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  Universality of long-range correlations in expansion-randomization systems

Messer, P., Lässig, M., & Arndt, P. F. (2005). Universality of long-range correlations in expansion-randomization systems. Journal of Statistical Mechanics: Theory and Experiment, (10), P10004-P10004. doi:10.1088/1742-5468/2005/10/P10004.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-8584-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-8585-E
Genre: Journal Article

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 Creators:
Messer, Philipp1, Author
Lässig, M., Author
Arndt, Peter F.2, Author              
Affiliations:
1Max Planck Society, ou_persistent13              
2Evolutionary Genomics (Peter Arndt), Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society, ou_1479638              

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Free keywords: dynamics (theory) models for evolution (theory) mutational and evolutionary processes (theory)
 Abstract: We study the stochastic dynamics of sequences evolving by single-site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion–randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent χ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of χ, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.

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Language(s): eng - English
 Dates: 2005-10-06
 Publication Status: Published in print
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 Identifiers: eDoc: 267512
DOI: 10.1088/1742-5468/2005/10/P10004
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Title: Journal of Statistical Mechanics: Theory and Experiment
Source Genre: Journal
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Pages: - Volume / Issue: (10) Sequence Number: - Start / End Page: P10004 - P10004 Identifier: -