Prediction of the native conformation of a polypeptide by a statistical‐mechanical procedure. I. Backbone structure of enkephalin

Abstract A new methodology for theoretically predicting the native, three‐dimensional structure of a polypeptide is presented. Based on equilibrium statistical mechanics, an algorithm has been designed to determine the probable conformation of a polypeptide by calculating conditional free‐energy maps for each residue of the macromolecule. The conditional free‐energy map of each residue is computed from a set of probability integrals, obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. By locating the region(s) of lowest free energy for each map, the probable conformation for each residue can be identified. The native structure of the polypeptide is assumed to be the combination of the probable conformations of the individual residues. All multidimensional probability integrals are evaluated by an adaptive Monte Carlo algorithm ( SMAPPS —Statistical‐Mechanical Algorithm for Predicting Protein Structure). The Monte Carlo algorithm searches the entire conformational space, adjusting itself automatically to concentrate its sampling in regions where the magnitude of the integrand is largest (“importance sampling”). No assumptions are made about the native conformation. The only prior knowledge necessary for the prediction of the native conformation is the amino acid sequence of the polypeptide. To test the effectiveness of the algorithm, SMAPPS was applied to the prediction of the native conformation of the backbone of Met‐enkephalin, a pentapeptide. In the calculations, only the backbone dihedral angles (ϕ and ψ) were allowed to vary; all side‐chain (χ) and peptide‐bond (ω) dihedral angles were kept fixed at the values corresponding to the alleged global minimum energy previously determined by direct energy minimization. For each conformation generated randomly by the Monte Carlo algorithm, the total conformational energy of the polypeptide was obtained from established empirical potential energy functions. Solvent effects were not included in the computations. With this initial application of SMAPPS , three distinct low‐free‐energy β‐bend structures of Met‐enkephalin were found. In particular, one of the structures has a conformation remarkably similar to the one associated with the previously alleged global minimum energy. The two additional structures of the pentapeptide have conformational energies lower than the previously computed low‐energy structure. However, the Monte Carlo results are in agreement with an improved energy‐minimization procedure. These initial results on the backbone structure of Met‐enkephalin indicate that an equilibrium statistical‐mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.