Diminishing return for increased Mappability with longer sequencing reads: implications of the k-mer distributions in the human genome

Range-limited Heaps' law for functional DNA words in the human genome

Heaps' or Herdan-Heaps' law is a linguistic law describing the relationship between the vocabulary/dictionary size (type) and word counts (token) to be a power-law function. Its existence in genomes with certain definition of DNA words is unclear partly because the dictionary size in genome could be much smaller than that in a human language. We define a DNA word as a coding region in a genome that codes for a protein domain. Using human chromosomes and chromosome arms as individual samples, we establish the existence of Heaps' law in the human genome within limited range. Our definition of words in a genomic or proteomic context is different from other definitions such as over-represented k-mers which are much shorter in length. Although an approximate power-law distribution of protein domain sizes due to gene duplication and the related Zipf's law is well known, their translation to the Heaps' law in DNA words is not automatic. Several other animal genomes are shown herein also to exhibit range-limited Heaps' law with our definition of DNA words, though with various exponents. When tokens were randomly sampled and sample sizes reach to the maximum level, a deviation from the Heaps' law was observed, but a quadratic regression in log-log type-token plot fits the data perfectly. Investigation of type-token plot and its regression coefficients could provide an alternative narrative of reusage and redundancy of protein domains as well as creation of new protein domains from a linguistic perspective.

Small extrachromosomal circular DNA (eccDNA): major functions in evolution and cancer

Extrachromosomal circular DNA (eccDNA) refers to a type of circular DNA that originate from but are likely independent of chromosomes. Due to technological advancements, eccDNAs have recently emerged as multifunctional molecules with numerous characteristics. The unique topological structure and genetic characteristics of eccDNAs shed new light on the monitoring, early diagnosis, treatment, and prediction of cancer. EccDNAs are commonly observed in both normal and cancer cells and function via different mechanisms in the stress response to exogenous and endogenous stimuli, aging, and carcinogenesis and in drug resistance during cancer treatment. The structural diversity of eccDNAs contributes to the function and numerical diversity of eccDNAs and thereby endows eccDNAs with powerful roles in evolution and in cancer initiation and progression by driving genetic plasticity and heterogeneity from extrachromosomal sites, which has been an ignored function in evolution in recent decades. EccDNAs show great potential in cancer, and we summarize the features, biogenesis, evaluated functions, functional mechanisms, related methods, and clinical utility of eccDNAs with a focus on their role in evolution and cancer.

PB-Motif-A Method for Identifying Gene/Pseudogene Rearrangements With Long Reads: An Application to CYP21A2 Genotyping

Long read sequencing technologies have the potential to accurately detect and phase variation in genomic regions that are difficult to fully characterize with conventional short read methods. These difficult to sequence regions include several clinically relevant genes with highly homologous pseudogenes, many of which are prone to gene conversions or other types of complex structural rearrangements. We present PB-Motif, a new method for identifying rearrangements between two highly homologous genomic regions using PacBio long reads. PB-Motif leverages clustering and filtering techniques to efficiently report rearrangements in the presence of sequencing errors and other systematic artifacts. Supporting reads for each high-confidence rearrangement can then be used for copy number estimation and phased variant calling. First, we demonstrate PB-Motif's accuracy with simulated sequence rearrangements of PMS2 and its pseudogene PMS2CL using simulated reads sweeping over a range of sequencing error rates. We then apply PB-Motif to 26 clinical samples, characterizing CYP21A2 and its pseudogene CYP21A1P as part of a diagnostic assay for congenital adrenal hyperplasia. We successfully identify damaging variation and patient carrier status concordant with clinical diagnosis obtained from multiplex ligation-dependent amplification (MLPA) and Sanger sequencing. The source code is available at: github.com/zstephens/pb-motif.

Expansion sequencing: Spatially precise in situ transcriptomics in intact biological systems

Methods for highly multiplexed RNA imaging are limited in spatial resolution and thus in their ability to localize transcripts to nanoscale and subcellular compartments. We adapt expansion microscopy, which physically expands biological specimens, for long-read untargeted and targeted in situ RNA sequencing. We applied untargeted expansion sequencing (ExSeq) to the mouse brain, which yielded the readout of thousands of genes, including splice variants. Targeted ExSeq yielded nanoscale-resolution maps of RNAs throughout dendrites and spines in the neurons of the mouse hippocampus, revealing patterns across multiple cell types, layer-specific cell types across the mouse visual cortex, and the organization and position-dependent states of tumor and immune cells in a human metastatic breast cancer biopsy. Thus, ExSeq enables highly multiplexed mapping of RNAs from nanoscale to system scale.

Probably Correct: Rescuing Repeats with Short and Long Reads

Ever since the introduction of high-throughput sequencing following the human genome project, assembling short reads into a reference of sufficient quality posed a significant problem as a large portion of the human genome-estimated 50-69%-is repetitive. As a result, a sizable proportion of sequencing reads is multi-mapping, i.e., without a unique placement in the genome. The two key parameters for whether or not a read is multi-mapping are the read length and genome complexity. Long reads are now able to span difficult, heterochromatic regions, including full centromeres, and characterize chromosomes from "telomere to telomere". Moreover, identical reads or repeat arrays can be differentiated based on their epigenetic marks, such as methylation patterns, aiding in the assembly process. This is despite the fact that long reads still contain a modest percentage of sequencing errors, disorienting the aligners and assemblers both in accuracy and speed. Here, I review the proposed and implemented solutions to the repeat resolution and the multi-mapping read problem, as well as the downstream consequences of reference choice, repeat masking, and proper representation of sex chromosomes. I also consider the forthcoming challenges and solutions with regards to long reads, where we expect the shift from the problem of repeat localization within a single individual to the problem of repeat positioning within pangenomes.

Unique k-mer sequences for validating cancer-related substitution, insertion and deletion mutations

Cancer genome sequencing has led to important discoveries such as the identification of cancer genes. However, challenges remain in the analysis of cancer genome sequencing. One significant issue is that mutations identified by multiple variant callers are frequently discordant even when using the same genome sequencing data. For insertion and deletion mutations, oftentimes there is no agreement among different callers. Identifying somatic mutations involves read mapping and variant calling, a complicated process that uses many parameters and model tuning. To validate the identification of true mutations, we developed a method using k-mer sequences. First, we characterized the landscape of unique versus non-unique k-mers in the human genome. Second, we developed a software package, KmerVC, to validate the given somatic mutations from sequencing data. Our program validates the occurrence of a mutation based on statistically significant difference in frequency of k-mers with and without a mutation from matched normal and tumor sequences. Third, we tested our method on both simulated and cancer genome sequencing data. Counting k-mer involving mutations effectively validated true positive mutations including insertions and deletions across different individual samples in a reproducible manner. Thus, we demonstrated a straightforward approach for rapidly validating mutations from cancer genome sequencing data.

Evidence of constraint in the 3D genome for trans-splicing in human cells

Fusion transcripts are commonly found in eukaryotes, and many aberrant fusions are associated with severe diseases, including cancer. One class of fusion transcripts is generated by joining separate transcripts through trans-splicing. However, the mechanism of trans-splicing in mammals remains largely elusive. Here we showed evidence to support an intuitive hypothesis that attributes trans-sphcing to the spatial proximity between premature transcripts. A novel trans-splicing detection tool (TSD) was developed to reliably identify intra-chromosomal trans-splicing events (iTSEs) from RNA-seq data. TSD can maintain a remarkable balance between sensitivity and accuracy, thus distinguishing it from most state-of-the-art tools. The accuracy of TSD was experimentally demonstrated by excluding potential false discovery from mosaic genome or template switching during PCR. We showed that iTSEs identified by TSD were frequently found between genomic regulatory elements, which are known to be more prone to interact with each other. Moreover, iTSE sites may be more physically adjacent to each other than random control in the tested human lymphoblastoid cell line according to Hi-C data. Our results suggest that trans-splicing and 3D genome architecture may be coupled in mammals and that our pipeline, TSD, may facilitate investigations of trans-splicing on a systematic and accurate level previously thought impossible.

Mapping RNA-chromatin interactions by sequencing with iMARGI

RNA-chromatin interactions represent an important aspect of the transcriptional regulation of genes and transposable elements. However, analyses of chromatin-associated RNAs (caRNAs) are often limited to one caRNA at a time. Here, we describe the iMARGI (in situ mapping of RNA-genome interactome) technique, which is used to discover caRNAs and reveal their respective genomic interaction loci. iMARGI starts with in situ crosslinking and genome fragmentation, followed by converting each proximal RNA-DNA pair into an RNA-linker-DNA chimeric sequence. These chimeric sequences are subsequently converted into a sequencing library suitable for paired-end sequencing. A standardized bioinformatic software package, iMARGI-Docker, is provided to decode the paired-end sequencing data into caRNA-DNA interactions. Compared to its predecessor MARGI (mapping RNA-genome interactions), the number of input cells for iMARGI is 3-5 million (a 100-fold reduction), experimental time is reduced, and clear checkpoints have been established. It takes a few hours a day and a total of 8 d to complete the construction of an iMARGI sequencing library and 1 d to carry out data processing with iMARGI-Docker.

Alignment-free approaches for predicting novel Nuclear Mitochondrial Segments (NUMTs) in the human genome

The nuclear human genome harbors sequences of mitochondrial origin, indicating an ancestral transfer of DNA from the mitogenome. Several Nuclear Mitochondrial Segments (NUMTs) have been detected by alignment-based sequence similarity search, as implemented in the Basic Local Alignment Search Tool (BLAST). Identifying NUMTs is important for the comprehensive annotation and understanding of the human genome. Here we explore the possibility of detecting NUMTs in the human genome by alignment-free sequence similarity search, such as k-mers (k-tuples, k-grams, oligos of length k) distributions. We find that when k=6 or larger, the k-mer approach and BLAST search produce almost identical results, e.g., detect the same set of NUMTs longer than 3 kb. However, when k=5 or k=4, certain signals are only detected by the alignment-free approach, and these may indicate yet unrecognized, and potentially more ancestral NUMTs. We introduce a "Manhattan plot" style representation of NUMT predictions across the genome, which are calculated based on the reciprocal of the Jensen-Shannon divergence between the nuclear and mitochondrial k-mer frequencies. The further inspection of the k-mer-based NUMT predictions however shows that most of them contain long-terminal-repeat (LTR) annotations, whereas BLAST-based NUMT predictions do not. Thus, similarity of the mitogenome to LTR sequences is recognized, which we validate by finding the mitochondrial k-mer distribution closer to those for transposable sequences and specifically, close to some types of LTR.

Rank ordered beta distributions of nonlinear map symbolic dynamics families with a first-order transition between dynamical regimes

Rank-ordered distributions have been a matter of intense study. Often Zipf type invariant scaling is invoked; however, in the last decade the ubiquity of a Discrete Generalized Beta Distribution, DGBD, with two scaling exponents has been established. This distribution incorporates deviations from the power law at the extremes. A proper understanding of the meaning of these exponents is still lacking. Here, using two families of unimodal maps on the [0,1] interval, we construct binary sequences via standard symbolic dynamics. In both cases, the tent map, which is at the convex-concave border of the mapping families, separates intermittent regimes from chaotic dynamics. We show that the frequencies of n-tuples of the generated symbolic sequences are remarkably well fitted by the DGBD. We argue that in the underlying dynamics an order-disorder competition takes place and that one of the exponents is related to multiple range correlations, while the other is sensitive to disorder. In our study, we implement thermodynamic formalisms with which we can readily calculate n-tuple frequencies, in some particular cases, analytically. We show that for the convex mappings there is a first-order thermodynamic phase transition, while concave mappings have smooth free energy densities. Within our DGBD study, the transition between these two regimes coincides with a zero value for both exponents; in this sense, they may even be considered as indicators of the transition. An analysis of the difference between the exponents reinforces the interpretation we have assigned to them. Furthermore, the two regimes can be identified by the sign of such a difference. We also show that divergences in the invariant densities are responsible for the first order phase transitions observed in a range of the rank-frequency distributions. Our findings give further support to previous studies based on expansion-modification algorithms, birth-death processes, and random variable subtraction dynamics.

miR-MaGiC improves quantification accuracy for small RNA-seq

Objective

Many tools have been developed to profile microRNA (miRNA) expression from small RNA-seq data. These tools must contend with several issues: the small size of miRNAs, the small number of unique miRNAs, the fact that similar miRNAs can be transcribed from multiple loci, and the presence of miRNA isoforms known as isomiRs. Methods failing to address these issues can return misleading information. We propose a novel quantification method designed to address these concerns.

Results

We present miR-MaGiC, a novel miRNA quantification method, implemented as a cross-platform tool in Java. miR-MaGiC performs stringent mapping to a core region of each miRNA and defines a meaningful set of target miRNA sequences by collapsing the miRNA space to “functional groups”. We hypothesize that these two features, mapping stringency and collapsing, provide more optimal quantification to a more meaningful unit (i.e., miRNA family). We test miR-MaGiC and several published methods on 210 small RNA-seq libraries, evaluating each method’s ability to accurately reflect global miRNA expression profiles. We define accuracy as total counts close to the total number of input reads originating from miRNAs. We find that miR-MaGiC, which incorporates both stringency and collapsing, provides the most accurate counts.

Electronic supplementary material

The online version of this article (10.1186/s13104-018-3418-2) contains supplementary material, which is available to authorized users.

Efficient Mining Multi-mers in a Variety of Biological Sequences

Counting the occurrence frequency of each -mer in a biological sequence is a preliminary yet important step in many bioinformatics applications. However, most -mer counting algorithms rely on a given k to produce single-length -mers, which is inefficient for sequence analysis for different k. Moreover, existing -mer counters focus more on DNA and RNA sequences and less on protein ones. In practice, the analysis of -mers in protein sequences can provide substantial biological insights in structure, function and evolution. To this end, an efficient algorithm, called MulMer (Multiple-Mer mining), is proposed to mine -mers of various lengths termed multi-mers via inverted-index technique, which is orders of magnitude faster than the conventional forward-index methods. Moreover, to the best of our knowledge, MulMer is the first able to mine multi-mers in a variety of sequences, including DNARNA and protein sequences.

Intricate and Cell Type-Specific Populations of Endogenous Circular DNA (eccDNA) in Caenorhabditis elegans and Homo sapiens

Investigations aimed at defining the 3D configuration of eukaryotic chromosomes have consistently encountered an endogenous population of chromosome-derived circular genomic DNA, referred to as extrachromosomal circular DNA (eccDNA). While the production, distribution, and activities of eccDNAs remain understudied, eccDNA formation from specific regions of the linear genome has profound consequences on the regulatory and coding capabilities for these regions. Here, we define eccDNA distributions in Caenorhabditis elegans and in three human cell types, utilizing a set of DNA topology-dependent approaches for enrichment and characterization. The use of parallel biophysical, enzymatic, and informatic approaches provides a comprehensive profiling of eccDNA robust to isolation and analysis methodology. Results in human and nematode systems provide quantitative analysis of the eccDNA loci at both unique and repetitive regions. Our studies converge on and support a consistent picture, in which endogenous genomic DNA circles are present in normal physiological states, and in which the circles come from both coding and noncoding genomic regions. Prominent among the coding regions generating DNA circles are several genes known to produce a diversity of protein isoforms, with mucin proteins and titin as specific examples.

Beyond Zipf's Law: The Lavalette Rank Function and Its Properties

Although Zipf’s law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf’s law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf’s law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

From NGS assembly challenges to instability of fungal mitochondrial genomes: A case study in genome complexity

The presence of repetitive or non-unique DNA persisting over sizable regions of a eukaryotic genome can hinder the genome's successful de novo assembly from short reads: ambiguities in assigning genome locations to the non-unique subsequences can result in premature termination of contigs and thus overfragmented assemblies. Fungal mitochondrial (mtDNA) genomes are compact (typically less than 100 kb), yet often contain short non-unique sequences that can be shown to impede their successful de novo assembly in silico. Such repeats can also confuse processes in the cell in vivo. A well-studied example is ectopic (out-of-register, illegitimate) recombination associated with repeat pairs, which can lead to deletion of functionally important genes that are located between the repeats. Repeats that remain conserved over micro- or macroevolutionary timescales despite such risks may indicate functionally or structurally (e.g., for replication) important regions. This principle could form the basis of a mining strategy for accelerating discovery of function in genome sequences. We present here our screening of a sample of 11 fully sequenced fungal mitochondrial genomes by observing where exact k-mer repeats occurred several times; initial analyses motivated us to focus on 17-mers occurring more than three times. Based on the diverse repeats we observe, we propose that such screening may serve as an efficient expedient for gaining a rapid but representative first insight into the repeat landscapes of sparsely characterized mitochondrial chromosomes. Our matching of the flagged repeats to previously reported regions of interest supports the idea that systems of persisting, non-trivial repeats in genomes can often highlight features meriting further attention.

Cracking the Code of Human Diseases Using Next-Generation Sequencing: Applications, Challenges, and Perspectives

Next-generation sequencing (NGS) technologies have greatly impacted on every field of molecular research mainly because they reduce costs and increase throughput of DNA sequencing. These features, together with the technology's flexibility, have opened the way to a variety of applications including the study of the molecular basis of human diseases. Several analytical approaches have been developed to selectively enrich regions of interest from the whole genome in order to identify germinal and/or somatic sequence variants and to study DNA methylation. These approaches are now widely used in research, and they are already being used in routine molecular diagnostics. However, some issues are still controversial, namely, standardization of methods, data analysis and storage, and ethical aspects. Besides providing an overview of the NGS-based approaches most frequently used to study the molecular basis of human diseases at DNA level, we discuss the principal challenges and applications of NGS in the field of human genomics.

Designing alternative splicing RNA-seq studies. Beyond generic guidelines

MOTIVATION

Designing an RNA-seq study depends critically on its specific goals, technology and underlying biology, which renders general guidelines inadequate. We propose a Bayesian framework to customize experiments so that goals can be attained and resources are not wasted, with a focus on alternative splicing.

RESULTS

We studied how read length, sequencing depth, library preparation and the number of replicates affects cost-effectiveness of single-sample and group comparison studies. Optimal settings varied strongly according to the target organism or tissue (potential 50-500% cost cuts) and, interestingly, short reads outperformed long reads for standard analyses. Our framework learns key characteristics for study design from the data, and predicts if and how to continue experimentation. These predictions matched several follow-up experimental datasets that were used for validation. We provide default pipelines, but the framework can be combined with other data analysis methods and can help assess their relative merits.

AVAILABILITY AND IMPLEMENTATION

casper package at www.bioconductor.org/packages/release/bioc/html/casper.html, Supplementary Manual by typing casperDesign() at the R prompt.

CONTACT

rosselldavid@gmail.com

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Principles for the organization of gene-sets

A gene-set, an important concept in microarray expression analysis and systems biology, is a collection of genes and/or their products (i.e. proteins) that have some features in common. There are many different ways to construct gene-sets, but a systematic organization of these ways is lacking. Gene-sets are mainly organized ad hoc in current public-domain databases, with group header names often determined by practical reasons (such as the types of technology in obtaining the gene-sets or a balanced number of gene-sets under a header). Here we aim at providing a gene-set organization principle according to the level at which genes are connected: homology, physical map proximity, chemical interaction, biological, and phenotypic-medical levels. We also distinguish two types of connections between genes: actual connection versus sharing of a label. Actual connections denote direct biological interactions, whereas shared label connection denotes shared membership in a group. Some extensions of the framework are also addressed such as overlapping of gene-sets, modules, and the incorporation of other non-protein-coding entities such as microRNAs.

Mappability and read length

Power-law distributions are the main functional form for the distribution of repeat size and repeat copy number in the human genome. When the genome is broken into fragments for sequencing, the limited size of fragments and reads may prevent an unique alignment of repeat sequences to the reference sequence. Repeats in the human genome can be as long as 10⁴ bases, or 10⁵ − 10⁶ bases when allowing for mismatches between repeat units. Sequence reads from these regions are therefore unmappable when the read length is in the range of 10³ bases. With a read length of 1000 bases, slightly more than 1% of the assembled genome, and slightly less than 1% of the 1 kb reads, are unmappable, excluding the unassembled portion of the human genome (8% in GRCh37/hg19). The slow decay (long tail) of the power-law function implies a diminishing return in converting unmappable regions/reads to become mappable with the increase of the read length, with the understanding that increasing read length will always move toward the direction of 100% mappability.

Characterizing regions in the human genome unmappable by next-generation-sequencing at the read length of 1000 bases

Repetitive and redundant regions of a genome are particularly problematic for mapping sequencing reads. In the present paper, we compile a list of the unmappable regions in the human genome based on the following definition: hypothetical reads with length 1 kb which cannot be uniquely mapped with zero-mismatch alignment for the described regions, considering both the forward and reverse strand. The respective collection of unmappable regions covers 0.77% of the sequence of human autosomes and 8.25% of the sex chromosomes in the reference genome GRCh37/hg19 (overall 1.23%). Not surprisingly, our unmappable regions overlap greatly with segmental duplication, transposable elements, and structural variants. About 99.8% of bases in our unmappable regions are part of either segmental duplication or transposable elements and 98.3% overlap structural variant annotations. Notably, some of these regions overlap units with important biological functions, including 4% of protein-coding genes. In contrast, these regions have zero intersection with the ultraconserved elements, very low overlap with microRNAs, tRNAs, pseudogenes, CpG islands, tandem repeats, microsatellites, sensitive non-coding regions, and the mapping blacklist regions from the ENCODE project.