title: Analysis of genomic sequences by Chaos Game Representation.
abstract: BACKGROUND
  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 find the coordinates for their position in a continuous space. This distribution of positions has two properties: it is unique, and the source sequence can be recovered from the coordinates such that distance between positions measures similarity between the corresponding sequences. The possibility of using the latter property to identify succession schemes have been entirely overlooked in previous studies which raises the possibility that CGR may be upgraded from a mere representation technique to a sequence modeling tool.
  
  
  RESULTS
  The distribution of positions in the CGR plane were shown to be a generalization of Markov chain probability tables that accommodates non-integer orders. Therefore, Markov models are particular cases of CGR models rather than the reverse, as currently accepted. In addition, the CGR generalization has both practical (computational efficiency) and fundamental (scale independence) advantages. These results are illustrated by using Escherichia coli K-12 as a test data-set, in particular, the genes thrA, thrB and thrC of the threonine operon.
authors.affiliation: ITQB/Universidade Nova Lisboa, PO Box 127, 2780 Oeiras, Portugal. almeidaj@musc.edu
authors.forename: J S
authors.initials: JS
authors.lastname: Almeida
authors.forename: J A
authors.initials: JA
authors.lastname: Carriço
authors.forename: A
authors.initials: A
authors.lastname: Maretzek
authors.forename: P A
authors.initials: PA
authors.lastname: Noble
authors.forename: M
authors.initials: M
authors.lastname: Fletcher
mesh_terms: D000465:Algorithms; D001483:Base Sequence; D004269:DNA, Bacterial / Q000235:genetics; D004926:Escherichia coli / Q000235:genetics; D005716:Game Theory; D016678:Genome; D016680:Genome, Bacterial; D017711:Nonlinear Dynamics; D016415:Sequence Alignment / Q000706:statistics & numerical data; D017422:Sequence Analysis, DNA / Q000706:statistics & numerical data*; D013912:Threonine / Q000235:genetics
chemical_list: D004269:DNA, Bacterial; D013912:Threonine