Multifractal and correlation analyses of protein sequences from complete genomes

A measure representation of protein sequences similar to the measure representation of DNA sequences proposed in our previous paper [Yu et al., Phys. Rev. E 64, 031903 (2001)] and another induced measure are introduced. Multifractal analysis is then performed on these two kinds of measures of a large number of protein sequences derived from corresponding complete genomes. From the values of the Dq (generalized dimensions)spectra and related Cq (analogous specific heat) curves, it is concluded that these protein sequences are not completely random sequences. For substrings with length K=5, the Dq spectra of all organisms studied are multifractal-like and sufficiently smooth for the Cq curves to be meaningful. The Cq curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of higher organisms studied exhibit the shape of double-peaked specific heat function. But for the classification problem, the multifractal property is not sufficient. When the measure representations of protein sequences from complete genomes are considered as time series, a method based on correlation analysis after removing some memory from the time series is proposed to construct a phylogenetic tree. This construction is shown to be reasonably satisfactory