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CHAPTER 4 PROBLEMS


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3. A Bayesian method for estimating evolutionary distance between nucleic acid sequences.

A great deal can be learned about the use of PAM matrices using the DNA PAM matrices as an example (p. 95).
1. First an alignment between two DNA sequences without any gaps is found. The object is to figure out how long ago (in PAM units of time where 1 PAM equals 10 million years) the sequences might have diverged to give the observed variation (the number of mismatches) in the alignment.
2. A PAM1 matrix is made for an expected model of evolution, e.g., each base can change into any other base and the overall rate of change in the sequences is 1% (see Table 3.4, p. 107).
3. For longer periods, e.g., PAM10, the PAM1 matrix is multiplied by itself n times (10 for PAM10).
4. The more time, the greater the amount of change expected and these changes are reflected in the log odds scores of each particular PAM matrix. These are shown in the table of nucleic acid substitution matrices (Table 3.6 on p. 108) that assumes a uniform rate of mutation among nucleotides and that a 1% change in sequence represents 10 my (million years) of mutation.
5. Examine the substitution rates in the following sequences and decide approximately how many years ago they became separated.
  AGTTG ACTAA GCCAG GTCAC
  ACTTG CCGGA GCCTC GTGTC
What log odds and odds scores are found for the alignment for PAM distances of 10, 25, 50, 100, and 125, and which score is highest?
Add up the odds scores and determine the ratio of each to the total. What is the sum of these numbers, and what do these numbers represent?

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