Metrization

A metrization procedure to improve the consistency of the chosen distances is available. Briefly, the bounds matrix is smoothed for one root, the distance from the root atom to another atom is chosen, and the procedure is repeated, changing roots after the distances from the current root to all other atoms have been chosen. This procedure ensures that later interatom distance choices are consistent with earlier ones. However, it requires considerably more CPU time than the actual embedding because the bounds matrix is frequently resmoothed. It also creates a sampling problem because the order in which distances are chosen has a great impact on which parts of the molecule explore their conformational space completely. If, e.g., the distances are chosen starting from the N terminus of a protein, the molecule's coordinates will be almost completely determined before the distances from the C terminus are chosen. The resulting coordinates show good sampling for the N terminus only, with the C terminus usually lying in an extended loop.

This ordered metrization protocol can be modified to improve the conformational sampling of the coordinates produced. Random metrization picks the root atoms in random order, so that the molecule's conformational freedom is not necessarily used up in just one region.

A modification of these two metrization algorithms in the X-PLOR distance geometry routines gives equally good conformational sampling and reduces the CPU time requirements. In partial metrization, the bounds matrix is resmoothed after choosing distances from only a fraction of the root atoms, after which distances are chosen from the other atoms without resmoothing. This procedure works reliably, even with only four root atoms used in the retightening phase. If very large structures are calculated, the number of root atoms may have to be increased beyond four. The variable $NON_MET_GAP is automatically set by the program to the size of the largest interval in the bounds matrix after (partial) metrization. If $NON_MET_GAP exceeds a few Å, the number of root atoms has to be increased.