Interpolated Markov Models Research Articles

Higher-order Markov models for metagenomic sequence classification.

Alignment-free, stochastic models derived from k-mer distributions representing reference genome sequences have a rich history in the classification of DNA sequences. In particular, the variants of Markov models have previously been used extensively. Higher-order Markov models have been used with caution, perhaps sparingly, primarily because of the lack of enough training data and computational power. Advances in sequencing technology and computation have enabled exploitation of the predictive power of higher-order models. We, therefore, revisited higher-order Markov models and assessed their performance in classifying metagenomic sequences. Comparative assessment of higher-order models (HOMs, 9th order or higher) with interpolated Markov model, interpolated context model and lower-order models (8th order or lower) was performed on metagenomic datasets constructed using sequenced prokaryotic genomes. Our results show that HOMs outperform other models in classifying metagenomic fragments as short as 100 nt at all taxonomic ranks, and at lower ranks when the fragment size was increased to 250 nt. HOMs were also found to be significantly more accurate than local alignment which is widely relied upon for taxonomic classification of metagenomic sequences. A novel software implementation written in C++ performs classification faster than the existing Markovian metagenomic classifiers and can therefore be used as a standalone classifier or in conjunction with existing taxonomic classifiers for more robust classification of metagenomic sequences. The software has been made available at https://github.com/djburks/SMM. Rajeev.Azad@unt.edu. Supplementary data are available at Bioinformatics online.

A framework for space-efficient variable-order Markov models.

Markov models with contexts of variable length are widely used in bioinformatics for representing sets of sequences with similar biological properties. When models contain many long contexts, existing implementations are either unable to handle genome-scale training datasets within typical memory budgets, or they are optimized for specific model variants and are thus inflexible. We provide practical, versatile representations of variable-order Markov models and of interpolated Markov models, that support a large number of context-selection criteria, scoring functions, probability smoothing methods, and interpolations, and that take up to four times less space than previous implementations based on the suffix array, regardless of the number and length of contexts, and up to ten times less space than previous trie-based representations, or more, while matching the size of related, state-of-the-art data structures from Natural Language Processing. We describe how to further compress our indexes to a quantity related to the redundancy of the training data, saving up to 90% of their space on very repetitive datasets, and making them become up to 60 times smaller than previous implementations based on the suffix array. Finally, we show how to exploit constraints on the length and frequency of contexts to further shrink our compressed indexes to half of their size or more, achieving data structures that are a hundred times smaller than previous implementations based on the suffix array, or more. This allows variable-order Markov models to be used with bigger datasets and with longer contexts on the same hardware, thus possibly enabling new applications. https://github.com/jnalanko/VOMM. Supplementary data are available at Bioinformatics online.

Exploration of multivariate analysis in microbial coding sequence modeling

BackgroundGene finding is a complicated procedure that encapsulates algorithms for coding sequence modeling, identification of promoter regions, issues concerning overlapping genes and more. In the present study we focus on coding sequence modeling algorithms; that is, algorithms for identification and prediction of the actual coding sequences from genomic DNA. In this respect, we promote a novel multivariate method known as Canonical Powered Partial Least Squares (CPPLS) as an alternative to the commonly used Interpolated Markov model (IMM). Comparisons between the methods were performed on DNA, codon and protein sequences with highly conserved genes taken from several species with different genomic properties.ResultsThe multivariate CPPLS approach classified coding sequence substantially better than the commonly used IMM on the same set of sequences. We also found that the use of CPPLS with codon representation gave significantly better classification results than both IMM with protein (p < 0.001) and with DNA (p < 0.001). Further, although the mean performance was similar, the variation of CPPLS performance on codon representation was significantly smaller than for IMM (p < 0.001).ConclusionsThe performance of coding sequence modeling can be substantially improved by using an algorithm based on the multivariate CPPLS method applied to codon or DNA frequencies.

The Binning of Metagenomic Contigs for Microbial Physiology of Mixed Cultures

So far, microbial physiology has dedicated itself mainly to pure cultures. In nature, cross feeding and competition are important aspects of microbial physiology and these can only be addressed by studying complete communities such as enrichment cultures. Metagenomic sequencing is a powerful tool to characterize such mixed cultures. In the analysis of metagenomic data, well established algorithms exist for the assembly of short reads into contigs and for the annotation of predicted genes. However, the binning of the assembled contigs or unassembled reads is still a major bottleneck and required to understand how the overall metabolism is partitioned over different community members. Binning consists of the clustering of contigs or reads that apparently originate from the same source population. In the present study eight metagenomic samples from the same habitat, a laboratory enrichment culture, were sequenced. Each sample contained 13–23 Mb of assembled contigs and up to eight abundant populations. Binning was attempted with existing methods but they were found to produce poor results, were slow, dependent on non-standard platforms or produced errors. A new binning procedure was developed based on multivariate statistics of tetranucleotide frequencies combined with the use of interpolated Markov models. Its performance was evaluated by comparison of the results between samples with BLAST and in comparison to existing algorithms for four publicly available metagenomes and one previously published artificial metagenome. The accuracy of the new approach was comparable or higher than existing methods. Further, it was up to a 100 times faster. It was implemented in Java Swing as a complete open source graphical binning application available for download and further development (http://sourceforge.net/projects/metawatt).

Improved accuracy of supervised CRM discovery with interpolated Markov models and cross-species comparison

Despite recent advances in experimental approaches for identifying transcriptional cis-regulatory modules (CRMs, ‘enhancers’), direct empirical discovery of CRMs for all genes in all cell types and environmental conditions is likely to remain an elusive goal. Effective methods for computational CRM discovery are thus a critically needed complement to empirical approaches. However, existing computational methods that search for clusters of putative binding sites are ineffective if the relevant TFs and/or their binding specificities are unknown. Here, we provide a significantly improved method for ‘motif-blind’ CRM discovery that does not depend on knowledge or accurate prediction of TF-binding motifs and is effective when limited knowledge of functional CRMs is available to ‘supervise’ the search. We propose a new statistical method, based on ‘Interpolated Markov Models’, for motif-blind, genome-wide CRM discovery. It captures the statistical profile of variable length words in known CRMs of a regulatory network and finds candidate CRMs that match this profile. The method also uses orthologs of the known CRMs from closely related genomes. We perform in silico evaluation of predicted CRMs by assessing whether their neighboring genes are enriched for the expected expression patterns. This assessment uses a novel statistical test that extends the widely used Hypergeometric test of gene set enrichment to account for variability in intergenic lengths. We find that the new CRM prediction method is superior to existing methods. Finally, we experimentally validate 12 new CRM predictions by examining their regulatory activity in vivo in Drosophila; 10 of the tested CRMs were found to be functional, while 6 of the top 7 predictions showed the expected activity patterns. We make our program available as downloadable source code, and as a plugin for a genome browser installed on our servers.

Clustering metagenomic sequences with interpolated Markov models.

BackgroundSequencing of environmental DNA (often called metagenomics) has shown tremendous potential to uncover the vast number of unknown microbes that cannot be cultured and sequenced by traditional methods. Because the output from metagenomic sequencing is a large set of reads of unknown origin, clustering reads together that were sequenced from the same species is a crucial analysis step. Many effective approaches to this task rely on sequenced genomes in public databases, but these genomes are a highly biased sample that is not necessarily representative of environments interesting to many metagenomics projects.ResultsWe present SCIMM (Sequence Clustering with Interpolated Markov Models), an unsupervised sequence clustering method. SCIMM achieves greater clustering accuracy than previous unsupervised approaches. We examine the limitations of unsupervised learning on complex datasets, and suggest a hybrid of SCIMM and supervised learning method Phymm called PHYSCIMM that performs better when evolutionarily close training genomes are available.ConclusionsSCIMM and PHYSCIMM are highly accurate methods to cluster metagenomic sequences. SCIMM operates entirely unsupervised, making it ideal for environments containing mostly novel microbes. PHYSCIMM uses supervised learning to improve clustering in environments containing microbial strains from well-characterized genera. SCIMM and PHYSCIMM are available open source from http://www.cbcb.umd.edu/software/scimm.

Phymm and PhymmBL: metagenomic phylogenetic classification with interpolated Markov models

Metagenomics projects collect DNA from uncharacterized environments that may contain thousands of species per sample. One main challenge facing metagenomic analysis is phylogenetic classification of raw sequence reads into groups representing the same or similar taxa, a prerequisite for genome assembly and for analyzing the biological diversity of a sample. New sequencing technologies have made metagenomics easier, by making sequencing faster, and more difficult, by producing shorter reads than previous technologies. Classifying sequences from reads as short as 100 base pairs has until now been relatively inaccurate, requiring researchers to use older, long-read technologies. We present Phymm, a classifier for metagenomic data, that has been trained on 539 complete, curated genomes and can accurately classify reads as short as 100 bp, representing a substantial leap forward over previous composition-based classification methods. We also describe how combining Phymm with sequence alignment algorithms, further improves accuracy.

Identifying bacterial genes and endosymbiont DNA with Glimmer

The Glimmer gene-finding software has been successfully used for finding genes in bacteria, archaea and viruses representing hundreds of species. We describe several major changes to the Glimmer system, including improved methods for identifying both coding regions and start codons. We also describe a new module of Glimmer that can distinguish host and endosymbiont DNA. This module was developed in response to the discovery that eukaryotic genome sequencing projects sometimes inadvertently capture the DNA of intracellular bacteria living in the host. The new methods dramatically reduce the rate of false-positive predictions, while maintaining Glimmer's 99% sensitivity rate at detecting genes in most species, and they find substantially more correct start sites, as measured by comparisons to known and well-curated genes. We show that our interpolated Markov model (IMM) DNA discriminator correctly separated 99% of the sequences in a recent genome project that produced a mixture of sequences from the bacterium Prochloron didemni and its sea squirt host, Lissoclinum patella. Glimmer is OSI Certified Open Source and available at http://cbcb.umd.edu/software/glimmer.

GlimmerM, Exonomy and Unveil: three ab initio eukaryotic genefinders.

We present three programs for ab initio gene prediction in eukaryotes: Exonomy, Unveil and GlimmerM. Exonomy is a 23-state Generalized Hidden Markov Model (GHMM), Unveil is a 283-state standard Hidden Markov Model (HMM) and GlimmerM is a previously-described genefinder which utilizes decision trees and Interpolated Markov Models (IMMs). All three are readily re-trainable for new organisms and have been found to perform well compared to other genefinders. Results are presented for Arabidopsis thaliana. Cases have been found where each of the genefinders outperforms each of the others, demonstrating the collective value of this ensemble of genefinders. These programs are all accessible through webservers at http://www.tigr.org/software.

Interpolated Markov Models for Eukaryotic Gene Finding

Computational gene finding research has emphasized the development of gene finders for bacterial and human DNA. This has left genome projects for some small eukaryotes without a system that addresses their needs. This paper reports on a new system, GlimmerM, that was developed to find genes in the malaria parasite Plasmodium falciparum. Because the gene density in P. falciparum is relatively high, the system design was based on a successful bacterial gene finder, Glimmer. The system was augmented with specially trained modules to find splice sites and was trained on all available data from the P. falciparum genome. Although a precise evaluation of its accuracy is impossible at this time, laboratory tests (using RT-PCR) on a small selection of predicted genes confirmed all of those predictions. With the rapid progress in sequencing the genome of P. falciparum, the availability of this new gene finder will greatly facilitate the annotation process.

Microbial gene identification using interpolated Markov models.

This paper describes a new system, GLIMMER, for finding genes in microbial genomes. In a series of tests on Haemophilus influenzae , Helicobacter pylori and other complete microbial genomes, this system has proven to be very accurate at locating virtually all the genes in these sequences, outperforming previous methods. A conservative estimate based on experiments on H.pylori and H. influenzae is that the system finds >97% of all genes. GLIMMER uses interpolated Markov models (IMMs) as a framework for capturing dependencies between nearby nucleotides in a DNA sequence. An IMM-based method makes predictions based on a variable context; i.e., a variable-length oligomer in a DNA sequence. The context used by GLIMMER changes depending on the local composition of the sequence. As a result, GLIMMER is more flexible and more powerful than fixed-order Markov methods, which have previously been the primary content-based technique for finding genes in microbial DNA.