Motivation: Linkage disequilibrium (LD) block construction is required for research in population genetics and genetic epidemiology, including specification of sets of single nucleotide polymorphisms (SNPs) for analysis of multi-SNP based association and identification of haplotype blocks in high density sequencing data. Existing methods based on a narrow sense definition do not allow intermediate regions of low LD between strongly associated SNP pairs and tend to split high density SNP data into small blocks having high between-block correlation. Results: We present Big-LD, a block partition method based on interval graph modeling of LD bins which are clusters of strong pairwise LD SNPs, not necessarily physically consecutive. Big-LD uses an agglomerative approach that starts by identifying small communities of SNPs, i.e. the SNPs in each LD bin region, and proceeds by merging these communities. We determine the number of blocks using a method to find maximum-weight independent set. Big-LD produces larger LD blocks compared to existing methods such as MATILDE, Haploview, MIG ++, or S-MIG ++ and the LD blocks better agree with recombination hotspot locations determined by sperm-typing experiments. The observed average runtime of Big-LD for 13 288 240 non-monomorphic SNPs from 1000 Genomes Project autosome data (286 East Asians) is about 5.83 h, which is a significant improvement over the existing methods. Availability and implementation: Source code and documentation are available for download at http://github.com/sunnyeesl/BigLD. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Proteins interact with each other to regulate their functionality and localization. The accumulated protein interaction evidences are represented by protein interaction network using a graph abstraction. Topological properties of protein interaction networks have been explored to characterize proteins and predict undiscovered interactions. Meanwhile, many researchers have tried to explain how protein interaction network is formed through evolutionary process. While one group of researchers have made efforts to simulate current protein interaction starting from hypothetical infant state of protein interaction networks through suggested evolutionary models, another group of researchers have made efforts to estimate the phylogenetic age of proteins from evolutionary relationship. Recently, these efforts gave rise to the database of phylogenetic age of proteins and this allows many researchers to estimate phylogenetic age of proteins of their interest easily. As seen by their terms, the evolutionary model of protein interaction networks and phylogenetic age of proteins are closely related, thus topological properties of protein interactions, which is important in studies of the evolutionary models, can be linked to the phylogenetic age of proteins. In this paper, we construct a weighted human protein interaction network from a human protein interaction network, which is provided by BioGRID database. The weight of an edge is defined as the number of triangles which contains this edge in the protein interaction network and we call this weight as the triangle score. From the weighted protein interaction network, we extract proteins that are incident to an edge that has a high triangle score. We obtain phylogenetic age of proteins and measure various statistical values to observe correlation between phylogenetic age and the triangle score. As a result, we show that the proteins, that participate in interactions with high triangle score, are old in terms of phylogenetic age. Also we show that for interactions within a same phylogenetic age category tend to have higher triangle scores than the interactions with only one of its participant protein contained in the given age category.

Linkage disequilibrium structure (LD) is the main source of the study of population genetics and disease-gene association. Especially, analyzing extended long haplotypes carrying a derived allele and examining LD block patterns can provide evidence for positive selection. We investigated the LD block structure of East Asian, European, and African populations for the previously reported sites of positive selection by comparing LD block construction results based on 1000 Genomes Project data. We confirmed that differences of LD block size in EDAR, LCT, PCDH15, and LARGE region among different populations is consistent with previous reports. We found new evidence for positive selection in SLC30A19, PDE11A and BCAS3 in East Asian and European populations based on the LD block patterns.

If $D = ( V,A )$ is a digraph, its p-competition graph for p a positive integer has vertex set V and an edge between x and y if and only if there are distinct vertices $a_1, \cdots ,a_p $ in D with $( x,a_i )$ and $( y,a_i )$ arcs of D for each $i = 1, \cdots ,p$. This notion generalizes the notion of ordinary competition graph, which has been widely studied and is the special case where $p = 1$. Results about the case where $p = 2$ are obtained. In particular, the paper addresses the question of which complete bipartite graphs are 2-competition graphs. This problem is formulated as the following combinatorial problem: Given disjoint sets A and B such that $| A \cup B | = n$, when can one find n subsets of $A \cup B$ so that every a in A and b in B are together contained in at least two of the subsets and so that the intersection of every pair of subsets contains at most one element from A and at most one element from B?