Chaos game representation of protein sequences based on the detailed HP model and their multifractal and correlation analyses

Similar to the chaos game representation (CGR) of DNA sequences proposed by Jeffrey (Nucleic Acid Res. 18 (1990) 2163), a new CGR of protein sequences based on the detailed HP model is proposed. Multifractal and correlation analyses of the measures based on the CGR of protein sequences from complete genomes are performed. The D, spectra of all organisms studied are multifractal-like and sufficiently smooth for the C-q curves to be meaningful. The C-q curves of bacteria resemble a classical phase transition at a critical point. The correlation distance of the difference between the measure based on the CGR of protein sequences and its fractal background is also proposed to construct a more precise phylogenctic tree of bacteria. (C) 2003 Elsevier Ltd. All rights reserved.