# Introduction to the kmeRs package

## Introduction

The package contains tools to calculate similarity score matrix for DNA k-mers. The pairwise similarity score is calculated using PAM or BLOSUM substitution matrix. The results are evaluated by similarity score calculated by Needleman-Wunsch (global) (Needleman and Wunsch 1970) or Smith-Waterman (local) alignment. (Smith and Waterman 1981). Higher similarity score indicates more similar sequences for BLOSUM and less similar sequences for PAM matrix; 30, 40, 70, 120, 250 and 62, 45, 50, 62, 80, 100 matrix versions are available for PAM and BLOSUM, respectively.

### Import the package first

# Import the package
library(kmeRs)

### Example 1. How to display PAM or BLOSUM matrix used for calculation?

Simply apply the kmeRs_similarity_matrix function and mark as an input the vector contains the nucleotides letters for witch the score should be calculated.

# Simple BLOSUM62 similarity matrix for all DNA nucleotides
result <- kmeRs_similarity_matrix(kmers_given = c("A", "T", "C", "G"), submat = "BLOSUM62")
# Fancy knitr table
knitr::kable(result)
A T C G
A 4 0 0 0
T 0 5 -1 -2
C 0 -1 9 -3
G 0 -2 -3 6

### 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
result <- kmeRs_similarity_matrix(kmers_given = c("GATTACA"), compare_to = kmers_given , submat = "BLOSUM62")
# Fancy knitr table
knitr::kable(result) 
GATTACA
GATTACA 37
ACAGATT 1
GAATTAC 15
GAAATCT 19
CTATAGA 7
GTACATA 12
AACGATT 4

Now, applying kmeRs_score_and_sort function the total score is calculated and the matrix is sorted by decreasing 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
result <- kmeRs_score_and_sort(result)
# Fancy knitr table
knitr::kable(result)
GATTACA score_total
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
result <- kmeRs_similarity_matrix(kmers_given = kmers_given, submat = "BLOSUM62")
# Score the matrix and sort by decreasing score
result <- kmeRs_score_and_sort(result)
# Fancy knitr table
knitr::kable(result)
GATTACA ACAGATT GAATTAC GAAATCT CTATAGA GTACATA AACGATT score_total
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 (here, result matrix from example 3) the basic statistics can be calculated as additional columns. 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.

# Score the matrix and sort by decreasing score
result <- kmeRs_statistics(result)
# Fancy knitr table
knitr::kable(result[ , 1:(length(result[1, ])-4)])
GATTACA ACAGATT GAATTAC GAAATCT CTATAGA GTACATA AACGATT score_total
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

## 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. doi: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. doi:10.1016/0022-2836(81)90087-5.

1. BioTesseract Cambridge Bioinformatics Solutions, Cambridgeshire, Cambridge, UK