Multidimensional scaling for large genomic data sets

<p>Abstract</p> <p>Background</p> <p>Multi-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over <it>O(N</it>²<it>)</it>, so that it is difficult to process a data set of a large number of genes <it>N</it>, such as in the case of whole genome microarray data.</p> <p>Results</p> <p>We developed a new rapid metric MDS method with a low computational complexity, making metric MDS applicable for large data sets. Computer simulation showed that the new method of split-and-combine MDS (SC-MDS) is fast, accurate and efficient. Our empirical studies using microarray data on the yeast cell cycle showed that the performance of K-means in the reduced dimensional space is similar to or slightly better than that of K-means in the original space, but about three times faster to obtain the clustering results. Our clustering results using SC-MDS are more stable than those in the original space. Hence, the proposed SC-MDS is useful for analyzing whole genome data.</p> <p>Conclusion</p> <p>Our new method reduces the computational complexity from <it>O</it>(<it>N</it>³) to <it>O</it>(<it>N</it>) when the dimension of the feature space is far less than the number of genes <it>N</it>, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent high dimensional large data set in a low dimensional space not only efficiently but also effectively.</p

chroGPS, a global chromatin positioning system for the functional analysis and visualization of the epigenome

Development of tools to jointly visualize the genome and the epigenome remains a challenge. chroGPS is a computational approach that addresses this question. chroGPS uses multidimensional scaling techniques to represent similarity between epigenetic factors, or between genetic elements on the basis of their epigenetic state, in 2D/3D reference maps. We emphasize biological interpretability, statistical robustness, integration of genetic and epigenetic data from heterogeneous sources, and computational feasibility. Although chroGPS is a general methodology to create reference maps and study the epigenetic state of any class of genetic element or genomic region, we focus on two specific kinds of maps: chroGPSfactors, which visualizes functional similarities between epigenetic factors, and chroGPSgenes, which describes the epigenetic state of genes and integrates gene expression and other functional data. We use data from the modENCODE project on the genomic distribution of a large collection of epigenetic factors in Drosophila, a model system extensively used to study genome organization and function. Our results show that the maps allow straightforward visualization of relationships between factors and elements, capturing relevant information about their functional properties that helps to interpret epigenetic information in a functional context and derive testable hypotheses

Mapping the Space of Genomic Signatures

We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is computed for each pair of graphical representations of DNA sequences, and the distances are visualized as a Molecular Distance Map: Each point on the map represents a DNA sequence, and the spatial proximity between any two points reflects the degree of structural similarity between the corresponding sequences. The graphical representation of DNA sequences utilized, Chaos Game Representation (CGR), is genome- and species-specific and can thus act as a genomic signature. Consequently, Molecular Distance Maps could inform species identification, taxonomic classifications and, to a certain extent, evolutionary history. The image distance employed, Structural Dissimilarity Index (DSSIM), implicitly compares the occurrences of oligomers of length up to $k$ (herein $k=9$) in DNA sequences. We computed DSSIM distances for more than 5 million pairs of complete mitochondrial genomes, and used Multi-Dimensional Scaling (MDS) to obtain Molecular Distance Maps that visually display the sequence relatedness in various subsets, at different taxonomic levels. This general-purpose method does not require DNA sequence homology and can thus be used to compare similar or vastly different DNA sequences, genomic or computer-generated, of the same or different lengths. We illustrate potential uses of this approach by applying it to several taxonomic subsets: phylum Vertebrata, (super)kingdom Protista, classes Amphibia-Insecta-Mammalia, class Amphibia, and order Primates. This analysis of an extensive dataset confirms that the oligomer composition of full mtDNA sequences can be a source of taxonomic information.Comment: 14 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1307.375

Worldwide genetic variation of the IGHV and TRBV immune receptor gene families in humans.

The immunoglobulin heavy variable (IGHV) and T cell beta variable (TRBV) loci are among the most complex and variable regions in the human genome. Generated through a process of gene duplication/deletion and diversification, these loci can vary extensively between individuals in copy number and contain genes that are highly similar, making their analysis technically challenging. Here, we present a comprehensive study of the functional gene segments in the IGHV and TRBV loci, quantifying their copy number and single-nucleotide variation in a globally diverse sample of 109 (IGHV) and 286 (TRBV) humans from over a 100 populations. We find that the IGHV and TRBV gene families exhibit starkly different patterns of variation. In addition to providing insight into the different evolutionary paths of the IGHV and TRBV loci, our results are also important to the adaptive immune repertoire sequencing community, where the lack of frequencies of common alleles and copy number variants is hampering existing analytical pipelines

Uncertainty in phylogenetic tree estimates

Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly model the multivariate uncertainty of tree estimates. We consider both the cases where uncertainty information arises extrinsically (through covariate information) and intrinsically (through the tree estimates themselves). The importance of accounting for tree uncertainty in tree space is demonstrated in two case studies. In the first instance, differences between gene trees are small relative to their uncertainties, while in the second, the differences are relatively large. Our main goal is visualization of tree uncertainty, and we demonstrate advantages of our method with respect to reproducibility, speed and preservation of topological differences compared to visualization based on multidimensional scaling. The proposal highlights that phylogenetic trees are estimated in an extremely high-dimensional space, resulting in uncertainty information that cannot be discarded. Most importantly, it is a method that allows biologists to diagnose whether differences between gene trees are biologically meaningful, or due to uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical Statistic

Soft topographic map for clustering and classification of bacteria

In this work a new method for clustering and building a topographic representation of a bacteria taxonomy is presented. The method is based on the analysis of stable parts of the genome, the so-called “housekeeping genes”. The proposed method generates topographic maps of the bacteria taxonomy, where relations among different type strains can be visually inspected and verified. Two well known DNA alignement algorithms are applied to the genomic sequences. Topographic maps are optimized to represent the similarity among the sequences according to their evolutionary distances. The experimental analysis is carried out on 147 type strains of the Gammaprotebacteria class by means of the 16S rRNA housekeeping gene. Complete sequences of the gene have been retrieved from the NCBI public database. In the experimental tests the maps show clusters of homologous type strains and present some singular cases potentially due to incorrect classification or erroneous annotations in the database

BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN

Consanguinity and rare mutations outside of MCCC genes underlie nonspecific phenotypes of MCCD.

Purpose3-Methylcrotonyl-CoA carboxylase deficiency (MCCD) is an autosomal recessive disorder of leucine catabolism that has a highly variable clinical phenotype, ranging from acute metabolic acidosis to nonspecific symptoms such as developmental delay, failure to thrive, hemiparesis, muscular hypotonia, and multiple sclerosis. Implementation of newborn screening for MCCD has resulted in broadening the range of phenotypic expression to include asymptomatic adults. The purpose of this study was to identify factors underlying the varying phenotypes of MCCD.MethodsWe performed exome sequencing on DNA from 33 cases and 108 healthy controls. We examined these data for associations between either MCC mutational status, genetic ancestry, or consanguinity and the absence or presence/specificity of clinical symptoms in MCCD cases.ResultsWe determined that individuals with nonspecific clinical phenotypes are highly inbred compared with cases that are asymptomatic and healthy controls. For 5 of these 10 individuals, we discovered a homozygous damaging mutation in a disease gene that is likely to underlie their nonspecific clinical phenotypes previously attributed to MCCD.ConclusionOur study shows that nonspecific phenotypes attributed to MCCD are associated with consanguinity and are likely not due to mutations in the MCC enzyme but result from rare homozygous mutations in other disease genes.Genet Med 17 8, 660-667