CorGen--measuring and generating long-range correlations for DNA sequence analysis

Bioinformatics tools for the sequence complexity estimates

We review current methods and bioinformatics tools for the text complexity estimates (information and entropy measures). The search DNA regions with extreme statistical characteristics such as low complexity regions are important for biophysical models of chromosome function and gene transcription regulation in genome scale. We discuss the complexity profiling for segmentation and delineation of genome sequences, search for genome repeats and transposable elements, and applications to next-generation sequencing reads. We review the complexity methods and new applications fields: analysis of mutation hotspots loci, analysis of short sequencing reads with quality control, and alignment-free genome comparisons. The algorithms implementing various numerical measures of text complexity estimates including combinatorial and linguistic measures have been developed before genome sequencing era. The series of tools to estimate sequence complexity use compression approaches, mainly by modification of Lempel-Ziv compression. Most of the tools are available online providing large-scale service for whole genome analysis. Novel machine learning applications for classification of complete genome sequences also include sequence compression and complexity algorithms. We present comparison of the complexity methods on the different sequence sets, the applications for gene transcription regulatory regions analysis. Furthermore, we discuss approaches and application of sequence complexity for proteins. The complexity measures for amino acid sequences could be calculated by the same entropy and compression-based algorithms. But the functional and evolutionary roles of low complexity regions in protein have specific features differing from DNA. The tools for protein sequence complexity aimed for protein structural constraints. It was shown that low complexity regions in protein sequences are conservative in evolution and have important biological and structural functions. Finally, we summarize recent findings in large scale genome complexity comparison and applications for coronavirus genome analysis.

Fractal genomics of SOD1 evolution

To understand the fundamental processes of gene evolution such as the impact of point mutations and segmental duplications on statistical topography, superoxide dismutase-1 (SOD1) orthologous sequences (n = 50) are studied. These demonstrate scale invariant self-similarity patterns and long-range correlations (LRCs) indicating fractal organization. Phylogenetic hierarchies change when SOD1 orthologs are grouped according to fractal measures, indicating that statistical topographies can be used to study gene evolution. Sliding window k-mer analysis show that majority of k-mers across all SOD1 orthologs are unique, with very few duplications. Orthologs from simpler species contribute minimally (< 1% of k-mers) to more complex species. Both simple and complex random processes fail to produce significant matching k-mer sequences for SOD1 orthologs. Point mutations causing amyotrophic lateral sclerosis do not impact the fractal organization of human SOD1. Hence, SOD1 did not evolve by a patchwork of repetitive sequences modified by point mutations. Moreover, fractal and other methods described here can be used to study the origin and evolution of genomes.

Large-Deviation Properties of Sequence Alignment of Correlated Sequences

The significance of alignment scores of optimally aligned DNA sequences can be estimated through the score distribution of pairs of random sequences. It is necessary to obtain statistics for the relevant high-scoring tail of the distribution. For local alignments of iid drawn sequences it has already been shown that the often assumed Gumbel distribution does not hold in the distribution tail, but has to be corrected by a Gaussian factor. Real DNA sequences were observed to show long-range correlations within sequences, which are not correctly modeled by iid random sequences. In this publication the large deviation method that was used in previous studies is applied to local and global alignment of such sequences with long-range correlations. We study the distributions over the full range of the support and obtained probabilities as low as [Formula: see text]. We show that again a correction to the Gumbel distribution is necessary to study the dependence of the parameters on the correlation strength. For global alignments the Gamma distribution, which was found heuristically to be a good fit in earlier simple sampling studies, is found to be a poor fit.

Ising-model description of long-range correlations in DNA sequences

We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 10(3) and 10(6) bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.

BiDaS: a web-based Monte Carlo BioData Simulator based on sequence/feature characteristics

BiDaS is a web-application that can generate massive Monte Carlo simulated sequence or numerical feature data sets (e.g. dinucleotide content, composition, transition, distribution properties) based on small user-provided data sets. BiDaS server enables users to analyze their data and generate large amounts of: (i) Simulated DNA/RNA and aminoacid (AA) sequences following practically identical sequence and/or extracted feature distributions with the original data. (ii) Simulated numerical features, presenting identical distributions, while preserving the exact 2D or 3D between-feature correlations observed in the original data sets. The server can project the provided sequences to multidimensional feature spaces based on: (i) 38 DNA/RNA features describing conformational and physicochemical nucleotide sequence features from the B-DNA-VIDEO database, (ii) 122 DNA/RNA features based on conformational and thermodynamic dinucleotide properties from the DiProDB database and (iii) Pseudo-aminoacid composition of the initial sequences. To the best of our knowledge, this is the first available web-server that allows users to generate vast numbers of biological data sets with realistic characteristics, while keeping between-feature associations. These data sets can be used for a wide variety of current biological problems, such as the in-depth study of gene, transcript, peptide and protein groups/families; the creation of large data sets from just a few available members and the strengthening of machine learning classifiers. All simulations use advanced Monte Carlo sampling techniques. The BiDaS web-application is available at http://bioserver-3.bioacademy.gr/Bioserver/BiDaS/.

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.

Multifractal analysis of HIV-1 genomes

Pathogens like HIV-1, which evolve into many closely related variants displaying differential infectivity and evolutionary dynamics in a short time scale, require fast and accurate classification. Conventional whole genome sequence alignment-based methods are computationally expensive and involve complex analysis. Alignment-free methodologies are increasingly being used to effectively differentiate genomic variations between viral species. Multifractal analysis, which explores the self-similar nature of genomes, is an alignment-free methodology that has been applied to study such variations. However, whether multifractal analysis can quantify variations between closely related genomes, such as the HIV-1 subtypes, is an open question. Here we address the above by implementing the multifractal analysis on four retroviral genomes (HIV-1, HIV-2, SIVcpz, and HTLV-1), and demonstrate that individual multifractal properties can differentiate between different retrovirus types easily. However, the individual multifractal measures do not resolve within-group variations for different known subtypes of HIV-1 M group. We show here that these known subtypes can instead be classified correctly using a combination of the crucial multifractal measures. This method is simple and computationally fast in comparison to the conventional alignment-based methods for whole genome phylogenetic analysis.

Scale-free duplication dynamics: a model for ultraduplication

Empirical studies of the genome-wide length distribution of duplicated sequences have revealed an algebraic tail common to nearly all clades. The decay of the tail is often well approximated by a single exponent that takes values within a limited range. We propose and study here scale-free duplication dynamics, a class of model for genome sequence evolution that generates the observed shapes of this distribution. A transition between self-similar and non-self-similar regimes is exhibited. Our model accounts plausibly for the observed form of the algebraic tail, which is not produced by standard models for generating long-range sequence correlations.

Multifractal analysis of nonhyperbolic coupled map lattices: application to genomic sequences

Symbolic sequences generated by coupled map lattices (CMLs) can be used to model the chaotic-like structure of genomic sequences. In this study it is shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a shift of four symbols) very closely reproduce the multifractal spectrum D(q) of human genomic sequences for coupling constant α = 0.35 ± 0.01 if q > 0. The presence of rare configurations causes deviations for q < 0, which disappear if the rare event statistics of the CML is modified. Such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements.

Hierarchical multifractal representation of symbolic sequences and application to human chromosomes

The two-dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size. The multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences. This method is applied to entire human chromosomes, shuffled human chromosomes, reconstructed human genomic sequences and to artificial random sequences. It is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size. Small deviations are observed between the longer and the shorter chromosomes, especially for the higher (in absolute values) statistical moments. The correlations are crucial for the form of the multifractal spectrum; surrogate shuffled chromosomes present randomlike spectrum, distinctly different from the actual chromosomes. Analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra, especially in the region of negative exponents, due to the underrepresentation of various functional units (such as the cytosine-guanine CG combination and its complementary GC complex). Retaining higher-order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences. This hierarchical approach is generic and is applicable to other correlated symbolic sequences.

Genomic DNA from animals shows contrasting strand bias in large and small subsequences

Background

For eukaryotes, there is almost no strand bias with regard to base composition, with exceptions for origins of replication and transcription start sites and transcribed regions. This paper revisits the question for subsequences of DNA taken at random from the genome.

Results

For a typical mammal, for example mouse or human, there is a small strand bias throughout the genomic DNA: there is a correlation between (G - C) and (A - T) on the same strand, (that is between the difference in the number of guanine and cytosine bases and the difference in the number of adenine and thymine bases). For small subsequences – up to 1 kb – this correlation is weak but positive; but for large windows – around 50 kb to 2 Mb – the correlation is strong and negative. This effect is largely independent of GC%. Transcribed and untranscribed regions give similar correlations both for small and large subsequences, but there is a difference in these regions for intermediate sized subsequences. An analysis of the human genome showed that position within the isochore structure did not affect these correlations. An analysis of available genomes of different species shows that this contrast between large and small windows is a general feature of mammals and birds. Further down the evolutionary tree, other organisms show a similar but smaller effect. Except for the nematode, all the animals analysed showed at least a small effect.

Conclusion

The correlations on the large scale may be explained by DNA replication. Transcription may be a modifier of these effects but is not the fundamental cause. These results cast light on how DNA mutations affect the genome over evolutionary time. At least for vertebrates, there is a broad relationship between body temperature and the size of the correlation. The genome of mammals and birds has a structure marked by strand bias segments.

Strand bias structure in mouse DNA gives a glimpse of how chromatin structure affects gene expression

Background

On a single strand of genomic DNA the number of As is usually about equal to the number of Ts (and similarly for Gs and Cs), but deviations have been noted for transcribed regions and origins of replication.

Results

The mouse genome is shown to have a segmented structure defined by strand bias. Transcription is known to cause a strand bias and numerous analyses are presented to show that the strand bias in question is not caused by transcription. However, these strand bias segments influence the position of genes and their unspliced length. The position of genes within the strand bias structure affects the probability that a gene is switched on and its expression level. Transcription has a highly directional flow within this structure and the peak volume of transcription is around 20 kb from the A-rich/T-rich segment boundary on the T-rich side, directed away from the boundary. The A-rich/T-rich boundaries are SATB1 binding regions, whereas the T-rich/A-rich boundary regions are not.

Conclusion

The direct cause of the strand bias structure may be DNA replication. The strand bias segments represent a further biological feature, the chromatin structure, which in turn influences the ease of transcription.