CHAPTER 35

WAVELET ALGORITHMS FOR DNA ANALYSIS

35.1 INTRODUCTION

One of the main tasks of the genome project is to understand completely the underlying biological function from a possible interpretation of the given sequence of nucleotides that is from the distribution of the four symbols A, C, G, T along the sequence [21, 24, 25]. The main hypotheses of this project are as follows:

1. The activity (functional) of the organism is a result of the distribution of nucleotides.

2. The distribution of nucleotides should follow some hidden rules.

3. It should be possible to discover these rules by singling out some regular features like periodicity, typical patterns, trends, sequence evolution, and so on.

In recent years, the analysis of DNA sequences has been focused mainly on the existence of hidden law, periodicities, and autocorrelation [14, 17, 24, 34]. The main task is to find (if any) some kind of mathematical rules or meaningful statistics in the nucleotides distribution. This would help us to characterize each DNA sequence to construct a possible classification. From a mathematical point a view, the DNA sequence is a symbolic sequence (of nucleotides) with some empty spaces (no coding regions). To get some numerical information from this sequence, it must be transformed into a digital sequence. It follows that the symbolic sequence is transformed into a very large time series (from one half of a million digits for the primitive organisms such as fungus, eukaryotes, ...