Substitution matrix: Difference between revisions

Revision as of 01:22, 28 November 2018

Revision as of 01:39, 9 March 2019

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We express the [[probability|probabilities]] of transformation in what are called [[log-odds]] [[Score (statistics)|score]]s. The scores matrix S is defined as

: <math>S_{i,j} = \log \frac {p_i \cdot M_{i,j}} {p_i \cdot p_j} = \log \frac {M_{i,j}}{p_j} = \log \frac {observed\;text{observed frequency} }{expected\;text{expected frequency}},</math>

where <math>M_{i,j}</math> is the probability that amino acid <math>i</math> transforms into amino acid <math>j</math>, and <math>p_i</math>, <math>p_j</math> are the frequencies of amino acids ''i'' and ''j''. The base of the logarithm is not important, and you will often see the same substitution matrix is often expressed in different bases.

=== PAM ===