Reviews in Computational Chemistry Volume 18

54 The Use of Scoring Functions in Drug Discovery Applications
that use this concept are called ‘‘empirical scoring functions.’’ Several reviews
summarize details of individual parameterizations. 17,146–151 The individual
terms in empirical scoring functions are usually chosen so as to intuitively
cover important contributions of the total binding free energy. Most empirical
scoring functions are derived by evaluating the functions fi for a set of protein–
ligand complexes and fitting the coefficients Gi to experimental binding
affinities of these complexes by multiple linear regression or by supervised
learning techniques. The relative weight of the individual contributions
depends on the training set. Usually, between 50 and 100 complexes are
used to derive the weighting factors, but in a recent study it was shown that
many more than 100 complexes were needed to achieve convergence. 75 The
reason for this large number is probably due to the fact that the publicly available
protein–ligand complexes fall in a few heavily populated classes of
proteins, such that in small sets of complexes few interaction types dominate.
Empirical scoring functions usually contain individual terms for hydrogen
bonds, ionic interactions, hydrophobic interactions, and for binding
entropy. Hydrogen bonds are typically scored by simply counting the number
of donor–acceptor pairs falling within a given distance and angle range considered
to be favorable for hydrogen bonding, weighted by penalty functions for
deviations from preset ideal values. 56,71,73 The amount of error-tolerance in
these penalty functions is critical to the success of scoring methodology.
When large deviations from ideality are tolerated, the scoring function may
be unable to discriminate between different orientations of a ligand. Contrarily,
small tolerances lead to situations where many structurally similar complex
structures result in very similar scores. Attempts have been made to
reduce the localized nature of such interaction terms by using continuous modulating
functions on an atom-pair basis. 69 Other workers have avoided the use
of penalty functions altogether and introduced separate regression coefficients
for strong, medium, and weak hydrogen bonds. 75 For example, at Agouron a
simple four-parameter potential, which is called the piecewise linear potential
(PLP), was developed that is an approximation of a potential well without
angular terms. 62 Most empirical scoring functions treat all types of hydrogenbond
interactions equally, but some attempts have been made to
distinguish between different donor–acceptor functional group pairs. Hydrogenbond
scoring in the docking program GOLD, 60,61 for example, is based on
a list of hydrogen-bond energies for all combinations of 12 defined donor and
6 acceptor atom types derived from ab initio calculations of model systems
incorporating those atom types. A similar differentiation of donor and acceptor
groups is made in the hydrogen-bond functions in the program GRID, 152 a
program commonly used for the characterization of binding sites. 115–117 The
inclusion of such lookup tables in scoring functions is presumed to avoid
errors originating from the oversimplification of individual interactions.
Reducing the weight of hydrogen bonds formed at the outer surface of
the binding site is a useful measure for reducing the number of false positive