Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

Abstract

The cause of symmetry is usually subtle, and its study often leads to a deeper understanding of the bearer of the symmetry. To gain insight into the dynamics driving the growth and evolution of genomes, we conducted a comprehensive study of textual symmetries in 786 complete chromosomes. We focused on symmetry based on our belief that, in spite of their extreme diversity, genomes must share common dynamical principles and mechanisms that drive their growth and evolution, and that the most robust footprints of such dynamics are symmetry related. We found that while complement and reverse symmetries are essentially absent in genomic sequences, inverse–complement plus reverse–symmetry is prevalent in complex patterns in most chromosomes, a vast majority of which have near maximum global inverse symmetry. We also discovered relations that can quantitatively account for the long observed but unexplained phenomenon of -mer skews in genomes. Our results suggest segmental and whole-genome inverse duplications are important mechanisms in genome growth and evolution, probably because they are efficient means by which the genome can exploit its double-stranded structure to enrich its code-inventory.

Attaining the 2nd Chargaff Rule by Tandem Duplications

“…Similar bounds on R 10 X can be derived for other values of d using Figures 2 and 3. Note that the choice of = 0.00005 for generating the plot in Figure 4 is arbitrary here and similar plots can be obtained for other values of by using (12). Moreover, similar bounds can be obtained for other values of k by calculating ∆ (k,g) .…”

“…There have been several papers in the past that have verified this symmetry for different values of k for more than 700 different species [1] [2] [12] [16] [17]. Given a genome of length n, the k-limit or the value of k upto which the 2nd Chargaff rule holds was empirically observed to be about 0.7 ln n [19].…”

“…The presence of IS makes it plausible that most of the species share common dynamics of evolution. In [12] [19], the authors also showed that this symmetry only holds for reverse complement pairs and not for complement or any random pair of k-mers. [12] also argued that IS may be due to whole genome or segmental inverse duplications.…”

“…In [12] [19], the authors also showed that this symmetry only holds for reverse complement pairs and not for complement or any random pair of k-mers. [12] also argued that IS may be due to whole genome or segmental inverse duplications. Duplication based sequence generating models have been analysed in the past from a combinatorial [7] [9] [11] [13] [14] and probabilistic [8] [10] perspective.…”

A novel approach for constructing reversible codes and applications to DNA codes over the ring F2[u]/(u<

“…In these regions reversible-complement DNA 8-mers have been shown to appear intensively. Moreover the reversible-complement property has been shown to be of importance one a single DNA strand as illustrated in [14,22], which show that the numbers of a DNA k-mer and its reversible complement are close in the same DNA strand. Having these facts, our goal in this paper is to be able to match k-mers with ring elements of R 2k = F 2 [u]/(u 2k − 1).…”