Global vs Local lignment - example Global alignment GGGG -G---G--G GGGG -GG-----G 1 = GGGG 2 = GGG Local alignment GGGG -GG-G---- Which is better? Glo

Size: px

Start display at page:

Download "Global vs Local lignment - example Global alignment GGGG -G---G--G GGGG -GG-----G 1 = GGGG 2 = GGG Local alignment GGGG -GG-G---- Which is better? Glo"

帚禹
5 years ago
Views:

1 BB 444/544 Lecture 7 Still more: Dynamic Programming Global vs Local lignment Scoring Matrices & lignment Statistics BLS #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? 2004 Nature Biotechnol 22:909 Wed Sept 5 - for Lecture 7 & Lab 3 Database Similarity Searching: BLS (more DP!!) hp 4 - pp Fri Sept - for Lecture 8 BLS variations; BLS vs FS hp 4 - pp BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 1 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 2 ssignments & nnouncements hp 3- Sequence lignment ues Sept 4 - Lab #2 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#2 posted online & sent via & handed out in class Fri Sept 14 - HW#2 Due by 5 PM Fri Sept 21 - Exam #1 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 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, 2007, with some slides from: ltman, Fernandez-Baca, Batzoglou, raven, Hunter, Page. BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 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 2 sequences ligned sequences assumed to be generally similar over entire length Local alignment Finds local regions with highest similarity between 2 sequences ligns these without regard for rest of sequence Sequences are not assumed to be similar over entire length BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 5 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 6 BB 444/544 Fall 07 Dobbs 1

2 Global vs Local lignment - example Global alignment GGGG -G---G--G GGGG -GG-----G 1 = GGGG 2 = 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? 1. Searching for conserved motifs in DN or protein sequences? 2. 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 F07 ISU Dobbs #7 - Still More DP 9/5/07 7 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 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? 1. Searching for conserved motifs in DN or protein sequences? Local 2. 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: 1. Dot matrix analysis - practice in HW2 2. Dynamic programming - more today & in HW2 3. Word or k-tuple methods (later, in hp 4) BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 9 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 10 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 F07 ISU Dobbs #7 - Still More DP 9/5/07 11 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 12 BB 444/544 Fall 07 Dobbs 2

3 Global lignment: Scoring lignment lgorithms Reward for matches: 10 Mismatch penalty: -2 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 = 11 We could have done better!! BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 13 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 14 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-1, j-1) PLUS the score for aligning x i and y j Global lignment: DP Problem Formulation & Notations Given two sequences (strings) X = x 1 x 2 x N of length N x = G N = 3 Y = y 1 y 2 y M of length M y = M = 4 onstruct a matrix with (N+1) x (M+1) elements, where S(i,j) = Score of best alignment of x[1..i]=x 1 x 2 x i with y[1..j]=y 1 y 2 y j x 1 x 2 x 3 Which means: S(i,j) = Score of best alignment of a prefix of X and a prefix of Y y 1 y 2 y 3 S(2,3) = score of best alignment of G (x 1 x 2 ) to (y 1 y 2 y 3 ) y 4 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 15 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 16 Dynamic Programming - 4 Steps: 1. Define score of optimal alignment, using recursion 2. 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 F07 ISU Dobbs #7 - Still More DP 9/5/07 17 Define: 1- Define Score of Optimal lignment using Recursion S(i, j) = Score of optimal alignment of x 1..i and y 1..j Initial conditions: x 1..i = Prefix of length i of x y 1.. j = Prefix of length j of y S(i,0) = "i #$ S(0, j) = " j #$ Recursive definition: For 1 i N, 1 j M: % S(i "1, j "1) +# (x i,y j ) S(i, j) = max& S(i "1, j) "$ ( S(i, j "1) "$ α = Match Reward β = Mismatch Penalty γ = Gap penalty σ(x i,y j ) = α or β γ = Gap penalty BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 18 BB 444/544 Fall 07 Dobbs 3

4 2- Initialize & Fill in DP Matrix for Storing Optimal Scores of Subproblems onstruct sequence vs sequence matrix Fill in from [0,0] to [N,M] (row by row), calculating best possible score for each alignment ending at residues at [i,j] 0 1 N 0 S(0,0)=0 1 S(i,j) How do we calculate S(i,j)? i.e., Score for alignment of x[1..i] to y[1..j]? 1 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 1 x 2... x i-1 x i y 1 y 2... y j-1 y j S(i-1,j-1) + σ(x i,y j ) x 1 x 2... x i-1 x i y 1 y 2... y j S(i-1,j) x 1 x 2... x i y 1 y 2... y j-1 y j S(i,j-1) M S(N,M) BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 19 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 20 Specific Example: ase 1: Line up x i with y j i - 1 i x: - G y: - j - 1 j ase 2: Line up x i with space i - 1 i x: - G - y: - - j ase 3: Line up y j with space i x: - G - y: - - j -1 j Note: I changed sequences on this slide (to match the rest of DP example) Scoring onsequence? Match Bonus Space Penalty Space Penalty BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 21 α = Match Reward β = Mismatch Penalty γ = Gap penalty Ready? Fill in DP Matrix Keep track of dependencies of scores (in a pointer matrix) 0 1 N 0 S(0,0)=0 1 + σ(x i,y j ) = α or β M Initialization S(i,0) = "i #$ S(0, j) = " j #$ S(i-1,j-1) S(i,j-1) S(i-1,j) S(i,j) S(N,M) Recursion % S(i "1, j "1) +# (x i, y j ) S(i, j) = max& S(i "1, j) "$ ( S(i, j "1) "$ BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 22 Fill in the DP matrix!! G G alculate Score S(N,M) of Optimal lignment - for Global lignment G G BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 23 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 24 BB 444/544 Fall 07 Dobbs 4

5 3- alculate Score S(N,M) of Optimal lignment - for Global lignment G G 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 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 25 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 26 raceback - for Global lignment raceback to Recover 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 G G an have >1 optimal alignment; this example has 2 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 27 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 28 raceback to Recover lignment G G Where did red arrows come from? BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 29 raceback to Recover lignment G G BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 30 Where did 33 come from? Match = 10, so 33-10= 23 Must have come from diagonal Where did 23 come from? (Not a match) Left? 28-5= 23; Diag? 13-2= 11; op? 8-5= 3 BB 444/544 Fall 07 Dobbs 5

6 raceback to Recover lignment G G raceback to Recover lignment G G with - with with with - G with with with G with - with Where did 8 come from? wo possibilities: 13-5= 8 or 10-2=8 hen, follow both paths Great - but what are the alignments? #1 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 31 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 32 raceback to Recover lignment G G with - with with with G with - with with G with - with 1: 2: What are the 2 Global lignments with Optimal Score = 33? op: G G Left: - G G - G G Great - but what are the alignments? #2 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 F07 ISU Dobbs #7 - Still More DP 9/5/07 33 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/ : 2: What are the 2 Global lignments with Optimal Score = 33? op: G G Left: - G G G G - - heck raceback? G G d v d 1 h d 2 d d h d h d horizontal move puts a gap in left sequence vertical move puts a gap in top sequence diagonal move uses one character from each sequence 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 F07 ISU Dobbs #7 - Still More DP 9/5/07 35 BB 444/544 F07 ISU Dobbs #7 - Still More DP 9/5/07 36 BB 444/544 Fall 07 Dobbs 6

& BLS 9/7/7 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

& BLS 9/7/7 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 & BLS 9/7/7 BB 444/544 Lecture 8 Finish: Dynamic Programming Global vs Local lignment Scoring Matrices & lignment Statistics BLS #8_Sept7 Required Reading (before lecture) Last week: - for Lectures 4-7