Chaos Game Representation (GCR) stack

lehvaslaiho at cc.helsinki.fi lehvaslaiho at cc.helsinki.fi
Thu Aug 9 18:27:46 EST 1990

       a HyperCard stack for presenting nucleotide sequence data
                    using Chaos Game Representation 

Recently, M. Joel Jeffrey (Jeffrey 1990) published a way of presenting 
nucleotide sequences in graphical form, that he called Chaos Game 
Representation (CGR). It is, to my knowladge, the first published attempt 
to apply the nonlinear approach to nucleotide sequences data (excluding 
Ohno 1988). While the complete mathematical description of this approach 
waits its completion, I felt its present state to be important enough to 
make it widely available and let as many molecular biologists as possible 
to try it out.

Shortly, CGR plots nucleotides in a square where the corners are labelled 
A, C, G and T. Beginning at the centre, successive nucleotides in a sequence 
are plotted halfway between the corner carrying the corresponding label and 
the previous point. Estimates of relative oligonucleotide (<10 b) frequencies 
can be seen in a glance from the fractal plot. The possible implications of 
this approach are discussed in detail in the original article.

CGR HyperCard stack reads sequence data in EMBL or GenBank form or in plain 
sequences from text only files. Introns or other sequence regions can be 
excluded from the plot by entering their base range. Contrary to what is 
suggested in the original article, both plotting and calculation are 
interrupted these regions. For easy modification, the file and excluded 
region information are transferred to the new card when RNew cardS button i

Also included in the stack is my own modification of the CGR approach for 
comparing nucleotide frequencies in codons. Three plots, one for each base 
in codons are plotted separately. For most sequences, the resulting plots 
show clearly the increasing randomness from first to third codon base and 
can be used, for example, to determine the actual reading frame from 
overlapping ORFS. This approach loses much of the accuracy of a 
mathematical approach (e.g. Tavar and Song 1989), but gains in presenting
the data in easily understood graphical form. For molecular biologists, 
this might be more useful. 

The users are strongly encouraged to try their own ideas and modify the 
scripts of CGR. I am interested in any developments in CGR approach to 
gene structure. For example, has someone developed a way of plotting 
amino acid sequences? Joel?

CGR 1.0 is available from the EMBL Network File Server 
(Internet address: NETSERV at EMBL.BITNET).


Jeffrey JM 1990: Chaos game representation of gene structure. 
Nucl Acid Res 18:2163-21270.

Ohno S 1988. Codon preference is but an illusion created by the construction 
principle of coding sequences. Proc Natl Acad Sci USA 85: 4378-4382.

Tavare S and Song B 1989: Codon preference and primary sequence structure
in protein-coding regions. Bulletin of Mathematical Biology 51:95-115

Heikki Lehva
Cancer Biology Laboratory, Departments of Pathology and Virology
University of Helsinki, Haartmaninkatu 3, SF-00290 Helsinki, FINLAND

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