The goal of {grantham}
is to provide a minimal set of routines to
calculate the Grantham distance (Grantham
(1974)).
The Grantham distance attempts to provide a proxy for the evolutionary distance between two amino acids based on three key side chain chemical properties: composition, polarity and molecular volume. In turn, evolutionary distance is used as a proxy for the impact of missense substitutions. The higher the distance, the more deleterious the substitution is expected to be.
Install {grantham}
from CRAN:
install.packages("grantham")
Grantham distance between two amino acids:
library(grantham)
grantham_distance(x = "Ser", y = "Phe")
#> # A tibble: 1 × 3
#> x y d
#> <chr> <chr> <dbl>
#> 1 Ser Phe 155
The function grantham_distance()
is vectorised with amino acids being
matched element-wise to form pairs for comparison:
grantham_distance(x = c("Ser", "Arg"), y = c("Phe", "Leu"))
#> # A tibble: 2 × 3
#> x y d
#> <chr> <chr> <dbl>
#> 1 Ser Phe 155
#> 2 Arg Leu 102
The two vectors of amino acids must have compatible sizes in the sense of vec_recycle() for element recycling to be possible, i.e., either the two vectors have the same length, or one of them is of length one, and it is recycled up to the length of the other.
# `'Ser'` is recycled to match the length of the second vector, i.e. 3.
grantham_distance(x = "Ser", y = c("Phe", "Leu", "Arg"))
#> # A tibble: 3 × 3
#> x y d
#> <chr> <chr> <dbl>
#> 1 Ser Phe 155
#> 2 Ser Leu 145
#> 3 Ser Arg 110
Use the function amino_acid_pairs()
to generate all 20 x 20 amino acid
pairs:
aa_pairs <- amino_acid_pairs()
aa_pairs
#> # A tibble: 400 × 2
#> x y
#> <chr> <chr>
#> 1 Ser Ser
#> 2 Ser Arg
#> 3 Ser Leu
#> 4 Ser Pro
#> 5 Ser Thr
#> 6 Ser Ala
#> 7 Ser Val
#> 8 Ser Gly
#> 9 Ser Ile
#> 10 Ser Phe
#> # ℹ 390 more rows
And now calculate all Grantham distances for all pairs aa_pairs
:
grantham_distance(x = aa_pairs$x, y = aa_pairs$y)
#> # A tibble: 400 × 3
#> x y d
#> <chr> <chr> <dbl>
#> 1 Ser Ser 0
#> 2 Ser Arg 110
#> 3 Ser Leu 145
#> 4 Ser Pro 74
#> 5 Ser Thr 58
#> 6 Ser Ala 99
#> 7 Ser Val 124
#> 8 Ser Gly 56
#> 9 Ser Ile 142
#> 10 Ser Phe 155
#> # ℹ 390 more rows
Because distances are symmetric, and for pairs formed by the same amino acid are trivially zero, you might want to exclude these pairs:
# `keep_self = FALSE`: excludes pairs such as ("Ser", "Ser")
# `keep_reverses = FALSE`: excludes reversed pairs, e.g. ("Arg", "Ser") will be
# removed because ("Ser", "Arg") already exists.
aa_pairs <- amino_acid_pairs(keep_self = FALSE, keep_reverses = FALSE)
# These amino acid pairs are the 190 pairs shown in Table 2 of Grantham's
# original publication.
aa_pairs
#> # A tibble: 190 × 2
#> x y
#> <chr> <chr>
#> 1 Ser Arg
#> 2 Ser Leu
#> 3 Ser Pro
#> 4 Ser Thr
#> 5 Ser Ala
#> 6 Ser Val
#> 7 Ser Gly
#> 8 Ser Ile
#> 9 Ser Phe
#> 10 Ser Tyr
#> # ℹ 180 more rows
# Grantham distance for the 190 unique amino acid pairs
grantham_distance(x = aa_pairs$x, y = aa_pairs$y)
#> # A tibble: 190 × 3
#> x y d
#> <chr> <chr> <dbl>
#> 1 Ser Arg 110
#> 2 Ser Leu 145
#> 3 Ser Pro 74
#> 4 Ser Thr 58
#> 5 Ser Ala 99
#> 6 Ser Val 124
#> 7 Ser Gly 56
#> 8 Ser Ile 142
#> 9 Ser Phe 155
#> 10 Ser Tyr 144
#> # ℹ 180 more rows
The Grantham distance $d_{i,j}$ for two amino acids $i$ and $j$ is:
$$d_{i,j} = \rho (\alpha (c_i-c_j)^2+\beta (p_i-p_j)^2+ \gamma (v_i-v_j)^2)^{1/2}\ .$$
The distance is based on three chemical properties of amino acid side chains:
We provide a data set with these properties:
amino_acids_properties
#> # A tibble: 20 × 4
#> amino_acid c p v
#> <chr> <dbl> <dbl> <dbl>
#> 1 Ser 1.42 9.2 32
#> 2 Arg 0.65 10.5 124
#> 3 Leu 0 4.9 111
#> 4 Pro 0.39 8 32.5
#> 5 Thr 0.71 8.6 61
#> 6 Ala 0 8.1 31
#> 7 Val 0 5.9 84
#> 8 Gly 0.74 9 3
#> 9 Ile 0 5.2 111
#> 10 Phe 0 5.2 132
#> 11 Tyr 0.2 6.2 136
#> 12 Cys 2.75 5.5 55
#> 13 His 0.58 10.4 96
#> 14 Gln 0.89 10.5 85
#> 15 Asn 1.33 11.6 56
#> 16 Lys 0.33 11.3 119
#> 17 Asp 1.38 13 54
#> 18 Glu 0.92 12.3 83
#> 19 Met 0 5.7 105
#> 20 Trp 0.13 5.4 170
If you want to calculate the Grantham distance from these property
values you may use the function grantham_equation()
.
Other sources we’ve found in the R ecosystem that also provide code for calculation of the Grantham distance:
calculate_grantham()
, see
Fetch_Grantham.R.{midasHLA}
package includes the unexported function
distGrantham()
in
utils.R.{HLAdivR}
package exports a data set with the Grantham distances
in the format of a matrix, see
data.R.{MSA2dist}
by Kristian K. Ullrich provides
the function
aastring2dist()
.Please note that the {grantham}
package is released with a
Contributor Code of
Conduct.
By contributing to this project, you agree to abide by its terms.
1. Grantham, R. Amino acid difference formula to help explain protein evolution. Science 185, 862–864 (1974). doi: 10.1126/science.185.4154.862.
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