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Lecture 9. Thursday, September 28. Similarity Scores. Introduction to Energy

# Lecture 9. Thursday, September 28. Similarity Scores. Introduction to Energy

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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 1 John Kuriyan : University of California, Berkeley Chem 130/MCB 100A, Fall 2006, Lecture 9 Amino acid substitution score: S ij = 2 log 2 L ij Here i and j are two amino acids, e.g. L and F. L ij is the likelihood, based on observed statistics in aligned sequences, of seeing the i and j residues together in the same column of a sequence alignment. L ij = frequency of seeing the i , j pair in an aligned sequence block expected frequency of seeing them together based on random chance L ij is symmetric. Suppose I=L and j=W L LL = L LW , but L WW L LL That is, Trp is more conserved than leucine but that difference shows up in the diagonal, not the off-diagonal element of the likelihood matrix.

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Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 2 1.The calculation of amino acid substitution frequencies from blocks of aligned sequences If we shuffle all the sequences completely (i.e., randomize the sequence block), then the probability, p i , of finding the i th kind of amino acid at any position is given by: p i = n i N x M For a random distributions, the joint probability that we find the i th type of amino acid at 1 position, and the j th type of amino acid at a 2 nd position is given by: p ij = 2 x p i p j (i j) COLUMNS THAT HAVE BOTH F & L n L = 18 n F = 26 : total number of Fs and Ls in the block
Restricted: For students enrolled in Chem130/MCB100A, UC Berkeley, Fall 2005 ONLY 3 The factor of 2 arises because we don t consider the order: F-L pairing is counted as an equivalent occurance to L-F pairings. That is: p ij is the chance of finding an i-j pairing, and we consider i-j and j-i to be equivalent. For the sequence block in the example, p L = 18 8 x 24 = 0.09375 p F = 25 8 x 24 = 0.1354 Thus the probability of finding an F-L pairing in the randomized alignment is: P FL = 2 x 0.09375 x 0.1354 = 0.0254

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Lecture 9. Thursday, September 28. Similarity Scores. Introduction to Energy

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