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
rhoparameter 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.