  Background. Protein dihedral angles provide a detailed description of protein
local conformation. Predicted dihedral angles can be used to narrow down the
conformational space of the whole polypeptide chain significantly, thus aiding
protein tertiary structure prediction. However, direct angle prediction from
sequence alone is challenging.
  Method. In this study, we present a novel method to predict real-valued
angles by combining clustering and deep learning. That is, we first generate
certain clusters of angles (each assigned a label) and then apply a deep
residual neural network to predict the label posterior probability. Finally, we
output real-valued prediction by a mixture of the clusters with their predicted
probabilities. At the same time, we also estimate the bound of the prediction
errors at each residue from the predicted label probabilities.
  Result. In this article, we present a novel method (named RaptorX-Angle) to
predict real-valued angles by combining clustering and deep learning. Tested on
a subset of PDB25 and the targets in the latest two Critical Assessment of
protein Structure Prediction (CASP), our method outperforms the existing
state-of-art method SPIDER2 in terms of Pearson Correlation Coefficient (PCC)
and Mean Absolute Error (MAE). Our result also shows approximately linear
relationship between the real prediction errors and our estimated bounds. That
is, the real prediction error can be well approximated by our estimated bounds.
  Conclusions. Our study provides an alternative and more accurate prediction
of dihedral angles, which may facilitate protein structure prediction and
functional study.
