Chaos Game Representation (CGR) was proposed as a scale-independent representation for genomic sequences by Jeffrey in 1990 (Jeffrey, H. J. 1990). The technique, formally an iterative map, can be traced further back to the foundations of statistical mechanics, in particular to Chaos theory (Bar-Yam,1997). The original proposition has been considerably expanded and generalized for sequences of arbitrary symbols (Tino, 1999), and therefore including other biological sequences such as proteins (Basu et al., 1997; Pleißner et al., 1997).
Jeffry plotted CGR of Human Beta Globin Region on Chromosome 11 and noticed a double scoop in it. In 1993 Goldman pointed out that the double scoop is due to relative rarity of CG dinucleotides . (Goldman, 1993).
Three years after the original proposition, the translation of CGR quadrant frequencies into oligonucleotide frequencies was demonstrated and interpreted as an indication that ‘it is unlikely that CGRs can be more useful than simple evaluation of nucleotide, dinucleotide and trinucleotide frequencies’ (Goldman, 1993). So for several years, the possibility that the CGR format can be used for representing the nucleotide sequence as well as identifying the resulting sequence scheme had not been fully explored. In 2001 Almeida proved that the distribution of positions in the CGR plane are generalization of Markov chain probability tables that accommodates non-integer orders(Almeida 2001). This brought CGR to the main stream again.
In CGR representation for promoter, corners are taken as A at position (0,0), G at position (1,0), T at position (1,1) and C at (0,1) which is different from conventional corner assignment viz. A at(0,0) T at (1,0) G at(1,1) and C at(0,1) (Deschavanne PJ, Giron A, Vilain J, Fagot G, Fertil B. 1999). The reason for this variation is the AT rich and GC rich nature of the promoter region. The increase in their concentrations is represented as diagonals and can be easily observable. But in the standard case it is represented as bands and cannot be observed prominently. |
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