is

or

to

it

fragments,

active

above

variations

of

fragments

our

the

insights

particular

recognition

From

our

search,

as

compounds

fragments.

to

the

the

automatically

fragments

why

the

approaches

indicated,

to

for

for

for biological

statistical

relevant

as

atomic intuition

chemical

efficiently

responsible

fragments

corresponding

selecting

can

contrast,

have

structural

in

in

one

fragments.

to

This

resolved.

a distinction

descriptors.

influence

serve

now

substances.

reflected

is

offered

is,

is

previously

to a larger fragment

CONCLUDING

other

larger

which

fragments,

among active

Inactive

G

structure points

being responsible

as active)

sufficiently

consider

to

"active"

features.

structural to

G

that the compound

of

F(1)

therefore

no

present

This suggests

not

compounds

"deactivating"

behavior

but

scheme

is twice

less apparent. does

respect

has

necessarily

anomalous

and

shows

The two compounds

Both

but

the

observation

observed

The

F

the

for

the

G the opposite

within

The discrepancy

perturbed.

see

F

activity

we conclude

(not

we

parallels

with

to A.

activity

relative

G,

(with

(which

the

the

compounds.

and

some

well

F

our model

the

reasons.

Rosenkranz.

while

section

discrepancy,

while

activity,

fragments, has

to

shows

fit

and

comparable

Within

G

not

left

similarity.

a

different

similarity

do

F

relative

F(l)),

case:

one

mutgenicity

showing

for

shown

between

right

similarity

the

the

is

the corresponding

the

fragment

is

Here

structures

structures

G,

F

the

of

relative

decrease two

4.

relationship

mutagenicities Except

order

ambiguities

arising

size of the fragments.

A and B. ACKNOWLEDGMENTS

TESTING

ADDITIONAL

FRAGMENTS This

In order

to understand

components and

its

are

we

different the

additional

carbon

the

same

F(4)

reproduces

more

structures of

G,

shows

the

for

which

A,

of

by

B and

has

F(Z)),

C.

The

it

to

of

this

the Fulbright

University

We

also

Research

project.

One

travel

Office

Ames

Department under

thank for

of

the

authors

assistance

in Cairo,

the

partial

from

Egypt.

REFERENCES

Grossman,

leading ordering slightly

S.C., B. Jerman-Blafi?,

Randid

(1986).

approach

Quantum

Harary,

F. Wesley,

Klopman,

A

to

relationships.

that

activity,

the

only

State

Naval

acknowledges

crossings.

relative is

of

(S.E.)

leads

time,

limited

similarity

Iowa

support

however,

though several

for the U.S.

W-7405-Eng-82.

Office

by the Office

Laboratory.

further

obtained

F(6),

first

by

in part

Ames

fragment

already

the

structures

there

of

is operated

Energy

U.S.

supported

produces

the

with

but

contract

an

was

Director

Laboratory of

of the compounds.

fragment

work the

several

including

fragment

of

related

When we enlarge

even

diagram

reduced

other

activity

examine

ordering

interesting,

structure also

family

Similarly,

the

now,

the

(fragment

smaller

The 13-atom

observe

structural

F(2) does not merit a

result.

to a comparison We

a to

in the ordering

because

from F(3).

for

F(1)

atom

the fragment

attention

which

fragments.

fragment

is no change

is

within

decided

molecular

7-atom

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