Shannon information and self-similarity in whole genomes

Chen, Ta-Yuan; Hsieh, Li-Ching; Lee, Hoong-Chien

doi:10.1016/j.cpc.2005.03.050

Cited by 4 publications

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“…In the up-and-up and up-and-down types, the approximate constant of the slope of the cumulative skew is a reflection of the typical approximate uniformity of -mer-content on a scale greater than 25 kb in most chromosomes [36], [37]. Eq.…”

Section: Discussionmentioning

confidence: 99%

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

et al. 2009

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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.

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Section: Discussionmentioning

confidence: 99%

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

et al. 2009

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“…For small , is diminutive relative to genome length: 0.35 and 1.0 kb when = 2 and 4, respectively, growing to 600 kb when = 10. Within a genome, the apparent invariance of (not ) with respect to segment length was noted in [47] – [49] and the relation between Shannon information and a quantity similar to was discussed in [50] .…”

Section: Resultsmentioning

confidence: 99%

Universal Global Imprints of Genome Growth and Evolution – Equivalent Length and Cumulative Mutation Density

et al. 2010

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BackgroundSegmental duplication is widely held to be an important mode of genome growth and evolution. Yet how this would affect the global structure of genomes has been little discussed.Methods/Principal FindingsHere, we show that equivalent length, or , a quantity determined by the variance of fluctuating part of the distribution of the -mer frequencies in a genome, characterizes the latter's global structure. We computed the s of 865 complete chromosomes and found that they have nearly universal but (-dependent) values. The differences among the of a chromosome and those of its coding and non-coding parts were found to be slight.ConclusionsWe verified that these non-trivial results are natural consequences of a genome growth model characterized by random segmental duplication and random point mutation, but not of any model whose dominant growth mechanism is not segmental duplication. Our study also indicates that genomes have a nearly universal cumulative “point” mutation density of about 0.73 mutations per site that is compatible with the relatively low mutation rates of (15)10/site/Mya previously determined by sequence comparison for the human and E. coli genomes.

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Quantitative measure of randomness and order for complete genomes

et al. 2009

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We propose an order index, phi, which gives a quantitative measure of randomness and order of complete genomic sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length. The 786 complete genomic sequences in GenBank were found to have phi values in a very narrow range, phig=0.031(-0.015)+0.028. We show this implies that genomes are halfway toward being completely random, or, at the "edge of chaos." We further show that artificial "genomes" converted from literary classics have phi 's that almost exactly coincide with phig, but sequences of low information content do not. We infer that phig represents a high information-capacity "fixed point" in sequence space, and that genomes are driven to it by the dynamics of a robust growth and evolution process. We show that a growth process characterized by random segmental duplication can robustly drive genomes to the fixed point.

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Shannon information and self-similarity in whole genomes

Cited by 4 publications

References 4 publications

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

Universal Global Imprints of Genome Growth and Evolution – Equivalent Length and Cumulative Mutation Density

Quantitative measure of randomness and order for complete genomes

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