Abstract
The √ n-rule of Schrödinger in his discussion of DNA is based onnormal statistics and equilibrium physics. Herein the kurtosis is used tomeasure the deviation from normality of the stistics of non-equilibrium DNAsequences. A pattern for this deviation from normality is identified andthis signature is found in prokaryotes. The signature is explained by atheory of DNA sequences that involves finite length DNA walks withdynamically generated long-range correlations.
Keywords: DNA walk, inverse power law, Lévy statistics, nonlinear dynamics
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References
- 1.Schrödinger E. What is Life? Cambridge: Cambridge University Press; 1995. [Google Scholar]
- 2.Li W., Kaneko K. Europhys. Lett. 1992;17:655. [Google Scholar]
- 3.Peng C.K., Buldyrev S., Goldberger A.L., Havlin S., Sciotino F., Simons M., Stanley H.E. Long-range correlations in nucleotide sequences. Nature. 1992;356:168–172. doi: 10.1038/356168a0. [DOI] [PubMed] [Google Scholar]
- 4.Stanley H.E., Budyrev S.V., Goldberger A.L., Goldberg Z.D., Havlin S., Mantegna R.N., Ossadnik S.M., Peng C.K., Simon S.M. Statistical mechanics in biology: how ubiquitous are long-range correlations. Physica A. 1994;205:214–235. doi: 10.1016/0378-4371(94)90502-9. [DOI] [PubMed] [Google Scholar]
- 5.Voss R. Evolution of long-range fractal correlations and 1/f noise in DNA base sequences. Phys. Rev. Lett. 1992;68:3805–3808. doi: 10.1103/PhysRevLett.68.3805. [DOI] [PubMed] [Google Scholar]
- 6.Allegrini P., Barbi M., Grigolini P., West B.J. Dynamical model for DNA sequences. Phys. Rev. E. 1995;52:5281–5286. doi: 10.1103/physreve.52.5281. [DOI] [PubMed] [Google Scholar]
- 7.Arneodo A., Bacry E., Graves P.V., Muzy J.F. Phys. Rev. Lett. 1995;74:3293–3296. doi: 10.1103/PhysRevLett.74.3293. [DOI] [PubMed] [Google Scholar]
- 8.Klafter J., Zumofen G. Physica A. 1993;196:102–111. [Google Scholar]
- 9.Trefán G., Florian E., West B.J., Grigolini P. Dynamical approach to anomalous diffusion: Response of Lévy processes to a perturbation. Phys. Rev. E. 1994;50:2564–2579. doi: 10.1103/physreve.50.2564. [DOI] [PubMed] [Google Scholar]
- 10.Allegrini P., Grigolini P., West B.J. Dynamical approach to Lévy processes. Phys. Rev. E. 1996;54:4760–4767. doi: 10.1103/physreve.54.4760. [DOI] [PubMed] [Google Scholar]
- 11.Araujio M., Havlin S., Weiss G.H., Stanley H.E. Diffusion of walkers with persistent velocities. Phys. Rev. 1991;43:5240–5247. doi: 10.1103/physreva.43.5207. [DOI] [PubMed] [Google Scholar]
- 12.Buldyrev S.V., Goldberger A.L., Havlin S., Peng C.-K., Simons M., Stanley H.E. Generalized Lévy-walk model for DNA nucleotide sequences. Phys. Rev. E. 1993;47:4514–4521. doi: 10.1103/physreve.47.4514. [DOI] [PubMed] [Google Scholar]
- 13.Allegrini P., Buiatti M., Grigolini P., West B.J. Non-Gaussian statistics of anomalous diffusion: the DNA sequences of prokaryotes. Phys. Rev. E. 1998;57:1–11. [Google Scholar]
- 14.Montroll E.W., West B.J. An enriched collection of stochastic processes. In: Montroll E.W., Lebowitz J.L., editors. Fluctuation Phenomena. 2nd ed. Amsterdam: North-Holland; 1987. [Google Scholar]
- 15.West B.J., Seshadri V. Linear systems with Lévy fluctuations. Physica A. 1982;113:203–216. [Google Scholar]
- 16.West B.J. Physiology, Promiscuity and Prophecy at the Millennium: A Tale of Tails. Singapore: World Scientific; 1999. [Google Scholar]