Most protein substitution models use a single amino acid replacement matrix summarizing the biochemical properties of amino acids. However, site evolution is highly heterogeneous and depends on many factors that influence the substitution patterns. In this paper, we investigate the use of different substitution matrices for different site evolutionary rates. Indeed, the variability of evolutionary rates corresponds to one of the most apparent heterogeneity factors among sites, and there is no reason to assume that the substitution patterns remain identical regardless of the evolutionary rate. We first introduce LG4M, which is composed of four matrices, each corresponding to one discrete gamma rate category (of four). These matrices differ in their amino acid equilibrium distributions and in their exchangeabilities, contrary to the standard gamma model where only the global rate differs from one category to another. Next, we present LG4X, which also uses four different matrices, but leaves aside the gamma distribution and follows a distribution-free scheme for the site rates. All these matrices are estimated from a very large alignment database, and our two models are tested using a large sample of independent alignments. Detailed analysis of resulting matrices and models shows the complexity of amino acid substitutions and the advantage of flexible models such as LG4M and LG4X. Both significantly outperform single-matrix models, providing gains of dozens to hundreds of log-likelihood units for most data sets. LG4X obtains substantial gains compared with LG4M, thanks to its distribution-free scheme for site rates. Since LG4M and LG4X display such advantages but require the same memory space and have comparable running times to standard models, we believe that LG4M and LG4X are relevant alternatives to single replacement matrices. Our models, data, and software are available from http://www.atgc-montpellier.fr/models/lg4x.

Summary Background Improvements to prognostic models in metastatic castration-resistant prostate cancer have the potential to augment clinical trial design and guide treatment strategies. In partnership with Project Data Sphere, a not-for-profit initiative allowing data from cancer clinical trials to be shared broadly with researchers, we designed an open-data, crowdsourced, DREAM (Dialogue for Reverse Engineering Assessments and Methods) challenge to not only identify a better prognostic model for prediction of survival in patients with metastatic castration-resistant prostate cancer but also engage a community of international data scientists to study this disease. Methods Data from the comparator arms of four phase 3 clinical trials in first-line metastatic castration-resistant prostate cancer were obtained from Project Data Sphere, comprising 476 patients treated with docetaxel and prednisone from the ASCENT2 trial, 526 patients treated with docetaxel, prednisone, and placebo in the MAINSAIL trial, 598 patients treated with docetaxel, prednisone or prednisolone, and placebo in the VENICE trial, and 470 patients treated with docetaxel and placebo in the ENTHUSE 33 trial. Datasets consisting of more than 150 clinical variables were curated centrally, including demographics, laboratory values, medical history, lesion sites, and previous treatments. Data from ASCENT2, MAINSAIL, and VENICE were released publicly to be used as training data to predict the outcome of interest—namely, overall survival. Clinical data were also released for ENTHUSE 33, but data for outcome variables (overall survival and event status) were hidden from the challenge participants so that ENTHUSE 33 could be used for independent validation. Methods were evaluated using the integrated time-dependent area under the curve (iAUC). The reference model, based on eight clinical variables and a penalised Cox proportional-hazards model, was used to compare method performance. Further validation was done using data from a fifth trial—ENTHUSE M1—in which 266 patients with metastatic castration-resistant prostate cancer were treated with placebo alone. Findings 50 independent methods were developed to predict overall survival and were evaluated through the DREAM challenge. The top performer was based on an ensemble of penalised Cox regression models (ePCR), which uniquely identified predictive interaction effects with immune biomarkers and markers of hepatic and renal function. Overall, ePCR outperformed all other methods (iAUC 0·791; Bayes factor >5) and surpassed the reference model (iAUC 0·743; Bayes factor >20). Both the ePCR model and reference models stratified patients in the ENTHUSE 33 trial into high-risk and low-risk groups with significantly different overall survival (ePCR: hazard ratio 3·32, 95% CI 2·39–4·62, p<0·0001; reference model: 2·56, 1·85–3·53, p<0·0001). The new model was validated further on the ENTHUSE M1 cohort with similarly high performance (iAUC 0·768). Meta-analysis across all methods confirmed previously identified...

Amino acid substitution models play a crucial role in phylogenetic analyses. Maximum likelihood (ML) methods have been proposed to estimate amino acid substitution models, however, they are typically complicated and slow. In this paper, we propose QMaker, a new ML method to estimate a general time-reversible Q matrix from a large protein dataset consisting of multiple sequence alignments. QMaker combines an efficient ML tree search algorithm, a model selection for handling the model heterogeneity among alignments, and the consideration of rate mixture models among sites. We provide QMaker as a user-friendly function in the IQ-TREE software package (http://www.iqtree.org) supporting the use of multiple CPU cores so that biologists can easily estimate amino acid substitution models from their own protein alignments. We used QMaker to estimate new empirical general amino acid substitution models from the current Pfam database as well as five clade-specific models for mammals, birds, insects, yeasts, and plants. Our results show that the new models considerably improve the fit between model and data and in some cases influence the inference of phylogenetic tree topologies.

BackgroundThe amino acid substitution model is the core component of many protein analysis systems such as sequence similarity search, sequence alignment, and phylogenetic inference. Although several general amino acid substitution models have been estimated from large and diverse protein databases, they remain inappropriate for analyzing specific species, e.g., viruses. Emerging epidemics of influenza viruses raise the need for comprehensive studies of these dangerous viruses. We propose an influenza-specific amino acid substitution model to enhance the understanding of the evolution of influenza viruses.ResultsA maximum likelihood approach was applied to estimate an amino acid substitution model (FLU) from ~113, 000 influenza protein sequences, consisting of ~20 million residues. FLU outperforms 14 widely used models in constructing maximum likelihood phylogenetic trees for the majority of influenza protein alignments. On average, FLU gains ~42 log likelihood points with an alignment of 300 sites. Moreover, topologies of trees constructed using FLU and other models are frequently different. FLU does indeed have an impact on likelihood improvement as well as tree topologies. It was implemented in PhyML and can be downloaded from ftp://ftp.sanger.ac.uk/pub/1000genomes/lsq/FLU or included in PhyML 3.0 server at http://www.atgc-montpellier.fr/phyml/.ConclusionsFLU should be useful for any influenza protein analysis system which requires an accurate description of amino acid substitutions.

BackgroundAmino acid substitution models play an essential role in inferring phylogenies from mitochondrial protein data. However, only few empirical models have been estimated from restricted mitochondrial protein data of a hundred species. The existing models are unlikely to represent appropriately the amino acid substitutions from hundred thousands metazoan mitochondrial protein sequences.ResultsWe selected 125,935 mitochondrial protein sequences from 34,448 species in the metazoan kingdom to estimate new amino acid substitution models targeting metazoa, vertebrates and invertebrate groups. The new models help to find significantly better likelihood phylogenies in comparison with the existing models. We noted remarkable distances from phylogenies with the existing models to the maximum likelihood phylogenies that indicate a considerable number of incorrect bipartitions in phylogenies with the existing models. Finally, we used the new models and mitochondrial protein data to certify that Testudines, Aves, and Crocodylia form one separated clade within amniotes.ConclusionsWe introduced new mitochondrial amino acid substitution models for metazoan mitochondrial proteins. The new models outperform the existing models in inferring phylogenies from metazoan mitochondrial protein data. We strongly recommend researchers to use the new models in analysing metazoan mitochondrial protein data.