The cyclic coordinate descent (CCD) method is a popular loop closure method in protein structure modeling. It is a robotics algorithm originally developed for inverse kinematic applications. We demonstrate an effective method of building the backbone of protein structure models using the principle of CCD and a guiding trace. For medium-resolution 3-dimensional (3D) images derived using cryo-electron microscopy (cryo-EM), it is possible to obtain guiding traces of secondary structures and their skeleton connections. Our new method, constrained cyclic coordinate descent (CCCD), builds α-helices, β-strands, and loops quickly and fairly accurately along predefined traces. We show that it is possible to build the entire backbone of a protein fairly accurately when the guiding traces are accurate. In a test of 10 proteins, the models constructed using CCCD show an average of 3.91 Å of backbone root mean square deviation (RMSD). When the CCCD method is incorporated in a simulated annealing framework to sample possible shift, translation, and rotation freedom, the models built with the true topology were ranked high on the list, with an average backbone RMSD100 of 3.76 Å. CCCD is an effective method for modeling atomic structures after secondary structure traces and skeletons are extracted from 3D cryo-EM images.

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 Å RMSD error for the mainchain N, Cα, C, and O atoms; the average accuracies were 0.59 ± 0.05, 1.16 ± 0.10, and 2.61 ± 0.16 Å, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 Å, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.