Dynamical model for DNA sequences

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This article discusses a dynamical model for DNA sequences based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated.

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16 p.

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Allegrini, Paolo; Barbi, M.; Grigolini, Paolo & West, Bruce J. November 1995.

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This article discusses a dynamical model for DNA sequences based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated.

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16 p.

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Copyright 1995 American Physical Society. The following article appeared in Physical Review E, 1995, 52:5, pp. 5281-5296, http://link.aps.org/doi/10.1103/PhysRevE.52.5281

Abstract: We address the problem of DNA sequences, developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated. The generator of the deterministic evolution is a nonlinear map belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules that determine the DNA path, whereas the noise mimics the influence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are canceled on the short-range scale, but show up in the long-range one. We denote their prescription to generate statistical sequences as the copying mistake map (CMM). We carry out their analysis of several DNA sequences and their CMM realizations with a variety of techniques and the authors especially focus on a method of regression to equilibrium, which they call the Onsager analysis. With these techniques the authors establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are difficult to detect, since the exon "dynamics" is shown to be determined by the entanglement of three distinct and independent CMM's.

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  • Physical Review E, 1995, College Park: American Physical Society, pp. 5281-5296

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  • Publication Title: Physical Review E
  • Volume: 52
  • Issue: 5
  • Page Start: 5281
  • Page End: 5296
  • Peer Reviewed: Yes

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  • November 1995

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  • Feb. 1, 2013, 9:58 a.m.

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  • July 18, 2013, 12:20 p.m.

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Allegrini, Paolo; Barbi, M.; Grigolini, Paolo & West, Bruce J. Dynamical model for DNA sequences, article, November 1995; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc139499/: accessed December 15, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.