Chaos game representation walk model for the protein sequences

A new chaos game representation of protein sequences based on the detailed hydrophobic--hydrophilic (HP) model has been proposed by Yu et al (Physica A 337 (2004) 171). A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CGR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA(p, d, q) model is introduced into the protein sequence analysis. This model is applied to simulating real CGR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA(p, d, q) model.