Practical Protein Chemistry - A. Darbre 1989

Prediction of Peptide and Protein Conformation
The Arsenal of Modern Theoretical Methods
Periodic Evaluation and Mapping

Periodic energy evaluation is a Procedure that employs a fixed molecular geometry, with calculations performed while varying rotation angles at regular intervals. The system's energy is calculated at each point in space, and the resulting values are recorded in a dedicated two-dimensional array designed for convenient subsequent visual presentation of the data.

To facilitate this presentation, the tabulated values are converted into a map, i.e., contours of isoenergetic points. If the molecule has more than two torsion angles, the remaining angles are treated as less significant compared to the angles being minimized. If necessary, the energy of the molecule at each point in the space defined by the two map angles can be minimized as a function of the remaining angles not involved in constructing the map.

Since the map provides a clear cross-section of the potential surface at a resolution determined by the intervals between points, it can be used for various purposes. For example, one can quickly find Conformations with the lowest and highest energies, as well as determine the shape of the minima. The energy values plotted on the contour can be used to calculate A number of quantities using Statistical Mechanics Methods: mean values of configurational Entropy, circular dichroism spectra, etc. Contour mapping inherently involves interpolating energy values between points, which is essential when averaging physical properties under conditions of a limited number of evaluation points. Such averaging should also take into account the aforementioned Jacobian, although this is rarely done. If the primary goal is computation rather than mere visualization of results, it matters little whether a one- or two-dimensional data array is used. This array can be employed for automated energy Minimization, which in this context means minimization via an "exhaustive periodic scan" (i.e., surveying the entire potential energy surface). If the data array corresponds to the potential surface of a statistical polymer coil monomer unit, applying the approximation of statistical polymer theory allows one to calculate the hydrodynamic and light-scattering Properties of the studied molecule.

Periodic energy evaluation serves not only for generating contour maps. It can also be used to find approximate energy values at any point on the potential surface covered by the minimization procedure.