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Long-range correlations and generalized Lévy walks in DNA sequences. (English) Zbl 0828.92016
Shlesinger, Michael F. (ed.) et al., Lévy flights and related topics in physics. Proceedings of the international workshop, held at Nice, France, 27-30 June, 1994. Berlin: Springer-Verlag. Lect. Notes Phys. 450, 331-347 (1995).
In recent years long-range power-law correlations have been discovered in a remarkably wide variety of systems. Such long-range power-law correlations are a physical fact that in turn gives rise to the increasingly appreciated “fractal geometry of nature”. So if fractals are indeed so widespread, it makes sense to anticipate that long-range power-law correlations may be similarly widespread. Indeed, recognizing the ubiquity of long-range power-law correlations can help us in our efforts to understand nature, since as soon as we find power-law correlations we can quantify them with a critical exponent. Quantification of this kind of scaling behavior for apparently unrelated systems allows us to recognize similarities between different systems, leading to underlying unifications that might otherwise have gone unnoticed.
In the following we attempt to summarize some recent findings concerning the possibility that – under suitable conditions – the sequence of base pairs or “nucleotides” in DNA also displays power-law correlations. The underlying basis of such power law correlations is not understood at present, but this discovery has intriguing implications for molecular evolution, as well as potential practical applications for distinguishing coding and noncoding regions in long nucleotide chains. It also may be related to the presence of a language in noncoding DNA.
For the entire collection see [Zbl 0823.00016].

MSC:
92C40 Biochemistry, molecular biology
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
92D20 Protein sequences, DNA sequences
60G50 Sums of independent random variables; random walks
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