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Calculation of Log Odds and Odds Scores by the BLOSUM Method

In one column of an alignment of a set of related, similar sequences, amino acid D changes to amino acid E at a frequency of 0.10, and the number of times this change is expected based on the number of occurrences of D and E in the column is 0.05.

  1. What is the odds score of finding a D-to-E substitution in an alignment?
  2. What is the log odds score for the D-to-E substitution in bits? (Note: log to base 2 = natural log / 0.693.)
  3. What would be the entry in the BLOSUM amino acid scoring matrix for this substitution? Compare your result to the actual entry in the BLOSUM62 matrix.
  4. In the same column, D does not change at all at a frequency of 0.80, and the expected frequency of D not changing is 0.10. Calculate the corresponding log odds score and the BLOSUM62 entry for D not changing.

Log Odds and Odds Score of a Short Alignment

  1. Using the above values, what is the log odds score of the following alignment in bits?
    (Note that these two short sequences have very low sequence complexity by having only two amino acids of the available 20. These sequences were chosen to simplify the calculations. Alignments of low complexity sequences can give quite high scores that are misleading of the sequence similarity, as discussed in Chapter 6.)
  2. What is the odds score of the above alignment?


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