Finding the global minimum: a fuzzy end elimination implementation

Abstract

The 'fuzzy end elimination theorem' (FEE) is a mathematically proven theorem that identifies rotameric states in proteins which are incompatible with the global minimum energy conformation. While implementing the FEE we noticed two different aspects that directly affected the final results at convergence. First, the identification of a single dead-ending rotameric state can trigger a 'domino effect' that initiates the identification of additional rotameric states which become dead-ending. A recursive check for dead-ending rotameric states is therefore necessary every time a dead-ending rotameric state is identified. It is shown that, if the recursive check is omitted, it is possible to miss the identification of some dead-ending rotameric states causing a premature termination of the elimination process. Second, we examined the effects of removing dead-ending rotameric states from further considerations at different moments of time. Two different methods of rotameric state removal were examined for an order dependence. In one case, each rotamer found to be incompatible with the global minimum energy conformation was removed immediately following its identification. In the other, dead-ending rotamers were marked for deletion but retained during the search, so that they influenced the evaluation of other rotameric states. When the search was completed, all marked rotamers were removed simultaneously. In addition, to expand further the usefulness of the FEE, a novel method is presented that allows for further reduction in the remaining set of conformations at the FEE convergence. In this method, called a tree-based search, each dead-ending pair of rotamers which does not lead to the direct removal of either rotameric state is used to reduce significantly the number of remaining conformations. In the future this method can also be expanded to triplet and quadruplet sets of rotameric states. We tested our implementation of the FEE by exhaustively searching ten protein segments and found that the FEE identified the global minimum every time. For each segment, the global minimum was exhaustively searched in two different environments: (i) the segments were extracted from the protein and exhaustively searched in the absence of the surrounding residues; (ii) the segments were exhaustively searched in the presence of the remaining residues fixed at crystal structure conformations. We also evaluated the performance of the method for accurately predicting side chain conformations. We examined the influence of factors such as type and accuracy of backbone template used, and the restrictions imposed by the choice of potential function, parameterization and rotamer database. Conclusions are drawn on these results and future prospects are given.

Modeling the Conformation of Side Chains in Proteins: Approaches, Problems and Possible Developments

“…Several methods to enhance DEE have been developed [25,26,[62][63][64][65][66][67][68]. For example, the combination of rotamers from multiple residues in "super-rotamers" was adopted to allow the elimination of multiple rotamers in a single step [63].…”

Modern Genome Annotation

“…3). These preferences, tabulated in so called rotamer libraries (Godzik and Skolnick 1992;Holm and Sander 1992;Chinea et al 1995;Keller et al 1995), are usually used as a starting point for subsequent refinement of the overall structure.…”

Expanded Explorations into the Optimization of an Energy Function for Protein Design

“…However, due to computational limitations the search requires: 1) a coarse-graining of the structure as a sequence of discrete side chain rotamers [19], [20], [21], 2) an assumption of minimal backbone conformational flexibility, where a fixed backbone or a feasible set of backbones are used [22], [23], [24], 3) an approximation of the energy model as a pairwise decomposition ), and 4) an efficient algorithm for searching the configurational space of rotamers and backbones, such as dead-end elimination [25], [26], [27], [28], [29], [30], Monte Carlo [31], [32], [33], genetic algorithm [5], [34] and branch-and-bound algorithm [35], [36], [37], and algorithms for sampling backbone conformations [38], [39], [40], [41]. These assumptions strike a compromise between speed and accuracy.…”