Predicting Backbone Cα Angles and Dihedrals from Protein Sequences by Stacked Sparse Auto-Encoder Deep Neural Network

Because a nearly constant distance between two neighbouring Ca atoms, local backbone structure of proteins can be represented accurately by the angle between C alpha(i-1)-C alpha(i)-C alpha(i+1) (h) and a dihedral angle rotated about the C alpha(i) AC alpha(i+1) bond (tau). h and s angles, as the representative of structural properties of three to four amino-acid residues, offer a description of backbone conformations that is complementary to phi and psi angles (single residue) and secondary structures (> 3 residues). Here, we report the first machine-learning technique for sequencebased prediction of theta and tau angles. Predicted angles based on an independent test have a mean absolute error of 9 degrees for h and 34 degrees for s with a distribution on the theta-tau plane close to that of native values. The average root-mean-square distance of 10-residue fragment structures constructed from predicted h and s angles is only 1.9 angstrom from their corresponding native structures. Predicted theta and tau angles are expected to be complementary to predicted phi and psi angles and secondary structures for using in model validation and template-based as well as template-free structure prediction. The deep neural network learning technique is available as an on-line server called Structural Property prediction with Integrated DEep neuRal network (SPIDER) at http://sparks-lab. org. (C) 2014 Wiley Periodicals, Inc.