Energy minimization

From DrugPedia: A Wikipedia for Drug discovery

Energy minimization involves identifying the conformation of a molecule that has lowest potential energy.

For all except the very simplest systems the potential energy is a complicated, multi-dimensional function of the coordinates. For example, the energy of a conformation of ethane is a function of the 18 internal coordinates or 24 Cartesian coordinates that are required to completely specify the structure. The way in which the energy varies with the corrdinates is referred to as the potential energy surface. For a system with N atoms the energy is thus a function of 3N - 6 internal of 3N Cartesian coordinates. It is therefore impossible to visualize the entire energy surface except for some simple cases where the energy is a function of just one or two coordinates. For example, the vander Waals energy of two argon atoms depends upon just one coordinate: the interatomic distance. Sometimes one may wish to visualize just a part of the energy surface. For example, suppose we take an extended conformation of pentane and rotate the two central carbon-carbon bonds so that the torsional angles vary from 0 degree to 360 degrees, calculating the energy of each structure generated. The energy in this case is a function of just two variables.

In molecular modelling, we are especially interested in minimum points on the energy surface. Minimum energy arrangements of the atoms correspond to stable states of the system; any movement away from a minimum gives a configuration with a higher energy. There may be a very large number of minima on the energy surface. The minimum with the very lowest energy is known as the global energy minimum. To identify those conformations of the system that correspond to minimum points on the energy surface we use energy minimization algorithm. Although global minimum energy structure or minimum energy strucutres are stable conformations but they may not correspond to the active structure (i.e. biologically active conformation of a drug molecule or a protein).

The highest point between two minima is of special interest and is known as the saddle point, with the arrangement of the atoms being the transition structure. A geographical analogy can be used to illustrate many of these concepts. In the analogy minimum points correspond to the bottom of valleys. A minimum may be described as being in a 'long and narrow valley' or a 'flat and featureless plain'. Saddle points correspond to mountain passes.

The input to a minimization program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. They may also be obtained from theoretical techniques such as homology modeling.