Solving the master equation for Indels

Insertions and deletions as phylogenetic signal in an alignment-free context

Most methods for phylogenetic tree reconstruction are based on sequence alignments; they infer phylogenies from substitutions that may have occurred at the aligned sequence positions. Gaps in alignments are usually not employed as phylogenetic signal. In this paper, we explore an alignment-free approach that uses insertions and deletions (indels) as an additional source of information for phylogeny inference. For a set of four or more input sequences, we generate so-called quartet blocks of four putative homologous segments each. For pairs of such quartet blocks involving the same four sequences, we compare the distances between the two blocks in these sequences, to obtain hints about indels that may have happened between the blocks since the respective four sequences have evolved from their last common ancestor. A prototype implementation that we call Gap-SpaM is presented to infer phylogenetic trees from these data, using a quartet-tree approach or, alternatively, under the maximum-parsimony paradigm. This approach should not be regarded as an alternative to established methods, but rather as a complementary source of phylogenetic information. Interestingly, however, our software is able to produce phylogenetic trees from putative indels alone that are comparable to trees obtained with existing alignment-free methods.

Phylogenetic tree inference based on DNA or protein sequence comparison is a fundamental task in computational biology. Given a multiple alignment of a set of input sequences, most approaches compare aligned sequence positions to each other, to find a suitable tree, based on a model of molecular evolution. Insertions and deletions that may have happened since the input sequences evolved from their last common ancestor are ignored by most phylogeny methods. Herein, we show that insertions and deletions can provide an additional source of information for phylogeny inference, and that such information can be obtained with a simple alignment-free approach. We provide an implementation of this idea that we call Gap-SpaM. The proposed approach is complementary to existing phylogeny methods since it is based on a completely different source of information. It is, thus, not meant to be an alternative to those existing methods but rather as a possible additional source of information for tree inference.

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.

Alignment-Integrated Reconstruction of Ancestral Sequences Improves Accuracy

Ancestral sequence reconstruction (ASR) uses an alignment of extant protein sequences, a phylogeny describing the history of the protein family and a model of the molecular-evolutionary process to infer the sequences of ancient proteins, allowing researchers to directly investigate the impact of sequence evolution on protein structure and function. Like all statistical inferences, ASR can be sensitive to violations of its underlying assumptions. Previous studies have shown that, whereas phylogenetic uncertainty has only a very weak impact on ASR accuracy, uncertainty in the protein sequence alignment can more strongly affect inferred ancestral sequences. Here, we show that errors in sequence alignment can produce errors in ASR across a range of realistic and simplified evolutionary scenarios. Importantly, sequence reconstruction errors can lead to errors in estimates of structural and functional properties of ancestral proteins, potentially undermining the reliability of analyses relying on ASR. We introduce an alignment-integrated ASR approach that combines information from many different sequence alignments. We show that integrating alignment uncertainty improves ASR accuracy and the accuracy of downstream structural and functional inferences, often performing as well as highly accurate structure-guided alignment. Given the growing evidence that sequence alignment errors can impact the reliability of ASR studies, we recommend that future studies incorporate approaches to mitigate the impact of alignment uncertainty. Probabilistic modeling of insertion and deletion events has the potential to radically improve ASR accuracy when the model reflects the true underlying evolutionary history, but further studies are required to thoroughly evaluate the reliability of these approaches under realistic conditions.

The Cumulative Indel Model: Fast and Accurate Statistical Evolutionary Alignment

Sequence alignment is essential for phylogenetic and molecular evolution inference, as well as in many other areas of bioinformatics and evolutionary biology. Inaccurate alignments can lead to severe biases in most downstream statistical analyses. Statistical alignment based on probabilistic models of sequence evolution addresses these issues by replacing heuristic score functions with evolutionary model-based probabilities. However, score-based aligners and fixed-alignment phylogenetic approaches are still more prevalent than methods based on evolutionary indel models, mostly due to computational convenience. Here, I present new techniques for improving the accuracy and speed of statistical evolutionary alignment. The "cumulative indel model" approximates realistic evolutionary indel dynamics using differential equations. "Adaptive banding" reduces the computational demand of most alignment algorithms without requiring prior knowledge of divergence levels or pseudo-optimal alignments. Using simulations, I show that these methods lead to fast and accurate pairwise alignment inference. Also, I show that it is possible, with these methods, to align and infer evolutionary parameters from a single long synteny block ($\approx$530 kbp) between the human and chimp genomes. The cumulative indel model and adaptive banding can therefore improve the performance of alignment and phylogenetic methods. [Evolutionary alignment; pairHMM; sequence evolution; statistical alignment; statistical genetics.].

Eleven grand challenges in single-cell data science

The recent boom in microfluidics and combinatorial indexing strategies, combined with low sequencing costs, has empowered single-cell sequencing technology. Thousands-or even millions-of cells analyzed in a single experiment amount to a data revolution in single-cell biology and pose unique data science problems. Here, we outline eleven challenges that will be central to bringing this emerging field of single-cell data science forward. For each challenge, we highlight motivating research questions, review prior work, and formulate open problems. This compendium is for established researchers, newcomers, and students alike, highlighting interesting and rewarding problems for the coming years.

Phylogenetic Signal of Indels and the Neoavian Radiation

The early radiation of Neoaves has been hypothesized to be an intractable “hard polytomy”. We explore the fundamental properties of insertion/deletion alleles (indels), an under-utilized form of genomic data with the potential to help solve this. We scored >5 million indels from >7000 pan-genomic intronic and ultraconserved element (UCE) loci in 48 representatives of all neoavian orders. We found that intronic and UCE indels exhibited less homoplasy than nucleotide (nt) data. Gene trees estimated using indel data were less resolved than those estimated using nt data. Nevertheless, Accurate Species TRee Algorithm (ASTRAL) species trees estimated using indels were generally similar to nt-based ASTRAL trees, albeit with lower support. However, the power of indel gene trees became clear when we combined them with nt gene trees, including a striking result for UCEs. The individual UCE indel and nt ASTRAL trees were incongruent with each other and with the intron ASTRAL trees; however, the combined indel+nt ASTRAL tree was much more congruent with the intronic trees. Finally, combining indel and nt data for both introns and UCEs provided sufficient power to reduce the scope of the polytomy that was previously proposed for several supraordinal lineages of Neoaves.

The Molecular Clock in the Evolution of Protein Structures

The molecular clock hypothesis, which states that substitutions accumulate in protein sequences at a constant rate, plays a fundamental role in molecular evolution but it is violated when selective or mutational processes vary with time. Such violations of the molecular clock have been widely investigated for protein sequences, but not yet for protein structures. Here, we introduce a novel statistical test (Significant Clock Violations) and perform a large scale assessment of the molecular clock in the evolution of both protein sequences and structures in three large superfamilies. After validating our method with computer simulations, we find that clock violations are generally consistent in sequence and structure evolution, but they tend to be larger and more significant in structure evolution. Moreover, changes of function assessed through Gene Ontology and InterPro terms are associated with large and significant clock violations in structure evolution. We found that almost one third of significant clock violations are significant in structure evolution but not in sequence evolution, highlighting the advantage to use structure information for assessing accelerated evolution and gathering hints of positive selection. Clock violations between closely related pairs are frequently significant in sequence evolution, consistent with the observed time dependence of the substitution rate attributed to segregation of neutral and slightly deleterious polymorphisms, but not in structure evolution, suggesting that these substitutions do not affect protein structure although they may affect stability. These results are consistent with the view that natural selection, both negative and positive, constrains more strongly protein structures than protein sequences. Our code for computing clock violations is freely available at https://github.com/ugobas/Molecular_clock.

Estimation of duplication history under a stochastic model for tandem repeats

BACKGROUND

Tandem repeat sequences are common in the genomes of many organisms and are known to cause important phenomena such as gene silencing and rapid morphological changes. Due to the presence of multiple copies of the same pattern in tandem repeats and their high variability, they contain a wealth of information about the mutations that have led to their formation. The ability to extract this information can enhance our understanding of evolutionary mechanisms.

RESULTS

We present a stochastic model for the formation of tandem repeats via tandem duplication and substitution mutations. Based on the analysis of this model, we develop a method for estimating the relative mutation rates of duplications and substitutions, as well as the total number of mutations, in the history of a tandem repeat sequence. We validate our estimation method via Monte Carlo simulation and show that it outperforms the state-of-the-art algorithm for discovering the duplication history. We also apply our method to tandem repeat sequences in the human genome, where it demonstrates the different behaviors of micro- and mini-satellites and can be used to compare mutation rates across chromosomes. It is observed that chromosomes that exhibit the highest mutation activity in tandem repeat regions are the same as those thought to have the highest overall mutation rates. However, unlike previous works that rely on comparing human and chimpanzee genomes to measure mutation rates, the proposed method allows us to find chromosomes with the highest mutation activity based on a single genome, in essence by comparing (approximate) copies of the pattern in tandem repeats.

CONCLUSION

The prevalence of tandem repeats in most organisms and the efficiency of the proposed method enable studying various aspects of the formation of tandem repeats and the surrounding sequences in a wide range of settings.

AVAILABILITY

The implementation of the estimation method is available at http://ips.lab.virginia.edu/smtr .