Energy-based reconstruction of a protein backbone from its alpha-carbon trace by a Monte-Carlo method

An automatic procedure is proposed for reconstruction of a protein backbone from its C(alpha)-trace; it is based on optimization of a simplified energy function of a peptide backbone, given its alpha-carbon trace. The energy is expressed as a sum of the energies of interaction between backbone peptide groups that are not neighbors in the sequence, the energies of local interactions within all amino acid residues, and a harmonic penalty function accounting for the conservation of standard bond angles. The energy of peptide group interactions is calculated using the assumption that each peptide group acts as a point dipole. For local interaction energy, use is made of a two-dimensional Fourier series expansion of the energies of model terminally blocked amino acid residues, calculated with the Empirical Conformational Energy Program for Peptides (ECEPP/3) force field in the angles lambda((1)) and lambda((2)) defining the rotation of peptide groups adjacent to a C(alpha) carbon atom about the corresponding C(alpha) em leader C(alpha) virtual-bond axes. To explore all possible rotations of peptide groups within a fixed C(alpha)-trace, a Monte Carlo search is carried out. The initial lambda angles are calculated by aligning the dipoles of the peptide groups that are close in space, subject to the condition of favorable local interactions. After the Monte Carlo search is accomplished with the simplified energy function, the energy of the structure is minimized with the ECEPP/3 force field, with imposition of distance constraints corresponding to the initial C(alpha)-trace geometry. The procedure was tested on model alpha-helices and beta-sheets, as well as on the crystal structure of the immunoglobulin binding protein (PDB code: 1IGD, an alpha/beta protein). In all cases, complete backbone geometry was reconstructed with a root-mean-square (rms) deviation of 0.5 A from the all-atom target structure.