On unrooted and root-uncertain variants of several well-known phylogenetic network problems

The hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view accurately inferring the root location in a phylogenetic tree is notoriously difficult and poor root placement can artificially inflate the hybridization number. To this end we study a number of relaxed variants of this problem. We start by showing that the fundamental problem of determining whether an \emph{unrooted} phylogenetic network displays (i.e. embeds) an \emph{unrooted} phylogenetic tree, is NP-hard. On the positive side we show that this problem is FPT in reticulation number. In the rooted case the corresponding FPT result is trivial, but here we require more subtle argumentation. Next we show that the hybridization number problem for unrooted networks (when given two unrooted trees) is equivalent to the problem of computing the Tree Bisection and Reconnect (TBR) distance of the two unrooted trees. In the third part of the paper we consider the "root uncertain" variant of hybridization number. Here we are free to choose the root location in each of a set of unrooted input trees such that the hybridization number of the resulting rooted trees is minimized. On the negative side we show that this problem is APX-hard. On the positive side, we show that the problem is FPT in the hybridization number, via kernelization, for any number of input trees.Comment: 28 pages, 8 Figure

On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems

International audienceThe hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view accurately inferring the root location in a phylogenetic tree is notoriously difficult and poor root placement can artificially inflate the hybridization number. To thisend we study a number of relaxed variants of this problem. We start by showing that the fundamental problem of determining whether an unrooted phylogenetic network displays (i.e. embeds) an unrooted phylogenetic tree, is NP-hard. On the positive side we show that this problem is FPT in reticulation number. In the rooted case the corresponding FPT result is trivial, but here we require more subtle argumentation. Next we show that the hybridization number problem for unrooted networks (when given two unrooted trees) is equivalent to the problem of computing the tree bisection and reconnect distance of the two unrooted trees. In the third part of the paper we consider the “root uncertain” variant of hybridization number. Here we are free to choose the root location in each of a set of unrooted input trees such that the hybridization number of the resulting rooted trees is minimized. On the negative side we show that this problem is APX-hard. On the positive side, we show that the problem is FPT in the hybridization number, via kernelization, for any number of input trees

Accounting for a Quantitative Trait Locus for Plasma Triglyceride Levels: Utilization of Variants in Multiple Genes

For decades, research efforts have tried to uncover the underlying genetic basis of human susceptibility to a variety of diseases. Linkage studies have resulted in highly replicated findings and helped identify quantitative trait loci (QTL) for many complex traits; however identification of specific alleles accounting for linkage remains elusive. The purpose of this study was to determine whether with a sufficient number of variants a linkage signal can be fully explained.We used comprehensive fine-mapping using a dense set of single nucleotide polymorphisms (SNPs) across the entire quantitative trait locus (QTL) on human chromosome 7q36 linked to plasma triglyceride levels. Analyses included measured genotype and combined linkage association analyses.Screening this linkage region, we found an over representation of nominally significant associations in five genes (MLL3, DPP6, PAXIP1, HTR5A, INSIG1). However, no single genetic variant was sufficient to account for the linkage. On the other hand, multiple variants capturing the variation in these five genes did account for the linkage at this locus. Permutation analyses suggested that this reduction in LOD score was unlikely to have occurred by chance (p = 0.008).With recent findings, it has become clear that most complex traits are influenced by a large number of genetic variants each contributing only a small percentage to the overall phenotype. We found that with a sufficient number of variants, the linkage can be fully explained. The results from this analysis suggest that perhaps the failure to identify causal variants for linkage peaks may be due to multiple variants under the linkage peak with small individual effect, rather than a single variant of large effect

Genome-wide association identifies nine common variants associated with fasting proinsulin levels and provides new insights into the pathophysiology of type 2 diabetes.

OBJECTIVE: Proinsulin is a precursor of mature insulin and C-peptide. Higher circulating proinsulin levels are associated with impaired β-cell function, raised glucose levels, insulin resistance, and type 2 diabetes (T2D). Studies of the insulin processing pathway could provide new insights about T2D pathophysiology. RESEARCH DESIGN AND METHODS: We have conducted a meta-analysis of genome-wide association tests of ∼2.5 million genotyped or imputed single nucleotide polymorphisms (SNPs) and fasting proinsulin levels in 10,701 nondiabetic adults of European ancestry, with follow-up of 23 loci in up to 16,378 individuals, using additive genetic models adjusted for age, sex, fasting insulin, and study-specific covariates. RESULTS: Nine SNPs at eight loci were associated with proinsulin levels (P < 5 × 10(-8)). Two loci (LARP6 and SGSM2) have not been previously related to metabolic traits, one (MADD) has been associated with fasting glucose, one (PCSK1) has been implicated in obesity, and four (TCF7L2, SLC30A8, VPS13C/C2CD4A/B, and ARAP1, formerly CENTD2) increase T2D risk. The proinsulin-raising allele of ARAP1 was associated with a lower fasting glucose (P = 1.7 × 10(-4)), improved β-cell function (P = 1.1 × 10(-5)), and lower risk of T2D (odds ratio 0.88; P = 7.8 × 10(-6)). Notably, PCSK1 encodes the protein prohormone convertase 1/3, the first enzyme in the insulin processing pathway. A genotype score composed of the nine proinsulin-raising alleles was not associated with coronary disease in two large case-control datasets. CONCLUSIONS: We have identified nine genetic variants associated with fasting proinsulin. Our findings illuminate the biology underlying glucose homeostasis and T2D development in humans and argue against a direct role of proinsulin in coronary artery disease pathogenesis

Improving the Needleman-Wunsch algorithm with the Dynamine predictor -- Informatique

info:eu-repo/semantics/nonPublishe

A Linear Bound on the Number of States in Optimal Convex Characters for Maximum Parsimony Distance

Given two phylogenetic trees on the same set of taxa X, the maximum parsimony distance d(MP) is defined as the maximum, ranging over all characters chi on X, of the absolute difference in parsimony score induced by chi on the two trees. In this note, we prove that for binary trees there exists a character achieving this maximum that is convex on one of the trees (i.e., the parsimony score induced on that tree is equal to the number of states in the character minus 1) and such that the number of states in the character is at most 7d(MP) - 5. This is the first non-trivial bound on the number of states required by optimal characters, convex or otherwise. The result potentially has algorithmic significance because, unlike general characters, convex characters with a bounded number of states can be enumerated in polynomial time