Exploring the conformational space of cyclic peptides by a stochastic search method

A stochastic search algorithm is applied in order to probe the conformations of cyclic peptides. The search is conducted in two stages. In the first stage, random conformations are generated and evaluated by a penalty function for ring closure ability, following a stepwise construction of each amino acid into the peptide by a random choice of one of its allowed conformations. The allowed conformational ranges of backbone dihedral angles for each amino acid have been extracted from a Data Bank of diverse proteins. Values of dihedral angles that do not contribute favorably to the scoring of ring closure are retained or discarded by a statistical test. Values are discarded up to a point from which all remaining combinations of angles are constructed, scored, sorted, and clustered. In the second stage, side chains have been added and fast optimization was applied to the set of diverse conformations in a “united atoms” approach, with the “Kollman forcefield” of Sybyl 6.8. This iterative stochastic elimination algorithm finds the global minimum and most of the best results, when compared to a full exhaustive search in appropriately sized problems. In larger problems, we compare the results to experimental structures. The root mean square deviation (RMSD) of our best results compared to crystal structures of cyclic peptides with sizes from 4 to 15 amino acids are mostly below 1.0 Å up to 8 mers and under 2.0 Å for larger cyclic peptides.