SUMMARY: Simulated sequence alignments are frequently used to test bioinformatics tools, but current sequence simulators are limited to defined state spaces. Here, we present the COMPletely Arbitrary Sequence Simulator (COMPASS), which is able to simulate the evolution of absolutely any discrete state space along a tree, for any form of time-reversible model. AVAILABILITY AND IMPLEMENTATION: COMPASS is implemented in Python 2.7, and is freely available for all platforms with the Supplementary Information, as well as at http://labs.carleton.ca/eme/software-and-data. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In recent years, there has been an increasing interest in the potential of codon substitution models for a variety of applications. However, the computational demands of these models have sometimes lead to the adoption of oversimplified assumptions, questionable statistical methods or a limited focus on small data sets. RESULTS: Here, we offer a scalable, message-passing-interface-based Bayesian implementation of site-heterogeneous codon models in the mutation-selection framework. Our software jointly infers the global mutational parameters at the nucleotide level, the branch lengths of the tree and a Dirichlet process governing across-site variation at the amino acid level. We focus on an example estimation of the distribution of selection coefficients from an alignment of several hundred sequences of the influenza PB2 gene, and highlight the site-specific characterization enabled by such a modeling approach. Finally, we discuss future potential applications of the software for conducting evolutionary inferences. AVAILABILITY AND IMPLEMENTATION: The models are implemented within the PhyloBayes-MPI package, (available at phylobayes.org) along with usage details in the accompanying manual.

MOTIVATION: Mapping character state changes over phylogenetic trees is central to the study of evolution. However, current probabilistic methods for generating such mappings are ill-suited to certain types of evolutionary models, in particular, the widely used models of codon substitution. RESULTS: We describe a general method, based on a uniformization technique, which can be utilized to generate realizations of a Markovian substitution process conditional on an alignment of character states and a given tree topology. The method is applicable under a wide range of evolutionary models, and to illustrate its usefulness in practice, we embed it within a data augmentation-based Markov chain Monte Carlo sampler, for approximating posterior distributions under previously proposed codon substitution models. The sampler is found to be more efficient than the conventional pruning-based sampler with the decorrelation times between draws from the posterior reduced by a factor of 20 or more.

BACKGROUND: The aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility. RESULTS: We propose a formulation of the protein design problem in terms of model-based statistical inference. Our framework uses the maximum likelihood principle to optimize the unknown parameters of a statistical potential, which we call an inverse potential to contrast with classical potentials used for structure prediction. We propose an implementation based on Markov chain Monte Carlo, in which the likelihood is maximized by gradient descent and is numerically estimated by thermodynamic integration. The fit of the models is evaluated by cross-validation. We apply this to a simple pairwise contact potential, supplemented with a solvent-accessibility term, and show that the resulting models have a better predictive power than currently available pairwise potentials. Furthermore, the model comparison method presented here allows one to measure the relative contribution of each component of the potential, and to choose the optimal number of accessibility classes, which turns out to be much higher than classically considered. CONCLUSION: Altogether, this reformulation makes it possible to test a wide diversity of models, using different forms of potentials, or accounting for other factors than just the constraint of thermodynamic stability. Ultimately, such model-based statistical analyses may help to understand the forces shaping protein sequences, and driving their evolution.