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\section*{Discovering drug structure-activity rules}
A central concern of chemistry is understanding the 
relationships between chemical structure and activity.  In most cases, these
relationships cannot be derived solely from physical theory and experimental
evidence is essential.  Such empirically derived relationships are
called Structure Activity Relationships (SARs).  In a typical SAR problem, a
set of chemicals of known structure and activity are given, and the problem is
to construct a predictive theory relating the structure of a compound
to its activity.  This relationship can them be used to select for
structures with high or low activity.  Typically, knowledge of such relationships form
the basis for devising clinically effective, non-toxic drugs.

The data here concerns the classic drug design 
problem of inhibition of E. Coli Dihydrofolate Reductase by
pyrimidines and triazines.
Pyrimadine compounds are antibiotics.  They act by inhibiting
Dihydrolate Reductase, an enzyme on the pathway to forming DNA.  They 
inhibit bacterial forms of the enzyme preferentially to 
the human form and therefore kill bacteria. 
Further details on using ILP for this problem are available in
\cite{king:drugs,ashking:newgen}.

The pyrimidine problem is as follows. The
chemicals structures of all compounds used to induce the SAR can be considered
to have a common template (see Figure \ref{fig:pyramidines}).
To this template, chemical groups
can be added at three possible substitution positions, 3, 4, and 5.  A chemical
group is an atom or set of structurally connected atoms that can be substituted
together as a unit and have well defined chemical properties.

\begin{figure*}[htb]
\epsfysize=0.4\textheight
\centerline{\epsfbox{trimethoprim.eps}}
\caption{Chemical structure of pyramidine compounds. (A) Generic template
for all compounds in the study; and (B) An example compound: $3-Cl$, $4-NH_2$, $5-CH_3$}
\label{fig:pyramidines}
\end{figure*}

The existence of a template with only three possible substitution positions
gives the pyrimidine problem a relatively small structural component.  
The chemical structure of the example compound in Figure
\ref{fig:pyramidines} is adequately represented by a Prolog
fact of the form:
\begin{tabbing}
\ \ \ \ \ \ \ \ \ \ \ \=struc(d55,  cl,  nh2  ch3) \\
\end{tabbing}

which is intended to represent that drug 55 has a chlorine atom
substituted at position 3, a amino group (${NH}_2$) group substituted at
position 4, and a methyl (${CH}_3$) group at position 5.

In \cite{king:drugs}, the authors use
9 integer-valued attributes to represent chemical 
properties of the substituents.  These were encoded as predicates of the form:
\begin{tabbing}
\ \ \ \ \ \ \ \ \ \ \ \= polar(br, polar3)\\
\end{tabbing}
which states that a bromine atom has a polarity of value 3

Positive examples are pairs of drugs, the activity of one being known
to be higher than the other. For example:
\begin{tabbing}
\ \ \ \ \ \ \ \ \ \ \ \= great(d1,d2)\\
\end{tabbing}
states that the E. Coli Dihydrofolate Reductase inhibition by drug $d1$
is higher than that by $d2$.

A more difficult problem concerns the inhibition of
E. Coli Dihydrofolate reductase by triazines.  
Triazines act as anti-cancer agents by inhibiting the enzyme Dihydrolate Reductase.
They act by preferentially inhibiting reproducing cells.
Like the pyrimidines, the triazines can also be considered to have a common template 
structure (see Figure \ref{fig:triazines}).
However, the chemical groups substituted onto the 
template are much more complicated than the pyrimidine drugs.
Further, many of the substituting groups can more naturally be considered as sub-
templates with substitutions.  There are seven (7) regions where a substituent
might be present: the 2, 3, and 4 positions of the phenyl ring as shown in Figure
\ref{fig:triazines}. Each substituent can in turn, itself contain a ring
structure. In this case, further substitutions are possible into positions
3 and 4 of these rings.

\begin{figure*}[htb]
\epsfysize=0.4\textheight
\centerline{\epsfbox{triazine.eps}}
\caption{Chemical structure of triazine compounds. (A) Generic template
for all compounds in the study; and (B) An example compound:
$3-Cl$, $4-{({CH_2})_2}C_6H_3-{4}-Cl$, $5-CH_3$}
\label{fig:triazines}
\end{figure*}

The first-order representation of the triazines is best explained using an 
example.  The example compound in Figure \ref{fig:triazines} is represented
by the following Prolog facts:

\begin{tabbing}
\ \ \ \ \ \ \ \ \ \ \ \=struc3(d217, cl, absent).\\
\> struc4(d217, (ch2)24, subst14).\\
\> subst(subst14, so2f, cl).
\end{tabbing}

The first clause represents substitutions at position 3 on the basic template: a 
$Cl$ is present and there is an absence of a further phenyl ring.  The second 
clause represents substitutions at position 4 on the basic template: there is a 
($CH_2$)4 bridge to a second phenyl ring (implicit in the representation).  This 
second phenyl ring has a $S0_2F$ group substituted at position 3 and a $Cl$ group 
substituted at position 4.  This is represented using the linker constant subst14 
to the third clause.  There is no substitution at position 2 on the basic 
template.  Each of the chemical groups had 10 attributes, 9 of which were the same
as used in the study of pyrimidines.  One further attribute
was added to capture flexibility of a substituent.  The degree of
flexibility is represented by one of 9 values.


The data files are stored in compressed TAR format.
within that, they are as used in the original {\em Golem\/} \cite{mugfeng:golem}
experiments. That is, background knowledge files have a ``.b'' suffix,
positive example files have a ``.f'' suffix, and negative example files
have a ``.n'' suffix.

\begin{thebibliography}{}

\bibitem{king:drugs}
King R.D, Muggleton S., and Sternberg M.J.E. (1992).
Drug design by machine learning: The use of inductive logic
programming to model the structure-activity relationships of trimethoprim
analogues binding to dihydrofolate reductase.
{\sl Proc. of the National Academy of Sciences}, 89(23):11322--11326,

\bibitem{ashking:newgen}
King, R.D., Srinivasan, A. and Sternberg, M.J.E. (1995).
Relating chemical activity to structure: an examination of ILP successes.
{\sl New Gen. Comput.} (to appear).

\bibitem{mugfeng:golem}
Muggleton S.H. and Feng C. (1990).
Efficient induction of logic programs.
{\sl Proceedings of the First Conference on Algorithmic Learning Theory},
Tokyo.

\end{thebibliography}


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