The dead-end elimination theorem and its use in protein side-chain positioning

The prediction of a protein's tertiary structure is still a considerable problem because the huge amount of possible conformational space¹ makes it computationally difficult. With regard to side-chain modelling, a solution has been attempted by the grouping of side-chain conformations into representative sets of rotamers²⁻⁵. Nonetheless, an exhaustive combinatorial search is still limited to carefully indentified packing units⁵⁶ containing a limited number of residues. For larger systems other strategies had to be developed, such as the Monte Carlo Procedure⁶⁷ and the genetic algorithm and clustering approach⁸. Here we present a theorem, referred to as the 'dead-end elimination' theorem, which imposes a suitable condition to identify rotamers that cannot be members of the global minimum energy conformation. Application of this theorem effectively controls the computational explosion of the rotamer combinatorial problem, thereby allowing the determination of the global minimum energy conformation of a large collection of side chains.