complexcgr

complexcgr contains classes around the Chaos Game Representation for DNA sequences.

The FCGR helps to visualize a k-mer distribution The FCGR of a sequence is an image showing the distribution of the $k$-mers given a chosen $k$. The frequencies of all $k$-mers are distributed in the position of a matrix of $2^k \times 2^k$, which considers all the possible $k$-mers: $4^k$.

The position that a $k$-mer uses in the matrix depends on the encoding given by the CGR.

Some examples of bacterial assemblies (see reference) are shown below. The name of the species and the sample_id is in the title of each image (see an example with the first image). These images were created using the 6-mers of each assembly and the class FCGR of this library.

10 different species of bacteria represented by their FCGR (6-mers)

Installation

pypi

---

pip install complexcgr

to update to the latest version

pip install complexcgr --upgrade

version 0.8.0:
A list of available classes and functionalities are listed below:

Encoders The encoders are functions that map a sequence $s \in {A,C,G,T}$ to a point in the plane. CGR, iCGR, and ComplexCGR.

CGR Chaos Game Representation: encodes a DNA sequence in 3 numbers $(N,x,y)$

• encode a sequence.
• recover a sequence from a CGR encoding.

iCGR integer CGR: encodes a DNA sequence in 3 integers $(N,x,y)$.

CGR Chaos Game Representation: encodes a DNA sequence in 3 numbers $(N,x,y)$

• encode a sequence.
• recover a sequence from a CGR encoding.

iCGR integer CGR: encodes a DNA sequence in 3 integers $(N,x,y)$.

• encode a sequence
• recover a sequence from an iCGR encoding

ComplexCGR: encodes a DNA sequence in 2 integers $(k,N)$.

• encode a sequence
• recover a sequence from a ComplexCGR encoding
• plot sequence of ComplexCGR encodings

Image for distribution of k-mers

• FCGR Frequency Matrix CGR: representation as an image for k-mer representativity, based on CGR.
  • generates FCGR from an arbitrary n-long sequence.
  • plot FCGR.
  • save FCGR generated.
  • save FCGR in different bits.
• FCGRKmc Same as FCGR but receives as input the file with k-mer counts generated with KMC
• ComplexFCGR: Frequency ComplexCGR: representation as an image (circle) for k-mer representativity, based on ComplexCGR.
  • generates ComplexFCGR from an arbitrary n-long sequence.
  • plot ComplexFCGR.
  • save ComplexFCGR generated.

How to use

---

1. CGR Chaos Game Representation of DNA

from complexcgr import CGR

# Instantiate class CGR
cgr = CGR()

# encode a sequence
cgr.encode("ACGT")
# > CGRCoords(N=4, x=0.1875, y=-0.5625)

# recover a sequence from CGR coordinates
cgr.decode(N=4,x=0.1875,y=-0.5625)
# > "ACGT"

2. FCGR Frequency Matrix of Chaos Game Representation of DNA

Input for FCGR only accept sequences in ${A,C,G,T,N}$, but all $k$-mers that contains an $N$ will not be considered for the calculation of the frequency matrix CGR

import random; random.seed(42)
from complexcgr import FCGR

# set the k-mer
fcgr = FCGR(k=8) # (256x256) array

# Generate a random sequence without T's
seq = "".join(random.choice("ACG") for _ in range(300_000))
chaos = fcgr(seq) # an array with the frequencies of each k-mer
fcgr.plot(chaos)

FCGR representation for a sequence without T's

You can save the image with

fcgr.save_img(chaos, path="img/ACG.jpg")

Formats allowed are defined by PIL.

You can also generate the image in 16 (or more bits), to avoid losing information of k-mer frequencies

# Generate image in 16-bits (default is 8-bits)
fcgr = FCGR(k=8, bits=16) # (256x256) array. When using plot() it will be rescaled to [0,65535] colors

# Generate a random sequence without T's and lots of N's
seq = "".join(random.choice("ACGN") for _ in range(300_000))
chaos = fcgr(seq) # an array with the probabilities of each k-mer
fcgr.plot(chaos)

FCGR representation for a sequence without T's and lots of N's

3. iCGR integer Chaos Game Representation of DNA

from complexcgr import iCGR

# Instantiate class CGR
icgr = iCGR()

# encode a sequence
icgr.encode("ACGT")
# > CGRCoords(N=4, x=3, y=-9)

# recover a sequence from CGR coordinates
icgr.decode(N=4,x=3,y=-9)
# > "ACGT"

4. ComplexCGR Complex Chaos Game Representation of DNA (ComplexCGR)

from complexcgr import ComplexCGR

# Instantiate class CGR
ccgr = ComplexCGR()

# encode a sequence
ccgr.encode("ACGT")
# > CGRCoords(k=228,N=4)

# recover a sequence from ComplexCGR coordinates
ccgr.decode(k=228,N=4)
# > "ACGT"

5. ComplexFCGR Frequency Matrix of Complex Chaos Game Representation of DNA

Input for FCGR only accept sequences in ${A,C,G,T,N}$, but all $k$-mers that contains an $N$ will not be considered for the calculation of the frequency matrix CGR

import random; random.seed(42)
from complexcgr import FCGR

# set the k-mer desired
cfcgr = ComplexFCGR(k=8) # 8-mers

# Generate a random sequence without T's
seq = "".join(random.choice("ACG") for _ in range(300_000))
fig = cfcgr(seq)

ComplexFCGR representation for a sequence without T's

You can save the image with

cfcgr.save(fig, path="img/ACG-ComplexCGR.png")

Currently the plot must be saved as png

---

Advice for Real applications

Count k-mers could be the bottleneck for large sequences (> 100000 bp). Note that the class FCGR (and ComplexCGR) has implemented a naive approach to count k-mers, this is intended since in practice state-of-the-art tools like KMC or Jellyfish are used to count k-mers very efficiently.

We provide the class FCGRKmc, that receives as input the file generated by the following pipeline using KMC3

Make sure to have kmc installed. One recommended way is to create a conda environment and install it there

kmer_size=6
input="path/to/sequence.fa"
output="path/to/count-kmers.txt"

mkdir -p tmp-kmc
kmc -v -k$kmer_size -m4 -sm -ci0 -cs100000 -b -t4 -fa $input $input "tmp-kmc"
kmc_tools -t4 -v transform $input dump $output 
rm -r $input.kmc_pre $input.kmc_suf

the output file path/to/count-kmers.txt can be used with FCGRKmc

from complexcgr import FCGRKmc

kmer = 6
fcgr = FCGRKmc(kmer)

arr = fcgr("path/to/count-kmers.txt") # k-mer counts ordered in a matrix of 2^k x 2^k


# to visualize the distribution of k-mers. 
# Frequencies are scaled between [min, max] values. 
# White color corresponds to the minimum value of frequency
# Black color corresponds to the maximum value of frequency
fcgr.plot(arr) 

# Save it with numpy
import numpy as np
np.save("path_save/fcgr.npy",arr)

---

Videos

CGR encoding

CGR encoding of all k-mers This will define the positions of k-mers in the FCGR image.

ComplexCGR encoding

ComplexCGR and Symmetry