A General Coverage Theory for Shotgun DNA Sequencing

PROBABILISTIC MODELING AND ANALYSIS OF DNA FRAGMENTATION

Deoxyribonucleic Acid (DNA) sequencing has become indispensable to the modern biological and medicine sciences. DNA fragmentation is a preliminary step in a dominant technique called shotgun sequencing that provides a time and cost effective strategy for the DNA sequencing. In this paper, we propose a probabilistic model for the random DNA fragmentation and derive an average number of fragments with the suitable length along with the probability of covering the entire DNA strand through the de novo assembly or the referenced-based mapping assembly. We formulate the coverage problem in terms of the probability of bond breaking between nucleotides and the number of DNA molecules participating in the fragmentation process, and provide insights into the optimal DNA fragmentation. We obtain the lower bound for the minimum number of suitable fragments required to reconstruct the DNA strand with the specified reliability. We evaluate the derived results with our DNA Fragmentation Tool which demonstrate, the validity of these results based on our model. Finally, we update our model with respect to the fragments’ size distribution of real data.

Nonpareil 3: Fast Estimation of Metagenomic Coverage and Sequence Diversity

Estimations of microbial community diversity based on metagenomic data sets are affected, often to an unknown degree, by biases derived from insufficient coverage and reference database-dependent estimations of diversity. For instance, the completeness of reference databases cannot be generally estimated since it depends on the extant diversity sampled to date, which, with the exception of a few habitats such as the human gut, remains severely undersampled. Further, estimation of the degree of coverage of a microbial community by a metagenomic data set is prohibitively time-consuming for large data sets, and coverage values may not be directly comparable between data sets obtained with different sequencing technologies. Here, we extend Nonpareil, a database-independent tool for the estimation of coverage in metagenomic data sets, to a high-performance computing implementation that scales up to hundreds of cores and includes, in addition, a k-mer-based estimation as sensitive as the original alignment-based version but about three hundred times as fast. Further, we propose a metric of sequence diversity (N_d ) derived directly from Nonpareil curves that correlates well with alpha diversity assessed by traditional metrics. We use this metric in different experiments demonstrating the correlation with the Shannon index estimated on 16S rRNA gene profiles and show that N_d additionally reveals seasonal patterns in marine samples that are not captured by the Shannon index and more precise rankings of the magnitude of diversity of microbial communities in different habitats. Therefore, the new version of Nonpareil, called Nonpareil 3, advances the toolbox for metagenomic analyses of microbiomes. IMPORTANCE Estimation of the coverage provided by a metagenomic data set, i.e., what fraction of the microbial community was sampled by DNA sequencing, represents an essential first step of every culture-independent genomic study that aims to robustly assess the sequence diversity present in a sample. However, estimation of coverage remains elusive because of several technical limitations associated with high computational requirements and limiting statistical approaches to quantify diversity. Here we described Nonpareil 3, a new bioinformatics algorithm that circumvents several of these limitations and thus can facilitate culture-independent studies in clinical or environmental settings, independent of the sequencing platform employed. In addition, we present a new metric of sequence diversity based on rarefied coverage and demonstrate its use in communities from diverse ecosystems.

An Enumerative Combinatorics Model for Fragmentation Patterns in RNA Sequencing Provides Insights into Nonuniformity of the Expected Fragment Starting-Point and Coverage Profile

RNA sequencing (RNA-seq) has emerged as the method of choice for measuring the expression of RNAs in a given cell population. In most RNA-seq technologies, sequencing the full length of RNA molecules requires fragmentation into smaller pieces. Unfortunately, the issue of nonuniform sequencing coverage across a genomic feature has been a concern in RNA-seq and is attributed to biases for certain fragments in RNA-seq library preparation and sequencing. To investigate the expected coverage obtained from fragmentation, we develop a simple fragmentation model that is independent of bias from the experimental method and is not specific to the transcript sequence. Essentially, we enumerate all configurations for maximal placement of a given fragment length, F, on transcript length, T, to represent every possible fragmentation pattern, from which we compute the expected coverage profile across a transcript. We extend this model to incorporate general empirical attributes such as read length, fragment length distribution, and number of molecules of the transcript. We further introduce the fragment starting-point, fragment coverage, and read coverage profiles. We find that the expected profiles are not uniform and that factors such as fragment length to transcript length ratio, read length to fragment length ratio, fragment length distribution, and number of molecules influence the variability of coverage across a transcript. Finally, we explore a potential application of the model where, with simulations, we show that it is possible to correctly estimate the transcript copy number for any transcript in the RNA-seq experiment.

Recovering complete and draft population genomes from metagenome datasets

Assembly of metagenomic sequence data into microbial genomes is of fundamental value to improving our understanding of microbial ecology and metabolism by elucidating the functional potential of hard-to-culture microorganisms. Here, we provide a synthesis of available methods to bin metagenomic contigs into species-level groups and highlight how genetic diversity, sequencing depth, and coverage influence binning success. Despite the computational cost on application to deeply sequenced complex metagenomes (e.g., soil), covarying patterns of contig coverage across multiple datasets significantly improves the binning process. We also discuss and compare current genome validation methods and reveal how these methods tackle the problem of chimeric genome bins i.e., sequences from multiple species. Finally, we explore how population genome assembly can be used to uncover biogeographic trends and to characterize the effect of in situ functional constraints on the genome-wide evolution.

Nonpareil: a redundancy-based approach to assess the level of coverage in metagenomic datasets

MOTIVATION

Determining the fraction of the diversity within a microbial community sampled and the amount of sequencing required to cover the total diversity represent challenging issues for metagenomics studies. Owing to these limitations, central ecological questions with respect to the global distribution of microbes and the functional diversity of their communities cannot be robustly assessed.

RESULTS

We introduce Nonpareil, a method to estimate and project coverage in metagenomes. Nonpareil does not rely on high-quality assemblies, operational taxonomic unit calling or comprehensive reference databases; thus, it is broadly applicable to metagenomic studies. Application of Nonpareil on available metagenomic datasets provided estimates on the relative complexity of soil, freshwater and human microbiome communities, and suggested that ∼200 Gb of sequencing data are required for 95% abundance-weighted average coverage of the soil communities analyzed.

AVAILABILITY AND IMPLEMENTATION

Nonpareil is available at https://github.com/lmrodriguezr/nonpareil/ under the Artistic License 2.0.

A user's guide to quantitative and comparative analysis of metagenomic datasets

Metagenomics has revolutionized microbiological studies during the past decade and provided new insights into the diversity, dynamics, and metabolic potential of natural microbial communities. However, metagenomics still represents a field in development, and standardized tools and approaches to handle and compare metagenomes have not been established yet. An important reason accounting for the latter is the continuous changes in the type of sequencing data available, for example, long versus short sequencing reads. Here, we provide a guide to bioinformatic pipelines developed to accomplish the following tasks, focusing primarily on those developed by our team: (i) assemble a metagenomic dataset; (ii) determine the level of sequence coverage obtained and the amount of sequencing required to obtain complete coverage; (iii) identify the taxonomic affiliation of a metagenomic read or assembled contig; and (iv) determine differentially abundant genes, pathways, and species between different datasets. Most of these pipelines do not depend on the type of sequences available or can be easily adjusted to fit different types of sequences, and are freely available (for instance, through our lab Web site: http://www.enve-omics.gatech.edu/). The limitations of current approaches, as well as the computational aspects that can be further improved, will also be briefly discussed. The work presented here provides practical guidelines on how to perform metagenomic analysis of microbial communities characterized by varied levels of diversity and establishes approaches to handle the resulting data, independent of the sequencing platform employed.

Microbiome in human health and disease

Metagenomic studies have truly revolutionised biology and medicine, and changed the way we study genomics. As genome sequencing becomes cheaper it is being applied to study complex metagenomes. 'Metagenome' is the genetic material recovered directly from an environmental sample or niche. By delivering fast, cheap, and large volumes of data Next Generation Sequencing (NGS) platforms have facilitated a deeper understanding of the fundamentals of genomes, gene functions and regulation. Metagenomics, also referred to as environmental or community genomics, has brought about radical changes in our ability to analyse complex microbial communities by direct sampling of their natural habitat paving the way for the creation of innovative new areas for biomedical research. Many metagenomic studies involving the 'human microbiome'have been undertaken to date. Samples from of a number of diverse habitats including different human body sites have been subject to metagenomic examinations. Huge national and international projects with the purpose of elucidating the biogeography of microbial communities living within and on the human body, are well underway. The analysis of human microbiome data has brought about a paradigm shift in our understanding of the role of resident microflora in human health and disease and brings non-traditional areas such as gut ecology to the forefront of personalised medicine. In this chapter we present an overview of the state-of-the-art in current literature and projects pertaining to human microbiome studies.

Coverage theories for metagenomic DNA sequencing based on a generalization of Stevens' theorem

Metagenomic project design has relied variously upon speculation, semi-empirical and ad hoc heuristic models, and elementary extensions of single-sample Lander–Waterman expectation theory, all of which are demonstrably inadequate. Here, we propose an approach based upon a generalization of Stevens’ Theorem for randomly covering a domain. We extend this result to account for the presence of multiple species, from which are derived useful probabilities for fully recovering a particular target microbe of interest and for average contig length. These show improved specificities compared to older measures and recommend deeper data generation than the levels chosen by some early studies, supporting the view that poor assemblies were due at least somewhat to insufficient data. We assess predictions empirically by generating roughly 4.5 Gb of sequence from a twelve member bacterial community, comparing coverage for two particular members, Selenomonas artemidis and Enterococcus faecium, which are the least (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}3 %) and most (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}12 %) abundant species, respectively. Agreement is reasonable, with differences likely attributable to coverage biases. We show that, in some cases, bias is simple in the sense that a small reduction in read length to simulate less efficient covering brings data and theory into essentially complete accord. Finally, we describe two applications of the theory. One plots coverage probability over the relevant parameter space, constructing essentially a “metagenomic design map” to enable straightforward analysis and design of future projects. The other gives an overview of the data requirements for various types of sequencing milestones, including a desired number of contact reads and contig length, for detection of a rare viral species.

Coverage statistics for sequence census methods

Background

We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce a coding of the shape of the coverage depth function as a tree and explain how this can be used to detect regions with anomalous coverage. This modeling perspective is especially germane to current high-throughput sequencing experiments, where both sample preparation protocols and sequencing technology particulars can affect fragment length distributions.

Results

Under the mild assumptions that fragment start sites are Poisson distributed and successive fragment lengths are independent and identically distributed, we observe that, regardless of fragment length distribution, the fragments produced in a sequencing experiment can be viewed as resulting from a two-dimensional spatial Poisson process. We then study the successive jumps of the coverage function, and show that they can be encoded as a random tree that is approximately a Galton-Watson tree with generation-dependent geometric offspring distributions whose parameters can be computed.

Conclusions

We extend standard analyses of shotgun sequencing that focus on coverage statistics at individual sites, and provide a null model for detecting deviations from random coverage in high-throughput sequence census based experiments. Our approach leads to explicit determinations of the null distributions of certain test statistics, while for others it greatly simplifies the approximation of their null distributions by simulation. Our focus on fragments also leads to a new approach to visualizing sequencing data that is of independent interest.

Occupancy modeling, maximum contig size probabilities and designing metagenomics experiments

Mathematical aspects of coverage and gaps in genome assembly have received substantial attention by bioinformaticians. Typical problems under consideration suppose that reads can be experimentally obtained from a single genome and that the number of reads will be set to cover a large percentage of that genome at a desired depth. In metagenomics experiments genomes from multiple species are simultaneously analyzed and obtaining large numbers of reads per genome is unlikely. We propose the probability of obtaining at least one contig of a desired minimum size from each novel genome in the pool without restriction based on depth of coverage as a metric for metagenomic experimental design. We derive an approximation to the distribution of maximum contig size for single genome assemblies using relatively few reads. This approximation is verified in simulation studies and applied to a number of different metagenomic experimental design problems, ranging in difficulty from detecting a single novel genome in a pool of known species to detecting each of a random number of novel genomes collectively sized and with abundances corresponding to given distributions in a single pool.

Aspects of coverage in medical DNA sequencing

Background

DNA sequencing is now emerging as an important component in biomedical studies of diseases like cancer. Short-read, highly parallel sequencing instruments are expected to be used heavily for such projects, but many design specifications have yet to be conclusively established. Perhaps the most fundamental of these is the redundancy required to detect sequence variations, which bears directly upon genomic coverage and the consequent resolving power for discerning somatic mutations.

Results

We address the medical sequencing coverage problem via an extension of the standard mathematical theory of haploid coverage. The expected diploid multi-fold coverage, as well as its generalization for aneuploidy are derived and these expressions can be readily evaluated for any project. The resulting theory is used as a scaling law to calibrate performance to that of standard BAC sequencing at 8× to 10× redundancy, i.e. for expected coverages that exceed 99% of the unique sequence. A differential strategy is formalized for tumor/normal studies wherein tumor samples are sequenced more deeply than normal ones. In particular, both tumor alleles should be detected at least twice, while both normal alleles are detected at least once. Our theory predicts these requirements can be met for tumor and normal redundancies of approximately 26× and 21×, respectively. We explain why these values do not differ by a factor of 2, as might intuitively be expected. Future technology developments should prompt even deeper sequencing of tumors, but the 21× value for normal samples is essentially a constant.

Conclusion

Given the assumptions of standard coverage theory, our model gives pragmatic estimates for required redundancy. The differential strategy should be an efficient means of identifying potential somatic mutations for further study.

Lessons learned from the initial sequencing of the pig genome: comparative analysis of an 8 Mb region of pig chromosome 17

BACKGROUND

We describe here the sequencing, annotation and comparative analysis of an 8 Mb region of pig chromosome 17, which provides a useful test region to assess coverage and quality for the pig genome sequencing project. We report our findings comparing the annotation of draft sequence assembled at different depths of coverage.

RESULTS

Within this region we annotated 71 loci, of which 53 are orthologous to human known coding genes. When compared to the syntenic regions in human (20q13.13-q13.33) and mouse (chromosome 2, 167.5 Mb-178.3 Mb), this region was found to be highly conserved with respect to gene order. The most notable difference between the three species is the presence of a large expansion of zinc finger coding genes and pseudogenes on mouse chromosome 2 between Edn3 and Phactr3 that is absent from pig and human. All of our annotation has been made publicly available in the Vertebrate Genome Annotation browser, VEGA. We assessed the impact of coverage on sequence assembly across this region and found, as expected, that increased sequence depth resulted in fewer, longer contigs. One-third of our annotated loci could not be fully re-aligned back to the low coverage version of the sequence, principally because the transcripts are fragmented over several contigs.

CONCLUSION

We have demonstrated the considerable advantages of sequencing at increased read depths and discuss the implications that lower coverage sequence may have on subsequent comparative and functional studies, particularly those involving complex loci such as GNAS.