Analysis of single-strand exceptional word symmetry in the human genome: new measures

Generalised interrelations among mutation rates drive the genomic compliance of Chargaff's second parity rule

Chargaff's second parity rule (PR-2), where the complementary base and k-mer contents are matching within the same strand of a double stranded DNA (dsDNA), is a phenomenon that invited many explanations. The strict compliance of nearly all nuclear dsDNA to PR-2 implies that the explanation should also be similarly adamant. In this work, we revisited the possibility of mutation rates driving PR-2 compliance. Starting from the assumption-free approach, we constructed kinetic equations for unconstrained simulations. The results were analysed for their PR-2 compliance by employing symbolic regression and machine learning techniques. We arrived to a generalised set of mutation rate interrelations in place in most species that allow for their full PR-2 compliance. Importantly, our constraints explain PR-2 in genomes out of the scope of the prior explanations based on the equilibration under mutation rates with simpler no-strand-bias constraints. We thus reinstate the role of mutation rates in PR-2 through its molecular core, now shown, under our formulation, to be tolerant to previously noted strand biases and incomplete compositional equilibration. We further investigate the time for any genome to reach PR-2, showing that it is generally earlier than the compositional equilibrium, and well within the age of life on Earth.

An Explanation of Exceptions from Chargaff's Second Parity Rule/Strand Symmetry of DNA Molecules

In this article, we show that mono/oligonucleotide quadruplets, as basic structures of DNA, along with our classification of trinucleotides, disclose an organization of genomes based on purine-pyrimidine symmetry. Moreover, the structure and stability of DNA are influenced by the Watson-Crick pairing and the natural law of DNA creation and conservation, according to which the same mono- or oligonucleotide insertion must be inserted simultaneously into both strands of DNA. Taken together, they lead to quadruplets with central mirror symmetry and bidirectional DNA strand orientation and are incorporated into Chargaff's second parity rule (CSPR). Performing our quadruplet frequency analysis of all human chromosomes and of Neuroblastoma BreakPoint Family (NBPF) genes, which code Olduvai protein domains in the human genome, we show that the coding part of DNA violates CSPR. This may shed new light and give rise to a novel hypothesis on DNA creation and its evolution. In this framework, the logarithmic relationship between oligonucleotide order and minimal DNA sequence length, to establish the validity of CSPR, automatically follows from the quadruplet structure of the genomic sequence. The problem of the violation of CSPR in rare symbionts is discussed.

Specificity Analysis of Genome Based on Statistically Identical K-Words With Same Base Combination

Goal: Individual characteristics are determined through a genome consisting of a complex base combination. This base combination is reflected in the k-word profile, which represents the number of consecutive k bases. Therefore, it is important to analyze the genome-specific statistical specificity in the k-word profile to understand the characteristics of the genome. In this paper, we propose a new k-word-based method to analyze genome-specific properties. Methods: We define k-words consisting of the same number of bases as statistically identical k-words. The statistically identical k-words are estimated to appear at a similar frequency by statistical prediction. However, this may not be true in the genome because it is not a random list of bases. The ratio between frequencies of two statistically identical k-words can then be used to investigate the statistical specificity of the genome reflected in the k-word profile. In order to find important ratios representing genomic characteristics, a reference value is calculated that results in a minimum error when classifying data by ratio alone. Finally, we propose a genetic algorithm-based search algorithm to select a minimum set of ratios useful for classification. Results: The proposed method was applied to the full-length sequence of microorganisms for pathogenicity classification. The classification accuracy of the proposed algorithm was similar to that of conventional methods while using only a few features. Conclusions: We proposed a new method to investigate the genome-specific statistical specificity in the k-word profile which can be applied to find important properties of the genome and classify genome sequences.

Novel look at DNA and life-Symmetry as evolutionary forcing

After explanation of the Chargaff´s first parity rule in terms of the Watson-Crick base-pairing between the two DNA strands, the Chargaff´s second parity rule for each strand of DNA (also named strand symmetry), which cannot be explained by Watson-Crick base-pairing only, is still a challenging issue already fifty years. We show that during evolution DNA preserves its identity in the form of quadruplet A+T and C+G rich matrices based on purine-pyrimidine mirror symmetries of trinucleotides. Identical symmetries are present in our classification of trinucleotides and the genetic code table. All eukaryotes and almost all prokaryotes (bacteria and archaea) have quadruplet mirror symmetries in structural form and frequencies following the principle of Chargaff's second parity rule and Natural symmetry law of DNA creation and conservation. Some rare symbionts have mirror symmetry only in their structural form within each DNA strand. Based on our matrix analysis of closely related species, humans and Neanderthals, we find that the circular cycle of inverse proportionality between trinucleotides preserves identical relative frequencies of trinucleotides in each quadruplet and in the whole genome. According to our calculations, a change in frequencies in quadruplet matrices could lead to the creation of new species. Violation of quadruplet symmetries is practically inconsistent with life. DNA symmetries provide a key for understanding the restriction of disorder (entropy) due to mutations in the evolution of DNA.

Comparing Reverse Complementary Genomic Words Based on Their Distance Distributions and Frequencies

In this work, we study reverse complementary genomic word pairs in the human DNA, by comparing both the distance distribution and the frequency of a word to those of its reverse complement. Several measures of dissimilarity between distance distributions are considered, and it is found that the peak dissimilarity works best in this setting. We report the existence of reverse complementary word pairs with very dissimilar distance distributions, as well as word pairs with very similar distance distributions even when both distributions are irregular and contain strong peaks. The association between distribution dissimilarity and frequency discrepancy is also explored, and it is speculated that symmetric pairs combining low and high values of each measure may uncover features of interest. Taken together, our results suggest that some asymmetries in the human genome go far beyond Chargaff's rules. This study uses both the complete human genome and its repeat-masked version.

DNA word analysis based on the distribution of the distances between symmetric words

We address the problem of discovering pairs of symmetric genomic words (i.e., words and the corresponding reversed complements) occurring at distances that are overrepresented. For this purpose, we developed new procedures to identify symmetric word pairs with uncommon empirical distance distribution and with clusters of overrepresented short distances. We speculate that patterns of overrepresentation of short distances between symmetric word pairs may allow the occurrence of non-standard DNA conformations, such as hairpin/cruciform structures. We focused on the human genome, and analysed both the complete genome as well as a version with known repetitive sequences masked out. We reported several well-defined features in the distributions of distances, which can be classified into three different profiles, showing enrichment in distinct distance ranges. We analysed in greater detail certain pairs of symmetric words of length seven, found by our procedure, characterised by the surprising fact that they occur at single distances more frequently than expected.

Exceptional Symmetry by Genomic Word : A Statistical Analysis

Single-strand DNA symmetry is pointed as a universal law observed in the genomes from all living organisms. It is a somewhat broadly defined concept, which has been refined into some more specific measurable effects. Here we discuss the exceptional symmetry effect. Exceptional symmetry is the symmetry effect beyond that expected in independence contexts, and it can be measured for each word, for each equivalent composition group, or globally, combining the effects of all possible words of a given length. Global exceptional symmetry was found in several species, but there are genomic words with no exceptional symmetry effect, whereas others show a very high exceptional symmetry effect. In this work, we discuss a measure to evaluate the exceptional symmetry effect by symmetric word pair, and compare it with others. We present a detailed study of the exceptional symmetry by symmetric pairs and take the CG content into account. We also introduce and discuss the exceptional symmetry profile for the DNA of each organism, and we perform a multiple comparison for 31 genomes: 7 viruses; 5 archaea; 5 bacteria; 14 eukaryotes.

Inversion symmetry of DNA k-mer counts: validity and deviations

Background

The generalization of the second Chargaff rule states that counts of any string of nucleotides of length k on a single chromosomal strand equal the counts of its inverse (reverse-complement) k-mer. This Inversion Symmetry (IS) holds for many species, both eukaryotes and prokaryotes, for ranges of k which may vary from 7 to 10 as chromosomal lengths vary from 2Mbp to 200 Mbp. The existence of IS has been demonstrated in the literature, and other pair-wise candidate symmetries (e.g. reverse or complement) have been ruled out.

Results

Studying IS in the human genome, we find that IS holds up to k = 10. It holds for complete chromosomes, also after applying the low complexity mask. We introduce a numerical IS criterion, and define the k-limit, KL, as the highest k for which this criterion is valid. We demonstrate that chromosomes of different species, as well as different human chromosomal sections, follow a universal logarithmic dependence of KL ~ 0.7 ln(L), where L is the length of the chromosome.

We introduce a statistical IS-Poisson model that allows us to apply confidence measures to our numerical findings. We find good agreement for large k, where the variance of the Poisson distribution determines the outcome of the analysis. This model predicts the observed logarithmic increase of KL with length. The model allows us to conclude that for low k, e.g. k = 1 where IS becomes the 2^nd Chargaff rule, IS violation, although extremely small, is significant. Studying this violation we come up with an unexpected observation for human chromosomes, finding a meaningful correlation with the excess of genes on particular strands.

Conclusions

Our IS-Poisson model agrees well with genomic data, and accounts for the universal behavior of k-limits. For low k we point out minute, yet significant, deviations from the model, including excess of counts of nucleotides T vs A and G vs C on positive strands of human chromosomes. Interestingly, this correlates with a significant (but small) excess of genes on the same positive strands.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-016-3012-8) contains supplementary material, which is available to authorized users.

Trinucleotide's quadruplet symmetries and natural symmetry law of DNA creation ensuing Chargaff's second parity rule

For almost 50 years the conclusive explanation of Chargaff's second parity rule (CSPR), the equality of frequencies of nucleotides A=T and C=G or the equality of direct and reverse complement trinucleotides in the same DNA strand, has not been determined yet. Here, we relate CSPR to the interstrand mirror symmetry in 20 symbolic quadruplets of trinucleotides (direct, reverse complement, complement, and reverse) mapped to double-stranded genome. The symmetries of Q-box corresponding to quadruplets can be obtained as a consequence of Watson-Crick base pairing and CSPR together. Alternatively, assuming Natural symmetry law for DNA creation that each trinucleotide in one strand of DNA must simultaneously appear also in the opposite strand automatically leads to Q-box direct-reverse mirror symmetry which in conjunction with Watson-Crick base pairing generates CSPR. We demonstrate quadruplet's symmetries in chromosomes of wide range of organisms, from Escherichia coli to Neanderthal and human genomes, introducing novel quadruplet-frequency histograms and 3D-diagrams with combined interstrand frequencies. These "landscapes" are mutually similar in all mammals, including extinct Neanderthals, and somewhat different in most of older species. In human chromosomes 1-12, and X, Y the "landscapes" are almost identical and slightly different in the remaining smaller and telocentric chromosomes. Quadruplet frequencies could provide a new robust tool for characterization and classification of genomes and their evolutionary trajectories.

The exceptional genomic word symmetry along DNA sequences

Background

The second Chargaff’s parity rule and its extensions are recognized as universal phenomena in DNA sequences. However, parity of the frequencies of reverse complementary oligonucleotides could be a mere consequence of the single nucleotide parity rule, if nucleotide independence is assumed. Exceptional symmetry (symmetry beyond that expected under an independent nucleotide assumption) was proposed previously as a meaningful measure of the extension of the second parity rule to oligonucleotides. The global exceptional symmetry was detected in long and short genomes.

Results

To explore the exceptional genomic word symmetry along the genome sequences, we propose a sliding window method to extract the values of exceptional symmetry (for all words or by word groups). We compare the exceptional symmetry effect size distribution in all human chromosomes against control scenarios (positive and negative controls), testing the differences and performing a residual analysis. We explore local exceptional symmetry in equivalent composition word groups, and find that the behaviour of the local exceptional symmetry depends on the word group.

Conclusions

We conclude that the exceptional symmetry is a local phenomenon in genome sequences, with distinct characteristics along the sequence of each chromosome. The local exceptional symmetry along the genomic sequences shows outlying segments, and those segments have high biological annotation density.