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
Cancer Biology Laboratory, Departments of Pathology and Virology
University of Helsinki, Haartmaninkatu 3, SF-00290 Helsinki, FINLAND
E-mail: LEHVASLAIHO at CC.HELSINKI.FI