Sequence Alignments

1. Sequence Alignments

2. Intro to Bioinformatics � Sequence Alignment 2 Sequence Alignments Cornerstone of bioinformatics What is a sequence? Nucleotide sequence Amino acid sequence Pairwise and multiple sequence alignments We will focus on pairwise alignments What alignments can help Determine function of a newly discovered gene sequence Determine evolutionary relationships among genes, proteins, and species Predicting structure and function of protein

3. Intro to Bioinformatics � Sequence Alignment 3 DNA Replication Prior to cell division, all the genetic instructions must be �copied� so that each new cell will have a complete set DNA polymerase is the enzyme that copies DNA Reads the old strand in the 3� to 5� direction

4. Intro to Bioinformatics � Sequence Alignment 4 Over time, genes accumulate mutations

5. Intro to Bioinformatics � Sequence Alignment 5 Codon deletion:ACG ATA GCG TAT GTA TAG CCG� Effect depends on the protein, position, etc. Almost always deleterious Sometimes lethal Frame shift mutation: ACG ATA GCG TAT GTA TAG CCG�  ACG ATA GCG ATG TAT AGC CG?� Almost always lethal Deletions

6. Intro to Bioinformatics � Sequence Alignment 6 Indels Comparing two genes it is generally impossible to tell if an indel is an insertion in one gene, or a deletion in another, unless ancestry is known:ACGTCTGATACGCCGTATCGTCTATCTACGTCTGAT---CCGTATCGTCTATCT

7. Intro to Bioinformatics � Sequence Alignment 7 The Genetic Code

8. Intro to Bioinformatics � Sequence Alignment 8 Comparing Two Sequences Point mutations, easy:ACGTCTGATACGCCGTATAGTCTATCTACGTCTGATTCGCCCTATCGTCTATCT Indels are difficult, must align sequences:ACGTCTGATACGCCGTATAGTCTATCTCTGATTCGCATCGTCTATCTACGTCTGATACGCCGTATAGTCTATCT----CTGATTCGC---ATCGTCTATCT

9. Intro to Bioinformatics � Sequence Alignment 9 Why Align Sequences? The draft human genome is available Automated gene finding is possible Gene: AGTACGTATCGTATAGCGTAA What does it do? One approach: Is there a similar gene in another species? Align sequences with known genes Find the gene with the �best� match

10. Intro to Bioinformatics � Sequence Alignment 10 Gaps or No Gaps Examples

11. Intro to Bioinformatics � Sequence Alignment 11 Scoring a Sequence Alignment Match score: +1 Mismatch score: +0 Gap penalty: �1ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT Matches: 18 � (+1) Mismatches: 2 � 0 Gaps: 7 � (� 1)

12. Intro to Bioinformatics � Sequence Alignment 12 Origination and Length Penalties We want to find alignments that are evolutionarily likely. Which of the following alignments seems more likely to you?ACGTCTGATACGCCGTATAGTCTATCTACGTCTGAT-------ATAGTCTATCTACGTCTGATACGCCGTATAGTCTATCTAC-T-TGA--CG-CGT-TA-TCTATCT We can achieve this by penalizing more for a new gap, than for extending an existing gap

13. Intro to Bioinformatics � Sequence Alignment 13 Scoring a Sequence Alignment (2) Match/mismatch score: +1/+0 Origination/length penalty: �2/�1ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT Matches: 18 � (+1) Mismatches: 2 � 0 Origination: 2 � (�2) Length: 7 � (�1)

14. Intro to Bioinformatics � Sequence Alignment 14 How can we find an optimal alignment? Finding the alignment is computationally hard:ACGTCTGATACGCCGTATAGTCTATCTCTGAT---TCG-CATCGTC--T-ATCT C(27,7) gap positions = ~888,000 possibilities It�s possible, as long as we don�t repeat our work! Dynamic programming: The Needleman & Wunsch algorithm

15. Intro to Bioinformatics � Sequence Alignment 15 Dynamic Programming Technique of solving optimization problems Find and memorize solutions for subproblems Use those solutions to build solutions for larger subproblems Continue until the final solution is found Recursive computation of cost function in a non-recursive fashion

16. Intro to Bioinformatics � Sequence Alignment 16 Global Sequence Alignment Needleman-Wunsch algorithm Suppose we are aligning: A with A�

17. Intro to Bioinformatics � Sequence Alignment 17 Dynamic Programming (DP) Concept Suppose we are aligning: CACGA CCGA

18. Intro to Bioinformatics � Sequence Alignment 18 DP � Recursion Perspective Suppose we are aligning:ACTCGACAGTAG Last position choices:

19. Intro to Bioinformatics � Sequence Alignment 19 What is the optimal alignment? ACTCGACAGTAG Match: +1 Mismatch: 0 Gap: �1

20. Intro to Bioinformatics � Sequence Alignment 20 Needleman-Wunsch: Step 1 Each sequence along one axis Mismatch penalty multiples in first row/column 0 in [1,1] (or [0,0] for the CS-minded)

21. Intro to Bioinformatics � Sequence Alignment 21 Needleman-Wunsch: Step 2 Vertical/Horiz. move: Score + (simple) gap penalty Diagonal move: Score + match/mismatch score Take the MAX of the three possibilities

22. Intro to Bioinformatics � Sequence Alignment 22 Needleman-Wunsch: Step 2 (cont�d) Fill out the rest of the table likewise�

23. Intro to Bioinformatics � Sequence Alignment 23 Needleman-Wunsch: Step 2 (cont�d) Fill out the rest of the table likewise�

24. Intro to Bioinformatics � Sequence Alignment 24 But what is the optimal alignment To reconstruct the optimal alignment, we must determine of where the MAX at each step came from�

25. Intro to Bioinformatics � Sequence Alignment 25 A path corresponds to an alignment = GAP in top sequence = GAP in left sequence = ALIGN both positions One path from the previous table: Corresponding alignment (start at the end): AC--TCG ACAGTAG

26. Intro to Bioinformatics � Sequence Alignment 26 Algorithm Analysis Brute force approach If the length of both sequences is n, number of possibility = C(2n, n) = (2n)!/(n!)2 ? 22n / (?n)1/2, using Sterling�s approximation of n! = (2?n)1/2e-nnn. O(4n) Dynamic programming O(mn), where the two sequence sizes are m and n, respectively O(n2), if m is in the order of n

27. Intro to Bioinformatics � Sequence Alignment 27 Practice Problem Find an optimal alignment for these two sequences: GCGGTT GCGT Match: +1 Mismatch: 0 Gap: �1

28. Intro to Bioinformatics � Sequence Alignment 28 Practice Problem Find an optimal alignment for these two sequences: GCGGTT GCGT

29. Intro to Bioinformatics � Sequence Alignment 29 Semi-global alignment Suppose we are aligning:GCGGGCG Which do you prefer?G-CG -GCGGGCG GGCG Semi-global alignment allows gaps at the ends for free.

30. Intro to Bioinformatics � Sequence Alignment 30 Semi-global alignment

31. Intro to Bioinformatics � Sequence Alignment 31 Local alignment Global alignments � score the entire alignment Semi-global alignments � allow unscored gaps at the beginning or end of either sequence Local alignment � find the best matching subsequence CGATGAAATGGA This is achieved by allowing a 4th alternative at each position in the table: zero.

32. Intro to Bioinformatics � Sequence Alignment 32 Local Sequence Alignment Why local sequence alignment? Subsequence comparison between a DNA sequence and a genome Protein function domains Exons matching Smith-Waterman algorithm

33. Intro to Bioinformatics � Sequence Alignment 33 Local alignment Score: Match = 1, Mismatch = -1, Gap = -1

34. Intro to Bioinformatics � Sequence Alignment 34 Local alignment Another example

35. Intro to Bioinformatics � Sequence Alignment 35 More Example Align ATGGCCTC ACGGCTC Mismatch ? = -3 Gap ? = -4

36. Intro to Bioinformatics � Sequence Alignment 36 More Example

37. Intro to Bioinformatics � Sequence Alignment 37 Scoring Matrices for DNA Sequences Transition: A ?? G C ?? T Transversion: a purine (A or G) is replaced by a pyrimadine (C or T) or vice versa

38. Intro to Bioinformatics � Sequence Alignment 38 Scoring Matrices for Protein Sequence PAM (Percent Accepted Mutations) 250

39. Intro to Bioinformatics � Sequence Alignment 39 Scoring Matrices for Protein Sequence BLOSUM (BLOcks SUbstitution Matrix) 62

40. Intro to Bioinformatics � Sequence Alignment 40 Using Protein Scoring Matrices Divergence BLOSUM 80 BLOSUM 62 BLOSUM 45 PAM 1 PAM 120 PAM 250 Closely related Distantly related Less divergent More divergent Less sensitive More sensitive Looking for Short similar sequences ? use less sensitive matrix Long dissimilar sequences ? use more sensitive matrix Unknown ? use range of matrices Comparison PAM � designed to track evolutionary origin of proteins BLOSUM � designed to find conserved regions of proteins