than merely providing structural information about geometries and conformations,
quantum pharmacology calculations may be employed to provide useful data central to
the drug design process.
An important application of quantum pharmacology calculations to small molecules
is in the area of quantitative structure-activity relationships (QSAR). QSAR will be dis-
cussed at length in chapter 3. Over the past 30 years, QSAR has progressed from the
regression equations of Hansch, through 2D QSAR, to modern 3D QSAR methods. The
applications of quantum pharmacology calculations are well exemplified in 2D QSAR
studies. Typically, these studies start with 10–20 analogs of a bioactive molecule. These
analogs range from biologically active to inactive. Each analog, regardless of its bioac-
tivity, undergoes extensive calculations and is described by a series of descriptors.
Geometric descriptors reflect properties such as bond lengths, bond angles, and inter-
atomic distances within the analogue series. Electronic descriptorsrepresent properties
such as atomic charge densities, molecular dipoles, and energy of the highest occupied
molecular orbital. Topological descriptorsencode aspects of molecular shape and
branching and are frequently represented by graph theory indices, such as the Randic
indices.Physicochemical descriptorsreflect properties related to the ability of the mol-
ecules to traverse biological barriers such as the blood–brain barrier, and include values
such as the octanol–water partition coefficient. These descriptors, especially the geomet-
ric and electronic descriptors, may be ascertained using quantum mechanics calculations.
Once the descriptors have been determined, a data array is constructed with descriptors
along one axis of the array and biological activity along the other axis. Statistical
methods are then used to search the array and to identify the minimal descriptor set
capable of differentiating between biological activity and inactivity. As a corollary to
this, it is possible to deduce the bioactive face of the molecule, thereby identifying the
pharmacophore.
DRUG MOLECULES: STRUCTURE AND PROPERTIES 53Figure 1.14 Ab initio quantum mechanics calculations can be employed to rigorously provide
geometries (bond lengths, bond angles, torsional angles) for a drug molecule. This figure shows
such values for the anticonvulsant drug phenytoin.