Estimation of pairwise sequence similarity of mammalian enhancers with word neighbourhood counts

Interpreting alignment-free sequence comparison: what makes a score a good score?

Alignment-free methods are alternatives to alignment-based methods when searching sequence data sets. The output from an alignment-free sequence comparison is a similarity score, the interpretation of which is not straightforward. We propose objective functions to interpret and calibrate outputs from alignment-free searches, noting that different objective functions are necessary for different biological contexts. This leads to advantages: visualising and comparing score distributions, including those from true positives, may be a relatively simple method to gain insight into the performance of different metrics. Using an empirical approach with both DNA and protein sequences, we characterise different similarity score distributions generated under different parameters. In particular, we demonstrate how sequence length can affect the scores. We show that scores of true positive sequence pairs may correlate significantly with their mean length; and even if the correlation is weak, the relative difference in length of the sequence pair may significantly reduce the effectiveness of alignment-free metrics. Importantly, we show how objective functions can be used with test data to accurately estimate the probability of true positives. This can significantly increase the utility of alignment-free approaches. Finally, we have developed a general-purpose software tool called KAST for use in high-throughput workflows on Linux clusters.

K2Mem: Discovering Discriminative K-mers From Sequencing Data for Metagenomic Reads Classification

The major problem when analyzing a metagenomic sample is to taxonomically annotate its reads to identify the species they contain. Most of the methods currently available focus on the classification of reads using a set of reference genomes and their k-mers. While in terms of precision these methods have reached percentages of correctness close to perfection, in terms of recall (the actual number of classified reads) the performances fall at around 50%. One of the reasons is the fact that the sequences in a sample can be very different from the corresponding reference genome, e.g., viral genomes are highly mutated. To address this issue, in this paper we study the problem of metagenomic reads classification by improving the reference k-mers library with novel discriminative k-mers from the input sequencing reads. We evaluated the performance in different conditions against several other tools and the results showed an improved F-measure, especially when close reference genomes are not available. Availability: https://github.com.

Alignment-Free Sequence Comparison With Multiple k Values

Alignment-free sequence comparison approaches have become increasingly popular in computational biology, because alignment-based approaches are inefficient to process large-scale datasets. Still, there is no way to determine the optimal value of the critical parameter k for alignment-free approaches in general. In this article, we tried to solve the problem by involving multiple k values simultaneously. The method counts the occurrence of each k-mer with different k values in a sequence. Two weighting schemes, based on maximizing deviation method and genetic algorithm, are then used on these counts. We applied the method to enhance the three common alignment-free approaches D₂, D₂^S, and D₂^*, and evaluated its performance on similarity search and functionally related regulatory sequences recognition. The enhanced approaches achieve better performance than the original approaches in all cases, and much better performance than some other common measures, such as Pcc, Eu, Ma, Ch, Kld, and Cos.

An Information Gain-based Method for Evaluating the Classification Power of Features Towards Identifying Enhancers

Background:

Enhancers are cis-regulatory elements that enhance gene expression on DNA sequences. Since most of enhancers are located far from transcription start sites, it is difficult to identify them. As other regulatory elements, the regions around enhancers contain a variety of features, which can help in enhancer recognition.

Objective:

The classification power of features differs significantly, the performances of existing methods that use one or a few features for identifying enhancer vary greatly. Therefore, evaluating the classification power of each feature can improve the predictive performance of enhancers.

Methods:

We present an evaluation method based on Information Gain (IG) that captures the entropy change of enhancer recognition according to features. To validate the performance of our method, experiments using the Single Feature Prediction Accuracy (SFPA) were conducted on each feature.

Results:

The average IG values of the sequence feature, transcriptional feature and epigenetic feature are 0.068, 0.213, and 0.299, respectively. Through SFPA, the average AUC values of the sequence feature, transcriptional feature and epigenetic feature are 0.534, 0.605, and 0.647, respectively. The verification results are consistent with our evaluation results.

Conclusion:

This IG-based method can effectively evaluate the classification power of features for identifying enhancers. Compared with sequence features, epigenetic features are more effective for recognizing enhancers.

A survey and evaluations of histogram-based statistics in alignment-free sequence comparison

Motivation

Since the dawn of the bioinformatics field, sequence alignment scores have been the main method for comparing sequences. However, alignment algorithms are quadratic, requiring long execution time. As alternatives, scientists have developed tens of alignment-free statistics for measuring the similarity between two sequences.

Results

We surveyed tens of alignment-free k-mer statistics. Additionally, we evaluated 33 statistics and multiplicative combinations between the statistics and/or their squares. These statistics are calculated on two k-mer histograms representing two sequences. Our evaluations using global alignment scores revealed that the majority of the statistics are sensitive and capable of finding similar sequences to a query sequence. Therefore, any of these statistics can filter out dissimilar sequences quickly. Further, we observed that multiplicative combinations of the statistics are highly correlated with the identity score. Furthermore, combinations involving sequence length difference or Earth Mover’s distance, which takes the length difference into account, are always among the highest correlated paired statistics with identity scores. Similarly, paired statistics including length difference or Earth Mover’s distance are among the best performers in finding the K-closest sequences. Interestingly, similar performance can be obtained using histograms of shorter words, resulting in reducing the memory requirement and increasing the speed remarkably. Moreover, we found that simple single statistics are sufficient for processing next-generation sequencing reads and for applications relying on local alignment. Finally, we measured the time requirement of each statistic. The survey and the evaluations will help scientists with identifying efficient alternatives to the costly alignment algorithm, saving thousands of computational hours.

Availability

The source code of the benchmarking tool is available as Supplementary Materials.

HLMethy: a machine learning-based model to identify the hidden labels of m6A candidates

We developed a machine learning-based model to identify the hidden labels of m⁶A candidates from noisy m6A-seq data. Peak-calling approaches, such as MeRIP-seq or m⁶A-seq, are commonly used to map m⁶A modifications. However, these technologies can only map m⁶A sites with 100-200 nt resolution and cannot reveal the precise location or the number of modified residues in a transcript. To address this challenge, we developed a novel machine learning-based approach, named HLMethy, to assign labels to m⁶A candidates from noisy m⁶A-seq data. The multiple instance learning framework was adopted and two different training strategies were used to generate the classification model. To test the performance of our model, the m⁶A sites with single-base resolution were used and our model achieved comparable performance against existing instance-level predictors, which suggest that our model has the potential to improve the data quality of m⁶A-seq at reduced costs. What's more, our generic framework can be extended to other newly found modifications that are found by peak-calling approaches. The source code of HLMethy is available at https://github.com/liuze-nwafu/HLMethy.

Alignment-free inference of hierarchical and reticulate phylogenomic relationships

We are amidst an ongoing flood of sequence data arising from the application of high-throughput technologies, and a concomitant fundamental revision in our understanding of how genomes evolve individually and within the biosphere. Workflows for phylogenomic inference must accommodate data that are not only much larger than before, but often more error prone and perhaps misassembled, or not assembled in the first place. Moreover, genomes of microbes, viruses and plasmids evolve not only by tree-like descent with modification but also by incorporating stretches of exogenous DNA. Thus, next-generation phylogenomics must address computational scalability while rethinking the nature of orthogroups, the alignment of multiple sequences and the inference and comparison of trees. New phylogenomic workflows have begun to take shape based on so-called alignment-free (AF) approaches. Here, we review the conceptual foundations of AF phylogenetics for the hierarchical (vertical) and reticulate (lateral) components of genome evolution, focusing on methods based on k-mers. We reflect on what seems to be successful, and on where further development is needed.

Alignment-Free Sequence Analysis and Applications

Genome and metagenome comparisons based on large amounts of next generation sequencing (NGS) data pose significant challenges for alignment-based approaches due to the huge data size and the relatively short length of the reads. Alignment-free approaches based on the counts of word patterns in NGS data do not depend on the complete genome and are generally computationally efficient. Thus, they contribute significantly to genome and metagenome comparison. Recently, novel statistical approaches have been developed for the comparison of both long and shotgun sequences. These approaches have been applied to many problems including the comparison of gene regulatory regions, genome sequences, metagenomes, binning contigs in metagenomic data, identification of virus-host interactions, and detection of horizontal gene transfers. We provide an updated review of these applications and other related developments of word-count based approaches for alignment-free sequence analysis.

Alignment-free sequence comparison: benefits, applications, and tools

Alignment-free sequence analyses have been applied to problems ranging from whole-genome phylogeny to the classification of protein families, identification of horizontally transferred genes, and detection of recombined sequences. The strength of these methods makes them particularly useful for next-generation sequencing data processing and analysis. However, many researchers are unclear about how these methods work, how they compare to alignment-based methods, and what their potential is for use for their research. We address these questions and provide a guide to the currently available alignment-free sequence analysis tools.

Optimal choice of word length when comparing two Markov sequences using a χ 2-statistic

Background

Alignment-free sequence comparison using counts of word patterns (grams, k-tuples) has become an active research topic due to the large amount of sequence data from the new sequencing technologies. Genome sequences are frequently modelled by Markov chains and the likelihood ratio test or the corresponding approximate χ²-statistic has been suggested to compare two sequences. However, it is not known how to best choose the word length k in such studies.

Results

We develop an optimal strategy to choose k by maximizing the statistical power of detecting differences between two sequences. Let the orders of the Markov chains for the two sequences be r₁ and r₂, respectively. We show through both simulations and theoretical studies that the optimal k= max(r₁,r₂)+1 for both long sequences and next generation sequencing (NGS) read data. The orders of the Markov chains may be unknown and several methods have been developed to estimate the orders of Markov chains based on both long sequences and NGS reads. We study the power loss of the statistics when the estimated orders are used. It is shown that the power loss is minimal for some of the estimators of the orders of Markov chains.

Conclusion

Our studies provide guidelines on choosing the optimal word length for the comparison of Markov sequences.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-017-4020-z) contains supplementary material, which is available to authorized users.

Prediction of virus-host infectious association by supervised learning methods

Background

The study of virus-host infectious association is important for understanding the functions and dynamics of microbial communities. Both cellular and fractionated viral metagenomic data generate a large number of viral contigs with missing host information. Although relative simple methods based on the similarity between the word frequency vectors of viruses and bacterial hosts have been developed to study virus-host associations, the problem is significantly understudied. We hypothesize that machine learning methods based on word frequencies can be efficiently used to study virus-host infectious associations.

Methods

We investigate four different representations of word frequencies of viral sequences including the relative word frequency and three normalized word frequencies by subtracting the number of expected from the observed word counts. We also study five machine learning methods including logistic regression, support vector machine, random forest, Gaussian naive Bayes and Bernoulli naive Bayes for separating infectious from non-infectious viruses for nine bacterial host genera with at least 45 infecting viruses. Area under the receiver operating characteristic curve (AUC) is used to compare the performance of different machine learning method and feature combinations. We then evaluate the performance of the best method for the identification of the hosts of contigs in metagenomic studies. We also develop a maximum likelihood method to estimate the fraction of true infectious viruses for a given host in viral tagging experiments.

Results

Based on nine bacterial host genera with at least 45 infectious viruses, we show that random forest together with the relative word frequency vector performs the best in identifying viruses infecting particular hosts. For all the nine host genera, the AUC is over 0.85 and for five of them, the AUC is higher than 0.98 when the word size is 6 indicating the high accuracy of using machine learning approaches for identifying viruses infecting particular hosts. We also show that our method can predict the hosts of viral contigs of length at least 1kbps in metagenomic studies with high accuracy. The random forest together with word frequency vector outperforms current available methods based on Manhattan and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d_{2}^{*}$\end{document}d2∗ dissimilarity measures. Based on word frequencies, we estimate that about 95% of the identified T4-like viruses in viral tagging experiment infect Synechococcus, while only about 29% of the identified non-T4-like viruses and 30% of the contigs in the study potentially infect Synechococcus.

Conclusions

The random forest machine learning method together with the relative word frequencies as features of viruses can be used to predict viruses and viral contigs for specific bacterial hosts. The maximum likelihood approach can be used to estimate the fraction of true infectious associated viruses in viral tagging experiments.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1473-7) contains supplementary material, which is available to authorized users.

Inference of Markovian properties of molecular sequences from NGS data and applications to comparative genomics

MOTIVATION

Next-generation sequencing (NGS) technologies generate large amounts of short read data for many different organisms. The fact that NGS reads are generally short makes it challenging to assemble the reads and reconstruct the original genome sequence. For clustering genomes using such NGS data, word-count based alignment-free sequence comparison is a promising approach, but for this approach, the underlying expected word counts are essential.A plausible model for this underlying distribution of word counts is given through modeling the DNA sequence as a Markov chain (MC). For single long sequences, efficient statistics are available to estimate the order of MCs and the transition probability matrix for the sequences. As NGS data do not provide a single long sequence, inference methods on Markovian properties of sequences based on single long sequences cannot be directly used for NGS short read data.

RESULTS

Here we derive a normal approximation for such word counts. We also show that the traditional Chi-square statistic has an approximate gamma distribution ,: using the Lander-Waterman model for physical mapping. We propose several methods to estimate the order of the MC based on NGS reads and evaluate those using simulations. We illustrate the applications of our results by clustering genomic sequences of several vertebrate and tree species based on NGS reads using alignment-free sequence dissimilarity measures. We find that the estimated order of the MC has a considerable effect on the clustering results ,: and that the clustering results that use a N: MC of the estimated order give a plausible clustering of the species.

AVAILABILITY AND IMPLEMENTATION

Our implementation of the statistics developed here is available as R package 'NGS.MC' at http://www-rcf.usc.edu/∼fsun/Programs/NGS-MC/NGS-MC.html

CONTACT

fsun@usc.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On the comparison of regulatory sequences with multiple resolution Entropic Profiles

Background

Enhancers are stretches of DNA (100–1000 bp) that play a major role in development gene expression, evolution and disease. It has been recently shown that in high-level eukaryotes enhancers rarely work alone, instead they collaborate by forming clusters of cis-regulatory modules (CRMs). Although the binding of transcription factors is sequence-specific, the identification of functionally similar enhancers is very difficult and it cannot be carried out with traditional alignment-based techniques.

Results

The use of fast similarity measures, like alignment-free measures, to detect related regulatory sequences is crucial to understand functional correlation between two enhancers. In this paper we study the use of alignment-free measures for the classification of CRMs. However, alignment-free measures are generally tied to a fixed resolution k. Here we propose an alignment-free statistic, called \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$EP^{*}_{2}$\end{document}EP2∗, that is based on multiple resolution patterns derived from the Entropic Profiles (EPs). The Entropic Profile is a function of the genomic location that captures the importance of that region with respect to the whole genome. As a byproduct we provide a formula to compute the exact variance of variable length word counts, a result that can be of general interest also in other applications.

Conclusions

We evaluate several alignment-free statistics on simulated data and real mouse ChIP-seq sequences. The new statistic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$EP^{*}_{2}$\end{document}EP2∗, is highly successful in discriminating functionally related enhancers and, in almost all experiments, it outperforms fixed-resolution methods. We implemented the new alignment-free measures, as well as traditional ones, in a software called EP-sim that is freely available: http://www.dei.unipd.it/~ciompin/main/EP-sim.html.

Dynamic transcription of distinct classes of endogenous retroviral elements marks specific populations of early human embryonic cells

About half of the human genome consists of highly repetitive elements, most of which are considered dispensable for human life. Here, we report that repetitive elements originating from endogenous retroviruses (ERVs) are systematically transcribed during human early embryogenesis in a stage-specific manner. Our analysis highlights that the long terminal repeats (LTRs) of ERVs provide the template for stage-specific transcription initiation, thereby generating hundreds of co-expressed, ERV-derived RNAs. Conversion of human embryonic stem cells (hESCs) to an epiblast-like state activates blastocyst-specific ERV elements, indicating that their activity dynamically reacts to changes in regulatory networks. In addition to initiating stage-specific transcription, many ERV families contain preserved splice sites that join the ERV segment with non-ERV exons in their genomic vicinity. In summary, we find that ERV expression is a hallmark of cellular identity and cell potency that characterizes the cell populations in early human embryos.

Clustering of reads with alignment-free measures and quality values

Background

The data volume generated by Next-Generation Sequencing (NGS) technologies is growing at a pace that is now challenging the storage and data processing capacities of modern computer systems. In this context an important aspect is the reduction of data complexity by collapsing redundant reads in a single cluster to improve the run time, memory requirements, and quality of post-processing steps like assembly and error correction. Several alignment-free measures, based on k-mers counts, have been used to cluster reads.

Quality scores produced by NGS platforms are fundamental for various analysis of NGS data like reads mapping and error detection. Moreover future-generation sequencing platforms will produce long reads but with a large number of erroneous bases (up to 15 %).

Results

In this scenario it will be fundamental to exploit quality value information within the alignment-free framework. To the best of our knowledge this is the first study that incorporates quality value information and k-mers counts, in the context of alignment-free measures, for the comparison of reads data. Based on this principles, in this paper we present a family of alignment-free measures called D^q-type. A set of experiments on simulated and real reads data confirms that the new measures are superior to other classical alignment-free statistics, especially when erroneous reads are considered. Also results on de novo assembly and metagenomic reads classification show that the introduction of quality values improves over standard alignment-free measures. These statistics are implemented in a software called QCluster (http://www.dei.unipd.it/~ciompin/main/qcluster.html).

Inferring phylogenies of evolving sequences without multiple sequence alignment

Alignment-free methods, in which shared properties of sub-sequences (e.g. identity or match length) are extracted and used to compute a distance matrix, have recently been explored for phylogenetic inference. However, the scalability and robustness of these methods to key evolutionary processes remain to be investigated. Here, using simulated sequence sets of various sizes in both nucleotides and amino acids, we systematically assess the accuracy of phylogenetic inference using an alignment-free approach, based on D₂ statistics, under different evolutionary scenarios. We find that compared to a multiple sequence alignment approach, D₂ methods are more robust against among-site rate heterogeneity, compositional biases, genetic rearrangements and insertions/deletions, but are more sensitive to recent sequence divergence and sequence truncation. Across diverse empirical datasets, the alignment-free methods perform well for sequences sharing low divergence, at greater computation speed. Our findings provide strong evidence for the scalability and the potential use of alignment-free methods in large-scale phylogenomics.

Assembly-free genome comparison based on next-generation sequencing reads and variable length patterns

Background

With the advent of Next-Generation Sequencing technologies (NGS), a large amount of short read data has been generated. If a reference genome is not available, the assembly of a template sequence is usually challenging because of repeats and the short length of reads. When NGS reads cannot be mapped onto a reference genome alignment-based methods are not applicable. However it is still possible to study the evolutionary relationship of unassembled genomes based on NGS data.

Results

We present a parameter-free alignment-free method, called Under2¯, based on variable-length patterns, for the direct comparison of sets of NGS reads. We define a similarity measure using variable-length patterns, as well as reverses and reverse-complements, along with their statistical and syntactical properties. We evaluate several alignment-free statistics on the comparison of NGS reads coming from simulated and real genomes. In almost all simulations our method Under2¯ outperforms all other statistics. The performance gain becomes more evident when real genomes are used.

Conclusion

The new alignment-free statistic is highly successful in discriminating related genomes based on NGS reads data. In almost all experiments, it outperforms traditional alignment-free statistics that are based on fixed length patterns.

Beyond Fixed-Resolution Alignment-Free Measures for Mammalian Enhancers Sequence Comparison

The cell-type diversity is to a large degree driven by transcription regulation, i.e., enhancers. It has been recently shown that in high-level eukaryotes enhancers rarely work alone, instead they collaborate by forming clusters of cis-regulatory modules (CRMs). Even if the binding of transcription factors is sequence-specific, the identification of functionally similar enhancers is very difficult. A similarity measure to detect related regulatory sequences is crucial to understand functional correlation between two enhancers. This will allow large-scale analyses, clustering and genome-wide classifications. In this paper we present Under2, a parameter-free alignment-free statistic based on variable-length words. As opposed to traditional alignment-free methods, which are based on fixed-length patterns or, in other words, tied to a fixed resolution, our statistic is built upon variable-length words, and thus multiple resolutions are allowed. This will capture the great variability of lengths of CRMs. We evaluate several alignment-free statistics on simulated data and real ChIP-seq sequences. The new statistic is highly successful in discriminating functionally related enhancers and, in almost all experiments, it outperforms fixed-resolution methods. Finally, experiments on mouse enhancers show that Under2 can separate enhancers active in different tissues.

AVAILABILITY

http://www.dei.unipd.it/~ciompin/main/UnderIICRMS.html.

Global view of enhancer-promoter interactome in human cells

Enhancer mapping has been greatly facilitated by various genomic marks associated with it. However, little is available in our toolbox to link enhancers with their target promoters, hampering mechanistic understanding of enhancer-promoter (EP) interaction. We develop and characterize multiple genomic features for distinguishing true EP pairs from noninteracting pairs. We integrate these features into a probabilistic predictor for EP interactions. Multiple validation experiments demonstrate a significant improvement over state-of-the-art approaches. Systematic analyses of EP interactions across 12 cell types reveal several global features of EP interactions: (i) a larger fraction of EP interactions are cell type specific than enhancers; (ii) promoters controlled by multiple enhancers have higher tissue specificity, but the regulating enhancers are less conserved; (iii) cohesin plays a role in mediating tissue-specific EP interactions via chromatin looping in a CTCF-independent manner. Our approach presents a systematic and effective strategy to decipher the mechanisms underlying EP communication.

Fast alignment-free sequence comparison using spaced-word frequencies

Motivation: Alignment-free methods for sequence comparison are increasingly used for genome analysis and phylogeny reconstruction; they circumvent various difficulties of traditional alignment-based approaches. In particular, alignment-free methods are much faster than pairwise or multiple alignments. They are, however, less accurate than methods based on sequence alignment. Most alignment-free approaches work by comparing the word composition of sequences. A well-known problem with these methods is that neighbouring word matches are far from independent.

Results: To reduce the statistical dependency between adjacent word matches, we propose to use ‘spaced words’, defined by patterns of ‘match’ and ‘don’t care’ positions, for alignment-free sequence comparison. We describe a fast implementation of this approach using recursive hashing and bit operations, and we show that further improvements can be achieved by using multiple patterns instead of single patterns. To evaluate our approach, we use spaced-word frequencies as a basis for fast phylogeny reconstruction. Using real-world and simulated sequence data, we demonstrate that our multiple-pattern approach produces better phylogenies than approaches relying on contiguous words.

Availability and implementation: Our program is freely available at http://spaced.gobics.de/.

Contact:chris.leimeister@stud.uni-goettingen.de

Supplementary information:Supplementary data are available at Bioinformatics online.

Evolutionary conservation of the eumetazoan gene regulatory landscape

Despite considerable differences in morphology and complexity of body plans among animals, a great part of the gene set is shared among Bilateria and their basally branching sister group, the Cnidaria. This suggests that the common ancestor of eumetazoans already had a highly complex gene repertoire. At present it is therefore unclear how morphological diversification is encoded in the genome. Here we address the possibility that differences in gene regulation could contribute to the large morphological divergence between cnidarians and bilaterians. To this end, we generated the first genome-wide map of gene regulatory elements in a nonbilaterian animal, the sea anemone Nematostella vectensis. Using chromatin immunoprecipitation followed by deep sequencing of five chromatin modifications and a transcriptional cofactor, we identified over 5000 enhancers in the Nematostella genome and could validate 75% of the tested enhancers in vivo. We found that in Nematostella, but not in yeast, enhancers are characterized by the same combination of histone modifications as in bilaterians, and these enhancers preferentially target developmental regulatory genes. Surprisingly, the distribution and abundance of gene regulatory elements relative to these genes are shared between Nematostella and bilaterian model organisms. Our results suggest that complex gene regulation originated at least 600 million yr ago, predating the common ancestor of eumetazoans.

The distribution of word matches between Markovian sequences with periodic boundary conditions

Word match counts have traditionally been proposed as an alignment-free measure of similarity for biological sequences. The D(2) statistic, which simply counts the number of exact word matches between two sequences, is a useful test bed for developing rigorous mathematical results, which can then be extended to more biologically useful measures. The distributional properties of the D(2) statistic under the null hypothesis of identically and independently distributed letters have been studied extensively, but no comprehensive study of the D(2) distribution for biologically more realistic higher-order Markovian sequences exists. Here we derive exact formulas for the mean and variance of the D(2) statistic for Markovian sequences of any order, and demonstrate through Monte Carlo simulations that the entire distribution is accurately characterized by a Pólya-Aeppli distribution for sequence lengths of biological interest. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulas for the mean and variance to be derived. We also carry out a preliminary comparison between the approximate D(2) distribution computed with the theoretical mean and variance under a Markovian hypothesis and an empirical D(2) distribution from the human genome.

New developments of alignment-free sequence comparison: measures, statistics and next-generation sequencing

With the development of next-generation sequencing (NGS) technologies, a large amount of short read data has been generated. Assembly of these short reads can be challenging for genomes and metagenomes without template sequences, making alignment-based genome sequence comparison difficult. In addition, sequence reads from NGS can come from different regions of various genomes and they may not be alignable. Sequence signature-based methods for genome comparison based on the frequencies of word patterns in genomes and metagenomes can potentially be useful for the analysis of short reads data from NGS. Here we review the recent development of alignment-free genome and metagenome comparison based on the frequencies of word patterns with emphasis on the dissimilarity measures between sequences, the statistical power of these measures when two sequences are related and the applications of these measures to NGS data.

Multiple alignment-free sequence comparison

MOTIVATION

Recently, a range of new statistics have become available for the alignment-free comparison of two sequences based on k-tuple word content. Here, we extend these statistics to the simultaneous comparison of more than two sequences. Our suite of statistics contains, first, C(*)1 and C(S)1, extensions of statistics for pairwise comparison of the joint k-tuple content of all the sequences, and second, C(*)2, C(S)2 and C(geo)2, averages of sums of pairwise comparison statistics. The two tasks we consider are, first, to identify sequences that are similar to a set of target sequences, and, second, to measure the similarity within a set of sequences.

RESULTS

Our investigation uses both simulated data as well as cis-regulatory module data where the task is to identify cis-regulatory modules with similar transcription factor binding sites. We find that although for real data, all of our statistics show a similar performance, on simulated data the Shepp-type statistics are in some instances outperformed by star-type statistics. The multiple alignment-free statistics are more sensitive to contamination in the data than the pairwise average statistics.

AVAILABILITY

Our implementation of the five statistics is available as R package named 'multiAlignFree' at be http://www-rcf.usc.edu/∼fsun/Programs/multiAlignFree/multiAlignFreemain.html.

CONTACT

reinert@stats.ox.ac.uk.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Robust k-mer frequency estimation using gapped k-mers

Oligomers of fixed length, k, commonly known as k-mers, are often used as fundamental elements in the description of DNA sequence features of diverse biological function, or as intermediate elements in the constuction of more complex descriptors of sequence features such as position weight matrices. k-mers are very useful as general sequence features because they constitute a complete and unbiased feature set, and do not require parameterization based on incomplete knowledge of biological mechanisms. However, a fundamental limitation in the use of k-mers as sequence features is that as k is increased, larger spatial correlations in DNA sequence elements can be described, but the frequency of observing any specific k-mer becomes very small, and rapidly approaches a sparse matrix of binary counts. Thus any statistical learning approach using k-mers will be susceptible to noisy estimation of k-mer frequencies once k becomes large. Because all molecular DNA interactions have limited spatial extent, gapped k-mers often carry the relevant biological signal. Here we use gapped k-mer counts to more robustly estimate the ungapped k-mer frequencies, by deriving an equation for the minimum norm estimate of k-mer frequencies given an observed set of gapped k-mer frequencies. We demonstrate that this approach provides a more accurate estimate of the k-mer frequencies in real biological sequences using a sample of CTCF binding sites in the human genome.

A geometric interpretation for local alignment-free sequence comparison

Local alignment-free sequence comparison arises in the context of identifying similar segments of sequences that may not be alignable in the traditional sense. We propose a randomized approximation algorithm that is both accurate and efficient. We show that under D2 and its important variant [Formula: see text] as the similarity measure, local alignment-free comparison between a pair of sequences can be formulated as the problem of finding the maximum bichromatic dot product between two sets of points in high dimensions. We introduce a geometric framework that reduces this problem to that of finding the bichromatic closest pair (BCP), allowing the properties of the underlying metric to be leveraged. Local alignment-free sequence comparison can be solved by making a quadratic number of alignment-free substring comparisons. We show both theoretically and through empirical results on simulated data that our approximation algorithm requires a subquadratic number of such comparisons and trades only a small amount of accuracy to achieve this efficiency. Therefore, our algorithm can extend the current usage of alignment-free-based methods and can also be regarded as a substitute for local alignment algorithms in many biological studies.

Real time classification of viruses in 12 dimensions

The International Committee on Taxonomy of Viruses authorizes and organizes the taxonomic classification of viruses. Thus far, the detailed classifications for all viruses are neither complete nor free from dispute. For example, the current missing label rates in GenBank are 12.1% for family label and 30.0% for genus label. Using the proposed Natural Vector representation, all 2,044 single-segment referenced viral genomes in GenBank can be embedded in [Formula: see text]. Unlike other approaches, this allows us to determine phylogenetic relations for all viruses at any level (e.g., Baltimore class, family, subfamily, genus, and species) in real time. Additionally, the proposed graphical representation for virus phylogeny provides a visualization of the distribution of viruses in [Formula: see text]. Unlike the commonly used tree visualization methods which suffer from uniqueness and existence problems, our representation always exists and is unique. This approach is successfully used to predict and correct viral classification information, as well as to identify viral origins; e.g. a recent public health threat, the West Nile virus, is closer to the Japanese encephalitis antigenic complex based on our visualization. Based on cross-validation results, the accuracy rates of our predictions are as high as 98.2% for Baltimore class labels, 96.6% for family labels, 99.7% for subfamily labels and 97.2% for genus labels.

Protection against experimental melioidosis following immunization with live Burkholderia thailandensis expressing a manno-heptose capsule

Melioidosis is a severe infectious disease caused by Burkholderia pseudomallei. It is highly resistant to antibiotic treatment, and there is currently no licensed vaccine. Burkholderia thailandensis is a close relative of Burkholderia pseudomallei but is essentially avirulent in mammals. In this report, we detail the protective efficacy of immunization with live B. thailandensis E555, a strain which has been shown to express an antigenic capsule similar to that of B. pseudomallei. Immunization with E555 induced significant protection against a lethal intraperitoneal B. pseudomallei challenge in a mouse model of infection, with no mice succumbing to infection over the course of the study, even with challenges of up to 6,000 median lethal doses. By comparison, mice immunized with B. thailandensis not expressing a B. pseudomallei-like capsule had significantly decreased levels of protection. E555-immunized mice had significantly higher levels of IgG than mice immunized with noncapsulated B. thailandensis, and these antibody responses were primarily directed against the capsule.

Indel-tolerant read mapping with trinucleotide frequencies using cache-oblivious kd-trees

Motivation: Mapping billions of reads from next generation sequencing experiments to reference genomes is a crucial task, which can require hundreds of hours of running time on a single CPU even for the fastest known implementations. Traditional approaches have difficulties dealing with matches of large edit distance, particularly in the presence of frequent or large insertions and deletions (indels). This is a serious obstacle both in determining the spectrum and abundance of genetic variations and in personal genomics.

Results: For the first time, we adopt the approximate string matching paradigm of geometric embedding to read mapping, thus rephrasing it to nearest neighbor queries in a q-gram frequency vector space. Using the L₁ distance between frequency vectors has the benefit of providing lower bounds for an edit distance with affine gap costs. Using a cache-oblivious kd-tree, we realize running times, which match the state-of-the-art. Additionally, running time and memory requirements are about constant for read lengths between 100 and 1000 bp. We provide a first proof-of-concept that geometric embedding is a promising paradigm for read mapping and that L₁ distance might serve to detect structural variations. TreQ, our initial implementation of that concept, performs more accurate than many popular read mappers over a wide range of structural variants.

Availability and implementation: TreQ will be released under the GNU Public License (GPL), and precomputed genome indices will be provided for download at http://treq.sf.net.

Contact:pavelm@cs.rutgers.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Next-generation phylogenomics

Thanks to advances in next-generation technologies, genome sequences are now being generated at breadth (e.g. across environments) and depth (thousands of closely related strains, individuals or samples) unimaginable only a few years ago. Phylogenomics--the study of evolutionary relationships based on comparative analysis of genome-scale data--has so far been developed as industrial-scale molecular phylogenetics, proceeding in the two classical steps: multiple alignment of homologous sequences, followed by inference of a tree (or multiple trees). However, the algorithms typically employed for these steps scale poorly with number of sequences, such that for an increasing number of problems, high-quality phylogenomic analysis is (or soon will be) computationally infeasible. Moreover, next-generation data are often incomplete and error-prone, and analysis may be further complicated by genome rearrangement, gene fusion and deletion, lateral genetic transfer, and transcript variation. Here we argue that next-generation data require next-generation phylogenomics, including so-called alignment-free approaches.