Sequence Alignment. part 2

Transcription

1 Sequence Alignment part 2

2 Dynamic programming with more realistic scoring scheme Using the same initial sequences, we ll look at a dynamic programming example with a scoring scheme that selects for matches and penalizes both mismatched and gaps, as follows: S i,j = 2 if residues match S i,j = -1 if there is a mismatch at the current position w = -2 (gap penalty)

3 Initialization same as before Example sequences: GAATTCAGTTA (sequence 1: M=11) GGATCGA (sequence 2: N=7) G 0 G 0 A 0 T 0 C 0 G 0 A 0 G A A T T C A G T T A

4 Filling matrix (scoring) Recall the scoring scheme: M i,j (matrix position to be filled in) = maximum of these 3 terms: M i-1, j-1 + S i,j (match/mismatch in diagonal) where: o S i,j = 2 for match o S i,j = -1 for mismatch M i, j-1 + w (gap in sequence 1) M i-1,j + w (gap in sequence 2) in either case, w = -2

5 Filling matrix (scoring) Since both sequences start with G, the maximum value for M 1,1 is = 2 for the match G A A T T C A G T T A G 0 2 G 0 A 0 T 0 C 0 G 0 A 0

6 Filling matrix (scoring) Continuing down column 2, we see that the G in the first position of sequence 1 also matches the G in the second position of sequence 2; this means that M1,2 will be the maximum of [2, -2, -2] which is 2 We also add a backward pointing arrow at each position to show where the maximum score came from (see next slide)

7 Filling matrix (scoring) G A A T T C A G T T A G 0 2 G 0 2 A 0 T 0 C 0 G 0 A 0

8 Filling matrix (scoring) At M 1,3 there is no match, so S 1,3 = -1 M 1,3 = MAX[M 0,2-1, M 1,2-2,M 0,3-2] = MAX[-1,0,-2] = 0 G A A T T C A G T T A G 0 2 G 0 2 A 0 0 T 0 C 0 G 0 A 0

9 Filling matrix (scoring) We can continue filling in column 1 using the same reasoning: G A A T T C A G T T A G 0 2 G 0 2 A 0 0 T 0-1 C 0-1 G 0 2 A 0 0

10 Filling matrix (scoring) We continue into column 2: G A A T T C A G T T A G G A T C G A 0 0 4

11 Filling matrix (scoring) At column 3 row 3 we encounter the following situation: M 3,2 = MAX[M 2,1-1, M 3,1-2,M 2,2-2] = MAX[-1,-3,-1] = -1 Since there are 2 different ways we could reach the maximum score, we provide arrows back to both cells that could get us there: G A A T T C A G T T A G G A T C G A 0 0 4

12 Completed matrix G A A T T C A G T T A G G A T C G A

13 Traceback Maximum global alignment is 3, the value in the last row of the last column; traceback step begins here The traceback step is simplified by the presence of the arrows we can follow them to get to the predecessor at each step Since some locations have multiple arrows, we may find multiple alignments, but there will be fewer than under the simple scoring scheme we used before

14 Second possible path Alternate path gives the following alignment: GAATTCAGTTA GGAT-C-G--A

15 Verifying the score(s) Recall our scoring scheme: match: +2 mismatch: -1 gap: -2 Final overall score in table was 3, so alignments should add up to 3, given the above Calculations on next slide verify that they do

16 Verifying the score(s) First alignment: GAATTCAGTTA GGA-TC-G--A = 3 Second alignment: GAATTCAGTTA GGAT-C-G--A = 3

17 Global alignments: pros & cons What they re good for: checking for minor differences between sequences comparing sequences that partly overlap What they re not good for: discovering similarities between 2 sequences exploring similarities within a family of sequences (for this we do multiple alignment)

18 Programming global alignment GA algorithms are based on dynamic programming which is a recursive technique Recursion can be summarized as follows: nature of the problem: must be divisible into smaller subproblems begin by solving the smallest subproblems solutions to smallest problems are used in solutions to larger problems process continues until entire (largest) problem is solved

19 Detailed algorithm: step 1: build scoring matrix 1. Read in 2 sequences to be aligned: lines 7-25 of program 2. Obtain match, mismatch & gap scores (from user): lines Create m+1 x n+1 matrix (see next slide): lines Prepend a blank character to the front of both sequences (so that position 0 of each sequence contains a blank, and sequence indices are consistent with matrix indices): lines 30 & 31

20 Arrays in Perl Array: single variable that holds multiple scalar values individual elements are accessible via index (subscript) one-dimensional array: vector two-dimensional array: matrix

21 Array declaration & notation To distinguish a vector or matrix from a scalar, the starting character of the array = (); # declares empty array We refer to the entire array we reference individual elements using $name and subscript(s): for ($i=0; $i<10; $i++) { $array[$i] = ; } # initializes 10-element vector to blank strings

22 Example program #!/usr/bin/perl # declare = (); # initialize with empty strings: for ($i=0; $i<10; $i++) { $array[$i]=''; } # print it all out backwards: for ($i=9; $i>=0; $i--) { print $array[$i]. "\n"; } # prompt for & read in some data: for ($i=0; $i<10; $i++) { print "Please enter a word or phrase:\n"; $array[$i] = <STDIN>; }

23 Back to algorithm 5. Initialize first row & first column of matrix by adding gap penalty to each successive cell: lines Fill remaining cells (lines 66-99): compute three candidate values for each cell by adding gap penalty or match score (as appropriate) to value in appropriate neighboring cell (lines 80-87) compare the three values to determine maximum score (lines 89-97)

24 Algorithm continued 7. Develop directional string to facilitate traceback: lines unlike the human observer, a program cannot see directional arrows in the matrix instead, we create a string containing directional indicators to develop a traceback path: H indicates left neighbor (horizontal gap) D indicates diagonal neighbor (match/mismatch) V indicates above neighbor (vertical gap)

25 Algorithm continued Perform traceback (lines ): Starting at the right end of each sequence, obtain the current character Read the first (leftmost) character of the directional string & align the retrieved sequence characters as directed Continue until you run out of directional characters

26 Terminal gaps & semiglobal alignments Terminal gaps occur when you align 2 sequences that differ significantly in length; our global alignment algorithm doesn t distinguish between these gaps and internal gaps, even though an alignment with only terminal gaps actually represents the optimal alignment For example, the three alignments below represent what the global alignment would consider optimal: CGCTATAG CGCTATAG CGCTATAG --CTA--- C--TA--- --C--TA- Eliminating the gap penalty for terminal gaps produces a semiglobal alignment

27 Local alignment Many pairs of sequences will include regions of high similarity (conserved regions) interspersed with dissimilar regions A global alignment algorithm on such sequences will result in poor scores and/or many equally (un)likely alignments reported as optimal In such situations, a local alignment algorithm is preferable

28 Local alignment Uses for local alignment: compare distantly-related sequences that share a few non-connected regions in common analysis of repeated elements within a single sequence Smith-Waterman: the original local alignment algorithm

29 Smith-Waterman algorithm Uses scoring system similar to Needleman-Wunsch for building matrix: M i,j = maximum of: 0 or M i-1, j-1 + S i,j or M i-1, j + w or M i, j Note that the inclusion of 0 as a possible maximum eliminates negative values from the matrix FASTA format originated with FASTA algorithm a fast (or fasta ) approximation of Smith-Waterman

30 Online resource for local alignment BLAST: bl2seq Lalign: slower but more accurate than BLAST BLAST returns only best alignment between query & target Lalign returns as many as specified, ranked from best to worst

31 Lalign output % identity within conserved regions length of alignment score: sum of gap/substitution penalties higher score = better alignment E-value better indicator of alignment quality lower = better

32 A look under the hood at BLAST BLAST algorithm splits query sequence into hot spots consisting of: words : short subsequences neighboring words : subsequences similar to words Sequence database is scanned for matches to these hot spots Identified matches used to extend hot spots Uses heuristics to identify best matches

33 BLAST algorithm illustrated