Finding the global minimum: a fuzzy end elimination implementation

The ‘fuzzy end elimination theorem’ (FEE) is a mathematicallyproven theorem that identifies rotameric states in proteinswhich are incompatible with the global minimum energy conformation.While implementing the FEE we noticed two different aspectsthat directly affected the final results at convergence. First,the identification of a single dead-ending rotameric state cantrigger a ‘domino effect’ that initiates the identificationof additional rotameric states which become dead-ending. A recursivecheck for deadending rotameric states is therefore necessaryevery time a dead-ending rotameric state is identified. It isshown that, if the recursive check is omitted, it is possibleto miss the identification of some dead-ending rotameric statescausing a premature termination of the elimination process.Second, we examined the effects of removing dead-ending rotamericstates from further considerations at different moments of time.Two different methods of rotameric state removal were examinedfor an order dependence. In one case, each rotamer found tobe incompatible with the global minimum energy conformationwas removed immediately following its identification. In theother, dead-ending rotamers were marked for deletion but retainedduring the search, so that they influenced the evaluation ofother rotameric states. When the search was completed, all markedrotamers were removed simultaneously. In addition, to expandfurther the usefulness of the FEE, a novel method is presentedthat allows for further reduction in the remaining set of conformationsat the FEE convergence. In this method, called a tree-basedsearch, each dead-ending pair of rotamers which does not leadto the direct removal of either rotameric state is used to reducesignificantly the number of remaining conformations. In thefuture this method can also be expanded to triplet and quadrupletsets of rotameric states. We tested our implementation of theFEE by exhaustively searching ten protein segments and foundthat the FEE identified the global minimum every time. For eachsegment, the global minimum was exhaustively searched in twodifferent environments: (i) the segments were extracted fromthe protein and exhaustively searched in the absence of thesurrounding residues; (ii) the segments were exhaustively searchedin the presence of the remaining residues fixed at crystal structureconformations. We also evaluated the performance of the methodfor accurately predicting side chain conformations. We examinedthe influence of factors such as type and accuracy of backbonetemplate used, and the restrictions imposed by the choice ofpotential function, parameterization and rotamer database. Conclusionsare drawn on these results and future prospects are given