Researches On Fractal Characteristic Of DNA Sequence Based On Wavelet Analysis

This paper dissertates the complexity and non-linearity of biologic system, indicates the necessity of systemic and integrative view in the study of biologic system. Fractal theory is fit for the non-linear system. The non- linearity of DNA can be described by it's fractal characteristics. This paper presented method about using wavelet analysis to study the fractal characteristics of DNA sequence on the basis of existing literature. Fractional Brownian motion(FBM) is used in the parameterized modeling of base distributing of DNA sequence. Using mexihat wavelet do wavelet transform and Hurst index is calculated which can describes the self-similarity of DNA sequence.This method introduces the parameterized analysis and calculate index by wavelet analysis. Compare to Fourier transform, it has better statistical stabilization and reliability. DNA sequence is composed of four bases which are Adenine(A), Guannine(G), Cytosine(C) and Thymine(T). They can not be processed as a signal directly. They are mapped to digital signals of AG walk, AC walk and AT walk using theory of DNA Walk. We calculate the Hurst indexes of each sequence and regard it as one dimension fractal characteristic of DNA sequence. Hurst index is an important statistic index which describes the self-similarity of time series. FBM is an representative self-similarity model and it can be used in parameterized modeling of DNA sequence. Wavelet transform has the merit of scale-irrespective. It is a very suitable tool for quantized analysis of fractal structure. DNA sequence of Human, bacteriophage , invertebrates and rat are studied in the experiment. Their Hurst indexes are calculated using the method above-mentioned. The results indicate that it can describe fractal characteristics of DNA sequence correctly and expediently. This study is the foundation of further study about genetic information and control mechanism of DNA sequence.