Algorithmic Approaches for Biological Data, Lecture #20
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1 Algorithmic Approaches for Biological Data, Lecture #20 Katherine St. John City University of New York American Museum of Natural History 20 April 2016
2 Outline Aligning with Gaps and Substitution Matrices K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
3 Outline Aligning with Gaps and Substitution Matrices Global versus Local Alignment K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
4 Outline Aligning with Gaps and Substitution Matrices Global versus Local Alignment Searching Graphs: Breadth First & Depth First K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
5 Pairwise Sequence Alignment A G A G A -1 1 G -2 G -3 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
6 Pairwise Sequence Alignment Pictorially: A G A G A -1 1 G -2 G -3 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
7 Pairwise Sequence Alignment Pictorially: A G A G A -1 1 G -2 G -3 As equations: where: K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
8 Aligning with Gaps and Substitution Matrices The basic dynamic programming format can be adjusted for different gaps and substitutions models. where: K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
9 Aligning with Gaps and Substitution Matrices The basic dynamic programming format can be adjusted for different gaps and substitutions models. δ: the gap penalty where: K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
10 Aligning with Gaps and Substitution Matrices The basic dynamic programming format can be adjusted for different gaps and substitutions models. δ: the gap penalty σ: scores matches/mismatches. where: K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
11 Gaps Are Treated Equally Commonly use affine gap penalty function: A G A G A -1 1 G -2 G -3 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
12 Gaps Are Treated Equally A G A G A -1 1 G -2 G -3 Commonly use affine gap penalty function: h: penalty associated with opening a gap g: (smaller) penalty associated with extending the gap. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
13 Gaps Are Treated Equally A G A G A -1 1 G -2 G -3 Commonly use affine gap penalty function: h: penalty associated with opening a gap g: (smaller) penalty associated with extending the gap. To implement this efficiently, use 2 additional matrices that keeps track of the gaps (one for each sequence). K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
14 Affine Gap Burr Settles, U Wisconsin, 2008 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
15 Using Substitution Matrices Can view σ(i, j) as a substitution matrix. A C G T A C G T K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
16 Using Substitution Matrices A C G T A C G T Can view σ(i, j) as a substitution matrix. Substitution matrices commonly used for protein seqeunces. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
17 Using Substitution Matrices A C G T A C G T Can view σ(i, j) as a substitution matrix. Substitution matrices commonly used for protein seqeunces. PAM = Percent Accepted Mutation K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
18 Using Substitution Matrices A C G T A C G T Can view σ(i, j) as a substitution matrix. Substitution matrices commonly used for protein seqeunces. PAM = Percent Accepted Mutation Dayhoff et al., 1978 Used for closely related protein sequences Based on global alignment K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
19 Using Substitution Matrices A C G T A C G T Can view σ(i, j) as a substitution matrix. Substitution matrices commonly used for protein seqeunces. PAM = Percent Accepted Mutation Dayhoff et al., 1978 Used for closely related protein sequences Based on global alignment BLOSUM = Blocks Substitution Matrix K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
20 Using Substitution Matrices A C G T A C G T Can view σ(i, j) as a substitution matrix. Substitution matrices commonly used for protein seqeunces. PAM = Percent Accepted Mutation Dayhoff et al., 1978 Used for closely related protein sequences Based on global alignment BLOSUM = Blocks Substitution Matrix Henikoff & Henikoff, 1992 Used for more divergent sequences Based on local alignment K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
21 Global versus Local Alignment Global: Needleman & Wunsch, Local: Smith & Waterman, Instead of looking for the global best score, look for the best score for subsequences of the initial sequences. Paul Reiners, IBM, 2008 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
22 Global versus Local Alignment Paul Reiners, IBM, 2008 Global: Needleman & Wunsch, Local: Smith & Waterman, Instead of looking for the global best score, look for the best score for subsequences of the initial sequences. Examples: finding motifs (conserved patterns) across sequences, comparing sequences against longer sequences (e.g. blast search). K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
23 Smith-Waterman Algorithm The equation is slightly different: Paul Reiners, IBM, 2008 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
24 Smith-Waterman Algorithm The equation is slightly different: σ(i, j) + s(i 1, j 1) δ + s(i, j 1) s(i, j) = max δ + s(i 1, j) 0 Paul Reiners, IBM, 2008 Initialize: first row and first column set to 0 s Traceback: find maximum value of s(i, j) anywhere in the the matrix, stop when we get to a cell with 0. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
25 Smith-Waterman Algorithm Paul Reiners, IBM, 2008 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
26 In Pairs: Local Alignment A A G A T T A A G Use σ from Monday, but δ = 2. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
27 In Pairs: Local Alignment A A G A T T A A G Use σ from Monday, but δ = 2. What are the best local alignments? K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
28 In Pairs: Local Alignment A A G A T 0 T 0 A 0 A 0 G 0 Use σ from Monday, but δ = 2. What are the best local alignments? K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
29 In Pairs: Local Alignment A A G A T T A A G Use σ from Monday, but δ = 2. What are the best local alignments? K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
30 In Pairs: Searching Graphs Develop a strategy to visit every node of the graph (i.e. what data structures are needed?) Bastert et al., 2002 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
31 In Pairs: Searching Graphs Develop a strategy to visit every node of the graph (i.e. what data structures are needed?) The bookkeeping is important. Bastert et al., 2002 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
32 In Pairs: Searching Graphs Develop a strategy to visit every node of the graph (i.e. what data structures are needed?) The bookkeeping is important. Bastert et al., 2002 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
33 In Pairs: Searching Graphs Two common strategies: Bastert et al., 2002 K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
34 In Pairs: Searching Graphs Bastert et al., 2002 Two common strategies: Breadth First Search (BFS): visit all the neighbors, then visit all the neighbors neighbors, etc. Depth First Search (DFS): for each neighbor, visit its neighbors, and continue as far down as possible. Bookkeeping is important: Keep a To Do list (priority queue) of nodes still to visit. Mark nodes as you visit them, so, you know not to visit again. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
35 Recap Dynamic Programming: will do local & global alignments in lab today. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
36 Recap Dynamic Programming: will do local & global alignments in lab today. More on searching graphs on Monday. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
37 Recap Dynamic Programming: will do local & global alignments in lab today. More on searching graphs on Monday. lab reports to K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
38 Recap Dynamic Programming: will do local & global alignments in lab today. More on searching graphs on Monday. lab reports to Challenges available at rosalind.info. K. St. John (CUNY & AMNH) Algorithms #20 20 April / 16
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