# Blosum matrix with probabilities instead of the positive and negative scores

I am trying to find a version of the BLOSUM matrix that has the frequencies instead of the scaled log-odds. i.e. instead of the common version that tells us that the score LEU/ASP is -4, I would like to know the probability of LEU replaced by ASP.

## 1 Answer

Download the BLOSUM data and source-code from here. Unzip the archive which has several files. The file called blosum'XX'.qij will have the co-occurence probabilities, and the subsitution probabilities can be calculated from them.

Also have a look at this article.

• Thank you for the answer and the link. For the benefit of anyone reading this: the frequencies in .qij files still need to be normalized before they can be used as substitution probability since they don't add up to 1 for each column or row (they add up to 1 for the entire matrix). i.e. If I want to know the probability of ALA being replaced by HIS, the table will say it is 0.0011 but actually it is 0.0011/0.0741 (the sum of the frequencies in the ALA column) = 0.014844804318488529 Jun 19, 2014 at 17:20
• So perhaps they are more called cooccurance probability than substitution probabilities. The probability of ALA substutited by HIS is p('His'|'Ala') but the table gives the joint probability p('His', 'Ala'). So we get the conditional probability p('His'|'Ala') = p(His,Ala)/p(Ala) and p(Ala) is basically p(Ala,x) for all x. so it is the sum of the Ala column. Jun 19, 2014 at 17:30
• oh yes you would need the $p_i$ for the calculation. I have not checked if that file exists in this archive. Jun 19, 2014 at 19:23