Manuel Lafond

Orthology and paralogy constraints: satisfiability and consistency

BackgroundA variety of methods based on sequence similarity, reconciliation, synteny or functional characteristics, can be used to infer orthology and paralogy relations between genes of a given gene family G. But is a given set C of orthology/paralogy constraints possible, i.e., can they simultaneously co-exist in an evolutionary history for G? While previous studies have focused on full sets of constraints, here we consider the general case where C does not necessarily involve a constraint for each pair of genes. The problem is subdivided in two parts: (1) Is C satisfiable, i.e. can we find an event-labeled gene tree G inducing C? (2) Is there such a G which is consistent, i.e., such that all displayed triplet phylogenies are included in a species tree?ResultsPrevious results on the Graph sandwich problem can be used to answer to (1), and we provide polynomial-time algorithms for satisfiability and consistency with a given species tree. We also describe a new polynomial-time algorithm for the case of consistency with an unknown species tree and full knowledge of pairwise orthology/paralogy relationships, as well as a branch-and-bound algorithm in the case when unknown relations are present. We show that our algorithms can be used in combination with ProteinOrtho, a sequence similarity-based orthology detection tool, to extract a set of robust orthology/paralogy relationships.

Gene tree correction guided by orthology

BackgroundReconciled gene trees yield orthology and paralogy relationships between genes. This information may however contradict other information on orthology and paralogy provided by other footprints of evolution, such as conserved synteny.ResultsWe explore a way to include external information on orthology in the process of gene tree construction. Given an initial gene tree and a set of orthology constraints on pairs of genes or on clades, we give polynomial-time algorithms for producing a modified gene tree satisfying the set of constraints, that is as close as possible to the original one according to the Robinson-Foulds distance. We assess the validity of the modifications we propose by computing the likelihood ratio between initial and modified trees according to sequence alignments on Ensembl trees, showing that often the two trees are statistically equivalent.AvailabilitySoftware and data available upon request to the corresponding author.

Efficient gene tree correction guided by genome evolution

Motivations Gene trees inferred solely from multiple alignments of homologous sequences often contain weakly supported and uncertain branches. Information for their full resolution may lie in the dependency between gene families and their genomic context. Integrative methods, using species tree information in addition to sequence information, often rely on a computationally intensive tree space search which forecloses an application to large genomic databases. Results We propose a new method, called ProfileNJ, that takes a gene tree with statistical supports on its branches, and corrects its weakly supported parts by using a combination of information from a species tree and a distance matrix. Its low running time enabled us to use it on the whole Ensembl Compara database, for which we propose an alternative, arguably more plausible set of gene trees. This allowed us to perform a genome-wide analysis of duplication and loss patterns on the history of 63 eukaryote species, and predict ancestral gene content and order for all ancestors along the phylogeny. Availability A web interface called RefineTree, including ProfileNJ as well as a other gene tree correction methods, which we also test on the Ensembl gene families, is available at: http://www-ens.iro.umontreal.ca/~adbit/polytomysolver.html. The code of ProfileNJ as well as the set of gene trees corrected by ProfileNJ from Ensembl Compara version 73 families are also made available.

The link between orthology relations and gene trees: a correction perspective

BackgroundWhile tree-oriented methods for inferring orthology and paralogy relations between genes are based on reconciling a gene tree with a species tree, many tree-free methods are also available (usually based on sequence similarity). Recently, the link between orthology relations and gene trees has been formally considered from the perspective of reconstructing phylogenies from orthology relations. In this paper, we consider this link from a correction point of view. Indeed, a gene tree induces a set of relations, but the converse is not always true: a set of relations is not necessarily in agreement with any gene tree. A natural question is thus how to minimally correct an infeasible set of relations. Another natural question, given a gene tree and a set of relations, is how to minimally correct a gene tree so that the resulting gene tree fits the set of relations.ResultsWe consider four variants of relation and gene tree correction problems, and provide hardness results for all of them. More specifically, we show that it is NP-Hard to edit a minimum of set of relations to make them consistent with a given species tree. We also show that the problem of finding a maximum subset of genes that share consistent relations is hard to approximate. We then demonstrate that editing a gene tree to satisfy a given set of relations in a minimum way is NP-Hard, where “minimum” refers either to the number of modified relations depicted by the gene tree or the number of clades that are lost. We also discuss some of the algorithmic perspectives given these hardness results.

Orthology Relation and Gene Tree Correction: Complexity Results

Tree-oriented methods for inferring orthology and paralogy relations between genes are based on reconciling a gene tree with a species tree. On the other hand, many tree-free methods, mainly based on sequence similarity, are also available. The link between orthology relations and gene trees has been formally considered recently from the angle of reconstructing phylogenies from orthology relations. Here, we rather consider this link from a correction point of view. While a gene tree induces a set of relations, the converse is not always true, as a set of relations is not necessarily in agreement with any gene tree. How can we minimally correct an infeasible set of relations? On the other hand, given a gene tree and a set of relations, how to minimally correct a gene tree in order to fit the set of relations? In this paper, various objective functions are considered for the minimality criterion, among them the Robinson-Foulds distance between the initial and corrected gene tree. All considered problem variants are shown to be NP-complete.

Correction of Weighted Orthology and Paralogy Relations - Complexity and Algorithmic Results

A relation graph for a gene family is a graph with vertices representing the genes, edges connecting pairs of orthologous genes and “missing” edges representing paralogs. While a gene tree directly leads to a set of orthology and paralogy relations, the converse is not always true. Indeed a relation graph cannot necessarily be inferred from any tree, and even if it is “satisfiable” by a tree, this tree is not necessarily “consistent”, i.e. does not necessarily reflect a valid history for the genes, in agreement with a species tree. Here, we consider the problems of minimally correcting a relation graph for satisfiability and consistency, when a degree of confidence is assigned to each orthology or paralogy relation, leading to a weighted relation graph. We provide complexity and algorithmic results for minimizing corrections on a weighted graph, and also for the maximization variant of the problems for unweighted graphs.

The Scourge of Internet Personal Data Collection

In todays age of exposure, websites and Internet services are collecting personal data-with or without the knowledge or consent of users. Not only does new technology provide an abundance of methods for organizations to gather and store information, but people are also willingly sharing data with increasing frequency, exposing their intimate lives on social media websites such as Facebook, Twitter, You tube, My space and others. Moreover, online data brokers, search engines, data aggregators and many other actors of the web are profiling people for various purposes such as the improvement of marketing through better statistics and an ability to predict consumer behaviour. Other less known reasons include understanding the newest trends in education, gathering peoples medical history or observing tendencies in political opinions. People who care about privacy use the Privacy Enhancing Technologies (PETs) to protect their data, even though clearly not sufficiently. Indeed, as soon as information is recorded in a database, it becomes permanently available for analysis. Consequently even the most privacy aware users are not safe from the threat of re-identification. On the other hand, there are many people who are willing to share their personal information, even when fully conscious of the consequences. A claim from the advocates of open access information is that the preservation of privacy should not be an issue, as people seem to be confortable in a world where their tastes, lifestyle or personality are digitized and publicly available. This paper deals with Internet data collection and voluntary information disclosure, with an emphasis on the problems and challenges facing privacy nowadays.

The SCJ Small Parsimony Problem for Weighted Gene Adjacencies

Reconstructing ancestral gene orders in a given phylogeny is a classical problem in comparative genomics. Most existing methods compare conserved features in extant genomes in the phylogeny to define potential ancestral gene adjacencies, and either try to reconstruct all ancestral genomes under a global evolutionary parsimony criterion, or, focusing on a single ancestral genome, use a scaffolding approach to select a subset of ancestral gene adjacencies, generally aiming at reducing the fragmentation of the reconstructed ancestral genome. In this paper, we describe an exact algorithm for the Small Parsimony Problem that combines both approaches. We consider that gene adjacencies at internal nodes of the species phylogeny are weighted, and we introduce an objective function defined as a convex combination of these weights and the evolutionary cost under the Single-Cut-or-Join (SCJ) model. The weights of ancestral gene adjacencies can, e.g., be obtained through the recent availability of ancient DNA sequencing data, which provide a direct hint at the genome structure of the considered ancestor, or through probabilistic analysis of gene adjacencies evolution. We show the NP-hardness of our problem variant and propose a Fixed-Parameter Tractable algorithm based on the Sankoff-Rousseau dynamic programming algorithm that also allows to sample co-optimal solutions. We apply our approach to mammalian and bacterial data providing different degrees of complexity. We show that including adjacency weights in the objective has a significant impact in reducing the fragmentation of the reconstructed ancestral gene orders. An implementation is available at http://github.com/nluhmann/PhySca.

Approximating the correction of weighted and unweighted orthology and paralogy relations

BackgroundGiven a gene family, the relations between genes (orthology/paralogy), are represented by a relation graph, where edges connect pairs of orthologous genes and “missing” edges represent paralogs. While a gene tree directly induces a relation graph, the converse is not always true. Indeed, a relation graph is not necessarily “satisfiable”, i.e. does not necessarily correspond to a gene tree. And even if that holds, it may not be “consistent”, i.e. the tree may not represent a true history in agreement with a species tree. Previous studies have addressed the problem of correcting a relation graph for satisfiability and consistency. Here we consider the weighted version of the problem, where a degree of confidence is assigned to each orthology or paralogy relation. We also consider a maximization variant of the unweighted version of the problem.ResultsWe provide complexity and algorithmic results for the approximation of the considered problems. We show that minimizing the correction of a weighted graph does not admit a constant factor approximation algorithm assuming the unique game conjecture, and we give an n-approximation algorithm, n being the number of vertices in the graph. We also provide polynomial time approximation schemes for the maximization variant for unweighted graphs.ConclusionsWe provided complexity and algorithmic results for variants of the problem of correcting a relation graph for satisfiability and consistency. For the maximization variants we were able to design polynomial time approximation schemes, while for the weighted minimization variants we were able to provide the first inapproximability results.

Efficient Non-Binary Gene Tree Resolution with Weighted Reconciliation Cost.

Polytomies in gene trees are multifurcated nodes corresponding to unresolved parts of the tree, usually due to insufficient differentiation between sequences of homologous gene copies. Apart from gene sequences, other information such as that contained in the species tree can be used to resolve such intricate parts of a gene tree. The problem of resolving a multifurcated tree has been considered by many authors, the objective function often being the number of duplications and losses reflected by the reconciliation of the resolved gene tree with the species tree. Here, we present PolytomySolver, an algorithm accounting for a more general model allowing different costs for duplications and losses per species. The time complexity of this algorithm is linear for the unit cost and is quadratic for the general cost, which outperforms the best known solutions so far by a linear factor. We show on simulated trees that the gain in theoretical complexity has a real practical impact on running times.