Reviews in Computational Chemistry Volume 18

Scoring Functions for Receptor–Ligand Interactions 57
distributions for a data set of interacting molecules can thus be converted to
sets of atom-pair potentials that are straightforward to evaluate.
The first applications of knowledge-based scoring functions in drug
research 164–166 were restricted to small data sets of HIV protease–inhibitor
complexes and did not result in generally applicable scoring functions. Recent
publications 82–86,92,93 have shown that useful general scoring functions can be
derived with this method. The de novo design program SMoG 82,83 contained
the first general-purpose implementation of such a potential.
The ‘‘PMF’’ function by Muegge 86 consists of a set of distancedependent
atom-pair potentials EijðrÞ that are written as
EijðrÞ ¼ kT ln½ fjðrÞr ij ðrÞ=r ij Š ½4Š
Here, r is the atom pair distance, and rijðrÞ is the number density of pairs ij
that occur in a given radius range around r. The term rij in the denominator
is the average density of receptor atoms j in the whole reference volume. The
number density is calculated in the following manner. A maximum search
radius is defined. This radius describes a reference sphere around each ligand
atom j, in which receptor atoms of type i are searched, and which is divided
into shells of a specified thickness. The number of receptor atoms i found in
each spherical shell is divided by the volume of the shell and averaged over all
occurrences of ligand atoms i in the database of protein–ligand complexes.
Muegge argues that the spherical reference volume around each ligand atom
needs to be corrected by eliminating the volume of the ligand itself, because
ligand–ligand interactions are not regarded. This correction is done by the
volume correction factor fjðrÞ that is a function of the ligand atom only and
gives a rough estimate of the preference of atom j to be solvent exposed rather
than buried within the binding pocket. Muegge could show that the volume
correction factor contributes significantly to the predictive power of the
PMF function. 90 Also, a relatively large reference radius of at least 7–8A˚ must be applied to implicitly include solvation effects, particularly the propensity
of individual atom types to be located inside a protein cavity or in contact
with solvent. 89 For docking calculations, the PMF scoring function is evaluated
in a grid-based manner and combined with a repulsive van der Waals
potential at short distances and minima extended slightly toward shorter
distances.
The DrugScore function created by Gohlke, Hendlich, and Klebe 92 is
based on roughly the same formalism, albeit with several differences in the
derivation leading to different potential forms. Most notably, the statistical
distance distributions rijðrÞ=rij for the individual atom pairs ij are divided
by a common reference state that is simply the average of the distance distributions
of all atom pairs rðrÞ ¼ P P
i j rijðrÞ=imax jmax , where the product in
the denominator yields the total number of pair functions. Furthermore, no