WGSUniFrac: Applying UniFrac Metric to Whole Genome Shotgun Data

The UniFrac metric has proven useful in revealing diversity across metagenomic communities. Due to the phylogeny-based nature of this measurement, UniFrac has historically only been applied to 16S rRNA data. Simultaneously, Whole Genome Shotgun (WGS) metagenomics has been increasingly widely employed and proven to provide more information than 16S data, but a UniFrac-like diversity metric suitable for WGS data has not previously been developed. The main obstacle for UniFrac to be applied directly to WGS data is the absence of phylogenetic distances in the taxonomic relationship derived from WGS data. In this study, we demonstrate a method to overcome this intrinsic difference and compute the UniFrac metric on WGS data by assigning branch lengths to the taxonomic tree obtained from input taxonomic profiles. We conduct a series of experiments to demonstrate that this WGSUniFrac method is comparably robust to traditional 16S UniFrac and is not highly sensitive to branch lengths assignments, be they data-derived or model-prescribed

Sparse Recovery by means of Nonnegative Least Squares

This short note demonstrates that sparse recovery can be achieved by an l₁-minimization ersatz easily implemented using a conventional nonnegative least squares algorithm. A connection with orthogonal matching pursuit is also highlighted. The preliminary results call for more investigations on the potential of the method and on its relations to classical sparse recovery algorithms.Keywords: Sparse recovery, Nonnegative least squares, k-mer frequency matrices, Orthogonal matching pursuit, Compressive sensing, Adjacency matrices of bipartite graphs, l₁-minimization, Gaussian matrices(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article can be found at: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97

EMDUniFrac: exact linear time computation of the UniFrac metric and identification of differentially abundant organisms

Both the weighted and unweighted UniFrac distances have been very successfully employed to assess if two communities differ, but do not give any information about how two communities differ. We take advantage of recent observations that the UniFrac metric is equivalent to the so-called earth mover's distance (also known as the Kantorovich-Rubinstein metric) to develop an algorithm that not only computes the UniFrac distance in linear time and space, but also simultaneously finds which operational taxonomic units are responsible for the observed differences between samples. This allows the algorithm, called EMDUniFrac, to determine why given samples are different, not just if they are different, and with no added computational burden. EMDUniFrac can be utilized on any distribution on a tree, and so is particularly suitable to analyzing both operational taxonomic units derived from amplicon sequencing, as well as community profiles resulting from classifying whole genome shotgun metagenomes. The EMDUniFrac source code (written in python) is freely available at: https://github.com/dkoslicki/EMDUniFrac

Coding sequence density estimation via topological pressure

We give a new approach to coding sequence (CDS) density estimation in genomic analysis based on the topological pressure, which we develop from a well known concept in ergodic theory. Topological pressure measures the ‘weighted information content’ of a finite word, and incorporates 64 parameters which can be interpreted as a choice of weight for each nucleotide triplet. We train the parameters so that the topological pressure fits the observed coding sequence density on the human genome, and use this to give ab initio predictions of CDS density over windows of size around 66,000bp on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While the differences between these genomes are too great to expect that training on the human genome could predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the ‘coarse scale’ problem of predicting CDS density. Inspired again by ergodic theory, the weightings of the nucleotide triplets obtained from our training procedure are used to define a probability distribution on finite sequences, which can be used to distinguish between intron and exon sequences from the human genome of lengths between 750bp and 5,000bp. At the end of the paper, we explain the theoretical underpinning for our approach, which is the theory of Thermodynamic Formalism from the dynamical systems literature. Mathematica and MATLAB implementations of our method are available at http://sourceforge.net/projects/topologicalpres/.This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/285Keywords: DNA sequence analysis, Topological pressure, Coding sequence density estimatio

WGSQuikr: Fast Whole-Genome Shotgun Metagenomic Classification

With the decrease in cost and increase in output of whole-genome shotgun technologies, many metagenomic studies are utilizing this approach in lieu of the more traditional 16S rRNA amplicon technique. Due to the large number of relatively short reads output from whole-genome shotgun technologies, there is a need for fast and accurate short-read OTU classifiers. While there are relatively fast and accurate algorithms available, such as MetaPhlAn, MetaPhyler, PhyloPythiaS, and PhymmBL, these algorithms still classify samples in a read-by-read fashion and so execution times can range from hours to days on large datasets. We introduce WGSQuikr, a reconstruction method which can compute a vector of taxonomic assignments and their proportions in the sample with remarkable speed and accuracy. We demonstrate on simulated data that WGSQuikr is typically more accurate and up to an order of magnitude faster than the aforementioned classification algorithms. We also verify the utility of WGSQuikr on real biological data in the form of a mock community. WGSQuikr is a Whole-Genome Shotgun QUadratic, Iterative, -mer based Reconstruction method which extends the previously introduced 16S rRNA-based algorithm Quikr. A MATLAB implementation of WGSQuikr is available at: http://sourceforge.net/projects/wgsquikr.At the author's request, we have also posted the author's accepted manuscript version