gd {agvgd} R Documentation

## Grantham deviation

### Description

This function calculates the Grantham deviation (\mathrm{gd}):

\mathrm{gd} = \rho \left((\alpha\ \mathrm{dev}^2(c_x, c_{min}, c_{max}) + \beta\ \mathrm{dev}^2(p_x, p_{min}, p_{max}) + \gamma\ \mathrm{dev}^2(v_x, v_{min}, v_{max})\right)^\frac{1}{2}

where c_x is the value for composition c of amino acid x, i.e. the atomic weight ratio of hetero (noncarbon) elements in end groups or rings to carbons in the side chain; p_x is the value for polarity p of amino acid x; and, v_x is the value for molecular volume v of amino acid x.

c_x, p_x and v_x are looked up in grantham::amino_acids_properties based on the amino acid identities passed in x. The function \mathrm{dev} is implemented in dev(). Remaining variables in the equation are arguments to gd() and hence are explained below in the Arguments section.

### Usage

gd(
x,
c_min,
c_max,
p_min,
p_max,
v_min,
v_max,
alpha = 1.833,
beta = 0.1018,
gamma = 0.000399,
rho = 50.723
)


### Arguments

 x A character vector of one-letter amino acid codes, indicating missense substitutions. c_min Amino acid composition, minimum value. c_max Amino acid, composition, maximum value. p_min Amino acid polarity, minimum value. p_max Amino acid polarity, maximum value. v_min Amino acid molecular volume, maximum value. v_max Amino acid molecular volume, maximum value. alpha The constant \alpha in Grantham's equation. It is the square inverse of the mean of the composition property. beta The constant \beta in Grantham's equation. It is the square inverse of the mean of the polarity property. gamma The constant \gamma in Grantham's equation. It is the square inverse of the mean of the molecular volume property. rho Grantham's distances reported in Table 2, Science (1974). 185(4154): 862–4 by R. Grantham, are scaled by a factor (here named \rho) such that the mean value of all distances are 100. The rho parameter allows this factor \rho to be changed. By default \rho=50.723, the same value used by Grantham. This value is originally mentioned in the caption of Table 2 of the aforementioned paper.

### Value

A numeric vector of Grantham deviations. Each deviation corresponds to one of the amino acids indicated in x.

gv(), dev()
gd('S', c_min = 0.39, c_max = 0.74, p_min =4.9, p_max =8.6, v_min = 3, v_max = 32.5)