The "clustered structure" of the purines/pyrimidines distribution in DNA distinguishes systematically between coding and non-coding sequences

Quantifying local randomness in human DNA and RNA sequences using Erdös motifs

In 1932, Paul Erdös asked whether a random walk constructed from a binary sequence can achieve the lowest possible deviation (lowest discrepancy), for the sequence itself and for all its subsequences formed by homogeneous arithmetic progressions. Although avoiding low discrepancy is impossible for infinite sequences, as recently proven by Terence Tao, attempts were made to construct such sequences with finite lengths. We recognize that such constructed sequences (we call these "Erdös sequences") exhibit certain hallmarks of randomness at the local level: they show roughly equal frequencies of short subsequences, and at the same time exclude trivial periodic patterns. For the human DNA we examine the frequency of a set of Erdös motifs of length-10 using three nucleotides-to-binary mappings. The particular length-10 Erdös sequence is derived from the length-11 Mathias sequence and is identical with the first 10 digits of the Thue-Morse sequence, underscoring the fact that both are deficient in periodicities. Our calculations indicate that: (1) the purine(A and G)/pyridimine(C and T) based Erdös motifs are greatly underrepresented in the human genome, (2) the strong(G and C)/weak(A and T) based Erdös motifs are slightly overrepresented, (3) the densities of the two are negatively correlated, (4) the Erdös motifs based on all three mappings being combined are slightly underrepresented, and (5) the strong/weak based Erdös motifs are greatly overrepresented in the human messenger RNA sequences.

Simple structural differences between coding and noncoding DNA

Background

The study of large-scale genome structure has revealed patterns suggesting the influence of evolutionary constraints on genome evolution. However, the results of these studies can be difficult to interpret due to the conceptual complexity of the analyses. This makes it difficult to understand how observed statistical patterns relate to the physical distribution of genomic elements. We use a simpler and more intuitive approach to evaluate patterns of genome structure.

Methodology/Principal Findings

We used randomization tests based on Morisita's Index of aggregation to examine average differences in the distribution of purines and pyrimidines among coding and noncoding regions of 261 chromosomes from 223 microbial genomes representing 21 phylum level groups. Purines and pyrimidines were aggregated in the noncoding DNA of 86% of genomes, but were only aggregated in the coding regions of 52% of genomes. Coding and noncoding DNA differed in aggregation in 94% of genomes. Noncoding regions were more aggregated than coding regions in 91% of these genomes. Genome length appears to limit aggregation, but chromosome length does not. Chromosomes from the same species are similarly aggregated despite substantial differences in length. Aggregation differed among taxonomic groups, revealing support for a previously reported pattern relating genome structure to environmental conditions.

Conclusions/Significance

Our approach revealed several patterns of genome structure among different types of DNA, different chromosomes of the same genome, and among different taxonomic groups. Similarity in aggregation among chromosomes of varying length from the same genome suggests that individual chromosome structure has not evolved independently of the general constraints on genome structure as a whole. These patterns were detected using simple and readily interpretable methods commonly used in other areas of biology.

Scaling properties and fractality in the distribution of coding segments in eukaryotic genomes revealed through a block entropy approach

Statistical methods, including block entropy based approaches, have already been used in the study of long-range features of genomic sequences seen as symbol series, either considering the full alphabet of the four nucleotides or the binary purine or pyrimidine character set. Here we explore the alternation of short protein-coding segments with long noncoding spacers in entire chromosomes, focusing on the scaling properties of block entropy. In previous studies, it has been shown that the sizes of noncoding spacers follow power-law-like distributions in most chromosomes of eukaryotic organisms from distant taxa. We have developed a simple evolutionary model based on well-known molecular events (segmental duplications followed by elimination of most of the duplicated genes) which reproduces the observed linearity in log-log plots. The scaling properties of block entropy H(n) have been studied in several works. Their findings suggest that linearity in semilogarithmic scale characterizes symbol sequences which exhibit fractal properties and long-range order, while this linearity has been shown in the case of the logistic map at the Feigenbaum accumulation point. The present work starts with the observation that the block entropy of the Cantor-like binary symbol series scales in a similar way. Then, we perform the same analysis for the full set of human chromosomes and for several chromosomes of other eukaryotes. A similar but less extended linearity in semilogarithmic scale, indicating fractality, is observed, while randomly formed surrogate sequences clearly lack this type of scaling. Genomic sequences always present entropy values much lower than their random surrogates. Symbol sequences produced by the aforementioned evolutionary model follow the scaling found in genomic sequences, thus corroborating the conjecture that "segmental duplication-gene elimination" dynamics may have contributed to the observed long rangeness in the coding or noncoding alternation in genomes.

Power-laws in the genomic distribution of coding segments in several organisms: an evolutionary trace of segmental duplications, possible paleopolyploidy and gene loss

Large-scale features of the spatial arrangement of protein-coding segments (PCS) are investigated by means of the inter-PCS spacers' size distributions, which have been found to follow power-laws. Linearity in double-logarithmic scale extends to several orders of magnitude in the genomes of organisms as disparate as mammals, insects and plants. This feature is also present in the most compact eukaryotic genomes and in half of the examined bacteria, despite their very limited non-coding space. We have tried to determine the sequence of events in the course of genomes' evolution which may account for the formation of the observed size distributions. The proposed mechanism essentially includes two types of events: (i) segmental duplications (and possibly paleopolyploidy), and (ii) the subsequent loss of most of the duplicated genes. It is shown by computer simulations that the formulated scenario generates power-law-like inter-PCS spacers' size distributions, which remain robust for a variety of parameter choices, even if insertion of external sequences, such as viruses or proliferating retroelements is included. Moreover, power-laws are preserved after most of the non-coding DNA has been removed, thus explaining the finding of this pattern in genomes as compact as that of Takifugu rubripes.

Long range clustering of oligonucleotides containing the CG signal

The distance distributions between successive occurrences of the same oligonucleotides in chromosomal DNA are studied, in different classes of higher eucaryotic organisms. A two-parameter modeling is undertaken and applied on the distance distribution of quintuplets (sequences of size five bps) and hexaplets (sequences of size six bps); the first parameter k refers to the short range exponential decay of the distributions, whereas the second parameter m refers to the power law behavior. A two-dimensional scatter plot representing the model equation demonstrates that the points corresponding to the distance distribution of oligonucleotides containing the CG consensus sequence (promoter of the RNA polymerase II) cluster together (group alpha), apart from all other oligonucleotides (group beta). This is shown for the available chordata Homo sapiens, Pan troglodytes, Mus musculus, Rattus norvegicus, Gallus gallus and Danio rerio. This clustering is less evident in lower Animalia and plants, such as Drosophila melanogaster, Caenorhabditis elegans and Arabidopsis thaliana. Moreover, in all organisms the oligonucleotides which contain any consensus sequence are found to be described by long range distributions, whereas all others have a stronger influence of short range decay. Various measures are introduced and evaluated, to numerically characterize the clustering of the two groups. The one which most clearly discriminates the two classes is shown to be the proximity factor.

“Word” Preference in the Genomic Text and Genome Evolution: Different Modes of n-tuplet Usage in Coding and Noncoding Sequences

Extensive work on n-tuplet occurrence in genomic sequences has revealed the correlation of their usage with sequence origin. Parallel to that, there exist different restrictions in the nucleotide composition of coding and noncoding sequences that may result in distinct modes of usage of n-tuplets. The relatively simple approaches described herein focus on such differences. They are based on simple summation measures of n-tuplet frequencies, computed after filtering the background nucleotide composition. Among the main targets of this work is to draw some conclusions on the qualitative differences in the composition of genomic sequences depending on their functionality. Moreover, an evolutionary model is formulated, including simple forms of ubiquitous events of genome dynamics: genomic fusions, genome shuffling due to transpositions, replication slippage, and point mutations. This model is shown to be able to reproduce all the statistical features of genomic sequences discussed herein.

An evolutionary model for the origin of non-randomness, long-range order and fractality in the genome

We present a model for genome evolution, comprising biologically plausible events such as transpositions inside the genome and insertions of exogenous sequences. This model attempts to formulate a minimal proposition accounting for key statistical properties of genomes, avoiding, as far as possible, unsupportable hypotheses for the remote evolutionary past. The statistical properties that are observed in genomic sequences and are reproduced by the proposed model are: (i) deviations from randomness at different length scales, measured by suitable algorithms, (ii) a special form of size distribution (power law distribution) characterising different levels of genome organisation in the non-coding, and (iii) extensive resemblance in the alternation of coding and non-coding regions at several length scales (self-similarity) in long genomic sequences of higher eukaryotes.