Download 2. Pam Calculate Matrices

RELATIVE MUTABILITY
If we talk about mutability, usually people know the meaning which is something that changes
from its original condition. But do they know what is mean by Relative Mutability? As described
by Dayhoff et al., relative mutability of each amino acid is the probability that amino acid will
change over a small evolutionary time period. Total numbers of every change that happen are
counted. Not only that, the total number of occurrences of each amino acid is also considered and
the ratio that we got is determined.
To know the whole relative mutability of the sequences of amino acid, we need to do some
calculation and to do this calculation, the relative mutability of the individual amino acids need
to be calculated. Why relative mutability of the individual amino acids need to be calculated?
This is because amino acids are not equally mutable. That is to say, some residues are observed
to mutate more frequently than others per occurrence. This is taken into consideration by
defining the relative mutability of amino acid j as the number of times amino acid j mutated
divided by the number of occurrences of amino acid j. The number of amino acid mutated j
divided by the number of occurrences of amino acid j is also the formula that we will used to
calculate and to know the relative mutability of amino acid j. Usually, after we do calculation to
know the relative mutability of the amino acids and the point accepted mutation matrix, the data
is then taken to be used to calculate the mutation probability matrix.
Relative mutability  [changes] / [occurrences]
Example:
sequence 1
ala
his
val
ala
sequence 2
ala
arg
ser
val
For ala, relative mutability = [1] / [3] = 0.33
For val, relative mutability = [2] / [2] = 1.0
SUBSTITUTION FREQUENCY
A substitution matrix contains values proportional to the probability that amino acid i mutates
into amino acid j for all pairs of amino acids.
Substitution matrices are constructed by assembling a large and diverse sample of verified
pairwise alignments (or multiple sequence alignments) of amino acids.
Substitution matrices should reflect the true probabilities of mutations occurring through a period
of evolution.
Example FG,A
Substitution may occur in A→G or G→A.
Therefore, F G,A = 3
MUTATION PROBABILITY
Just like what we have said before in relative mutability part, mutation probability matrix can be
done by taking the data that we have calculated from the relative mutability. Data from the
relative mutability of the amino acids and the point accepted mutation matrix is used to calculate
the mutation probability matrix.
For example:
FG,A
Mij= (mj*Fij)/ (sum_over_all_iFij)
Mij shows the probability that an original amino acid j (in columns) will be replaced by amino
acid i (in rows) over a defined evolutionary interval.
The entries, Ri,j are the Mi,j values divided by the frequency of occurrence, fi, of residue i.
•
f G = 10 G / 63 residues = 0.1587
•
R G,A = log (2.1/0.1587)
= log(13.2325)
= 1.1216
≈1
QUESTION (RELATIVE MUTABILITY)
1. You are given the sequences below:
There are how many G→X substitutions across all pairs of sequences?