Fractal landscapes in biological systems: Long-range correlations in DNA and interbeat heart intervals

H. E. Stanley, S. V. Buldyrev, A. L. Goldberger, J. M. Hausdorff, S. Havlin, J. Mietus, C. K. Peng, F. Sciortino, M. Simons

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46 Scopus citations


Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having in common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis. whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-4
StatePublished - 15 Dec 1992

Bibliographical note

Funding Information:
We wish to thank C. DeLisi, L. Liebovitch, R.D. Rosenberg, and M. Schwartzf or valuabled iscussionsP. artial supportw as provided to ALG by the G. Harold and Leila Y. Mathers Charitable Foundation, the National Heart, Lung and Blood Institute and the National Aeronauticsa nd SpaceA dministra-tion, to MS by the American Heart Association, and to HES by the NSF and ONR.


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