Statistical compression of protein sequences and inference of marginal probability landscapes over competing alignments using finite state models and Dirichlet priors

Gene-level alignment of single-cell trajectories

Single-cell data analysis can infer dynamic changes in cell populations, for example across time, space or in response to perturbation, thus deriving pseudotime trajectories. Current approaches comparing trajectories often use dynamic programming but are limited by assumptions such as the existence of a definitive match. Here we describe Genes2Genes, a Bayesian information-theoretic dynamic programming framework for aligning single-cell trajectories. It is able to capture sequential matches and mismatches of individual genes between a reference and query trajectory, highlighting distinct clusters of alignment patterns. Across both real world and simulated datasets, it accurately inferred alignments and demonstrated its utility in disease cell-state trajectory analysis. In a proof-of-concept application, Genes2Genes revealed that T cells differentiated in vitro match an immature in vivo state while lacking expression of genes associated with TNF signaling. This demonstrates that precise trajectory alignment can pinpoint divergence from the in vivo system, thus guiding the optimization of in vitro culture conditions.

Bridging the gaps in statistical models of protein alignment

Summary

Sequences of proteins evolve by accumulating substitutions together with insertions and deletions (indels) of amino acids. However, it remains a common practice to disconnect substitutions and indels, and infer approximate models for each of them separately, to quantify sequence relationships. Although this approach brings with it computational convenience (which remains its primary motivation), there is a dearth of attempts to unify and model them systematically and together. To overcome this gap, this article demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed using a time-parameterized substitution matrix and a time-parameterized alignment state machine. Methods to derive all parameters of such a model from any benchmark collection of aligned protein sequences are described here. This has not only allowed us to generate a unified statistical model for each of the nine widely used substitution matrices (PAM, JTT, BLOSUM, JO, WAG, VTML, LG, MIQS and PFASUM), but also resulted in a new unified model, MMLSUM. Our underlying methodology measures the Shannon information content using each model to explain losslessly any given collection of alignments, which has allowed us to quantify the performance of all the above models on six comprehensive alignment benchmarks. Our results show that MMLSUM results in a new and clear overall best performance, followed by PFASUM, VTML, BLOSUM and MIQS, respectively, amongst the top five. We further analyze the statistical properties of MMLSUM model and contrast it with others.

Supplementary information

Supplementary data are available at Bioinformatics online.

Three-dimensional Structure Databases of Biological Macromolecules

Databases of three-dimensional structures of proteins (and their associated molecules) provide: (a) Curated repositories of coordinates of experimentally determined structures, including extensive metadata; for instance information about provenance, details about data collection and interpretation, and validation of results. (b) Information-retrieval tools to allow searching to identify entries of interest and provide access to them. (c) Links among databases, especially to databases of amino-acid and genetic sequences, and of protein function; and links to software for analysis of amino-acid sequence and protein structure, and for structure prediction. (d) Collections of predicted three-dimensional structures of proteins. These will become more and more important after the breakthrough in structure prediction achieved by AlphaFold2. The single global archive of experimentally determined biomacromolecular structures is the Protein Data Bank (PDB). It is managed by wwPDB, a consortium of five partner institutions: the Protein Data Bank in Europe (PDBe), the Research Collaboratory for Structural Bioinformatics (RCSB), the Protein Data Bank Japan (PDBj), the BioMagResBank (BMRB), and the Electron Microscopy Data Bank (EMDB). In addition to jointly managing the PDB repository, the individual wwPDB partners offer many tools for analysis of protein and nucleic acid structures and their complexes, including providing computer-graphic representations. Their collective and individual websites serve as hubs of the community of structural biologists, offering newsletters, reports from Task Forces, training courses, and "helpdesks," as well as links to external software.Many specialized projects are based on the information contained in the PDB. Especially important are SCOP, CATH, and ECOD, which present classifications of protein domains.

OUP accepted manuscript

MOTIVATION

Alignments are correspondences between sequences. How reliable are alignments of amino acid sequences of proteins, and what inferences about protein relationships can be drawn? Using techniques not previously applied to these questions, by weighting every possible sequence alignment by its posterior probability we derive a formal mathematical expectation, and develop an efficient algorithm for computation of the distance between alternative alignments allowing quantitative comparisons of sequence-based alignments with corresponding reference structure alignments.

RESULTS

By analyzing the sequences and structures of 1 million protein domain pairs, we report the variation of the expected distance between sequence-based and structure-based alignments, as a function of (Markov time of) sequence divergence. Our results clearly demarcate the 'daylight', 'twilight' and 'midnight' zones for interpreting residue-residue correspondences from sequence information alone.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

ProPIP: a tool for progressive multiple sequence alignment with Poisson Indel Process

BACKGROUND

Current alignment tools typically lack an explicit model of indel evolution, leading to artificially short inferred alignments (i.e., over-alignment) due to inconsistencies between the indel history and the phylogeny relating the input sequences.

RESULTS

We present a new progressive multiple sequence alignment tool ProPIP. The process of insertions and deletions is described using an explicit evolutionary model-the Poisson Indel Process or PIP. The method is based on dynamic programming and is implemented in a frequentist framework. The source code can be compiled on Linux, macOS and Microsoft Windows platforms. The algorithm is implemented in C++ as standalone program. The source code is freely available on GitHub at https://github.com/acg-team/ProPIP and is distributed under the terms of the GNU GPL v3 license.

CONCLUSIONS

The use of an explicit indel evolution model allows to avoid over-alignment, to infer gaps in a phylogenetically consistent way and to make inferences about the rates of insertions and deletions. Instead of the arbitrary gap penalties, the parameters used by ProPIP are the insertion and deletion rates, which have biological interpretation and are contextualized in a probabilistic environment. As a result, indel rate settings may be optimised in order to infer phylogenetically meaningful gap patterns.