first draft of paper, designed experiments performed statistical analyses, performed bioinformatics analyses, performed data visualisation. M.T. wrote first draft of paper, designed experiments, generated tools & reagents, performed statistical analyses, performed bioinformatics analyses, performed data visualisation. S.M.G.E. wrote first draft of paper, generated tools & reagents, performed bioinformatics analyses, performed data visualisation. A.G.D. wrote first draft of paper, designed experiments, generated tools & reagents, performed bioinformatics analyses. M.D. generated tools & reagents. S.D. generated tools & reagents. L.Y.L. generated tools & reagents. S.S. generated tools & reagents. H.Z. generated tools & reagents. K.Z. generated tools & reagents, performed bioinformatics analyses. T.O.Y. generated tools & reagents, performed bioinformatics analyses. J.M.C. generated tools & reagents. A.B. generated tools & reagents. C.M.L. generated tools & reagents. I.U. generated tools & reagents. B.L. generated tools & reagents. W.Z. generated tools & reagents. A.D.E. generated tools & reagents, supervised research. NMW performed bioinformatics analyses, performed data visualisation. J.A.W. performed bioinformatics analyses. M.K.H.Z. performed bioinformatics analyses. C.V.A. performed bioinformatics analyses. C.P. performed data visualisation. J.T.S. supervised research. J.M.S. supervised research. D.A. supervised research. Y.G. supervised research. K.E. wrote first draft of paper, supervised research. D.C.W. designed experiments, supervised research. Q.D.M. wrote first draft of paper, designed experiments, generated tools & reagents, supervised research. P.V.L. wrote first draft of paper, designed experiments, supervised research. P.C.B. wrote first draft of paper, designed experiments, supervised research.

Phylogenetic inference is of fundamental importance to evolutionary as well as other fields of biology, and molecular sequences have emerged as the primary data for this task. Although many phylogenetic methods have been developed to explicitly take into account substitution models of sequence evolution, such methods could fail due to model misspecification or insufficiency, especially in the face of heterogeneities in substitution processes across sites and among lineages. In this study, we propose to infer topologies of four-taxon trees using deep residual neural networks, a machine learning approach needing no explicit modeling of the subject system and having a record of success in solving complex nonlinear inference problems. We train residual networks on simulated protein sequence data with extensive amino acid substitution heterogeneities. We show that the well-trained residual network predictors can outperform existing state-of-the-art inference methods such as the maximum likelihood method on diverse simulated test data, especially under extensive substitution heterogeneities. Reassuringly, residual network predictors generally agree with existing methods in the trees inferred from real phylogenetic data with known or widely believed topologies. Furthermore, when combined with the quartet puzzling algorithm, residual network predictors can be used to reconstruct trees with more than four taxa. We conclude that deep learning represents a powerful new approach to phylogenetic reconstruction, especially when sequences evolve via heterogeneous substitution processes. We present our best trained predictor in a freely available program named Phylogenetics by Deep Learning (PhyDL, https://gitlab.com/ztzou/phydl; last accessed January 3, 2020).

We tested two pipelines developed for template-free protein structure prediction in the CASP11 experiment. First, the QUARK pipeline constructs structure models by reassembling fragments of continuously distributed lengths excised from unrelated proteins. Five free-modeling (FM) targets have the model successfully constructed by QUARK with a TM-score above 0.4, including the first model of T0837-D1, which has a TM-score=0.736 and RMSD=2.9 Å to the native. Detailed analysis showed that the success is partly attributed to the high-resolution contact map prediction derived from fragment-based distance-profiles, which are mainly located between regular secondary structure elements and loops/turns and help guide the orientation of secondary structure assembly. In the Zhang-Server pipeline, weakly scoring threading templates are re-ordered by the structural similarity to the ab initio folding models, which are then reassembled by I-TASSER based structure assembly simulations; 60% more domains with length up to 204 residues, compared to the QUARK pipeline, were successfully modeled by the I-TASSER pipeline with a TM-score above 0.4. The robustness of the I-TASSER pipeline can stem from the composite fragment-assembly simulations that combine structures from both ab initio folding and threading template refinements. Despite the promising cases, challenges still exist in long-range beta-strand folding, domain parsing, and the uncertainty of secondary structure prediction; the latter of which was found to affect nearly all aspects of FM structure predictions, from fragment identification, target classification, structure assembly, to final model selection. Significant efforts are needed to solve these problems before real progress on FM could be made.

Supplementary data are available at Bioinformatics online.