Why PAM Works. An In-Depth Look at Scoring Matrices and Algorithms. Michael Darling Nazareth College. The Origin: Sequence Alignment

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1 Why PAM Works An In-Depth Look at Scoring Matrices and Algorithms Michael Darling Nazareth College The Origin: Sequence Alignment Scoring used in an evolutionary sense Compare protein sequences to find interspecies relationships Also find protein relationships within an organism Helps to explain life as we know it

2 Introduction: Scoring Sequences Find the relationship between sequences Compare matching and unmatching amino acids Simple Example: Sequences ACTCCA and GCACTA First, align the sequences side by side: ACTCCA GCACTA Use scoring system: Match=1, Mismatch=-1 First column is mismatch, second is match, etc. There are 3 matches and 3 mismatches, giving a score of: =0 With no mismatch penalty, score is 3 Gap Penalties Insertion of gaps provides a better relation Used to account for insertions or deletions Penalties include a subtraction from the score for the start of a gap, as well as for the length Consider the same example, but add gaps: ACTCCA GCACT A The creation of two gaps made a fourth match, but the score may not change depending on the scale of the penalty If origin penalty is -1 and length is 0, then we have 4 matches minus 2 gaps, giving us a score of 2. If origin penalty is -1 and length is length/2, we have 4 matches minus 2 gaps of length 2 (minus one each), bringing the score back to zero.

3 Creation of a Scoring Matrix Start by deriving a PAM (Accepted Point Mutation) Matrix M Ratio = Use data to find probability of protein substitutions in sequences Divide number of substitutions of specific amino acid by relative mutability ab where M ab is probability that the substitution can happenin nature, pb is the frequency of pb Relative mutability is the total number of times substituted by ANY other amino acid Substitutions P = Rl. Mutability occurenceof b Normalize this value with the probability of occurrence of the amino acids Resulting value is probability that a column amino acid is substituted by its corresponding row amino acid with 1% divergence This 1% substitution rate corresponds to one PAM unit, thus giving us PAM-1 PAM-1 A R N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V This PAM-1 Matrix was obtained from M.O. Dayhoff and colleagues, 1978

4 PAM Matrices on a Larger Scale The corresponding number, or PAM unit, of a PAM matrix represents the number of mutations per 100 residues How do we come up with PAM-2, PAM-3, PAM- 100, PAM-250?? Just use Matrix Multiplication: PAM-x = (PAM-1) x Questions to consider: For PAM-2, why do we use matrix multiplication and not just square each entry? The probability of A remaining A after one substitution squared should be the probability of A remaining A with two substitutions by the laws of probability, right? Why PAM-x = (PAM-1) x PAM Matrices consider probabilities of mutations Matrix Multiplication: Simple Example: Alanine(A) and Arginine(R).95.04» Assume P(A-A)=.95, P(A-R)=.04, P(R-A)=.05, P(R-R)= = » From this we can see that PAM takes into consideration not only A remaining A with 2 substitutions, but adds to this the probability that A is substituted by R, which is then in turn substituted by A, thus making the original A an A after 2 mutations. Note: Numbers used in example are arbitrary

5 Log-Odds Score Matrix Odds Ratio: R = M» where R is our desired ratio, M ab is the probability that the ab p ab mutation is accepted by nature, p b is the frequency of b occurrence of b Dayhoff took 10 times the log of this result to get a score for each mutation» Logs are used for counting purposes» Logs are more efficient than multiplying at each position S ( a, b) = 10 log( R) Quick Overview: Needleman & Wunsch Set up matrix for optimization of alignment Want to minimize gaps but maximize matches 4 possibilities at each point in matrix:» Match, Mismatch, Gap in Seq. 1, Gap in Seq. 2 Scores are input into matrix, looking to maximize score Quick Model of Process: Seq.1 Seq.2 Diagonal lines are alignments, vertical are gaps in sequence 1, horizontal are gaps in sequence 2

6 Sources Krane, Dan E. and Michael L. Raymer. Fundamental Concepts of Bioinformatics. San Francisco: Pearson Education Inc, 2003 Pevsner, Jonathon. Bioinformatics and Functional Genomics. New Jersey: John Wiley & Sons, 2003