The character of the correlations in DNA sequences

Although several authors proposed the existence of long-range correlations in DNA sequences [W. Li and K. Kaneko, Europhys. Lett. 17, 655 (1992); R.F. Voss, Phys. Rev. Lett. 68, 3805 (1992); C.-K. Peng et al., Nature 356, 168 (1992)], we claim that the real character of the correlations remains uncertain. To corroborate long-range correlations, one should prove that the correlation functions decay as an inverse power of the distance between the nucleotides in the DNA sequence. Instead of a direct calculation of the correlation functions, one can calculate either the Fourier transforms of the sequences or the characteristics of “DNA walk.” In our previous work we pointed out that the character of the results depends upon the way the DNA sequences are chosen. When looking for the correlations separately in introns and separately in exons, we found that the resulting correlations are short range. In this work, we discuss the numerical aspects of two computational approaches: the calculation of correlation function and the evaluation of “DNA walk” characteristics. We present the analytic results for the case of exponential correlations. © 1994 John Wiley & Sons, Inc.