Calculation of protein backbone geometry from α‐carbon coordinates based on peptide‐group dipole alignment

Abstract

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C" atoms) to an allatom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the a-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model a-helical and &sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these a-helical and P-sheet structures. Application to the a-carbon trace of the backbone of the crystallographic SPTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C"-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of SPTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.

Prediction of protein conformation on the basis of a search for compact structures: Test on avian pancreatic polypeptide

“…This is accomplished by optimizing the hydrogen-bonding arrangement between the backbone atoms but, at the same time, preserving the distances between a-carbons (virtual-bond structure) obtained in the united-residue treatment. This conversion was carried out with our recently developed dipole-path method, discussed in the accompanying paper (Liwo et al, 1993). Generation of the backbone is completed by carrying out EDMC (electrostatically driven Monte Carlo) simulations (Ripoll & Scheraga, 1988,1989Williams et al, 1992) in a "hybrid" representation of the polypeptide chain, Le., with an all-atom backbone and united side chains, still subject to the C"-distance constraints following from the united-residue simulations.…”

“…To obtain the average electrostatic energy for a given orientation of a pair of virtual-bond peptide groups (i andj), we averaged the dipole-dipole interaction energy over the angles of the rotation of the peptide groups, hi and A, (see Fig. 1 of Liwo et al [1993] and Fig. 3 for the definition of peptide-group arrangement).…”

“…The derivation of the average energy of interaction between peptide-group dipoles is given in the Appendix of Liwo et al (1993). The other (repulsion and dispersion) contributions to the energy are represented by a 6-12 term that also prevents the collapse of the peptide groups.…”

“…where aij, pij, and yij are angles that define the relative orientation of the peptide groups (defined in Equation A6 of Liwo et al [1993] and also shown in Fig. 1 of Liwo et al [1993]) and rij is the distance between the centers of the peptide groups.…”

Evolution of physics‐based methodology for exploring the conformational energy landscape of proteins

“…The united-residue chains are first converted to all-atom poly(L)-alanine backbones using the dipole-path algorithm, 161 i.e., the specific side chains are neglected. The side-chain conformations are then determined by several sweeps of a simple grid search of successive side-chain dihedral angles.…”