Substitution Matrix
Requirement
1. Must be able to give score>0
2. Should give scores <=0 for random sequences
Empirical Solution
● Estimate scores based on observed frequencies from sequence alignments
Real Substitution Matrix
Expected Value: The expected value per AA pair between random sequences
Here, it is -0.5206
Entropy: The amount of information on average from a AA pair.
Here it is 0.6979
● High entropy=mismatches penalized more
● Low entropy=permits more distant alignments
● BLOSUM/PAM with similar entropy~equivalent Calculating Scoring Matrix
𝑆𝑐𝑜𝑟𝑒(𝑎 → 𝑏) = λ𝑙𝑜𝑔
𝑃(𝑎→𝑏)
𝑃(𝑎)*𝑃(𝑏)
Numerator=> observed
Denominator=> Expected
ex) Lets take an example:Proline -> Glycine
𝑃(𝑎 → 𝑏) = probability Proline is substituted by glycine
𝑃(𝑎) = Probability a randomly selected amino acid is Proline
𝑃(𝑏) = Probability a randomly selected amino acid is Glycine
These are calculated form the same source
Substitutiution Matrix
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