Energy Minimization

The most common types of molecular mechanics calculation are conformational energy studies (2-4). Conformational energy calculations involve the search for the molecular geometry with the lowest potential energy, on the assumption that the structure with the lowest mechanical energy (as calculated from the semiempirical energy functions) will be the form primarily found in nature. This search is accomplished using automatic energy minimization algorithms, which minimize the gradient (derivative) of the potential energy. Predictions of the structure-dependent physical properties of the biopolymer system are then based on those calculated from the lowest energy conformation. Unfortunately, the major problem with this approach is that due to the enormous complexity of large systems, it is difficult to identify the lowest energy structure. The problem arises because for large systems, there will, in general, be many local minimum energy geometries that are locally stable, with a zero gradient of the potential energy, but that are higher in energy than the structure with the lowest energy, which is called the global energy minimum. There is no general mathematical procedure for finding this global energy minimum. Most minimization techniques will simply locate the nearest local stable geometry for which the gradient is zero and then be unable to proceed over any energy barriers that separate this local minimum from any lower energy structures. This multiple-minimum problem (5) is the reason that it is not yet possible to predict the tertiary conformation of a protein given its primary sequence, even though in principle the sequence for most proteins contains all of the information necessary for correct folding (see later). Even if the global minimum-energy structure is identified, there are other possible problems with this type of approach. Polymers such as proteins are not static, but actually fluctuate considerably, sampling a number of nearby thermally accessible conformations (6) (which are usually quite similar to the lowest energy structure), and the experimental, or physical, structure is actually an appropriately weighted average of all these structures. Energy minimization studies, however, generally cannot include such conformational averaging, or its entropic effects (7). Perhaps most important, energy minimization calculations cannot directly include the effects of solvation, which can be quite crucial in many biological systems.

In spite of their limitations, energy minimization calculations can be of great utility in studying certain limited questions, such as predicting the preferred binding geometries of substrates in enzyme active sites or the local effects of a single point mutation in a protein. This type of calculation can be especially useful when combined with computer graphics representations of molecular structures, as is now frequently done in the pharmaceutical (8) and food industries in binding studies. Visual inspection of computer-generated three-dimensional color images of interacting molecules such as a target protein and a drug molecule allow researchers to use their chemical intuition and experience to identify promising approximate binding configurations, which can subsequently be refined by the application of energy minimization calculations. In this way, the human-guided input can avoid calculations for many of the unpromising minima that blind energy minimizations would have wasted much computer time exploring needlessly.

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