dorsal/arxiv
View SchemaUniversality of Long-Range Correlations in Expansion-Randomization Systems
| Authors | Philipp W. Messer, Michael Lassig, Peter F. Arndt |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0509027 |
| URL | https://arxiv.org/abs/q-bio/0509027 |
| DOI | 10.1088/1742-5468/2005/10/P10004 |
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 $\chi$ 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 $\chi$, 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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"abstract": "We study the stochastic dynamics of sequences evolving by single site\nmutations, segmental duplications, deletions, and random insertions. These\nprocesses are relevant for the evolution of genomic DNA. They define a\nuniversality class of non-equilibrium 1D expansion-randomization systems with\ngeneric stationary long-range correlations in a regime of growing sequence\nlength. We obtain explicitly the two-point correlation function of the sequence\ncomposition and the distribution function of the composition bias in sequences\nof finite length. The characteristic exponent $\\chi$ of these quantities is\ndetermined by the ratio of two effective rates, which are explicitly calculated\nfor several specific sequence evolution dynamics of the universality class.\nDepending on the value of $\\chi$, we find two different scaling regimes, which\nare distinguished by the detectability of the initial composition bias. All\nanalytic results are accurately verified by numerical simulations. We also\ndiscuss the non-stationary build-up and decay of correlations, as well as more\ncomplex evolutionary scenarios, where the rates of the processes vary in time.\nOur findings provide a possible example for the emergence of universality in\nmolecular biology.",
"arxiv_id": "q-bio/0509027",
"authors": [
"Philipp W. Messer",
"Michael Lassig",
"Peter F. Arndt"
],
"categories": [
"q-bio.GN"
],
"doi": "10.1088/1742-5468/2005/10/P10004",
"title": "Universality of Long-Range Correlations in Expansion-Randomization Systems",
"url": "https://arxiv.org/abs/q-bio/0509027"
},
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