Fractal Dimension Analysis of Dna Sequences

This paper presents fractal measures for deoxyribonucleic acid (DNA) sequences using fractal and multifractal methodologies ([Kins94] and [RiKi99]), and demonstrates the intriguing possibility of identifying biological functionality using information contained within the DNA sequence. A vast amount of genetic material has been sequenced to date with an exponential growth rate. By 2005, human genome in a total of 3 x 109 base pairs will have been sequenced. But the rate of finding genes and their location at chromatosomes is relatively slow. Therefore, robust computational solutions to the DNA sequences analysis are a valuable way to the molecular biology. Most of the current research in the deciphering the meaning of DNA sequences is approached from the lowest level. Its main objective is to search for patterns or correlations existing in the DNA sequence related to codons, amino acids, and proteins using a variety of sophisticated computational techniques, including neural network algorithms, dynamic programming, rule-based methods, decision trees, probabilistic reasoning, and hidden Markov chain. Although none of them perform perfectly, the information they provide is so valuable that some of them are even used for recognition putative genes in uncharacterized DNA. In this paper, we have developed techniques that: (1) transform the DNA sequence alphabets to signal spectrum based on the Lévy-walk [BeRO96]; (2) estimate single fractal and multifractal dimensions; (3) power spectrum analysis. Experimental results show that (i) DNA is multifractal, and that the multifractality changes depending upon the location (coding or noncoding region) in the sequence; (ii) local polymer dimension fluctuated with the variation of the local DNA sequence; and (iii) there is a significant difference between coding region and noncoding region with DNA sequence power spectrum and the β value of them is around -1. AcknowledgmentsThis research has been supported in part by the Natural Sciences and Engineering Council (NSERC) of Canada. References[BeRO96] P. Bernaola-Galvan, R. Roman-Roldan, and J.L. Oliver, “Compositional seqmentation and long-rangefractal correlations in DNA sequences,” Phys. Rev. E, vol. 53, pp. 5181-5189, 1996.[Kins94] W. Kinsner, “Fractal dimensions: Morphological, entropy, spectrum, and variance classes,” TechnicalReport, DEL94-5, University of Manitoba, May 1994, 146 pp.[RiKi99] R. Rifaat and W. Kinsner, “Multifractal analysis of DNA sequences,” Proc. of IEEE CCECE’99,Edmonton, Canada, pp. 801-804,1999. ADVISOR: W. Kinsner, Ph. D., P. Eng.