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Everyday ideas of similarity are fundamental to the search for new drugs and
other useful molecules. If a particular molecule acts as a drug, for
instance, it seems reasonable to explore other molecules with similar
structures in the hope that these might be more effective, or perhaps have
fewer side effects. But this often means searching laboriously through
massive databases of likely candidates. In seeking ways of cutting short
this process, drug designers and industrial chemists face a tough question:
what, exactly, does similarity mean?

When people classify things according to how similar they are, they often
follow the simple rule that things that look alike tend to behave similarly.
But perceptions of what looks alike differ widely. Psychologists tell us
that in deciding whether or not two objects are similar we are influenced
by objective factors such as the size of the object relative to its
surroundings, and by subjective ones such as the significance of the
objects for the observer.

For molecular structures, matters are a little simpler. For one thing, the
emotive content of molecular structures is zero, even for chemists. And
since the late 1940s, chemists have been developing ways of describing
molecular structures in precise mathematical terms, which makes comparing
them much easier. With the advent of supercomputers, such studies have leapt
ahead. Determining the similarities of molecular structures now plays an
important role in designing all kinds of new molecules – mainly drugs, but
also pesticides, fuels, polymers and substitutes for blood and other body
fluids.

The many variations on this method, which have names like similarity
modelling, clustering and pattern recognition, still do not provide an
absolute measure of similarity. But they do give chemists a way of
quantifying how similar two or more structures are. Often, several methods
are used together on the same pair of molecules. Eventually, chemists arrive
at a set of structures that are most similar to some given structure.

All methods for establishing similarity consist of three basic steps. The
first is to characterise the molecule, using a set of ‘descriptors’ based on
some property whose value is unique to a particular substance or the
molecule of which it is made. Different descriptors are chosen to suit
different substances. A descriptor can be as ordinary a property as its
boiling point, or as specialised as the octanol/water partition coefficient
– a measure of how the substance distributes itself between oil and water.
Descriptors can also be based on theory: a descriptor might, for instance,
reflect the type of bonds between the atoms.

A descriptor can even be purely mathematical. The idea of describing
molecular structure mathematically dates back to 1842, when the German
chemist Hermann Kopp proposed that each atom in a molecule would contribute
a fixed amount to its overall behaviour. But within a few decades it was
realised that the behaviour of a molecule cannot be predicted simply by
adding up the contributions from its constituent atoms, and chemists began
to look for more subtle mathematical descriptors.

One descriptor that is increasingly used today is called a topological
index. To derive a topological index, chemists reduce a molecule’s structure
to a ‘skeleton’ or chemical graph, in which atoms are represented by points
and the chemical bonds between them by lines. This graph can be converted
fairly easily into a form that computers can handle. Usually, a mathematical
algorithm is applied to it to produce the index – a single number that is
characteristic of the structure of the molecule (see ‘Making molecules by
numbers’, New ÐÓ°ÉÔ­´´, 30 March 1991).

In the first modern topological index, which was proposed by the chemist
Harry Wiener in 1947, the algorithm adds up all possible linkages between
all pairs of atoms in the structure. Since the Wiener index, more than 100
different topological indices have been developed, notably by Monty Kier and
Lowell Hall in the US. Some of the more sophisticated algorithms weight the
atoms or linkages to reflect their different contributions to the overall
behaviour of the molecule.

The type and number of descriptors depend on the particular problem in hand.
In drug development, descriptors based on experimentally measured
properties have traditionally been regarded as more important than
mathematical descriptors such as topological indices. But things may be
changing. The recent discovery of a new series of molecules called the
bis(heteroaryl)-piperazines that are active against HIV, is an indication of
the growing importance of theoretical descriptors. Michael Lajiness and his
colleagues at the pharmaceuticals company Upjohn in Kalamazoo, Michigan,
made their discovery by searching a database of molecular structures with a
computer program developed in 1988 by Subhash Basak at the University of
Minnesota, which calculates 90 topological indices for each structure.

Once descriptors for a group of molecules have been chosen, the next step is
to compare them. Each molecule is plotted as a point in multidimensional
space, with the descriptors plotted along the axes – so for 20 descriptors,
for example, the plot is in 20-dimensional space. Plotting in more than
three dimensions is difficult to visualise, but computers can do it easily.

POINT OF REFERENCE

The final step in establishing how similar molecules are is to find out how
close the plotted points are to each other, or to some reference point in
multidimensional space. The assumption is that points which are close
together in the plot represent structures that will exhibit similar
behaviour. The distance between points is often worked out by a method which
interprets the distance geometrically, using a direct extension of
Pythagoras’s theorem. The measure of how similar two structures are can then
be derived by subtracting the cordinates of a pair of points to give their
distance apart. For convenience, the maximum distance apart for any two
points is taken to be 1, and the distances are scaled to give a measure
called a ‘similarity coefficient’.

Similarity can also be measured in terms of ‘fragments’ – individual atoms
or groups of atoms joined together in some specified way in a molecule. In
this method each molecular structure is usually encoded as a string of
numbers. For example, ‘1’ is used to indicate if the fragment is present,
‘0’ if it is absent. For consistency, the fragments are always listed in the
same order. In the late 1980s, Mark Johnson and his collaborators at Upjohn
developed computer programs that would identify the 100 structures that are
most similar to a target, measured by the Tanimoto coefficient and related
fragmental coefficients.

The Tanimoto coefficient is given by the formula A/A+B+C (see Figure 1),
where A is the number of molecular fragments that two structures have in
common, B is the number of features occurring in the first structure but not
in the second, and C is the number of features in the second structure that
are not in the first. As an example of what can be achieved, Figure 1 shows
the three structures most similar to a given target that were found by
Johnson and colleagues in a database search. Using only topological indices,
my group at the University of Georgia has predicted the properties of all
209 known polychlorinated biphenyls (PCBs) from similarities in their
structures, based on a randomly selected test set of only 10 of these
molecules.

Such codes are useful, not only for identifying molecules but also for
searching molecular databases. In the mid-1980s, Peter Willett and his
colleagues at the University of Sheffield developed the first techniques
designed to search for similar compounds in large chemical databases. Today,
large drugs companies in Britain and the US, including Abbott, Pfizer,
SmithKline Beecham, and Upjohn, are using similarity methods to search for
compounds that might be used as drugs to treat HIV, Alzheimer’s disease and
cancer, for example. Theoretically calculated descriptors are being used
increasingly for these searches.

The Tanimoto coefficient offers a simple way of pinning down the features
common to different drug molecules that cause them to bind to the same
receptor. These features in turn lead to the structure of the receptor,
because it is complementary to that of the drug. The mapping of enzymes and
other receptor systems was first automated in the early 1980s using Dock,
a computer program developed by Irwin Kuntz at the University of California,
San Francisco. Among the receptors whose features have been mapped is the
enzyme dihydrofolate reductase, which catalyses cell growth. It can be
inhibited by the anti-leukaemia drug methotrexate.

Until about ten years ago, drugs and other molecules were developed without
any detailed knowledge of how they worked. Neither the three-dimensional
structure of the drug molecule, nor the interaction between the drug and its
receptor were understood. But today, the search for new drugs is being
helped by similarity modelling in three dimensions. In 1987, Robert Pearlman
of the University of Texas at Austin developed a program called Concord,
which could convert a database of two-dimensional structures into its
three-dimensional equivalent. Abbott, Lederle and Pfizer were among the
first drugs companies to use three-dimensional databases to search for
similarity.

The key to obtaining a three-dimensional Wiener index, for example, is to
set up a geometrical distance matrix. For a molecule with n atoms (excluding
hydrogens, which for simplicity are often left out), each matrix entry
corresponds to one interatomic distance, and an n times n matrix of numbers
gives the distance between every pair of atoms in the structure
(see Figure 2). Then two structures can be compared by finding out how many entries are
similar in the two matrices, and how many are different. A pair of matrix
entries are taken to be similar if the distances they represent are the same
to within some preset tolerance, usually 0.5 angstroms, and the atoms being
compared are identical. Willett’s group, among others, has devised computer
programs that do all this automatically.

Working with a variety of collaborators, Willett has produced programs aimed
at discovering similarities between the three-dimensional structures of
proteins stored in the Brookhaven Protein Data Bank in the US. A target
protein structure is compared with each of the data bank structures in turn.
The interest lies in the close link between structure and function in
proteins. One discovery made by Willett and his colleagues is a previously
unrecognised link between two families of enzymes, the aminopeptidases and
carboxypeptidases, that may point to a remote evolutionary relationship
between them.

Information about the three-dimensional structure of receptors in the human
body requires knowledge of the structures of the proteins and nucleic acids
from which they are formed. The sequence of amino acids has been determined
for many proteins, even if the complete structure is not known. Some
researchers are interested in the practical question of whether proteins
with similar amino acid sequences have similar three-dimensional structures.
This approach, called homology modelling, has already had some success. A
computer program called Congen, written in 1987 by Robert Bruccolleri and
Martin Karplus of Harvard University, has been spectacularly successful in
predicting the shape of polypeptide segments in proteins. Applying the
procedure to study the structures of human and mouse antibodies, including
the immunoglobulins, Bruccolleri has predicted with great ac-curacy the
shape of the antigen binding sites on mouse and human antibodies. These
sites consist of six separate polypeptide loops on a fixed backbone.

There is no general agreement among researchers on the best way of
approaching similarity studies. One of the most interesting of the many
directions taken in the past few years (also see Box) is the growing use of
neural networks – computer systems that attempt to simulate the workings of
the human brain by exploiting parallel processing. Neural networks are
excellent for the pattern recognition problems inherent in drug design,
though there are still problems to be overcome. For example, neural networks
have difficulty processing chemical graphs, and to get round this Gerald
Maggiora of Upjohn has proposed that the input and output of the network
could be modelled as a so-called response surface, in which the peaks could
be used to identify classes of biologically active molecules. The approach
has enormous promise, though no drugs have yet been designed with these
networks, and they have solved only comparatively simple chemical problems.

At the Czech Academy of Sciences in Prague, Robert Ponec and his colleagues
are applying similarity to study how molecules behave during a chemical
reaction. They use similarity methods to compare the reacting molecules with
those that are produced, and from this they deduce how the molecules behave
during the reaction. Although in its infancy, their approach could prove
valuable in the theoretical analysis of chemical reactions, including those
involving drug molecules.

Johann Gasteiger and his colleagues at the Technical University in Munich
have taken this approach a stage further with a series of similarity
measures that they believe can be applied more generally to chemical
reactions. They have come up with similarity measures for molecular
structures, reaction conditions, and individual bonds broken and formed in
the reaction, which they have applied to a variety of organic reactions,
including the addition of ketones to olefins by a route that involves free
radicals. They have also used their techniques to search for starting
materials for synthesising 6-aminopenicillamic acid. Ultimately they hope to
reduce the number of reactions a chemist might have to try out when devising
a new synthesis.

Dennis Rouvray is a research professor in the chemistry department of the
University of Georgia at Athens, Georgia.

* * *

The British way

When designing a new drug, companies often start with a competitor’s patents
on an existing drug, and the information about the molecule’s structure that
it contains. From this they can create a three-dimensional picture on a
computer and then, they hope, a real molecule of the same shape which is not
covered by the patent. The new molecules can then be tested to see if they
have similar biological activity.

While some researchers look for similarity in terms of the molecular
framework of atoms and bonds, others have developed a more sophisticated
approach that takes into account a molecule’s shape and the electrostatic
potential on its surface. This makes sense when looking for potential drugs,
as it is the surface of a drug molecule that is the point of contact with
the body’s receptors.

Notions of how drugs interact with receptors have come a long way since Emil
Fischer, the pioneer of sugar chemistry, proposed his ‘lock and key’
hypothesis a century ago. Chemists now know that as a drug molecule
approaches its receptor it experiences first an attractive electrostatic
force, then one of repulsion. Today two of the most common descriptors used
in similarity studies are electron density, and electrostatic potential
which indicates which areas of the drug molecule are involved in bonding.
Electrostatic potential is a calculation of what the attractive force
between the drug and its receptor is likely to be, and gives a more detailed
picture of which atoms or groups of atoms are involved in the interaction. A
complicating factor in similarity modelling is that drug molecules are
generally much smaller than their receptors, so large parts of the receptor
play no role.

More than a decade ago, the Catalan chemist Ramon Carbo and his colleagues
suggested how the similarity of two molecules might be calculated by
comparing their electron densities. This approach was taken a step further
in 1988, when Graham Richards and Ed Hodgkin at Oxford proposed a similarity
index that compares molecules in terms of their electrostatic potential. In
1991 Kate Burt, another of Richards’ group, devised a computer program
called ASP that can do this automatically. The program has already been
widely used by drug designers to mimic peptide bonds, for example.

Richards and his team have devised a fast method based on a neural network
that could replace the statistical methods now used by drug companies to
decide which molecules to make next. They feed a matrix of similarity
indices of two sets of molecules, calculated from their electrostatic
potentials,into a neural network designed to select the most active
molecules. The network gives its answer in pictorial form. Richards and his
team have already used the method to look at a range of molecules: they
include corticosteroids; antibacterial triazines which bind to the same
receptors in the brain as tranquillisers; and compounds that bind in a
similar way to cocaine.

A second group, led by pharmacologist Philip Dean at the University of
Cambridge, has been developing methods of determining molecular similarity
for drug design. Real similarity, Dean says, is not concerned with bonds.
What is needed is an extended surface, as near as possible to that of the
target. He says the most complex problem is how to compare two apparently
dissimilar, physically flexible molecules – for example, those with bonds
that can rotate. His team is looking at molecules with up to 150 atoms,
using a statistical technique called simulated annealing inspired by the way
a metal cools to form crystals. This technique allows them to compare the
molecules atom by atom, by superimposing the best and near-best structures
on a computer screen. The result is a series of structures that have a high
probability of being similar, all in a low enough energy range to be stable.
Both Wellcome in Beckenham and Rhone-Poulenc in Dagenham are exploring this
method to design new drugs.

Large biological molecules such as proteins are often pictured in terms of
electron density maps, but these show mainly the ‘core’ electrons which do
not take part in chemical reactions. ‘The problem is that molecules such as
drug molecules contain a vast amount of information,’ says Neil Allan of the
University of Bristol, ‘and we need to find a way of reducing it.’ To do
this he has cooperated with theoretical chemist David Cooper of the
University of Liverpool to devise a method that instead of calculating where
electrons are, works out how fast they are moving. The electrons which take
part in chemical bonding happen to be the slowest moving, so by calculating
the velocity distribution of the electrons in the molecule they hope to
obtain a profile of its chemical activity. This can then be used to compare
molecules that do not appear to be similar.

Cooper and Allan are currently using this technique to look for similarities
in a series of anti-HIV lipids, as well as molecules related to the AIDS
drug AZT, starting from a list of formulae and information about the
activity of these molecules. Later this year they intend to work with a
major pharmaceuticals company to look at three or four molecules which could
act as a substitute molecule for cocaine.