Examining Substitution Matrices

1. Try running JTT with the -p option to get a substitution matrix:
   
   % ./JTT -p
   
   You may need to make the window wider to fit all the output to screen. The output shows the substitution probabilities for each amino acid evolving into another one after the default evolutionary change of 1% (1 substitution per 100 sites or ``PAM1''). Notice the following points:
   • The order of amino acids at the top. This is the same order of amino acids in columns. Each row gives the probability of that amino acid turning into another amino acid after a certain number of PAMs.
   • That most of the mass is (the biggest numbers are) on the diagonal, meaning that by far the most likely event is for any amino acid to stay the same.
   • The substitution probabilities for one amino acid turning into another are not symmetrical. A turning to R is not the same as R turning to A.
   • If you added up any row, it would be equal to 1. This just means that every amino acid has to turn into some other amino acid or not change at all, no other outcomes are allowed in this evolutionary model.
   • The matrix diagonal is also shown below the matrix. From these numbers you can compute the avergae %ID of a protein evolved according to this model at the given PAM distance, and that is shown at the top.
   • The amino acid composition of the data used to make this matrix is shown at the very bottom.
   
   
   
2. Try a higher PAM distance like so:
   
   % ./JTT -p 15
   
   Look at the top of the output.
   
   
3. Question 3: Does the %ID expected from this much change equal the evolutionary distance?
   
   
4. Question 4: Look at the bottom of the output giving the diagonal of the matrix. Which amino acid is most mutable? Which is least mutable? Please write your answers down.
   
   
5. Try even higher distances Go up in 5s from 15 to 30. eg:
   
   % ./JTT -p 20
   
   Where do you start seeing saturation?
   
   Take a quick look at PAM 100 and PAM 250.
   
   
6. Now try PAM1000. Question 5: What has happened to the substitution probabilities? What are they equal to? What does this mean -- why does it make sense that the substitution probabilities are equal to the stationary amino acid compositions regardless of the starting base?