Algebraic distribution of segmental duplication lengths in whole-genome sequence self-alignments

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.

Novel islands of GGC and GCC repeats coincide with human evolution

BACKGROUND

Because of high mutation rate, overrepresentation in genic regions, and link with various neurological, neurodegenerative, and movement disorders, GGC and GCC short tandem repeats (STRs) are prone to natural selection. Among a number of lacking data, the 3-repeats of these STRs remain widely unexplored.

RESULTS

In a genome-wide search in human, here we mapped GGC and GCC STRs of ≥3-repeats, and found novel islands of up to 45 of those STRs, populating spans of 1 to 2 kb of genomic DNA. RGPD4 and NOC4L harbored the densest (GGC)3 (probability 3.09061E-71) and (GCC)3 (probability 1.72376E-61) islands, respectively, and were human-specific. We also found prime instances of directional incremented density of STRs at specific loci in human versus other species, including the FOXK2 and SKI GGC islands. The genes containing those islands significantly diverged in expression in human versus other species, and the proteins encoded by those genes interact closely in a physical interaction network, consequence of which may be human-specific characteristics such as higher order brain functions.

CONCLUSION

We report novel islands of GGC and GCC STRs of evolutionary relevance to human. The density, and in some instances, periodicity of these islands support them as a novel genomic entity, which need to be further explored in evolutionary, mechanistic, and functional platforms.

A Model-Driven Quantitative Analysis of Retrotransposon Distributions in the Human Genome

Retrotransposons, DNA sequences capable of creating copies of themselves, compose about half of the human genome and played a central role in the evolution of mammals. Their current position in the host genome is the result of the retrotranscription process and of the following host genome evolution. We apply a model from statistical physics to show that the genomic distribution of the two most populated classes of retrotransposons in human deviates from random placement, and that this deviation increases with time. The time dependence suggests a major role of the host genome dynamics in shaping the current retrotransposon distributions. Focusing on a neutral scenario, we show that a simple model based on random placement followed by genome expansion and sequence duplications can reproduce the empirical retrotransposon distributions, even though more complex and possibly selective mechanisms can have contributed. Besides the inherent interest in understanding the origin of current retrotransposon distributions, this work sets a general analytical framework to analyze quantitatively the effects of genome evolutionary dynamics on the distribution of genomic elements.

Identical sequences found in distant genomes reveal frequent horizontal transfer across the bacterial domain

Horizontal gene transfer (HGT) is an essential force in microbial evolution. Despite detailed studies on a variety of systems, a global picture of HGT in the microbial world is still missing. Here, we exploit that HGT creates long identical DNA sequences in the genomes of distant species, which can be found efficiently using alignment-free methods. Our pairwise analysis of 93,481 bacterial genomes identified 138,273 HGT events. We developed a model to explain their statistical properties as well as estimate the transfer rate between pairs of taxa. This reveals that long-distance HGT is frequent: our results indicate that HGT between species from different phyla has occurred in at least 8% of the species. Finally, our results confirm that the function of sequences strongly impacts their transfer rate, which varies by more than three orders of magnitude between different functional categories. Overall, we provide a comprehensive view of HGT, illuminating a fundamental process driving bacterial evolution.

Primary orthologs from local sequence context

BACKGROUND

The evolutionary history of genes serves as a cornerstone of contemporary biology. Most conserved sequences in mammalian genomes don't code for proteins, yielding a need to infer evolutionary history of sequences irrespective of what kind of functional element they may encode. Thus, sequence-, as opposed to gene-, centric modes of inferring paths of sequence evolution are increasingly relevant. Customarily, homologous sequences derived from the same direct ancestor, whose ancestral position in two genomes is usually conserved, are termed "primary" (or "positional") orthologs. Methods based solely on similarity don't reliably distinguish primary orthologs from other homologs; for this, genomic context is often essential. Context-dependent identification of orthologs traditionally relies on genomic context over length scales characteristic of conserved gene order or whole-genome sequence alignment, and can be computationally intensive.

RESULTS

We demonstrate that short-range sequence context-as short as a single "maximal" match- distinguishes primary orthologs from other homologs across whole genomes. On mammalian whole genomes not preprocessed by repeat-masker, potential orthologs are extracted by genome intersection as "non-nested maximal matches:" maximal matches that are not nested into other maximal matches. It emerges that on both nucleotide and gene scales, non-nested maximal matches recapitulate primary or positional orthologs with high precision and high recall, while the corresponding computation consumes less than one thirtieth of the computation time required by commonly applied whole-genome alignment methods. In regions of genomes that would be masked by repeat-masker, non-nested maximal matches recover orthologs that are inaccessible to Lastz net alignment, for which repeat-masking is a prerequisite. mmRBHs, reciprocal best hits of genes containing non-nested maximal matches, yield novel putative orthologs, e.g. around 1000 pairs of genes for human-chimpanzee.

CONCLUSIONS

We describe an intersection-based method that requires neither repeat-masking nor alignment to infer evolutionary history of sequences based on short-range genomic sequence context. Ortholog identification based on non-nested maximal matches is parameter-free, and less computationally intensive than many alignment-based methods. It is especially suitable for genome-wide identification of orthologs, and may be applicable to unassembled genomes. We are agnostic as to the reasons for its effectiveness, which may reflect local variation of mean mutation rate.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Evolutionary dynamics of selfish DNA explains the abundance distribution of genomic subsequences

Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given length are distributed with a scale-free power-law tail, resembling properties of human texts, such as Zipf's law. Despite recent efforts, the understanding of this phenomenon is still lacking. Here we find that selfish DNA elements, such as those belonging to the Alu family of repeats, dominate the power-law tail. Interestingly, for the Alu elements the power-law exponent increases with the length of the considered subsequences. Motivated by these observations, we develop a model of selfish DNA expansion. The predictions of this model qualitatively and quantitatively agree with the empirical observations. This allows us to estimate parameters for the process of selfish DNA spreading in a genome during its evolution. The obtained results shed light on how evolution of selfish DNA elements shapes non-trivial statistical properties of genomes.

Size distribution of function-based human gene sets and the split-merge model

The sizes of paralogues-gene families produced by ancestral duplication-are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Comparing the Statistical Fate of Paralogous and Orthologous Sequences

For several decades, sequence alignment has been a widely used tool in bioinformatics. For instance, finding homologous sequences with a known function in large databases is used to get insight into the function of nonannotated genomic regions. Very efficient tools like BLAST have been developed to identify and rank possible homologous sequences. To estimate the significance of the homology, the ranking of alignment scores takes a background model for random sequences into account. Using this model we can estimate the probability to find two exactly matching subsequences by chance in two unrelated sequences. For two homologous sequences, the corresponding probability is much higher, which allows us to identify them. Here we focus on the distribution of lengths of exact sequence matches between protein-coding regions of pairs of evolutionarily distant genomes. We show that this distribution exhibits a power-law tail with an exponent [Formula: see text] Developing a simple model of sequence evolution by substitutions and segmental duplications, we show analytically and computationally that paralogous and orthologous gene pairs contribute differently to this distribution. Our model explains the differences observed in the comparison of coding and noncoding parts of genomes, thus providing a better understanding of statistical properties of genomic sequences and their evolution.

Human-chimpanzee alignment: ortholog exponentials and paralog power laws

Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.

How evolution of genomes is reflected in exact DNA sequence match statistics

Genome evolution is shaped by a multitude of mutational processes, including point mutations, insertions, and deletions of DNA sequences, as well as segmental duplications. These mutational processes can leave distinctive qualitative marks in the statistical features of genomic DNA sequences. One such feature is the match length distribution (MLD) of exactly matching sequence segments within an individual genome or between the genomes of related species. These have been observed to exhibit characteristic power law decays in many species. Here, we show that simple dynamical models consisting solely of duplication and mutation processes can already explain the characteristic features of MLDs observed in genomic sequences. Surprisingly, we find that these features are largely insensitive to details of the underlying mutational processes and do not necessarily rely on the action of natural selection. Our results demonstrate how analyzing statistical features of DNA sequences can help us reveal and quantify the different mutational processes that underlie genome evolution.

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.

Neutral evolution of duplicated DNA: an evolutionary stick-breaking process causes scale-invariant behavior

Recently, an enrichment of identical matching sequences has been found in many eukaryotic genomes. Their length distribution exhibits a power law tail raising the question of what evolutionary mechanism or functional constraints would be able to shape this distribution. Here we introduce a simple and evolutionarily neutral model, which involves only point mutations and segmental duplications, and produces the same statistical features as observed for genomic data. Further, we extend a mathematical model for random stick breaking to analytically show that the exponent of the power law tail is -3 and universal as it does not depend on the microscopic details of the model.