chaotic dynamical systems (Jeffery 1990), or simply chaos was a physics terminology. The common idea of chaos is lack of order, randomness. Yet, with proper application of maths, chaos can be given form and as such, quantified.
Thus, here comes chaos game, first described by Fractal modeling of real world images, Barnsly, 1988 and presented as a novel method, Chaos Game Representation, to present DNA structure, Chaos game representation of gene structure, H.Joel Jeffrey, 1990
This is a pythonic implementation (alpha stage) of cgr using biopython and matplotlib, to generate a cgr image of DNA fasta file.
Ability to compare two different cgr will eventually be added.
Ability to create cgr of anything other then DNA (e.g protein), is not planned for now.
CGR is an Iterated Function System (IFS), a derivative of fractals.
Mapping nucleotides in a two dimensional system will have the IFS constitute a pair of linear equation x = ax + by + e and y = cx + dy + f, providing the (x,y) coordinate of said nucleotide.
Each nucleotide n is assigned an original start coordinate (think of it as a corner in a graph) - with 4 nucleotide, A, T, G, C are assigned, (0,0), (1,0), (1,1), (0, 1) respectively.
With 4 individual loci, we have 8 equations, which can be summarized as: w(x, y) = (ax + by + e, cx + dy + f) and a probability, p for each loci. If the DNA sequence were completely random, an example IFS code might look like:
w a b c d e f p
1 0.5 0 0 0.5 0 0 0.25
2 0.5 0 0 0.5 0 0.5 0.25
3 0.5 0 0 0.5 0.5 0 0.25
4 0.5 0 0 0.5 0.5 0.5 0.25
TODO: Corresponding CGR TODO: Tweak the p to 0.1, 0.2, 0.3 and 0.5, the new CGR
For a DNA sequence with 4 nucleotide, A - T/U - G - C, we start with a graph
The center of the graph is (0.5, 0.5)
Algorithm to generate CGR:
LET SEQUENCE seq OF LEN s,
BEGIN
start_nt = seq[0]
center = (0.5, 0.5)
if start_nt == A: nt_pos = (0,0)
else if start_nt == T/U: nt_pos (1,0)
else if start_nt == G: nt_pos (1,1)
else if start_nt == C: nt_pos = (0,1)
else: Break
cgr_mark =
(
(nt_pos[0] + center[0])/2,
(nt_pos[1] + center[0])/2
)
plot(cgr_mark)
NEXT
while s:
if start_nt == A: nt_pos = (0,0)
else if start_nt == T/U: nt_pos (1,0)
else if start_nt == G: nt_pos (1,1)
else if start_nt == C: nt_pos = (0,1)
else: Break
cgr_mark = (
(nt_pos[0] + cgr_mark[0])/2,
(nt_pos[1] + cgr_mark[1])/2
)
plot(cgr_mark)
A plot is derived in linear time (baring the calculation of mid point)
For now, simply do python3 pycgr/dnacgr.py.
anaconda3 or appropriate virtual env is recommended.
Eventually, the setup.py will incorporate a proper installation system.
Requires: python3; biopython; matplotlib
usage: dnacgr.py [-h] [--dest-dir SAVE_DIR] [--show] [--save] [--dpi DPI]
[files [files ...]]
Chaos Game Representation
positional arguments:
files
optional arguments:
-h, --help show this help message and exit
--dest-dir SAVE_DIR, -d SAVE_DIR
Where do you want to save the resulting CGRs?
--show, -p Do you want to display resulting CGRs?
--save, -s Do you want to save resulting CGRs?
--dpi DPI, -i DPI Where do you want to save the resulting CGRs?
- Facility to compare two different CGRs
- Ability to create amino acid CGR
- Create PDF of CGR
- Save cgr to text file
- Use different color for different nucleotide
Jeffrey, H.J., 1990. Chaos game representation of gene structure. Nucleic Acids Res 18, 2163–2170.