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 Cα atoms, local backbone structure of proteins can be represented accurately by the angle between Cαi−1CαiCαi+1 (θ) and a dihedral angle rotated about the CαiCαi+1 bond (τ). θ and τ angles, as the representative of structural properties of three to four amino‐acid residues, offer a description of backbone conformations that is complementary to φ and ψ angles (single residue) and secondary structures (>3 residues). Here, we report the first machine‐learning technique for sequence‐based prediction of θ and τ angles. Predicted angles based on an independent test have a mean absolute error of 9° for θ and 34° for τ with a distribution on the θ‐τ plane close to that of native values. The average root‐mean‐square distance of 10‐residue fragment structures constructed from predicted θ and τ angles is only 1.9Å from their corresponding native structures. Predicted θ and τ angles are expected to be complementary to predicted ϕ and ψ 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. © 2014 Wiley Periodicals, Inc.