Ancestral sequence alignment under optimal conditions

BACKGROUND: Multiple genome alignment is an important problem in bioinformatics. An important subproblem used by many multiple alignment approaches is that of aligning two multiple alignments. Many popular alignment algorithms for DNA use the sum-of-pairs heuristic, where the score of a multiple alignment is the sum of its induced pairwise alignment scores. However, the biological meaning of the sum-of-pairs of pairs heuristic is not obvious. Additionally, many algorithms based on the sum-of-pairs heuristic are complicated and slow, compared to pairwise alignment algorithms. An alternative approach to aligning alignments is to first infer ancestral sequences for each alignment, and then align the two ancestral sequences. In addition to being fast, this method has a clear biological basis that takes into account the evolution implied by an underlying phylogenetic tree. In this study we explore the accuracy of aligning alignments by ancestral sequence alignment. We examine the use of both maximum likelihood and parsimony to infer ancestral sequences. Additionally, we investigate the effect on accuracy of allowing ambiguity in our ancestral sequences. RESULTS: We use synthetic sequence data that we generate by simulating evolution on a phylogenetic tree. We use two different types of phylogenetic trees: trees with a period of rapid growth followed by a period of slow growth, and trees with a period of slow growth followed by a period of rapid growth. We examine the alignment accuracy of four ancestral sequence reconstruction and alignment methods: parsimony, maximum likelihood, ambiguous parsimony, and ambiguous maximum likelihood. Additionally, we compare against the alignment accuracy of two sum-of-pairs algorithms: ClustalW and the heuristic of Ma, Zhang, and Wang. CONCLUSION: We find that allowing ambiguity in ancestral sequences does not lead to better multiple alignments. Regardless of whether we use parsimony or maximum likelihood, the success of aligning ancestral sequences containing ambiguity is very sensitive to the choice of gap open cost. Surprisingly, we find that using maximum likelihood to infer ancestral sequences results in less accurate alignments than when using parsimony to infer ancestral sequences. Finally, we find that the sum-of-pairs methods produce better alignments than all of the ancestral alignment methods

Global Alignment of Molecular Sequences via Ancestral State Reconstruction

Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on substitution-only models of sequence evolution. In practice these methods are extended beyond this simplified setting with the use of heuristics that produce global alignments of the input sequences--an important problem which has no rigorous model-based solution. In this paper we consider a new version of the multiple sequence alignment in the context of stochastic indel models. More precisely, we introduce the following {\em trace reconstruction problem on a tree} (TRPT): a binary sequence is broadcast through a tree channel where we allow substitutions, deletions, and insertions; we seek to reconstruct the original sequence from the sequences received at the leaves of the tree. We give a recursive procedure for this problem with strong reconstruction guarantees at low mutation rates, providing also an alignment of the sequences at the leaves of the tree. The TRPT problem without indels has been studied in previous work (Mossel 2004, Daskalakis et al. 2006) as a bootstrapping step towards obtaining optimal phylogenetic reconstruction methods. The present work sets up a framework for extending these works to evolutionary models with indels

The Mathematics of Phylogenomics

The grand challenges in biology today are being shaped by powerful high-throughput technologies that have revealed the genomes of many organisms, global expression patterns of genes and detailed information about variation within populations. We are therefore able to ask, for the first time, fundamental questions about the evolution of genomes, the structure of genes and their regulation, and the connections between genotypes and phenotypes of individuals. The answers to these questions are all predicated on progress in a variety of computational, statistical, and mathematical fields. The rapid growth in the characterization of genomes has led to the advancement of a new discipline called Phylogenomics. This discipline results from the combination of two major fields in the life sciences: Genomics, i.e., the study of the function and structure of genes and genomes; and Molecular Phylogenetics, i.e., the study of the hierarchical evolutionary relationships among organisms and their genomes. The objective of this article is to offer mathematicians a first introduction to this emerging field, and to discuss specific mathematical problems and developments arising from phylogenomics.Comment: 41 pages, 4 figure

Human-chimpanzee alignment: Ortholog Exponentials and Paralog Power Laws

Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.Comment: Main text: 31 pages, 13 figures, 1 table; Supplementary materials: 9 pages, 9 figures, 1 tabl

Polyploidy breaks speciation barriers in Australian burrowing frogs Neobatrachus

Polyploidy has played an important role in evolution across the tree of life but it is still unclear how polyploid lineages may persist after their initial formation. While both common and well-studied in plants, polyploidy is rare in animals and generally less understood. The Australian burrowing frog genus Neobatrachus is comprised of six diploid and three polyploid species and offers a powerful animal polyploid model system. We generated exome-capture sequence data from 87 individuals representing all nine species of Neobatrachus to investigate species-level relationships, the origin and inheritance mode of polyploid species, and the population genomic effects of polyploidy on genus-wide demography. We describe rapid speciation of diploid Neobatrachus species and show that the three independently originated polyploid species have tetrasomic or mixed inheritance. We document higher genetic diversity in tetraploids, resulting from widespread gene flow between the tetraploids, asymmetric inter-ploidy gene flow directed from sympatric diploids to tetraploids, and isolation of diploid species from each other. We also constructed models of ecologically suitable areas for each species to investigate the impact of climate on differing ploidy levels. These models suggest substantial change in suitable areas compared to past climate, which correspond to population genomic estimates of demographic histories. We propose that Neobatrachus diploids may be suffering the early genomic impacts of climate-induced habitat loss, while tetraploids appear to be avoiding this fate, possibly due to widespread gene flow. Finally, we demonstrate that Neobatrachus is an attractive model to study the effects of ploidy on the evolution of adaptation in animals

Origin and evolution of water oxidation before the last common ancestor of the Cyanobacteria

Photosystem II, the water oxidizing enzyme, altered the course of evolution by filling the atmosphere with oxygen. Here, we reconstruct the origin and evolution of water oxidation at an unprecedented level of detail by studying the phylogeny of all D1 subunits, the main protein coordinating the water oxidizing cluster (Mn4CaO5) of Photosystem II. We show that D1 exists in several forms making well-defined clades, some of which could have evolved before the origin of water oxidation and presenting many atypical characteristics. The most ancient form is found in the genome of Gloeobacter kilaueensis JS-1 and this has a C-terminus with a higher sequence identity to D2 than to any other D1. Two other groups of early evolving D1 correspond to those expressed under prolonged far-red illumination and in darkness. These atypical D1 forms are characterized by a dramatically different Mn4CaO5 binding site and a Photosystem II containing such a site may assemble an unconventional metal cluster. The first D1 forms with a full set of ligands to the Mn4CaO5 cluster are grouped with D1 proteins expressed only under low oxygen concentrations and the latest evolving form is the dominant type of D1 found in all cyanobacteria and plastids. In addition, we show that the plastid ancestor had a D1 more similar to those in early branching Synechococcus. We suggest each one of these forms of D1 originated from transitional forms at different stages towards the innovation and optimization of water oxidation before the last common ancestor of all known cyanobacteria

Distribution of Aligned Letter Pairs in Optimal Alignments of Random Sequences

Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges to a unique limiting distribution as $n$ tends to infinity. This result is interesting because it helps understanding the microscopic path structure of a special type of last passage percolation problem with correlated weights, an area of long-standing open problems. Characterizing the microscopic path structure yields furthermore a robust alternative to optimal alignment scores for testing the relatedness of genetic sequences

A deeply branching thermophilic bacterium with an ancient acetyl-CoA pathway dominates a subsurface ecosystem

<div><p>A nearly complete genome sequence of <em>Candidatus</em> ‘Acetothermum autotrophicum’, a presently uncultivated bacterium in candidate division OP1, was revealed by metagenomic analysis of a subsurface thermophilic microbial mat community. Phylogenetic analysis based on the concatenated sequences of proteins common among 367 prokaryotes suggests that <em>Ca.</em> ‘A. autotrophicum’ is one of the earliest diverging bacterial lineages. It possesses a folate-dependent Wood-Ljungdahl (acetyl-CoA) pathway of CO₂ fixation, is predicted to have an acetogenic lifestyle, and possesses the newly discovered archaeal-autotrophic type of bifunctional fructose 1,6-bisphosphate aldolase/phosphatase. A phylogenetic analysis of the core gene cluster of the acethyl-CoA pathway, shared by acetogens, methanogens, some sulfur- and iron-reducers and dechlorinators, supports the hypothesis that the core gene cluster of <em>Ca.</em> ‘A. autotrophicum’ is a particularly ancient bacterial pathway. The habitat, physiology and phylogenetic position of <em>Ca.</em> ‘A. autotrophicum’ support the view that the first bacterial and archaeal lineages were H₂-dependent acetogens and methanogenes living in hydrothermal environments.</p> </div