grantham_equation: Grantham distance

In grantham: Calculate the Grantham Distance

Grantham distance

Description

This function calculates Grantham's distance d_{i,j} between two amino acids (i and j) based on their chemical properties:

d_{i,j} = \rho ((\alpha (c_i-c_j)^2 + \beta (p_i-p_j)^2 + \gamma (v_i-v_j)^2)^\frac{1}{2}

This calculation is based on three amino acid side chain properties that were found to be the three strongest correlators with the relative substitution frequency (RSF) (references cited in Grantham (1974)), namely:

• composition c, meaning the atomic weight ratio of hetero (noncarbon) elements in end groups or rings to carbons in the side chain.

• polarity p;

• molecular volume v.

Each property difference is weighted by dividing by the mean distance found with it alone in the formula. The constants \alpha, \beta and \gamma are squares of the inverses of mean distances of each property, respectively.

The distances reported by Grantham (1974) are further scaled by a factor —here coined \rho— such that the mean of all distances is 100. Although this factor is not explicitly included in Grantham's distance formula, it is actually used for calculating the amino acid pair distances reported in Table 2 of Grantham's paper. So, for all intents and purposes, this factor should be regarded as part of the formula used to calculate Grantham distance, and therefore we include it explicitly in the equation above.

If you want to calculate Grantham's distance right off from the identity of the amino acids, instead of using their chemical properties, then use grantham_distance().

Usage

grantham_equation(
  c_i,
  c_j,
  p_i,
  p_j,
  v_i,
  v_j,
  alpha = 1.833,
  beta = 0.1018,
  gamma = 0.000399,
  rho = 50.723
)

Arguments

c_i	composition value for the ith amino acid.
c_j	composition value for the jth amino acid.
p_i	polarity value for the ith amino acid.
p_j	polarity value for the jth amino acid.
v_i	molecular volume value for the ith amino acid.
v_j	molecular volume value for the jth amino acid.
alpha	The constant \alpha in the equation of Grantham's paper, in page 863.
beta	The constant \beta in the equation of Grantham's paper, in page 863.
gamma	The constant \gamma in the equation of Grantham's paper, in page 863.
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 double vector of Grantham's distances.

See Also

Check amino_acids_properties for a table of the three property values that can be used with this formula. This data set is from Table 1, Science (1974). 185(4154): 862–4 by R. Grantham.

grantham documentation built on Sept. 11, 2024, 8:20 p.m.