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Local Alignment Tutorial 2. Conditions –Division to sub-problems possible –(Optimal) Sub-problem solution usable (many times?) –“Bottom-up” approach Dynamic.

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Presentation on theme: "Local Alignment Tutorial 2. Conditions –Division to sub-problems possible –(Optimal) Sub-problem solution usable (many times?) –“Bottom-up” approach Dynamic."— Presentation transcript:

1 Local Alignment Tutorial 2

2 Conditions –Division to sub-problems possible –(Optimal) Sub-problem solution usable (many times?) –“Bottom-up” approach Dynamic Programming

3 Examples –Shortest path –Fibonacci Dynamic Programming

4 Fibonacci Fib(x) = Fib(x-1)+Fib(x-2), Fib(0)=0 Fib(1)=1 Fib(5) = Fib(3)+Fib(4) = Fib(2)+Fib(1)+Fib(3)+Fib(2) = Fib(1)+Fib(0)+Fib(1)+Fib(2)+Fib(1)+Fib(1)+Fib(0)= Fib(1)+Fib(0)+Fib(1)+ Fib(1)+Fib(0)+Fib(1)+Fib(1)+Fib(0) = 1+0+1+1+0+1+1+0 = 5 Without using dynamic programming we will need to calculate Fib(2) three times.

5 Fibonacci Dynamic programming solution will work “bottom up”: 1. First calculate Fib(2) from known Fib(0) and Fib(1) 2. Calculate Fib(3) using calculated Fib(2) and known Fib(1). 3. Calculate Fib(4) using calculated Fib(3) and Fib(2). 4. Calculate Fib(5) using calculated Fib(4) and Fib(3).

6 Dynamic Programming algorithm for finding local matches between two sequences. What is a local match?: –It is a best-matching, highest-scoring region between two sequences. –It is a well conserved region between two sequences. Local Alignment

7 Alignment NnNn N1N1 M1M1 MmMm

8 NnNn N1N1 M1M1 MmMm [I,J] Best alignment M 1..I, N 1..J

9 Alignment All possible alignments encoded as path in matrix

10 The differences: 1.We can start a new match instead of extending a previous alignment. 2.Instead of looking only at the far corner, we look anywhere in the table for the best score Global vs Local Global Local Scoring System Match : +1 Mismatch: -2 Indel : -1

11 Local Alignment Scoring System –Match : +1N i =M j –Mismatch: -1N i =M j –Indel : -2 NnNn N1N1 M1M1 MmMm

12 Local Alignment Scoring System –Match : +1N i =M j –Mismatch : -1N i =M j –Indel : -2 NnNn N1N1 M1M1 MmMm

13 Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm

14 Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm N1-N1-

15 Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm -M1-M1

16 Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N1- M1M2

17 Local Alignment Fill: 1.We fill the table like in global alignment, but we don’t allow negative numbers (turn every negative number to 0) 2.No arrows coming out from cells with a 0. Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..

18 Local Alignment Trace: We trace back from the highest scoring cells. +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..

19 Local Alignment Question: Will there be gaps at the start/end? NnNn N2N2 N1N1 M1M1 M2M2 MmMm

20 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0 T 1 A 2 A 3 T 4 A 5

21 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 A 2 A 3 T 4 A 5

22 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0

23 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0 -T-T

24 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0 T-T-

25 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0? A 2 0 A 3 0 T 4 0 A 5 0

26 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0? A 2 0 A 3 0 T 4 0 A 5 0 -T T- -T T- -T +1 -2

27 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 01 A 2 0 A 3 0 T 4 0 A 5 0

28 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 010 A 2 0 A 3 0 T 4 0 A 5 0

29 0 0T 4 0A 3 0A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

30 0A 5 0T 4 0A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

31 0A 5 0T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

32 0A 5 1020010T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

33 1300200A 5 1020010T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

34 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 000000 010010 A 2 0020021 A 3 001101 3 T 4 0100201 A 5 00200 3 1

35 0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 000000 T 1 010010 A 2 0020021 A 3 0011013 T 4 0100201 A 5 0020031 Leave only paths from highest score

36 TAA TACTA TAATA

37 And Now… Global Alignment 1.We keep negative numbers. 2.Arrows coming out from any cell. 3.We trace back from right-bottom to left-top of the table. Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..

38 A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10 Match: +1 Mismatch:-1 Indel: -2 -12-10-8-6-4-2 -10 -8 -6 -4 -2 0 -9-7-5-31 130-3-4-7 -202-2-5 -3 10-3 -6-4-202

39 A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10 Match: +1 Mismatch:-1 Indel: -2 -12-10-8-6-4-2 -10 -8 -6 -4 -2 0 -9-7-5-31 130-3-4-7 -202-2-5 -3 10-3 -6-4-202

40 130-3-4-5A 5 02 -2 -4T 4 1 10-3 A 3 -20 02-2A 2 -6-4-2-31 T 1 -6-5-4-3-200 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

41 TACTAA TAATA- TACTAA TAAT-A

42 A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10

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