Temporal networks in biology and medicine: a survey on models, algorithms, and tools.

The use of static graphs for modelling and analysis of biological and biomedical data plays a key role in biomedical research. However, many real-world scenarios present dynamic behaviours resulting in both node and edges modification as well as feature evolution. Consequently, ad-hoc models for capturing these evolutions along the time have been introduced, also referred to as dynamic, temporal, time-varying graphs. Here, we focus on temporal graphs, i.e., graphs whose evolution is represented by a sequence of time-ordered snapshots. Each snapshot represents a graph active in a particular timestamp. We survey temporal graph models and related algorithms, presenting fundamentals aspects and the recent advances. We formally define temporal graphs, focusing on the problem setting and we present their main applications in biology and medicine. We also present temporal graph embedding and the application to recent problems such as epidemic modelling. Finally, we further state some promising research directions in the area. Main results of this study include a systematic review of fundamental temporal network problems and their algorithmic solutions considered in the literature, in particular those having application in computational biology and medicine. We also include the main software developed in this context.

Long-Term Outcomes of Two-Piece Mushroom Keratoplasty for Traumatic Corneal Scars.

PURPOSE: To report the outcomes of 2-piece microkeratome-assisted mushroom keratoplasty (MK) for eyes with full-thickness traumatic corneal scars and otherwise functional endothelium following corneal penetrating injury. DESIGN: This was an interventional case series. METHODS: In this single-center study, 41 consecutive eyes with traumatic corneal scars that underwent 2-piece microkeratome-assisted mushroom keratoplasty were evaluated. The 2-piece mushroom graft consisted of an anterior lamella 9 mm in diameter and a posterior lamella 6 mm in diameter. Outcome measures were best spectacle-corrected visual acuity (BSCVA), refractive astigmatism (RA), endothelial cell density, and postoperative complication rates. RESULTS: Of the 41 total cases, 38 eyes (93%) reached Snellen vision ≥20/100, 36 (88%) reached ≥20/60, 29 (71%) reached ≥20/40, and 13 (32%) reached ≥20/25 2 years following MK. Excluding eyes with vision-impairing comorbidities, baseline logMAR BSCVA (1.41 ± 0.73) significantly improved annually during the first 2 years (P < 0.001), reaching 0.16 ± 0.13 at year 2, which subsequently remained stable up to 10 years (P = .626). The RA exceeded 4.5 diopters in 2 cases (5%) after wound revision for high-degree astigmatism in 5 cases. Endothelial cell loss was 35.1% at 1 year, with an annual decline of 2.9% over 10 years. Elevation in IOP was observed postoperatively in 7 eyes, of which 6 had pre-existing glaucoma. The 10-year cumulative risk for graft rejection and failure was 8.5% and 10%, respectively. CONCLUSION: Two-piece microkeratome-assisted MK for traumatic corneal scars can allow excellent visual rehabilitation with relatively stable ECL and low rates of immunologic rejection and graft failure.

A novel algorithm for finding top-k weighted overlapping densest connected subgraphs in dual networks.

The use of networks for modelling and analysing relations among data is currently growing. Recently, the use of a single networks for capturing all the aspects of some complex scenarios has shown some limitations. Consequently, it has been proposed to use Dual Networks (DN), a pair of related networks, to analyse complex systems. The two graphs in a DN have the same set of vertices and different edge sets. Common subgraphs among these networks may convey some insights about the modelled scenarios. For instance, the detection of the Top-k Densest Connected subgraphs, i.e. a set k subgraphs having the largest density in the conceptual network which are also connected in the physical network, may reveal set of highly related nodes. After proposing a formalisation of the approach, we propose a heuristic to find a solution, since the problem is computationally hard. A set of experiments on synthetic and real networks is also presented to support our approach.

Computational Methods for Resting-State EEG of Patients With Disorders of Consciousness.

Patients who survive brain injuries may develop Disorders of Consciousness (DOC) such as Coma, Vegetative State (VS) or Minimally Conscious State (MCS). Unfortunately, the rate of misdiagnosis between VS and MCS due to clinical judgment is high. Therefore, diagnostic decision support systems aiming to correct any differentiation between VS and MCS are essential for the characterization of an adequate treatment and an effective prognosis. In recent decades, there has been a growing interest in the new EEG computational techniques. We have reviewed how resting-state EEG is computationally analyzed to support differential diagnosis between VS and MCS in view of applicability of these methods in clinical practice. The studies available so far have used different techniques and analyses; it is therefore hard to draw general conclusions. Studies using a discriminant analysis with a combination of various factors and reporting a cut-off are among the most interesting ones for a future clinical application.

Reconciling multiple genes trees via segmental duplications and losses.

Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families is interconnected. In this paper, we extend a previous approach to reconcile a set of gene trees with a species tree based on segmental macro-evolutionary events, where segmental duplication events and losses are associated with cost δ and λ , respectively. We show that the problem is polynomial-time solvable when δ ≤ λ (via LCA-mapping), while if δ > λ the problem is NP-hard, even when λ = 0 and a single gene tree is given, solving a long standing open problem on the complexity of multi-gene reconciliation. On the positive side, we give a fixed-parameter algorithm for the problem, where the parameters are δ / λ and the number d of segmental duplications, of time complexity O ⌈ δ λ ⌉ d · n · δ λ . Finally, we demonstrate the usefulness of this algorithm on two previously studied real datasets: we first show that our method can be used to confirm or raise doubt on hypothetical segmental duplications on a set of 16 eukaryotes, then show how we can detect whole genome duplications in yeast genomes.

Corrigendum: Computational Methods for Resting-State EEG of Patients With Disorders of Consciousness.

[This corrects the article DOI: 10.3389/fnins.2019.00807.].

Approximating the correction of weighted and unweighted orthology and paralogy relations.

BACKGROUND: Given 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. RESULTS: We 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. CONCLUSIONS: We 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.

On the Minimum Error Correction Problem for Haplotype Assembly in Diploid and Polyploid Genomes.

In diploid genomes, haplotype assembly is the computational problem of reconstructing the two parental copies, called haplotypes, of each chromosome starting from sequencing reads, called fragments, possibly affected by sequencing errors. Minimum error correction (MEC) is a prominent computational problem for haplotype assembly and, given a set of fragments, aims at reconstructing the two haplotypes by applying the minimum number of base corrections. MEC is computationally hard to solve, but some approximation-based or fixed-parameter approaches have been proved capable of obtaining accurate results on real data. In this work, we expand the current characterization of the computational complexity of MEC from the approximation and the fixed-parameter tractability point of view. In particular, we show that MEC is not approximable within a constant factor, whereas it is approximable within a logarithmic factor in the size of the input. Furthermore, we answer open questions on the fixed-parameter tractability for parameters of classical or practical interest: the total number of corrections and the fragment length. In addition, we present a direct 2-approximation algorithm for a variant of the problem that has also been applied in the framework of clustering data. Finally, since polyploid genomes, such as those of plants and fishes, are composed of more than two copies of the chromosomes, we introduce a novel formulation of MEC, namely the k-ploid MEC problem, that extends the traditional problem to deal with polyploid genomes. We show that the novel formulation is still both computationally hard and hard to approximate. Nonetheless, from the parameterized point of view, we prove that the problem is tractable for parameters of practical interest such as the number of haplotypes and the coverage, or the number of haplotypes and the fragment length.

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

BACKGROUND: While 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. RESULTS: We 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.

HapCol: accurate and memory-efficient haplotype assembly from long reads.

MOTIVATION: Haplotype assembly is the computational problem of reconstructing haplotypes in diploid organisms and is of fundamental importance for characterizing the effects of single-nucleotide polymorphisms on the expression of phenotypic traits. Haplotype assembly highly benefits from the advent of 'future-generation' sequencing technologies and their capability to produce long reads at increasing coverage. Existing methods are not able to deal with such data in a fully satisfactory way, either because accuracy or performances degrade as read length and sequencing coverage increase or because they are based on restrictive assumptions. RESULTS: By exploiting a feature of future-generation technologies-the uniform distribution of sequencing errors-we designed an exact algorithm, called HapCol, that is exponential in the maximum number of corrections for each single-nucleotide polymorphism position and that minimizes the overall error-correction score. We performed an experimental analysis, comparing HapCol with the current state-of-the-art combinatorial methods both on real and simulated data. On a standard benchmark of real data, we show that HapCol is competitive with state-of-the-art methods, improving the accuracy and the number of phased positions. Furthermore, experiments on realistically simulated datasets revealed that HapCol requires significantly less computing resources, especially memory. Thanks to its computational efficiency, HapCol can overcome the limits of previous approaches, allowing to phase datasets with higher coverage and without the traditional all-heterozygous assumption. AVAILABILITY AND IMPLEMENTATION: Our source code is available under the terms of the GNU General Public License at http://hapcol.algolab.eu/ CONTACT: bonizzoni@disco.unimib.it SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Polytomy refinement for the correction of dubious duplications in gene trees.

MOTIVATION: Large-scale methods for inferring gene trees are error-prone. Correcting gene trees for weakly supported features often results in non-binary trees, i.e. trees with polytomies, thus raising the natural question of refining such polytomies into binary trees. A feature pointing toward potential errors in gene trees are duplications that are not supported by the presence of multiple gene copies. RESULTS: We introduce the problem of refining polytomies in a gene tree while minimizing the number of created non-apparent duplications in the resulting tree. We show that this problem can be described as a graph-theoretical optimization problem. We provide a bounded heuristic with guaranteed optimality for well-characterized instances. We apply our algorithm to a set of ray-finned fish gene trees from the Ensembl database to illustrate its ability to correct dubious duplications. AVAILABILITY AND IMPLEMENTATION: The C++ source code for the algorithms and simulations described in the article are available at http://www-ens.iro.umontreal.ca/~lafonman/software.php. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Pure parsimony xor haplotyping.

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper, we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given single nucleotide polymorphisms (SNP). Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project.

Exemplar longest common subsequence.

In this paper, we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, we first present an efficient algorithm for the ELCS problem over instances of two sequences where each mandatory symbol can appear in total at most three times in the sequences. Furthermore, we present two fixed-parameter algorithms for the ELCS problem over instances of two sequences where the parameter is the number of mandatory symbols.

A novel method for signal transduction network inference from indirect experimental evidence.

In this paper, we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships as network paths and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. Our contributions are twofold: (a) We formalize our approach, study its computational complexity and prove new results for exact and approximate solutions of the computationally hard transitive reduction substep of the approach (Sections 2 and 5). (b) We validate the biological usability of our approach by successfully applying it to a previously published signal transduction network by Li et al. (2006) and show that our algorithm for the transitive reduction substep performs well on graphs with a structure similar to those observed in transcriptional regulatory and signal transduction networks.

Experimental analysis of a new algorithm for partial haplotype completion.

This paper deals with the computational problem of inferring complete information on haplotypes from haplotypes with missing data. This problem is one of the main issues in haplotyping, as the current DNA sequencing technology often produces haplotypes with missing bases and therefore the complete information on haplotypes has to be inferred through computational methods. In this paper, we propose a new algorithmic approach to the problem that assumes both the Coalescent and the Minimum Entropy models and we provide an experimental analysis relating it to the previously investigated approaches. In particular, the reconstruction of a perfect phylogeny from haplotypes with missing data is addressed.

A library of efficient bioinformatics algorithms.

In this paper we review some of the existing projects available in the bioinformatics field for facilitating the development of programs, but for which minimising the running time is not of primary importance. We point out the advantages of open source libraries for such tasks and we discuss some of the open source licenses available. Finally, we present the project ALiBio, which is aimed at facilitating the development of efficient programs in bioinformatics.