Introduction to the kmeRs package

Introduction

Similarity Score Matrix and HeatMap for nucleic and amino acid k-mers. Similarity score is evaluated by Point Accepted Mutation (PAM) and BLOcks SUbstitution Matrix (BLOSUM). Higher similarity score indicates more similar sequences for BLOSUM and less similar sequences for PAM matrix. The 30, 40, 70, 120, 250 and 62, 45, 50, 62, 80, 100 matrix versions are available for PAM and BLOSUM, respectively. Alignment is evaluated by Needleman-Wunsch (Needleman and Wunsch 1970) and Smith-Waterman (Smith and Waterman 1981).

Load the package first

# Import the package 
  library(kmeRs)

Example 1. How to display BLOSUM matrix used for amino acides calculation?

Simply apply the kmeRs_similarity_matrix function and mark the appropriate matrix, here BLOSUM62.

# Simple BLOSUM62 similarity matrix for all amino acid nucleotides
  BLOSUM62 <- kmeRs_similarity_matrix(submat = "BLOSUM62")
# Fancy knitr table
  knitr::kable(BLOSUM62)
G A L M F W K Q E S P V I C Y H R N D T
G 6 0 -4 -3 -3 -2 -2 -2 -2 0 -2 -3 -4 -3 -3 -2 -2 0 -1 -2
A 0 4 -1 -1 -2 -3 -1 -1 -1 1 -1 0 -1 0 -2 -2 -1 -2 -2 0
L -4 -1 4 2 0 -2 -2 -2 -3 -2 -3 1 2 -1 -1 -3 -2 -3 -4 -1
M -3 -1 2 5 0 -1 -1 0 -2 -1 -2 1 1 -1 -1 -2 -1 -2 -3 -1
F -3 -2 0 0 6 1 -3 -3 -3 -2 -4 -1 0 -2 3 -1 -3 -3 -3 -2
W -2 -3 -2 -1 1 11 -3 -2 -3 -3 -4 -3 -3 -2 2 -2 -3 -4 -4 -2
K -2 -1 -2 -1 -3 -3 5 1 1 0 -1 -2 -3 -3 -2 -1 2 0 -1 -1
Q -2 -1 -2 0 -3 -2 1 5 2 0 -1 -2 -3 -3 -1 0 1 0 0 -1
E -2 -1 -3 -2 -3 -3 1 2 5 0 -1 -2 -3 -4 -2 0 0 0 2 -1
S 0 1 -2 -1 -2 -3 0 0 0 4 -1 -2 -2 -1 -2 -1 -1 1 0 1
P -2 -1 -3 -2 -4 -4 -1 -1 -1 -1 7 -2 -3 -3 -3 -2 -2 -2 -1 -1
V -3 0 1 1 -1 -3 -2 -2 -2 -2 -2 4 3 -1 -1 -3 -3 -3 -3 0
I -4 -1 2 1 0 -3 -3 -3 -3 -2 -3 3 4 -1 -1 -3 -3 -3 -3 -1
C -3 0 -1 -1 -2 -2 -3 -3 -4 -1 -3 -1 -1 9 -2 -3 -3 -3 -3 -1
Y -3 -2 -1 -1 3 2 -2 -1 -2 -2 -3 -1 -1 -2 7 2 -2 -2 -3 -2
H -2 -2 -3 -2 -1 -2 -1 0 0 -1 -2 -3 -3 -3 2 8 0 1 -1 -2
R -2 -1 -2 -1 -3 -3 2 1 0 -1 -2 -3 -3 -3 -2 0 5 0 -2 -1
N 0 -2 -3 -2 -3 -4 0 0 0 1 -2 -3 -3 -3 -2 1 0 6 1 0
D -1 -2 -4 -3 -3 -4 -1 0 2 0 -1 -3 -3 -3 -3 -1 -2 1 6 -1
T -2 0 -1 -1 -2 -2 -1 -1 -1 1 -1 0 -1 -1 -2 -2 -1 0 -1 5

Example 2. How to find the most ‘different’ k-mer from the given set of k-mers?

In this example, the most ‘different’ k-mer to “GATTACA” sequence will be indicated from given set of heptamers. Here, 7 heptamer (being an anagram of the movie title “GATTACA”) are given, as follow:

# Given hexamers
  kmers_given <- c("GATTACA", "ACAGATT", "GAATTAC", "GAAATCT", "CTATAGA", "GTACATA", "AACGATT")
# Matrix calculation 
  kmers_mat <- kmeRs_similarity_matrix(q = c("GATTACA"), x = kmers_given , submat = "BLOSUM62") 
# Fancy knitr table
  knitr::kable(kmers_mat)
GATTACA
GATTACA 37
ACAGATT 1
GAATTAC 15
GAAATCT 19
CTATAGA 7
GTACATA 12
AACGATT 4

Now, applying kmeRs_score function the total score is calculated and the matrix is sorted by increasing score value. The lowest value (in case of BLOSUM) indicates the most ‘different’ sequence from given k-mers, in contrast to the highest value which indicates the most similar one.

# Score and sort the matrix  
  kmers_res <- kmeRs_score(kmers_mat)
# Fancy knitr table
  knitr::kable(kmers_res)
GATTACA Sum
ACAGATT 1 1
AACGATT 4 4
CTATAGA 7 7
GTACATA 12 12
GAATTAC 15 15
GAAATCT 19 19
GATTACA 37 37

As can be observed, the most ‘different’ sequence to GATTACA is ACAGATT with total score equal to 1 and the most similar to GATTACA sequence is of course GATTACA sequence with the highest score equal to 37.

Example 3. How to find the most ‘different’ k-mer to whole given set of k-mers?

In this example, the most ‘different’ k-mer to whole given set of heptamers will be indicated. The same heptamers as in example 2 are used.

# Given hexamers
  kmers_given <- c("GATTACA", "ACAGATT", "GAATTAC", "GAAATCT", "CTATAGA", "GTACATA", "AACGATT")
# Matrix calculation 
  kmers_mat <- kmeRs_similarity_matrix(q = kmers_given, submat = "BLOSUM62")
# Score the matrix and sort by decreasing score 
  kmers_res <- kmeRs_score(kmers_mat)
# Fancy knitr table
  knitr::kable(kmers_res)
GATTACA ACAGATT GAATTAC GAAATCT CTATAGA GTACATA AACGATT Sum
CTATAGA 7 3 6 -2 37 11 0 62
AACGATT 4 24 1 8 0 6 37 80
ACAGATT 1 37 1 8 3 9 24 83
GAATTAC 15 1 37 18 6 9 1 87
GTACATA 12 9 9 9 11 37 6 93
GATTACA 37 1 15 19 7 12 4 95
GAAATCT 19 8 18 37 -2 9 8 97

As can be observed, the most ‘different’ sequence to all given heptamers is CTATAGA with score equal to 62 and the most similar sequence is GAAATCT with the highest score equal to 97.

Example 4. How to calculate basic statistics for the matrix?

Applying function kmeRs_statistics to the result matrix the basic statistics can be calculated as additional rows. When summary_statistics_only is set to TRUE only summary table is returned. It is much more elegant way to present results, especially in case of ‘big data’ output.

# Calculate stats 
  kmers_stats <- kmeRs_statistics(kmers_res)
# Fancy knitr table
  knitr::kable(kmers_stats[ ,1:(dim(kmers_stats)[2] - 4) ])
GATTACA ACAGATT GAATTAC GAAATCT CTATAGA GTACATA AACGATT Sum
CTATAGA 7.00 3.00 6.00 -2.00 37.00 11.00 0.00 62.00
AACGATT 4.00 24.00 1.00 8.00 0.00 6.00 37.00 80.00
ACAGATT 1.00 37.00 1.00 8.00 3.00 9.00 24.00 83.00
GAATTAC 15.00 1.00 37.00 18.00 6.00 9.00 1.00 87.00
GTACATA 12.00 9.00 9.00 9.00 11.00 37.00 6.00 93.00
GATTACA 37.00 1.00 15.00 19.00 7.00 12.00 4.00 95.00
GAAATCT 19.00 8.00 18.00 37.00 -2.00 9.00 8.00 97.00
Min 1.00 1.00 1.00 -2.00 -2.00 6.00 0.00 62.00
Max 37.00 37.00 37.00 37.00 37.00 37.00 37.00 97.00
Mean 13.57 11.86 12.43 13.86 8.86 13.29 11.43 85.29
SD 12.08 13.64 12.62 12.40 13.16 10.63 13.83 12.04

Example 5. How to display a similarity matrix as a heatmap?

Simply applying function kmeRs_heatmap to the result matrix.

# Heatmap without sum column
  kmeRs_heatmap(kmers_res[, -8])

Acknowledgement

Special thanks to Jason Lin, PhD from Chiba Cancer Center Research Institute, Chiba, Japan for contribution in 2021 as implementing of heatmap function and update deprecated functions.

References

Needleman, Saul B., and Christian D. Wunsch. 1970. “A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins.” Journal of Molecular Biology 48 (3): 443–53. https://doi.org/10.1016/0022-2836(70)90057-4.
Smith, T. F., and M. S. Waterman. 1981. “Identification of Common Molecular Subsequences.” Journal of Molecular Biology 147 (1): 195–97. https://doi.org/10.1016/0022-2836(81)90087-5.

  1. OncoCDx Research Center, London, UK↩︎