#7 Still more DP, Scoring Matrices 9/5/07

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1 #7 Still more DP, Scoring Matrices 9/5/7 BB 444/544 Lecture 7 Still more: Dynamic Programming Global vs Local lignment Scoring Matrices & lignment Statistics BLS nope #7_Sept5 Required Reading (before lecture) Last week: - for Lectures 4-7 Pairwise Sequence lignment, Dynamic Programming, Global vs Local lignment, Scoring Matrices, Statistics Xiong: hp 3 Eddy: What is Dynamic Programming? 4 Nature Biotechnol :99 Wed Sept 5 - for Lecture 7 & Lab 3 Database Similarity Searching: BLS hp 4 - pp 5-6 Fri Sept - for Lecture 8 BLS variations; BLS vs FS hp 4 - pp 5-6 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 ssignments & nnouncements hp 3- Sequence lignment ues Sept 4 - Lab # Exercise Writeup due by 5 PM Send via to Pete Zaback petez@iastate.edu (For now, no late penalty - just send SP) Wed Sept 5 - Notes for Lecture 5 posted online - HW# posted online & sent via & handed out in class Fri Sept 4 - HW# Due by 5 PM Fri Sept - Exam # BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 SEION II SEQUENE LIGNMEN Xiong: hp 3 Pairwise Sequence lignment Evolutionary Basis Sequence Homology versus Sequence Similarity Sequence Similarity versus Sequence Identity Methods - cont Scoring Matrices Statistical Significance of Sequence lignment dapted from Brown and aragea, 7, with some slides from: ltman, Fernandez-Baca, Batzoglou, raven, Hunter, Page. BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 4 Methods Global and Local lignment lignment lgorithms Dot Matrix Method Dynamic Programming Method - cont Gap penalities DP for Global lignment DP for Local lignment Scoring Matrices mino acid scoring matrices PM BLOSUM omparisons between PM & BLOSUM Statistical Significance of Sequence lignment Global vs Local lignment Global alignment Finds best possible alignment across entire length of sequences ligned sequences assumed to be generally similar over entire length Local alignment Finds local regions with highest similarity between sequences ligns these without regard for rest of sequence Sequences are not assumed to be similar over entire length BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 5 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 6 BB 444/544 Fall 7 Dobbs

2 #7 Still more DP, Scoring Matrices 9/5/7 Global vs Local lignment - example Global alignment GGGG -G---G--G GGGG -GG-----G = GGGG = GGG Local alignment GGGG -GG-G---- Which is better? Global vs Local lignment Which should be used when? It is critical to choose correct method! Global lignment vs Local lignment? Shout out the answers!! Which should we use for?. Searching for conserved motifs in DN or protein sequences?. ligning two closely related sequences with similar lengths? 3. ligning highly divergent sequences? 4. Generating an extended alignment of closely related sequences? 5. Generating an extended alignment of closely related sequences with very different lengths? Hmmm - well work on that Excellent! BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 7 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 8 Global vs Local lignment Which should be used when? It is critical to choose correct method! Global lignment vs Local lignment? Shout out the answers!! Which should we use for?. Searching for conserved motifs in DN or protein sequences? Local. ligning two closely related sequences with similar lengths? Global 3. ligning highly divergent sequences? Local (at least initially) 4. Generating an extended alignment of closely related sequences? Global 5. Generating an extended alignment of closely related sequences with very different lengths? Hmmm - well work on that lignment lgorithms 3 major methods for pairwise sequence alignment:. Dot matrix analysis - practice in HW. Dynamic programming - more today & in HW 3. Word or k-tuple methods (later, in hp 4) BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 9 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 Dynamic Programming For Pairwise sequence alignment Idea: Display one sequence above another with spaces inserted in both to reveal similarity G G Global lignment: Scoring GG-GG -G-G-G---- Reward for matches: α Mismatch penalty: β Space/gap penalty: γ Score = αw βx y w = #matches x = #mismatches y = #spaces Note: I changed symbols & colors on this slide! BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 BB 444/544 Fall 7 Dobbs

3 #7 Still more DP, Scoring Matrices 9/5/7 Global lignment: Scoring lignment lgorithms Reward for matches: Mismatch penalty: - Space/gap penalty: -5 G G G - G G G Global: Needleman-Wunsch Local: Smith-Waterman Both NW and SW use dynamic programming Variations: Gap penalty functions Scoring matrices Note: I changed symbols & colors on this slide! otal = We could have done better!! BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 4 Dynamic Programming - Key Idea: he score of the best possible alignment that ends at a given pair of positions (i, j) is equal to: the score of best alignment ending just previous to those two positions (i.e., ending at i-, j-) PLUS the score for aligning x i and y j Global lignment: DP Problem Formulation & Notations Given two sequences (strings) X = x x x N of length N x = G N = 3 Y = y y y M of length M y = M = 4 onstruct a matrix with (N+) x (M+) elements, where S(i,j) = Score of best alignment of x[..i]=x x x i with y[..j]=y y y j x x x 3 Which means: S(i,j) = Score of best alignment of a prefix of X and a prefix of Y y y y 3 S(,3) = score of best alignment of G (x x ) to (y y y 3 ) y 4 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 5 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 6 Dynamic Programming - 4 Steps:. Define score of optimal alignment, using recursion. Initialize and fill in a DP matrix for storing optimal scores of subproblems, by solving smallest subproblems first (bottom-up approach) 3. alculate score of optimal alignment(s) 4. race back through matrix to recover optimal alignment(s) that generated optimal score BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 7 Define: - Define Score of Optimal lignment using Recursion S(i, j) = Score of optimal alignment of x..i and y..j Initial conditions: x..i = Prefix of length i of x y.. j = Prefix of length j of y S(i,) = "i #$ S(, j) = " j #$ Recursive definition: For i N, j M: % S(i ", j ") +# (x i,y j ) S(i, j) = max& S(i ", j) "$ ( S(i, j ") "$ α = Match Reward β = Mismatch Penalty γ = Gap penalty σ(x i,y j ) = α or β γ = Gap penalty BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 8 BB 444/544 Fall 7 Dobbs 3

4 #7 Still more DP, Scoring Matrices 9/5/7 - Initialize & Fill in DP Matrix for Storing Optimal Scores ofsubproblems onstruct sequence vs sequence matrix Fill in from [,] to [N,M] (row by row), calculating best possible score for each alignment ending at residues at [i,j] N S(,)= S(i,j) How do we calculate S(i,j)? i.e., Score for alignment of x[..i] to y[..j]? of 3 cases optimal score for this subproblem: x i aligns to y j x i aligns to a gap y j aligns to a gap x x... x i- x i y y... y j- y j S(i-,j-) + σ(x i,y j ) x x... x i- x i y y... y j S(i-,j) x x... x i y y... y j- y j S(i,j-) M S(N,M) BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 9 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 Specific Example: ase : Line up x i with y Scoring onsequence? j i - i x: - - G y: Mismatch Penalty j - j ase : Line up x i with space i - i x: - y: - G - j ase 3: Line up y j with space i x: - y: - - G j - j Note: I changed sequences on this slide (to match the rest of DP example) Space Penalty Space Penalty BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 α = Match Reward β = Mismatch Penalty γ = Gap penalty Ready? Fill in DP Matrix Keep track of dependencies of scores (in a pointer matrix) N S(,)= + σ(x i,y j ) = α or β M Initialization S(i,) = "i #$ S(, j) = " j #$ S(i-,j-) S(i,j-) S(i-,j) S(i,j) S(N,M) Recursion % S(i ", j ") +# (x i, y j ) S(i, j) = max& S(i ", j) "$ ( S(i, j ") "$ BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 Fill in the DP matrix!! G G alculate Score S(N,M) of Optimal lignment - for Global lignment G G + for match, - for mismatch, -5 for space + for match, - for mismatch, -5 for space BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 4 BB 444/544 Fall 7 Dobbs 4

5 #7 Still more DP, Scoring Matrices 9/5/7 4- race back through matrix to recover optimal alignment(s) that generated the optimal score How? "Repeat" alignment calculations in reverse order, starting at from position with highest score and following path, position by position, back through matrix Result? Optimal alignment(s) of sequences raceback - for Global lignment Start in lower right corner & trace back to upper left Each arrow introduces one character at end of alignment: horizontal move puts a gap in left sequence vertical move puts a gap in top sequence diagonal move uses one character from each sequence BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 5 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 6 raceback to Recover lignment G G d v d h d d d h d h d an have > optimal alignment; this example has : : What are the Global lignments with Optimal Score = 33? G G G G G G BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 7 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 8 Local lignment: Motivation o "ignore" stretches of non-coding DN: Non-coding regions (if "non-functional") are more likely to contain mutations than coding regions Local alignment between two protein-encoding sequences is likely to be between two exons o locate protein domains or motifs: Proteins with similar structures and/or similar functions but from different species (for example), often exhibit local sequence similarities Local sequence similarities may indicate functional modules Non-coding - "not encoding protein" Exons - "protein-encoding" parts of genes vs Introns = "intervening sequences" - segments of eukaryotic genes that "interrupt" exons Introns are transcribed into RN, but are later removed by RN processing & are not translated into protein BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 9 Local lignment: Example G G G G G Match: + Mismatch or space: - Best local alignment: G G G G G - Score = 5 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 BB 444/544 Fall 7 Dobbs 5

6 #7 Still more DP, Scoring Matrices 9/5/7 Local lignment: lgorithm S [i, j] = Score for optimally aligning a suffix of X with a suffix of Y Initialize top row & leftmost column of matrix with "" Recall: for Global lignment, S [i, j] = Score for optimally aligning a prefix of X with a prefix of Y Initialize top row & leftmost column of with gap penalty raceback - for Local lignment G G + for a match, - for a mismatch, -5 for a space BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 3 : : 3: 4: What are the 4 Local lignments with Optimal Score =? G G G G G G G G G G Some Results re: lignment lgorithms (for oms, pre & Math types!) Most pairwise sequence alignment problems can be solved in O(mn) time Space requirement can be reduced to O(m+n), while keeping run-time fixed [Myers88] Highly similar sequences can be aligned in O (dn) time, where d measures the distance between the sequences [Landau86] BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 33 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 34 ffine Gap Penalty Functions Methods ffine Gap Penalties = Differential Gap Penalties used to reflect cost differences between opening a gap and extending an existing gap otal Gap Penalty is linear function of gap length: W = γ + δ X (k - ) where γ = gap opening penalty δ = gap extension penalty k = length of gap an also be solved in O(nm) time using DP Sometimes, a onstant Gap Penalty is used, but it is usually least realistic than the ffine Gap Penalty Global and Local lignment lignment lgorithms Dot Matrix Method Dynamic Programming Method - cont Gap penalities DP for Global lignment DP for Local lignment Scoring Matrices mino acid scoring matrices PM BLOSUM omparisons between PM & BLOSUM Statistical Significance of Sequence lignment BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 35 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 36 BB 444/544 Fall 7 Dobbs 6

7 #7 Still more DP, Scoring Matrices 9/5/7 "Scoring" or "Substitution" Matrices Major types for mino cids: PM & BLOSUM PM = Point ccepted Mutation relies on "evolutionary model" based on observed differences in alignments of closely related proteins BLOSUM = BLOck SUbstitution Matrix based on % aa substitutions observed in blocks of conserved sequences within evolutionarily divergent proteins PM Matrix PM = Point ccepted Mutation relies on "evolutionary model" based on observed differences in closely related proteins Model includes defined rate for each type of sequence change Suffix number (n) reflects amount of "time" passed: rate of expected mutation if n% of amino acids had changed PM - for less divergent sequences (shorter time) PM5 - for more divergent sequences (longer time) BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 37 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 38 BLOSUM Matrix BLOSUM6 Substitution Matrix BLOSUM = BLOck SUbstitution Matrix based on % aa substitutions observed in blocks of conserved sequences within evolutionarily divergent proteins Doesnt rely on a specific evolutionary model Suffix number (n) reflects expected similarity: average % aa identity in the MS from which the matrix was generated s(a,b) corresponds to score of aligning character a with character b Match scores are often calculated based on frequency of mutations in very similar sequences (more details later) BLOSUM45 - for more divergent sequences BLOSUM6 - for less divergent sequences BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 39 BB 444/544 F7 ISU Dobbs #7 - Still more DP, Scoring Matrices 9/5/7 4 BB 444/544 Fall 7 Dobbs 7