Abstract Chaos game representation (CGR) is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to determine the coordinates of their positions in a continuous space. This distribution of positions has two features: one is unique, and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences. A CGR-walk model is proposed based on CGR coordinates for the DNA sequences. The CGR coordinates are converted into a time series, and a long-memory ARFIMA (p, d, q) model, where ARFIMA stands for autoregressive fractionally integrated moving average, is introduced into the DNA sequence analysis. This model is applied to simulating real CGR-walk sequence data of ten genomic sequences. Remarkably long-range correlations are uncovered in the data, and the results from these models are reasonably fitted with those from the ARFIMA (p, d, q) model.
Received: 24 April 2008
Revised: 27 August 2008
Accepted manuscript online:
PACS:
87.15.Cc
(Folding: thermodynamics, statistical mechanics, models, and pathways)
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 60575038) and the
Natural Science Foundation of Jiangnan University, China (Grant No
20070365).
Cite this article:
Gao Jie(高洁) and Xu Zhen-Yuan(徐振源) Chaos game representation (CGR)-walk model for DNA sequences 2009 Chin. Phys. B 18 370
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