computer modeling in molecular biology.pdf

8 Path Energy Minimization 237The results, shown in Table 8-3, show that the energy of individual forms changesby up to 2 kcal/mol but the energy barrier remains around 7 kcal/mol. The consistencybetween the results using a different representation for the metal ion is encouraging.8.5 Conclusions : Potential DevelopmentsThe PEM method has been shown to be a robust and powerful technique for findingreaction paths for conformational changes in macromolecules. It has advantagesover the SPW method (the only comparable technique), in that sampling is biasedtowards high energy regions of the path (thus ensuring that the transition state islocated), the continuity of the final result is assured and that the result is not dependenton the values taken for restraint parameters.The implementation of the PEM method presented here suffers from the problemof computational efficiency. This is in part due to the fact that the energy and forcecalculation routines in TIC have not been adjusted for maximum speed, for examplean atom based non-bonded cut-off procedure is used instead of the more efficientgroup based formalism and the code has not been vectorized. The PEM method wasalso designed with robustness rather than efficiency in mind, The present proceduretakes a specified number of equally spaced sample conformations between each pairof moving points but this could be changed so that the routine occasionally adjuststhe spacing to ensure the peak energy position of each interval is sampled.As shown in the D-xylose isomerase example, the PEM procedure can convergeto different paths depending on the starting set of conformations. It would be verydesirable for the method to always locate the path with the lowest peak energy. Thiswould require that the procedure should find the global minimum of the objectivefunction: a ubiquitous problem [48]. There are two partial solutions: to startminimization from different starting conformations (see below) and simulated annealing[49]. The molecular dynamics simulated annealing procedure has been appliedin a variant of SPW method [42] and could be expected to be useful in minimizingthe PEM objective function - allowing the method to avoid being trapped inlocal minima.An important potential improvement to the method would be to apply the procedurein dihedral angle coordinate space. This would require the molecular potentialenergy and force functions be calculable in terms of dihedral angle variables [61].This approach would result in several advantages compared to the present applicationin Cartesian space. Conformational change is clearly more naturally representedin internal coordinate space because of the division between “soft” (dihedral angles)and “hard” (bond lengths and angles) variables. This would allow the use of fewer