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.
Highlights
Symmetry has been considered as an aspect of beauty in mathematics [1], physics [2], chemistry [3], evolution [4], human appearance [5], and psychology [6]
Using the indexes we verified that all three symmetries are absent as expected in sufficiently long random sequences, and we found that: reverse and complement symmetries are absent, globally and locally, in the 786 complete chromosomes studied; in sharp contrast, a high level of global inverse symmetry (GIS) is ubiquitous in almost all complete chromosomes; the grand average of the GIS index in all complete chromosomes is 0:073+0:066; while broadly similar in their global behavior, chromosomes exhibit a wide variety of patterns in local inverse symmetry (LIS); coding and non-coding regions have essentially the same global and local symmetry properties
The Inverse Symmetry Database (ISDB) Data, in the form of numerical lists and plots, on local and global symmetries for 786 complete chromosomes are given in the Inverse Symmetry Database (ISDB) [23]
Summary
Symmetry has been considered as an aspect of beauty in mathematics [1], physics [2], chemistry [3], evolution [4], human appearance [5], and psychology [6]. Chargaff’s second parity rule (CPR2) states that at a lower level of accuracy the first rule extends to a single strand of DNA [9,10,11,12]. This monomeric base-complement symmetry has two possible generalizations to k-letter words, or k-mers: complement and reverse-complement, or inverse, symmetries. For a proper discussion of symmetry a quantitative description of the phenomenon, including its complete absence, is needed
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