Computational Approaches in Peptide and Protein Design: An Overview - Peptide and Protein Design for Biopharmaceutical Applications - page 29

rotamers in a peptide chain may be roughly estimated as 10 N , where N is
the number of residues in the sequence. Therefore, efficient sampling of
possible rotamers of side chains in peptides and proteins remains an
important problem, which is approached in several ways as briefly dis-
cussed below.
The theorem of the dead-end elimination proposes an energy-based
equation and an algorithm to eliminate any rotamers inconsistent with
the global energy minimum [91]. The theorem uses an assumption that the
sum energy of the interactions of a given residue in a given side-chain
rotamer consists of the energy of its interaction with the backbone and with
all other side chains. If, for a specific residue, it is possible to determine the
rotamer for which any combination of rotamers of all other residues would
be associated with an energy value larger than the energy values associated
with any other rotamer of the same residue, the former rotamer cannot be a
part of the structure corresponding to the global energy minimum; this
dead-end rotamer can be discarded from further consideration. Then
another rotamer in another residue may be determined as a dead-end one
and eliminated, and so on, until only one combination of side-chain
rotamers remains. This procedure may be appropriate for producing a
unique lowest-energy combination of the rotamers; obviously, it depends
on the accuracy of the energy estimations, i.e. on the force field used.
Though algorithms based on the dead-end elimination have been used
in several practical applications [92,93], most sampling procedures
employ selection of the rotamer combinations guided by libraries of
discrete side-chain conformations (see e.g. [94] and references therein).
Such libraries are obtained from statistical analysis of the PDB, and can
either be backbone-independent or backbone-dependent. The latter dif-
ferentiate distributions of rotamers that depend on backbone conforma-
tions, and the former ignore such dependence. Selection of side-chain
rotamers based on libraries can be performed by simple procedures such
as Monte Carlo sampling [95,96] or by more sophisticated algorithms
that estimate the energies of interactions between side chains of different
rotamers to determine the most energetically feasible combinations of
rotamers (e.g. the SCWRL procedure [94,97]). Usually, estimation of
energies involves simple steric energy combined with probabilities of
rotamer populations for each residue and each backbone conformation.
The library-based SCWRL procedure is computationally fast and pro-
duces several possible combinations of rotamers that are close to those
combinations observed in the X-ray structures of proteins (see [94,97]).
The procedure and its modifications have been used in many studies of
protein conformational space (e.g. the recent studies [74,88,90,98]).