drugs or drug receptors, molecular mechanics is preferred. For a small molecule that is
extremely flexible, one may wish to calculate many different conformations of the same
molecule. For such a problem, a preliminary series of molecular mechanics calculations
to identify a smaller number of low energy conformers, prior to performing a quantum
mechanics calculation, may be indicated.
At other times, quantum mechanics and molecular mechanics may be used together
in harmony. These are the so-called QM/MM calculations that have become popular
over the past several years. If one wishes to use quantum pharmacology calculations to
simulate a drug interacting with a site on a receptor protein, such calculations have both
small molecule and large molecule components. To approach this problem, one uses
QM calculations “nested” within MM calculations. The overall protein is studied using
molecular mechanics calculations; however, the small region around the receptor site
(and the drug interacting with that receptor via electrostatic interactions) is studied
using ab initio quantum mechanics calculations. Regions intermediate between these
two zones and at the interface between the molecular mechanics optimized region and
the quantum mechanics optimized region may be studied using intermediate semi-
empirical molecular orbital calculations.
1.6.1.4 Energy Minimization Algorithms
Whether one is using Schrödinger’s equation of quantum mechanics or the force field
equation of molecular mechanics, both approaches must be used in conjunction with an
energy minimization algorithm. These two mechanics approaches provide a single
energy for a single given geometry of the molecule; that is, they express geometry as a
function of energy—this function defines an energy surface such that all possible
geometries of the molecule are defined by a point on the energy surface. To obtain the
optimal geometry, one must minimize the energy function (as defined by either the
Schrodinger equation or a force field); that is, one must find the lowest point or deep-
est well on the energy surface. This is a multi-dimensional problem complicated by the
presence of many local energy troughs on the energy surface which are minima in a
mathematical sense, but which are higher in energy than the one single global energy
minimum. Many of the minimization algorithms in current use are based on either a
steepest descent method or a Newton–Raphson method, which require first and second
derivative information about the energy surface, respectively. The steepest descent
method is superior if the starting geometry of the drug molecule under consideration is
far from the global minimum on the energy surface. The Newton–Raphson method, on
the other hand, is superior when fine-tuning the geometry of the drug molecule within
the depths of the energy surface well. The two methods are frequently used in sequence,
with the steepest descent method being used prior to final optimization by a
Newton–Raphson method.
1.6.2 Methods of Quantum Pharmacology for Conformational Analysis:
Monte Carlo Methods, Molecular Dynamics, Genetic AlgorithmsThe ability of a drug molecule to interact with its receptor is dependent not only on
the geometry of the drug molecule (as defined by bond lengths, bond angles, and
DRUG MOLECULES: STRUCTURE AND PROPERTIES 49