xMaPAn Interpretable Alignment-Free Four-Dimensional Quantitative Structure–Activity Relationship Technique Based on Molecular Surface Properties and Conformer Ensembles

A novel alignment-free molecular
descriptor called xMaP (flexible
MaP descriptor) is introduced. The descriptor is the advancement of
the previously published translationally and rotationally invariant
three-dimensional (3D) descriptor MaP (mapping property distributions
onto the molecular surface) to the fourth dimension (4D). In addition
to MaP, xMaP is independent of the chosen starting conformation of
the encoded molecules and is therefore entirely alignment-free. This
is achieved by using ensembles of conformers, which are generated
by conformational searches. This step of the procedure is similar
to Hopfinger’s 4D quantitative structure–activity relationship
(QSAR). A five-step procedure is used to compute the xMaP descriptor.
First, a conformational search for each molecule is carried out. Next,
for each of the conformers an approximation to the molecular surface
with equally distributed surface points is computed. Third, molecular
properties are projected onto this surface. Fourth, areas of identical
properties are clustered to so-called patches. Fifth, the spatial
distribution of the patches is converted into an alignment-free descriptor
that is based on the entire conformer ensemble. The resulting descriptor
can be interpreted by superimposing the most important descriptor
variables and the molecules of the data set. The most important descriptor
variables are identified with chemometric regression tools. The novel
descriptor was applied to several benchmark data sets and was compared
to other descriptors and QSAR techniques comprising a binary fingerprint,
a topological pharmacophore descriptor (Cats2D), and the field-based
3D-QSAR technique GRID/PLS which is alignment-dependent. The use of
conformer ensembles renders xMaP very robust. It turns out that xMaP
performs very well on (almost) all data sets and that the statistical
results are comparable to GRID/PLS. In addition to that, xMaP can
also be used to efficiently visualize the derived quantitative structure–activity
relationships.