Global alignments - review

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Ruth Doyle
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1 Global alignments - review Take two sequences: X[j] and Y[j] M[i-1, j-1] ± 1 M[i, j] = max M[i, j-1] 2 M[i-1, j] 2 The best alignment for X[1 i] and Y[1 j] is called M[i, j] X[j] Initiation: M[,]= pply the equation Find the alignment with backtracing Y[i] G G G C G - 1 G 2 3 G 4 T 5 G 6 2

2 lgorithm time/space complexity - Big-O Notation a simple description of complexity: constant O(1), linear O(n), quadratic O(n 2 ), cubic O(n 3 )... asymptotic upper bound read: order of f n=o gn iff. simple,e.g.n 2 x, c f x cgx x x 2 lnx f x lnx x =17

3 Big-O Notation Example Time complexity of global alignment: M[i-1, j-1] ± 1 M[i, j] = max M[i, j-1] 2 M[i-1, j] 2 nm 1 init 1nm 1 =Onm calcm print

4 Global alignment linear space M[i-1, j-1] ± 1 M[i, j] = max M[i, j-1] 2 M[i-1, j] 2 We need O(nm) time, but only O(m) space how? problem with backtracking

5 Global alignment linear space, recursion LSpacei,i', j, j': i j k 1 j' LSpacei, n 2 1, j, k 1 n/2 LSpacei, n 2 1, j,k 2 i' k 2 space complexity: O(m)

6 Global alignment linear space, algorithm LSpacei,i ', j, j': i j k 1 j' return if areai,i', j, j'empty h:= i ' i 2 calc.musing Ommemory plusfind pathl h crossing therow h LSpacei,h 1,k 1, j' print L h LSpacei,h1,k 2, j' h=n/2 i' L h k 2 log 2 n time complexity: nm 2nm i= 2 i

7 lignments: Local alignment

8 Local alignment: Smith-Waterman algorithm Seq X: What s local? Seq Y: llow only parts of the sequence to match Locally maximal: can not make it better by trimming/extending the alignment

9 Local alignment Seq X: Seq Y: Why local? Parts of sequence diverge faster evolutionary pressure does not put constraints on the whole sequence seq X: seq Y: Proteins have modular construction sharing domains between sequences seq X: seq Y:

10 Domains - example Immunoglobulin domain

11 Global local alignment a) global align Take the global equation Look at the result of the global alignment - s e q - s b) retrieve the result e CGCCTTGGTTCTCG- C-C-----GTTCGT-G c) sum score along the result q u e sum align. pos.

12 Local alignment breaking the alignment recipe Just don t let the score go below Start the new alignment when it happens Where is the result in the matrix? Before: fter: - s e q u e - s e q u e - - s s e e q q sum sum sum align. pos. align. pos. align. pos.

13 Local alignment the equation M[i-1, j-1] + score(x[i],y[j]) M[i, j] = max M[i, j-1] g M[i-1, j] g Init the boundaries with s Great contribution to science! Run the algorithm Read the maximal value from anywhere in the matrix - s e q u e Find the result with backtracking - s e q

14 Finding second best alignment We can find the best local alignment in the sequence But where is the second best one? Scoring: 1 for match -2 for a gap G Best alignment G G clump 13 16

15 Clump of an alignment lignments sharing at least one aligned pair G G G clump

16 Clumps gene X gene Y

17 Finding second best alignment Don t let any matched pair to contribute to the next alignment G Clear the best alignment G Recalculate the clump G

18 Extraction of local alignments Waterman- Eggert algorithm 1. Repeat a. Calc M without taking cells into account b. Retrieve the highest scoring alignment c. Set it s trace to

19 Clumps gene X gene Y

20 Clumps gene X gene Y

21 Low complexity regions Local composition bias Replication slippage: e.g. triplet repeats Results in spurious hits Breaks down statistical models Different proteins reported as hits due to similar composition Up to ¼ of the sequence can be biased Huntington s disease Huntingtin gene of unknown (!) function Repeats #: 6-35: normal; 36-12: disease

22 Pitfalls of alignments lignment is not a reconstruction of the evolution (common ancestor is extinct by the time of alignment)

23 Pitfalls of alignments Matches to the same fragment rbitrary poor alignment regions seq X: seq Y:

24 What s the number of steps in these algorithms? How much memory is used? Summary 1. Global a.k.a. Needleman- Wunsch algorithm 2. Global-local 3. Local a.k.a. Smith- Waterman algorithm 4. Many local alignments a.k.a. Waterman- Eggert algorithm seq X: seq Y: seq X: seq Y: seq X: seq Y: seq X: seq Y:

25 mino acid substitution matrices

26 Percent ccepted Mutations distance and matrices ccepted by natural selection not lethal not silent Def.: S 1 and S 2 are PM 1 distant if on avg. there was one mutation per 1 aa Q.: If the seqs are PM 8 distant, how many residues may be diffent?

27 PM matrix Created from easy alignments pairwise gapless 85% id f proline f proline, valine i.e. frequency of occurenceof proline frequency of substitution proline with valine,for PM1 counta,b aligns f a,b= aligns c,d!=a,b M symmetricmatr ix, f a,a f a i.e. M=[ f b,a f b,b] countc,d

28 PM matrix How to calculte M for PM 2 distance? Take more distant seqs or extrapolate... M 2 =[ f a,a f b,a =[ f a f a,af a,af a,bf b,a f a,af a,bf a,bf b,b f b,b]2 ]

29 PM log odds matrix Making of the PM N matrix observed PMN[a, b] = log 2 f am N [a,b] f af b By chance alone Why log? Mutations and chance: More freq: PM N[a,b] > Less freq: PM N[a,b] < = log 2 M N [a,b] f b odds log odds

30 PM 25 matrix

31 BLOSUM matrix BLOcks SUbstitution Matrix Based on gapless alignments More often used than PM

32 BLOSUM N matrix Cluster together sequences N% identity f(a,b) frequency of occurrence a and b in the same column f a, b f a = f a,a a b 2 e(a,b) chance alone ea,b = 1 a b ea,a = f a 2 ea, b = 2 f af b for a b BLOSUM N [a,b] = log 2 f a,b ea,b log odds

33 BLOSUM 62 matrix # BLOSUM Clustered Scoring Matrix in 1/2 Bit Units # Blocks Database = /data/blocks_5./blocks.dat # Cluster Percentage: >= 62 # Entropy =.6979, Expected = R N D C Q E G H I L K M F P S T W Y V R N D C Q E G H I L K M F P S T W Y V

PM vs BLOSUM http://www.ncbi.nih.gov/education/blstinfo/scoring2.

34 PM vs BLOSUM PM is extrapolation from closely related seqs We are interested more distant relationships

Pairwise sequence alignment

Pairwise sequence alignment Department of Evolutionary Biology Example Alignment between very similar human alpha- and beta globins: GSAQVKGHGKKVADALTNAVAHVDDMPNALSALSDLHAHKL G+ +VK+HGKKV A+++++AH+D++ +++++LS+LH KL GNPKVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKL