Nonlinear analysis of random walks: a tool to analyze nucleic acid sequences

We have performed a comparison of computer-generated random sequences with tRNAs nucleotide sequences present in Bacteria represented as random walks. Nucleotide sequence data of tRNA genes were obtained from the Institute for Genomic Research (TIGR) and the GeneBank library. Random sequence data (white noise) were obtained from the algorithm by Press and Teukolsky. Random walks of nucleotide sequences were obtained by letting the orbit walk a unit step in one of four directions (down, left, right, and up), depending upon the next base (A,C,G, and T) in the sequence, and the distances from the origin calculated. The Visual Basic routines here applied to perform the analysis are presented. Relative Lempel-Ziv complexity. Entropy (sum of the positive Lyapunov indexes) and Hurst indexes of nucleotide sequences and of computer-generated random data were evaluated over the distances of their random walk. Our data show that the values of nonlinear parameters obtained from the bacteria are lower than the values of randomly generated sequences (p<0.01, p<0.05, p