Amino acid substitution matrices from protein blocks

[edit] Computing a log odds matrix

f_ij: The total number of amino acid i, j pairs (1 <= j <= i <= 20)

Observed probability of occurrence for each i, j pair:

Failed to parse (Cannot write to or create math temp directory): q_{ij} = f_{ij} / \sum_{i=1}^{20} \sum_{j=1}^{i} f_{ij}

Probability of occurrence of the ith amino acid in an i, j pair is:

Failed to parse (Cannot write to or create math temp directory): p_i = q_{ii} + \sum_{j \neq i} q_{ij} / 2

Expected probability of occurrence Failed to parse (Cannot write to or create math temp directory): e_{ij}

for each i, j pair is then Failed to parse (Cannot write to or create math temp directory): p_i p_j
for Failed to parse (Cannot write to or create math temp directory): i = j
and Failed to parse (Cannot write to or create math temp directory): p_i p_j + p_j p_i = 2 p_i p_j
for Failed to parse (Cannot write to or create math temp directory): i \neq j

Odds ratio: Failed to parse (Cannot write to or create math temp directory): q_{ij} / e_{ij}

Log odds ratio: Failed to parse (Cannot write to or create math temp directory): s_{ij} = log_2(q_{ij} / e_{ij}) , multiplied by a scaling factor of 2 and rounded to the nearest integer value

• Failed to parse (Cannot write to or create math temp directory): s_{ij} = 0

-- Observed frequencies are as expected

• Failed to parse (Cannot write to or create math temp directory): s_{ij} < 0

-- Less than expected

• Failed to parse (Cannot write to or create math temp directory): s_{ij} > 0

-- More than expected

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