computer modeling in molecular biology.pdf

8 Path Energy Minimization 223low energy parts of the path contribute very little to the objective function theseregions will not be optimized. If it is necessary to find the smooth overall path, avariety of methods can be used to locate routes downhill from the transition state[36]. These include “PEM descents”, an adaption of the PEM procedure which isused below. The method uses the fact that points immediately adjacent to the peakenergy position contribute to the PEM objective function. Only one fixed conformationand one moving conformation are considered (linked by a number of intermediates).The fixed position is initially set to the transition state conformationand the moving position to some point on one or other side of the transition state.The PEM procedure is then used to optimize the line section between the movingand fixed conformations. The highest energy intermediate conformation is “accepted”,output, and used to replace the fixed conformation. The process is thenrestarted. On each cycle the potential energy of the accepted position will be lowered.In this way PEM is used to descend from the transition state along a locally optimizedpath to the local energy minimum.The PEM method is inspired by, and shares some features with, the self penaltywalk (SPW) procedure developed by Elber and co-workers [44, 451 from the earlierGaussian chain approach [50]. The SPW procedure has been applied to study conformationaltransformations in peptides [44], ligand diffusion in leghemoglobin [45]and conformational transitions of DNA [51]. The Gaussian chain approach, withlow temperature molecular-dynamics simulated annealing, has recently been appliedto determine reaction paths for a conformational change of citrate synthase [42].The SPW procedure also considers a set of moving conformations [X,, X,, X,. . . xNmove] between fixed end points Xo and XNmove+, but unlike the PEM techniqueno sampled positions are taken between the moving conformations. The SPWmethod finds an optimal position for each intermediate by optimizing the objectivefunction:r!: sSPW = -kSchain -k Srepu/sion + (srigid body) (8-6)The first term of the expression is a summation of all the energies of the moving conformations.The term Schain imposes the requirement that the distances between adjacentmoving positions di,i+l should be equal (but does not specify the absolutevalue for the average distance):