Bios2cor (version 2.1)

mip: Mutual Information product (MIP) function

Description

Calculates a corrected mutual information score (MIP), by substraction of the average product from the probability of joint occurrence of events.

Usage

mip(align, gap_ratio = 0.2)

Arguments

align

An object of class 'align' created by the import.msf or the import.fasta function from a sequence alignment

gap_ratio

Numeric value between 0 and 1 indicating the maximal gap ratio at a given position in the MSA for this position to be taken into account. Default is 0.2, positions with more than 20 percent of gaps will not be taken into account in the analysis. When gap_ratio is 1 or close to 1, only positions with at least 1 aa are taken into account (positions with only gaps are excluded).

Value

A list of two elements which are numerical matrices containing the MIP scores and Z-scores for each pair of elements.

Details

The MIp score at position [i,j] has been computed with the following formula :

$${MIp(i,j)} = MI(i,j) - \frac{MI(i,\bar{j})MI(\bar{i},j)}{<MI>}$$

with :

• \({MI(i,j) = \sum_{x,y}^{ } p_{x,y}(i,j) ln\frac{p_{x,y}(i,j)}{p_{x}(i)p_{y}(j)}}\)

• \(MI(i,\bar{j}) = \frac{1}{n-1} \sum_{j \neq i}^{ } MI(i,j)\)

• \(MI(\bar{i},j) = \frac{1}{n-1} \sum_{i \neq j}^{ } MI(i,j)\)

• \(<MI> = \frac{2}{n(n-1)} \sum_{i,j}^{ }MI(i,j)\)

and where \(p_{x,y}(i,j)\) is the frequency of the amino acid pair (x,y) at positions i and j.

N.B. this formula has been widely applied in the field of sequence correlation/covariation but favors pairs with high entropy.

References

Dunn SD, Wahl LM, Gloor GB. Mutual information without the influence of phylogeny or entropy dramatically improves residue contact prediction. Bioinfor;atics 2008;24:333-340. Martin LC, Gloor GB, Dunn SD, Wahl LM. Using infor;ation theory to search for co-evolving residues in proteins. Bioinformatics 2005;21:4116-4124.

Examples

# NOT RUN {
  #Importing MSA file
  align <- import.fasta(system.file("msa/toy2_align.fa", package = "Bios2cor"))

  #Creating correlation object with MIP method for positions with gap ratio < 0.2 (Default) 
  mip <- mip(align)
# }