A rational approach to the optimal design of drugs

A RATIONAL

APPROACH

M. Randi@,

TO

THE

0. Jerman-Blazi&,

aDepartment

and Computer

Iowa State University,

P.O.B.

199, 61001 Ljubljana,

of Chemistry

and Computer

OF

DRUCS

Rouvrayd’

Science, Drake University,

- DOE,

bJozef Stefan Institute, CDepartment

DESIGN

S.C. Crossmanc, and D.H.

of Mathematics

and Ames Laboratory

OPTIMAL

Des Moines, Iowa 50311,

Ames, Iowa 50011, U.S.A. Slovenia, Yugoslavia.

Science, North

High School, 4323 North

37th Street,

Omaha, Nebraska 68111, U.S.A. dDepartment

of Chemistry,

University

of Georgia, Athens, Georgia 30602, U.S.A.

Recent advances in the rational

Abstract.

approach are briefly tive alternative Moreover,

reviewed.

to the empirical

researchers

We advocate here a novel yet simple After

by discussing molecules.

is indicated

similar

pharmacological

mathematical

behavior

in the development of new drugs.

formalism

the fundamental

how the essential

classification

prevailing

in this field are daunting in their great complexity.

comparison,

pharmacological

exhibit several differing

Keywords.

outlining

the characterization, It

displaying

of drug molecules based on a graph-theoretical

procedures currently

the problems confronting

avenue of research.

&sign

Graph theory has not been widely recognized to date as an effec-

which opens up a promising

premises

and quantification bioactive

of similarity

of 18 compounds, all of which are structurally

of major discoveries or as a result (Burger,

1983).

reason for this lacuna is a lack of knowledge

was recognized

of

drug

of

special

for

very

molecules

instance,

for

drugs.

Exactly

(1885),

the

the

the bioactivity

of

years

modern

It

medicinal

notable

exceptions)

to

bioactivity

studies

study.

investigating

group

difficult

problem

ledge.

Moreover,

pating

protein

existing

for

Ehrlich

chemistry,

Clearly,

small

He thereby

after

administration

such

difficulties

simplified

one involving

to one involving cular

level.

our current

the problem of drug interaction the

study

complexity

Ehrlich’s theories

work

of

cellular

complexity

at no more than the molelaid

the

of drug action,

foundation

observation from

for

drug metabolism,

theoretical

in one

small, large

an exceedingly

level of our know-

molecules

of the particiapproaches that

and until

our knowledge

steps which occur in an organism

of the drug becomes very detailed, are

likely

necessarily

a situation

into

unknown

our understanding

molecules,

of all the intermediate

more

problem

a relatively an

(with

much

itself

this represents

and enzyme

elucidated the role played by enzymes in living systems.

from

of with

given the current until

thus

resolves

interaction

By contrast,

molecules

fundamental

molecule

molecule.

small

and are

The

the

protein

as

therefore

characterized

(18681,

enzymes and an absence

of their active sites.

can be viewed

accessible

well

of curare-type

ago, Paul

drugs

few

of

presence

molecules.

ammonium

activity

a

however,

and Fraser

quaternary

one hundred

founder

in such

Brown

the blocking

most

erroneous procedures

on that

features

by Crum

that

was essential

serendipitously

was dependent upon the

structural out

early

of the relevant

of detailed descriptions

abounds in examples

In spite of this circumstance,

it

was pointed

totally

the

but which

techniques.

The principal

being made either

of following

similar

types of bioactivity.

Drug design; graph theory; optimization

of drug development

of compounds

We conclude by describing

of the structure history

it

among individual

component in molecules

may be identified.

INTRODUCTION

The

new

of our method, we exemplify

to

implies

remain that

with

we are

us. very

This far

where the use of any kind of rigorous

technique could be comtemplated.

and drug resistance. In coming to terms Unfortunately,

even today,

very

little

is known about

pragmatism

the mechanism of drug action or the underlying dynamics.

sacrificing 571

would

with

the present

seem to

our curiosity

point

state

in the

of affairs, direction

of

on how the whole process evolves

572

5th

and If

focusing

we

and

instead

adopt

Tauber,

of

an

19691,

and

the

of

over

however,

is

seem,

for

by

a

thus

appear

encompassing

which

have

the

accumu-

confronting

as

bleak

as

it

deal

of

evidence

apparently

the

statistical

good

similar

pharmacological

means

activity).

situation

-l-HE

reach.

may

us,

at

first which

compounds

exhibit

Currently,

of

the

the

structure

(1894) on

in

the

put

first

a

paper

action

of

i.e.

only

receptor

status

“Influence

of

drugs.

The

set

of

compounds

by

to

which

essential

more

reduces

and

normally

are

critical.

terms

of

the

role

probe

available

unknown ‘keys’

a ‘lock of

chemistry

the

will

can

with

be

the

of

of structural

of

drug

molecules,

the

Comparison

the

properties

is

structures

will

of

mathematical

example a

of

fair

parlance, a

reconstruction

number

of

the

optimal

input.

an

optimal

key

provide its

also

and biological

up

by

The

i.e.

a

structure

identified,

with

enhanced

without

some

out

the

small

the

usually

There

is

be

(Randit

an

or

more

of

astronomical

basis

expressed

lead

date

structures

ively

as drugs’

on

a

some which

can

not

to

This

cations,

has

mathematical

assumption

that

physical,

second of

the

such

chemical,

school

of

following

which

thought postulate

display

mattiematical

substantial

properties

simjlarity

detail:

(i)

The

be

soluble

terms.

picking

the

from

in

will

their

also

physical,

properties.

a

task those

even

than the lead can be recognized.

more

candieffect-

This

1983)

in

the

It

was

of

The

of

properties to

this

by

similar

for

studies.

approach years

has

(Kier

been

and Hall,

properties

reflect of view,

ions the

of of

structures chemical

mathematical

species

case,

natural

phenom-

Rouvray

be

used

(1973)

as

mathe-

molecules

feasibility amply

witness

(Bonchev,

by

candidate The

in

mathematical

indices

many

might

assess

chemical

be the

suggested indices

design

natural

merely

to

impli-

and

purely

topological

description first

of

in

wellknown

important

outline

properties

descriptors

drug

very

now

use of

topological

in recent (ii)

is

widespread

of

we

natural

type

becomes

number

characterized

ena.

in

a

which

be

matical

dozen from

few

of

various

that

number

(say)

has

each

of

starting

essential

postulate

may

modest

and

their

and biological

some

combinatorial

Thus,

function

the

terms

considerable

of

candidates.

of a

in

structures

molecules

possible

whereby

able

response,

method

even

the

chemical,

selecting

molecule

scheme

determine

lead compound,

active of

on

involved.

connectivity, be

would

substituents.

molecule,

to

structure

useful

the

of

in

Structures

similarity display

own

number with

sites

potential

devising

highly

number

associated

substitution

given

of

to

an

collecting

the

of

activity as

number

a

falling

1985a):

by

certainly

problem

biological

represents

a reliable

triggers

next

guidelines

possibilities

one

that the

its

about

once

enormous

of

would

information

In practice,

been

a

molecule

use

description

properties.

fundamental

may

employed

constructing

tries

of

Exclusive

structures

similar

of

similar

‘locks’.

above

one

inversion

display

of

the

similar

the

data

current

summed

problem:

responses, By

valuable

receptor.

the

having on

1969).

recognition

emphasis

the

this

(Stuper

a small

for

the of

structures

on

(Hansch,

value.

with

undertaken

drug

based

parameters

mathematicalproperties

in

can

candidate

compounds

therapeutic

here

parameters

being

between

is made the

now

of

dimension

recognition

analysis

set

all

parameters

considering

aim

similarity

POSTULATE: In

the

data

the

analysis.

lower

novel

pattern

entails

of

which

these of

regression

or

of of

methods

include

compounds,

size

schemes,

one

prediction

and

pharmacologic

the

to

design

large

statistical

indication

philosophy

at

analogy,

The

to

be

matching

being

view

fit

specific

key’

key.

are

a

better

degree

would

this

and

the

‘keys’

‘locks’

that

the

those

terms,

1979)

of

he

on

Representative

al.,

a

empirical

established,

the

thought

set

fragments with

informal

in

highly

in

of

Fischer

that

an

Once

be employed

of

problem

gives

rational

the

essentially

the

philosophies

the

considering

reducing

number

based

This

second

recognition

a drug,

precisely

playing

model

are i.e.

structural

up

medicinal

improved

host,

are

to

involves and

a

different

approaches

first

of

The

configuration

have

that

a

means

between

Emil

basic

enzymes

locations,

In

that

The

that

match

drug

of

stating

entitled enzymes.”

described

the

to

if

site.

be

with

was

Binding

molecule

can

drugs

receptor

possible drug

relationship

of

POSTULATE

fundamentally

various

of

school

activity

assumed

structurally.

the

the

molecules.

activities.

recognize

and

forward

sites,

to

two

underlie

et One

FUNDAMENTAL

(White

examine

might

to

drugs

The not

is

that

system then

rules,

routes on

perhaps

similar

the and

modelling

years.

there

indicates closely

our

approach

empirical

data

the

within

(pharmacological

reasonable

amount

lated

probe

mathematical

only

now

(drug)

schemes,

methods,

is

analysis

may

input

output

Approximate

vast

what

systems

we

appropriate

resultant

as

on

a typical

ICMM

of

this

demonstrated

1976); chemical

inherent concerned. species descriptors

species

are

mathematical According characterized will

be

OFTIHAL

possessed

of

biological to

saying

of

two

similar

which

the

are

will

isoteres,

broadly

(Langmuir,

1919;

Thornber,

formulation

places

that

the

In going cules

from

and

Although

refer

to

to

discrete that

very

Thus,

properties gaps

on making

and

their

initial

suitable

can

structures. selection

of

the

together slight

of

of

those

some

use

purpose defined

subject

of

of

the

test

two

of

Randit

of natural

need

set

we

the

cular

to

of

in

single,

this

isolated

drug-receptor the

pairs

alike

for

all

pair.

mathematical both

would

at

antipodal

reveal

and

were

that in

fact

the

display

only

shall

have

represent

by

Our

main

(iii)

and

within

displaying

1980;

the

also

of

a

set

differing

of

approach

et

For

1979a,

al.,

our

by

their

moleatoms

(Trinajstit

1983),

representation

weighted

path

however, the

structurally

will

of

numbers. be

essential related

pharmacological

thus

purposes

the

identifying

1981;

and

hydrogen

fashion

discuss

publi-

Wilkins,

compounds

first

many

1985),

nonessential

attention, of

al.,

given

significant The

in

and

here.

appropriately

means

compar-

two

the

Wilkins

et

customary

focus the

(RandiC

chemical

shall

much

addressed

elaborated

with

in the we

how

terms,

some

graph-theoretical

studies

further

represent

considered.

been

the

be neces-

to

mathematical

recognize

Jerman-Blazit

graphs

ents

around form

be

structures

criteria

this

not

to

will

(i)

prescribe

indicate (iii)

and Randie

1985a;

in to

it

viz

molecules

tasks

Wilkins

treatment,

(ii)

will

discussing

though

collection

will

SCHEMES

tasks,

interest

and

in

these

our

graphs;

that

suppressed

entail nature

mathematical

of

a

study

three

differ;

1979b;

specific

the

rest

from

a

comparison

with

structures

as chemical

structures

structures

the

from

GRAPH-THEORETICAL

accomplish

cations

that,

mathematical

of

not

to proceed

to

components of

significant

have

property

most

all

foregoing,

their

clustering

natural

matter

a

which of

of

were

OF

structures

range

range

and

structures

The

the

sary

ability

result

mathematical

terms

systems

of

because

consideration

drug-receptor sort

different

invalid

different.

i.e.

structures

of

would

the

in

con-

follows

the

structures

differences

descriptors. for

it

of

process

candidate

of

for

light

the

is

they

irrelevant

dramatically

arising

would

(since from

criticism

one

to structure-activity

&sired

realized the

characterization

our

will

selection any

be In

made

properties.

any

statement,

substituents,

properties

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continuous without

two

quite

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neighborhood

set

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display

under

rather

OUTLINE

changes;

above a

it

natural

less

no abrupt

the

by

of

or

but

apart

to

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not

criticism

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various accurate

molecules

their

can be generated

and with

Based

of

in

yet

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that

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the

reference

appropriate

more

of

in the

mole-

all

property

is

A

been

mathematical in

activities.

valid

the

has

postulated

be strictly

changes set

an

a

is in the

molecules,

changes

provided

chosen,

i.e.

the

minor

among it

never

be

concerned;

structure

when

small

within

only

can

objects,

relations

is

it

structure A

the

same

situation

pair.

approach

biological

the

may

drug-enzyme

of

reflections)

and

on

structures

properties

a continuum

a

assessing

continuum

biological

Such

a

the

the

bioactivity

573

identical

mirror

interest

similar,

a rough

to

in

closely

exist

species.

tention

to

have

brological

structures

by

as type

molecules

properties

of the

structure are

there

chemical,

of of

natural

features

which

that

focus

such

properties

1979).

predicted

and

mathematical (iii1

the

similar

properties

indicates

i.e.

DRUGS

are

structures

physicochemical

exhibit

compared

the

OF

our

descriptors

similar,

as

and

is equivalent

mathematical

related

which

chemical,

statement

closely

behave

have

mathematical

(iv)

This

if

that,

structures

concerned

and

physical,

properties.

DESIGA

on

task

componcompounds

activities.

the

presen-

tation.

Although in

our

postulate

specifying

how

around

some

reveal

how

natural the

manifested of

the

this

it

in set

of it

should

or

necessarily

property

of

is

apply

to

regarded

as

forming

contexts,

the

postulate

interest,

of

it

various

the

physics. postulate

individual

the

refer

to

be

properties

of

In

In

quantum Moreover, does

compounds

continuum.

not

will

investigated. axioms

that

a

does

natural

classical

can

paradigm be clustered

characteristics

unlike

mentioned

effective may

compounds

quite

laws

an

of

the

chemical

the be

as

structures

mathematical terms

respect,

theory

serves

chemical

which

not

appropriate

composite

FIG.

1.

Graph

of the

molecule

of phenylethylamine.

are

systems

Let

us

first

1 and assign

consider an arbitrary

the

compound

numbering

shown

to the

atoms

in

Figure therein.

5th

574

Drug

Q-cH+~I-HH~

ram Phartnacebgical

Therapeutic

Name

Classification

Applicaiien

Amphetamine __

CNS Stimulant

Antidepressant Anorexiant

CH,

Narcolepsy Minimal Brain Dysfunction

Phenylpropanoamine OH

3.

CH,

Q-w+;--NH--CH,

Methamphetamine

(1-Agonist

Decongestant

CNS Stimulant

Anorexiant

Anorexiant

CNS Stimulant

Antidepressant

CHs

Narcolepsy Minimal Brain Dysfunction

Phentermine

CNS Stimulant

Anorexiant

Hydroxyamphetamine

a -Agonist

Antihypotensive

Levarterenol

cx-Agonist

CH,

CY-CH,-NH,

6. HO

7.

CH- CH-NH, Ck

8.

Antihypctensive Vasoconstrictor

OH

Metaraminol

D -Agonist

Antihypotensive

Methamphetamine

CNS Stimulant

Anorexiant

dH,

T-cHrNH-cH’

Minimal Brain

OH

Dysfunction Antidepressant Narcolepsy

PIG. 2. Set of graphs of m~kcule~ closely related to the phenylethylami~

ml-le.

.

575

OPTIIUL DESIGIVOF DRUGS

Ephedrine

CH-CH-NH-CH, L

a-Agonist

Antihypotensivt

CNS Stimulant

Decongestant

C’H 3

Bronchodi later Antiarrhythmic

Mephentermine

CNS Stimulant

Antihypotensive

a-Agonist CH,

11.

Epinephrine

CH-CHi_NH-CH,

1

OH

HO

a-Agonist

Antihypotensive

B-Agonist

Bronchodilator Decongestant Antiarrhythmic

12.

Methoxyphenamine

B-Agonist

Bronchodilator

Ethylnorepinephrine

B-Agonist

Bronchodi later

Levodopa

CNS Agent

Antiparkinsonian

Methyldopa

CNS Agent

Antihypertensive

Methoxamine

(1-Agonist

Antiarrhythmic

HO

otl

Lo

14.

CH,--H-NH, HO

OH c=o

15.

HO

16.

Antihypotensive

17.

/ CH, H

0

O-PHO

18.

C;-CH,-NH-CH OH

lsoproterenol

6 -Agonist

\H,

Antiarrhythmic Bronchodi lator

Diethylpropion

FIG. 2. Set of graphs of molecules closely related

CNS Stimulant

to the phenylethylamine

Anorexiant

molecule. (continued)

576

5th

This

particular

the

compounds

molecular

compound

graphs

we

between

aromatic

do

distinguish

they

Our

interest 2,

Figure

from

context,

using

the

a

phenyl

ring

by

differentiation

be

of

no

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OF

PATHS:

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bond

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Figure

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more

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out

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once

1 thus

be

length

were

no

counts

1 ----_

of

bonds, for

for

the

atoms

(except

Figure

atoms counts

carrying

yet,

of

counts

having

atoms,

paths

paths

program

in

on

molecule cent

ALLPATH

impractical

whole. data

the

These

2

conven-

consecutive the

-____

containing By

atoms,

of

1

lengths.

k.

bonds,

of

1.

few

length

present

each

above

different

a fragment

of

row 6

the

the

a

particularly

last

12

for

of

of

pairs

1 we

For

and

becomes

The

of

use of

19791.

al.,

single

number

Figure

illustrated

represent

the

in

paths

a chain

number

length

at by making

of

zero

Table

depicted

compounds

represent

i.e.

length

count

on.

pound

k will

of

count

the

counts

bonds,

paths

two

of

from

7

I

remembered

1

length)

have

_____

atom.

The

end

9 bonds,

IO adja-

consecutive

bonds,

0 1 -----

and so on.

9 1

The

advantage

molecular

on

is that

the

is

mediate

local

on

isomeric

and Wilkins,

thus

such

that

in

variations

1980;

appear

two

the

small

10

9

counts,

a

compounds From

fact due

studies properties

role.

paths

it

has those

It

would of

the

in

NUMBER

order

abundant

greater

1977,

and

prominence.

a

effective

this

that

paths

counteracted,

on

Randic

weighting

TOTAL

75

inter-

especially

a crucial

9

Howof

1982).

paths,

introduce

atomic

paths

1979d;

----__---_

to

information

structure.

obscured.

Trinajstit

play to

opposed

physicochemical

shorter

three,

path

1979c,

Randicand

and

of

among

being

that

the

the

Wilkins,

desirable

some

similarities

in

(RandiCand

or

retain

number

in

as

bonds

within the

dominate

established

lengths

as

connectivity

result

numbers,

numbers

characteristics

of species

of

path

path

evident

length may

to

been

the

nonlocal it

which

using

fragments,

groups,

ever,

of

the

of

dominant

the

role

of

As of

for

purposes

Randie approach

1984a; here.

Randit

the

bond

shorter

types (Menon

1985a),

of

the

length

weighting

differentiation such

role

intermediate

of has

more

can paths

paths been

be given based found

and

Cammarata,

we

shall

adopt

OF'TIHALDESIGN OF DRUGS

To

carry

being

out

of

of

edges

of

the

in

(m

same

x

n)-f

procedure

many

provided

the

to

for

the

198513).

a modified

the

ALLPATH

weighting the

the

the

species,

though in

connectivity

index.

The

In

addition

to

counting

compound and

counts

output

different

atom

the

total

Thus,

for

2 it

of

atom

is only

environments;

the

to three

the

to

they

may

3.011

to

It appears

that

(ID)

be

with

the

these

in

each

0.025

0.574

as

a

been and

whole.

The

termed

the

has been

1984a)

total

not

of

for

1979c;

and

Wilkins,

1980;

of

the

relevant

is

restricted

as

line

of

in the

0.071

17.7005,

has

(identification

to be a highly

discriminating

(Randit

et al.,

index.

(Szymanski

on

the

OF

DIFFERENT

the

a set

molecule

of

similar such or

graph data

as a

set

numbers,

on a variety above

of

1985)

as

the

connectivity in

index

(Rand&

1975).

As

number

as

‘atomic’

information To

from

those

theory,

not it

may

of

basis

single

be

come

well as

even

yield

versed

something

comprised

sums,

where

the

summation

atoms

only,

as

illustrated

drugs

(Randi

antitumor

molecular

the

ID numbers

cases

for

of

purpose

made

the

several

only

individual

therapeutically antipsychotics,

and

good

structural

the

be

anticholinergics,

analgesics,

antiparkinsonians,

classifications

parameter

discuss among species

the

use

of

sum

of

of

atom

based

have

i.e. not

the

been

solely

obtained

the

finer

be

the

molecules

contain the

we

shall

compounds

compounds

will

of

of be

the

differ-

are

in

relatively

lo-15

atoms

hydrogen select

Figure

based

atoms

to

‘size’

pronoucned

than

suppressed

section, the

especially

more

3.00

such

illustrated

concerned

no

to

that structural

may

size-

considered

2.25

likely

effect

all

characteristics structures

of

are

have

compounds

following

the

quite

some

numbers

we

the

they

all

ID

among

counting

in

2,

around

seems

obscure

because

Table

compounds

contributes It

The

2.

In

the

number. may

present

such

from

For

existing

here

each,

to

evident

each ID

‘atomic’

a

2.

atoms. fragment

Comparison

solely

common

upon

the

all

the

to

considered.

CLUSTERING

useful

OF

THE

RELATED

THERAPEUTICALLY SPECIES

structures.

chemical a

Alterna-

sets

among

In

(RandiC Randit

1982). by

existing

be

will

small,

partial

between in

path

type

dopamines,

1979d;

represented

selected

defined position

aminotetralins

Wilkins, Trinajstil

be

be

the

similarities

As

lengths,

extremely

of

and

a vector

general

to

in

each

different

the

This

applied

can

1984133.

comparison

isomeric

a

are

used

of

can

together

(Randit,

index,

of

comparisons

especially

the

variations

e.g.

can

all

and

evident,

the

for

between

space.

Randitand

be

between

compounds

single

Figure

A sequence,

introduced

descriptor,

can

similarity

been

surprisingly

this

ences

in comparing

of

for

The

antihistamines,

dependent.

2 provides

topological

originally

numbers, the

list

the

to

structural

components

distance

optimal

of

values.

valuable

the

different

the

molecules

will a

used

structures.

properties

a

selected

a

alkane

physicochemical

single

as

a broader

(say)

be

paths

such

offers than

branching

the

of

1, Table

may

of other

list

numbers,

clearly

structures

that

amply of

number),

STRUCTURES

in Figure

invarrants

the

of

the

illustrated

the

origin,

numbers

existing

Randicand

of the

basis

effects For

as the

may

for

Use

clustering

here, COMPARISON

in

2

path

similarity

atomic

search

1985a).

on

molecule

ID

unique

hoc

important

Table

viewed

to

of

in

barbiturates,

Wilkins,

atomic

truncated

the

paths,

been

which

ad and

The

already

benzomorphans,

‘atomic’

0.276

counts

number

molecular

shown

though

path

be

n-dimensional

and

however, (weighted)

has

of

chemical

applications

ways.

antidepressants,

the

much with

numbers,

to

Euclidean

has

structures

0.007

represents

Such

established. the

analysis

ID 1.098

2.215

then

tively,

to

last

of

vectors

atom

referred

numbers

be

of

places:

4.431

9

observation manifold

presented

may

in terms

atom.

for

The

numbers.

here

that

between

therefore

so

associated

well-defined

degree

vectors

of

for

the

in

numbers

gives

whereas

differentiate

reproduced

decimal

the

also

pertaining

is

so on.

able

i.e.

output

paths

total

identification

output,

numbers,

the

this and

are

atomic

all

1

2.989,

numbers

path length,

capture

the

appear

different

of

program.

the

of

to

this

upon

information

several

of

paths

may based

able

information

invariants.

depicted

printed

is

corroborated

program

the

compound

number structural

1980)

Alternatively,

in

single

essential

in fact

widely

al.,

listed

a

uninitiated

connectivity

existing

2 are

represent

a

following

with

the

Table

cm,&,

This

et

to

of

results

bond,

weightings In

paths

The

each

as input.

added

vertices

types

the

as

numbers

terminal

(Randi&

entered

be

weighted 1.

to

the

bond

conjunction

introduce

(Randit

Figure

in

are

may

the

all

classified

are

1975).

used

weights

is

n

in computing

program

automatically

process

of

For

(Rand& be

ALLPATH

subroutine

each

adopted

bond

and

is assigned

molecules

available

a

from

m

question.

procedure

of

each

where

emanating

of

indices

weighting,

type,

bond

weight the

the

(m,n)

577

surprise

graph

The

compounds

that

are

therapeutically

represented very

in

Figure

efficacious,

2,

all

form

of

which

a

subset

5th

57%

_- - __

Icm

.-

1

.908248291

.S83333333

.291666667

.0463488515

.0104166667

5.20833334E-03

3.68284782E-03

.163092232

3.01199722

2 1

1

.454124145

.291666667

.0919627826

.0104166667

7.36569564E-03

0

.I3436437

2.98990033

3

-0833333334

1

.5

.204124145

.0294627826

0

0

.166666667

2.98358693 ---__ 4

.0919627826

1

.454124145

.291666667

.0104166667

7.36569564E-03

0

.13436437

2.98990033 __--5

.0463488515

.908248291

.583333333

.291666667

.0104166667

5.20833334E-03

3.68284782E-03

.163092232

3.01199722 -____ 6 1

1.22474487

.612372436

.348461713

.0510310363

0

0

0

.102062073

3.33867213 _---7 1

.908248291

.686886724

.166666667

.0416666667

.0208333333

0

0

1.20710678

.204124145

. 1666666667

.02083333333

.0104166667

0

1

.707106781

.353553391

.144337567

.0589255651

.0294627826

.0147313913

7.36569564E-03

9

4.43185165

2.21592583

1.09846171

.276623268

.0711294493

.025148058

7.36569564E-03

.0833333334

2.90763502 _---_ 8

.0416666667

.0833333334

2.73414759 ___-_ 9 .11785113

2.43333431 ___-___--_

TOTAL

NUMBER

OF

PATHS:

17.7005855

.57407987

OPTIML DESIGN OF

TABLE

3.

Atom

for

the

nine

atoms

common

to all

18 structures

of Fig. 2.

positions:

1

Drug

atomic ID number

The

579

DRUGS

2

3

4

5

6

7

8

9

1

3.016

2.992

2.985

2.992

3.016

3.349

2.933

2.993

2.394

2

3.015

2.992

2.985

2.992

3.015

3.347

3.156

2.967

2.379

3

3.025

2.997

2.989

2.997

3.025

3.369

2.982

3.112

2.693

4

3.017

2.993

2.9986

2.993

3.017

3.351

2.937

3.226

2.363

5

3.016

2.980

3.198

2.980

3.016

3.357

2.936

2.994

2.395

6

3.001

3.192

3.185

2.977

3.013

3.349

3.138

2.703

2.411

7

3.004

3.203

2.971

2.990

3.018

3.352

3.158

2.967

2.380

8

3.010

3.206

2.973

2.993

3.024

3.365

3.196

2.849

2.705

9

3.201

2.995

2.988

2.995

3.021

3.360

3.196

3.086

2.682

10

3.023

2.996

2.989

2.996

3.023

3.366

2.974

3.329

2.670 2.705

11

3.009

3.196

3.188

2.981

3.022

3.369

3.197

2.850

I2

3.350

3.028

3.013

3.019

3.049

3.408

2.998

3.119

2.696

13

3.009

3.196

3.188

2.981

3.022

3.370

3.199

3.088

2.449

14

3.009

3.196

3.188

2.981

3.021

3.369

2.962

3.054

2.430

15

3.008

3.196

3.188

2.981

3.021

3.368

2.960

3.279

2.389

16

3.362

3.045

3.040

3.341

3.074

3.410

3.177

2.974

2.383

17

3.014

3.198

3.190

2.984

3.027

3.381

3.233

2.936

2.877

18

2.983

2.973

2.970

2.973

2.983

3.272

3.138

3.083

3.155

of

a

and

collection

of

Cammarata

niques.

From

their

we

have

selected

no

cycles

other

18 compounds a single and

as

substituents,

All

of

the

selected

apart

have

a

pattern of

than

atoms

structurally:

investigated

using

collection

atoms.

all

compounds

(1977)

almost

no

40

group,

are a

three

fragmentID

tech-

mentioned

compounds,

no

quarternary

having

atom

Menon

molecules contain

whose phenyl

compounds

from

nitrogen

by

recognition

phenyl

fragment

leads

to

chlorine

produces

nitrogen

of

closely

bonds

the

the

ring,

they

IDS

the no

indicates

that

the

‘size’

effect

has

now

been

eliminated.

Use

to

order

the

compounds,

however,

disappointing significant

result

that

pharmacological

such

of

ordering

classification

compounds.

related

removed

numbers above

Q----

(al

from

N I

this

ring.

and

position

namely and

They

do differ, of

the

the

hydroxyl

occasionally characterization

with

only

nine

the

atoms

of

common

these

to

all

Figure

2 reveals

that

in

Figure

1

largest

the

number, they

methyl

group.

path

of

is

the

carbonyl

atomic

in the

substituents

group,

the

path

however,

various

or

of the

ethyl

In Table

compounds

numbers the

groups,

is

fragment

(b)

presented, for

compounds. we

c

3 a partial

appearing

structure

type,

contain,

the

N

Inspection have

depicted

common

to

all

the

18 compounds.

The

partial

nine

common

atoms six

sums

have

now

atoms

(for

later).

The

three

atoms

nitrogen); given

refer

to

the are

been

as

totals

the

the for case.

fragment

in

the

nine

groups:

the

are

become

(including

are

for

Analysis

fragments

thought

to be

essential for

(13 mutagenic nitroar-.

the the

fragment totals

The

the activity of (a) the morphins, 8) -oleptics.

apparent

4

numbers.

FIG. 3.

considered

Table

latter

the

The

chain

nine-atom

These

for

4.

two

ring will

side

ID

numbers Table

into

phenyl

entries

forming

each

in

which

remaining

in

path

the

reasons

the

atomic reported

partitioned

constituting

separately

also

of

atoms

are

we

shall of

the

The a an

nine-atom number essential

of

fraament other

is

grouoinas

pharmacophoric

comoarable identified role

in as

in

size

with

performing

various

drug

5th

580

ICnn

TABLE 4. Partial sums of atomic path numbers

_

for the ring and other atoms in the fragment kee Fig. 1). Drug

Ring ID

Side

Frag-

Chain

ment

ID

ID

Amphetamine

18.353

8.321

26.675

Pheny I propano Iamine

18.347

8.503

26.850

Metamphetamine

18.404

a.788

27.193

Phentermine

la.357

8.527

26.880

Hydroxyamphetamine

18.548

8.326

26.875

la.719

a.253

26.973

Metaraminol

18.541‘

8.506

27.047

Pheny lephrine

la.573

a.751

27.324

I

Levartereno

Ephedrine

18.382

8.965

27.347

10 Mephentermine

18.396

8.975

27.371

11 Epinephrine

la.767

8.753

27.521

12 Methoxyphenamine

18.870

8.814

27.685

13 Ethy lnorepinephrine

18.768

8.736

27.505

14 Levodopa

18.766

8.446

27.213

15 Methyidopa

18.764

8.629

27.393

16 Metoxamine

19.274

8.535

27.809

I

18.769

9.047

27.843

18 Diethylpropion

la.155

9.376

27.532

17 lsoprotereno

molecules.

For

fragment

(Lednicer

structure 1964),

the

The

three

our

case,

for

size

(Janssen, mutagenic

are

active,

What

at this point

_

.-Agonist

(II)

_

a-Agonist

(6)

= -

u-Agonist a-Agonist a-Agonist

(8) (5) (7)

B-Agonist (11) B-Agonist (13)

are

CNS CNS CNS CNS CNS CNS

ia.

all

=

a-Agonist

(9)

-

a-Agonist

(2)

in Figure

we consider

In Figure ring

3.

sums

for

in the there

the

six

i.e.

is a finer

is presented

interest.

is now a very evident

of the ring ID), and similar and the CNS agents. in the central within to

it

this

there

to

the

path

latter

ring

of all the central

for the 8-agonists

group,which

clusters

region of Figure 4, has too few compounds give

particular

is a wide

any

great

finding. scatter

for

statistical Moreover, the

significance by

a-agonists

contrast, over

the

whole range of ring ID values.

These observations, have

escaped

inspection

which are highly interesting,

attention

altogether

of the structures

if

18 compounds considered based on their ring ID numbers.

surprisingly,

(which have lower values

clusterings

The

phenly

Rather

clustering

nervous system (CNS) simulants

(18)

FIG. 4. Classification of the bicactivity of the

based only upon

constitutmg

of

CNS stimulant

18.

differentiation

the values of the atomic

atoms

18 compounds

(3) (IO) (9) (4) (I) (2)

In

though its action is nonspecific.

4 a histogram ID values,

stimulant stimulant stimulant stimulant stimulant stimulant

is clearly

among the 18 compounds under consideration.

the

CNS agent (15) CNS agent (14)

to be specific.

illustrated group

pharmacologically is required

1984)

B-Agonist (17)

rule’

action

is claimed

(12)

18.

1977), the fundamental

Rosenkranz,

6-Agonist

18.

in the

and

nine-atom

‘morphine

_

fragment

and each

fragments the

empirical

(16)

19.

neuroleptic

significant

(Klopman

a similar

the

and Mitscher,

proposed

and

nitroarenes of

instance,

a-Agonist

19.

only

had been made.

a

of all

the CNS

values

lying

a small

interval

ring

values

ID

within

18.35

compared (from

-

this

narrow

ponent logic

range

essential

This

activity.

to

unsubstituted

of

the

molecular

such

visual

case of the uent

rings

are

hydroxyl

that

18.00

E-agonists,

to

a specific

rings,

diagrams essential

ID

represents

for

19.25)

for

the

that rings lying within

particular

interval

phenyl

which

to the full range of possible

around

contain

for

the range of ring

18.40,

compounds under study, indicates

might

Clustering

stimulants

between

structural

relates,

of

and

careful

might CNS

cum-

type of pharmaco-

have

course,

revealed

stimulants.

only

inspection that In the

a phenyl ring with two substit-

groups appears

to be essential,

and the

DESIGPTOF

OPTIMAL

same

seems

certainly the

to

be

scatter

whole

of

range

(by

occur

the

CNS

as

that

is without

ID

must

for

ACKNOWLEDGMENTS

can

over

Ames

the

phenyl

in

ring

significance.

CONCLUDING

-

of

contract

activity

the

Laboratory

Department

as a negative

a-agonistic-type of

581

although

values

be seen

groups)

special

These

results,

ring

values

hydroxyl

agents.

positive

a-agonist

possible

finding

substitution may

in

the

of

The

result.

apply

interpreted

DRUGS

DOE

Energy

by

is

operated

for

Iowa

State

University

W-7405-ENC-82

part

by

and

the

U.S.

U.S.

Office

thanks

the

support

of this

Office

M.R.

of

of

was

the

Naval

the

U.S. under

supported

Director.

D.H.R.

Research

for

partial

project.

REMARKS REFERENCES

In

this

presentation

only

graph-theoretical activity

approach

relationships

identifying group

a

of

on

one

in discriminating

that

only

fragments

action,

but

not

logical be further

a

negative of

a

is

of

given

result,

to obtain

the

thing

it

suggests

to

may

be

used

for

that

other

in

that

any

the

that

A.

Crum

design

Ehrlich,

least

expensive which

is

die

compounds

listed

to

indicate

to

the

the

both

design

stimulants,

for

attempt

bility.

The

actual

depend

very

heavily

recommended most

that

S.C.,

A

dosage,

of

to

has

is much

the

1977; gained

better

known

characterization structures

that

are

str!;ctural

details,

for

drugs

dptimal

general to

will,

which least

the

approach previously

which

similar

certainly

of

Jerman-Blazit,

in

des

Configuration

auf

Chem.

2,

Ber.

VCH

Press,

not

Jerman-Blazit,

significant search

M.

Kloprmn,

3,

and

Seydel

M.

of

to

J.J.

and

psychotropic

Quant.

and

requirements

J.

Biol.

Symp.

Quant.

Biol.

Zerovnik

(Ed.),

of

(1985). derivation

QSAR

Bioactive

Germany,

RandiC

drug and

and

pp.

39-49.

(1983). for

Modelling

computer-assisted

structure-activity Simulation,

Strat-

Compounds,

relations.

AMSE

Press,

Tassin,

161-174.

L.H.

New

mental

Kaufman,

computer-aided

Design

Hall

Chemistry

C.

Quant.

approach

Chem.,

and

in

structures of

France,

Press,

by

Chem.,

Weinheim,

In Modelling

L.B.

J.

relationships.

Quant.

J.K.

B. and

studies

in

Int.

structure

Randie

the

molecular

Kier,

The

J.

(1985).

quantitative

?32-239.

Quant.

In

least

It

RandiC to

In press.

quoted

approach

in

and

2,

As

Int.

B.,

QSAR.

several

M.

quantitative

Res.,

J.

egies

1985a),

the

SOC.

259-26.

of

together

be eliminated.

1,

in

the

Symp.,

(1974).

Int.

new

molecular

and

A

(1964).

A

overall

uncertainties

Roy

Studie.

structure-activity

259-287.

are

insights.

more

der

approach

Biol.

Chem.

appear

clustering

in their

the and

Sauerstoff-Bedurfniss

Enzyme.

(1969).

drugs. 1,

Symp.

is

Trans.

relationship.

Kerman

course,

(Menon

the By

in

Randie,

additional

part

crucial.

it

pursued

1983;

E.

ring,

differ

II.

B. Jerman-Blazit

C.

P.A.

mathematical

should

and

Einfluss

Quant.

Accts.

be

standards

differ say

h,

Janssen,

possi-

of

Although

some can

phenyl

On

constitution

farbenanalytische

der

biochemical

CNS

allowed

fragments

important

most

would

molecule. the

is most

it

particular

Trinajstit,

now

that

an

Hansc

approaches of

(1868).

693-739.

graph-theoretical

serve

case

the be

as

can

the

adopted

reported

studies

Cammarata,

would

is

lead

adopt

In

substitute

in

regarded

unfruitful

Compounds

that

the

are.

Basis

Berlin.

Wirkung

Grossman,

irrelevant,

here

clear

which

would

of

unreasonable

one

on

fragment,

similar

to this

optimal.

characterization from

is

direction

as

promising

essential

and drugs. it

a-agonists

2

presented

enhanced instance,

to

whereas

Figure

productive

of

for

undesirable

in

analysis

I

Das

structure-activity

compounds,

Chemical

2985-2993.

unchanged.

the

lead

the

Fraser

eine

(1984).

Chem., If

United

York.

chemical

151-302,

(1885).

E.

to

T.R.

action. 2,

Hirschwald,

For

and

P.

Fischer,

derivative

as toxicity

and

Organismus:

behavior

studies.

Structures.

Chichester,

New

between

Edinburgh,

a

Guide

Wiley,

A.

Brown,

to

substitution,

drug

Design.

connection

Even

Indices

Chemical

Press,

A

(1983).

physiological

need

the

Studies

of Drug

correlation

selective

such

Burger,

role

pharmaco-

may

function.

substitution

factors,

for

of

Kingdom.

to recognize

a good

its

discovery

insensitive

major

Information-Theoretic

(1983).

Characterization

Research

a was

pharmacological

fragments

and

interest

one

provided

as

for

D. for

fragment.

a

be responsible

in order

is

the

is important

such

structure

considerable

remain

may that

such

fragment

it

Bonchev,

visually among

played

structures

the

attention

of

which

Thus,

subdivided

between

ring

between purposes.

drugs,

component

a

classification

After

fragment

valuable

critical

of

structure-

examined.

nine-atom

was

aspect

quantitative

been

common

component

particular

to

has

therapeutically

focused This

one

and

(1976).

Molecular

Drug

Connectivity

Research.

Academic

York. H.S. for

nitroarenes.

Rosenkranz the

(1984).

mutagenicity

Mutation

Res.,

Structural of

126,

environ227-238.

5th Iclal

582

Langmuir,

I.

Lednicer,

Isomorphism,

(1919).

covalence. D.

and

Chemistry

L.A.

Mitscher

of

Drug

Wiley-interscience, Menon,

C.K.

M.

The

Organic vo1:-

Stuper,

1.

(1977).

recog-

of structure-activity

rela-

On molecular

Syzmanski,

M. (1984b3.

activity

of

molecular

Biol. Symp., c, Rand&

Int.

M.

numbers.

Chem.,

studies:

antitumor

compounds.

Basis

Cancer,

approach

search

for

A,

Liss

to

optimal

In R. Rein (Ed.),

Part

Apple

Ile

Program

personal

written

Randie

M., GM.

(1979).

for

molecular graphs. Randie

in BASIC

pp.

Available

M. GM.

all

self-avoiding

Computers

and C.L.

paths for

ization

of

with

M. GA.

activity

studies.

bonds.

graphs

(1983).

as an approach Studies

Phys.

to structureTheor.

Chem.,

192-205. M. and C.L.

approach in

multiple

Krans, and B. Jerman-BlaziC of

Randit

graphs

Wilkins

character-

& Chem., 4, 27-43.

Ordering

2,

for

& Chem., 2, 5-13.

Brissey, R.B. Spencer,

molecular

to

Wilkins

(1979d3.

recognition

of

molecules.

J.

Chem.

Graph-theoretical

structural

Inf.

similarity

Comput.

Sci.,

3,

31-37. Randi&

M. and C.L.

study

of

Wilkins (1979b).

structural

Int. J. Quant. Chem., Randit,

and

M.

similarity

graph-theoretical

Graph-theoretical in benzomorphans.

Quant. Biol. Symp., 6, 55-71. Wilkins

C.L.

(1979c).

basis for ordering

On

a

of structures.

Chem. Phys. Lett., 63, 332-336. Rand&

M. and C.L.

ordering searches

of

Wilkins (1979a).

structures

for

Rand&

M.

and C.L.

Randit

Wilkins

molecular

(1980).

molecular

of

variations

in nonanes.

systematic data.

J-

Graph-theoretical

properties. Int.

J.

Quant.

lsomeric Chem.

2,

(1980).

M. and N. Trinajstic

variations

in

1525-1540.

analysis

1005-1027

Graph-theoretical

as a basis for

regularities

Phys. Chem., g,

in decanes.

C.W.

J.V. Knop, and N. Trinajstit

communication.

(1979).

lsosterism

in drug design.

N.

(1983).

Chemical

H.J.

and S. Tauber

(1982).

On

Math. Chem., 2,

and

molecular

Chem.

Graph

(196%

approach

Sot.

Theory,

isomeric 271-290.

Systems

Revs.

Vols

Analysis.

structure-activity

A graph-theoretical

structure-property

to

correlations.

Wilkins, C.L.,

M. Randie

Steiner,

and

Theor.

graph-theoretical

S.M.

Schuster,

L.

Dorgan

and

approach

structure-activity/reactivity Chim. Acta, 133, 637-645.

Wilkins

paths

Use of self-avoiding

Computers

upon

use is intended.

(1980).

Randit

for the

Brissey, R.B. Spencer, and C.L.

Search

Private

Chim.

Acta. 58, 45-68.

Molecular

Publishers,

computer.

request, provided no commercial

(1979).

Structure.

Saunders, Philadelphia.

S.

M. (1985b).

729-735. Jurs

Studies of Chemical

K. W.R. Muller,

Trinajstit

White,

Quant.

309-318. Randie

J.

Wilkins, C.L. and M. RandiC (1980).

Graph-theoretical

structure-activity

and

I and II. CRS Press, Boca Raton, Florida.

approach to structureQuant.

Amer. Sci., fi,

1, 563-580.

137-153.

(1985a).

of

J.

The search for useful topological

Brugger,

modification

6609-6615.

identification

Nonempirical

studies.

W.

(1985).

J. Chem. Inf. Comput. Sci., 24, 164-175. Randit

A.,

Thornber,

characterization

(1973).

Wiley, New York.

Pattern

J. Am. Chem. Sot., z,

D.H.

Computer-Assisted

New York, pp. 286-293.

On

M. (1984a).

Rouvray,

indices in chemistry.

J. Pharm. Sci., 66, 304-314.

(1975).

branching. Randit

and

559.

Synthesis,

II: Investigation

tionships. Randie

1543-1

(1977).

and A. Cammarata

nition

isosterism

J. Am. Chem. Soc.fl,

to

R.S.

Markin,

(1981).

A

quantitative

studies.

Anal.