1. Introduction to Bioinformatics
Sequence Alignments

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
Intro to Bioinformatics – Sequence Alignment
Acknowledgement: This notes is adapted from lecture notes of both Wright State University’s Bioinformatics Program and Professor Laurie Heyer of Davidson College with permission.

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
Intro to Bioinformatics – Sequence Alignment

4. Over time, genes accumulate mutations
Environmental factors
Radiation
Oxidation
Mistakes in replication or repair
Deletions, Duplications
Insertions, Inversions
Translocations
Point mutations
Intro to Bioinformatics – Sequence Alignment

5. Deletions 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
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: ACGTCTGATACGCCGTATCGTCTATCT ACGTCTGAT---CCGTATCGTCTATCT
Intro to Bioinformatics – Sequence Alignment

7. The Genetic Code
Substitutions are mutations accepted by natural selection.
Synonymous:
CGC  CGA
Non-synonymous:
GAU  GAA
Intro to Bioinformatics – Sequence Alignment

8. Comparing Two Sequences
Point mutations, easy: ACGTCTGATACGCCGTATAGTCTATCT ACGTCTGATTCGCCCTATCGTCTATCT
Indels are difficult, must align sequences: ACGTCTGATACGCCGTATAGTCTATCT CTGATTCGCATCGTCTATCT ACGTCTGATACGCCGTATAGTCTATCT ----CTGATTCGC---ATCGTCTATCT
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
Intro to Bioinformatics – Sequence Alignment

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

11. Scoring a Sequence Alignment
Given
Match score: +1
Mismatch score: +0
Gap penalty: –1
Sequences ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT 
Matches: 18 × (+1)
Mismatches: 2 × 0
Gaps: 7 × (– 1)
Score = +11
Intro to Bioinformatics – Sequence Alignment

12. Origination and Length Penalties
Note that a bioinformatics computational model or algorithm must be “biologically meaningful” or even “biologically significant”
We want to find alignments that are evolutionarily likely.
Which of the following alignments seems more likely to you? ACGTCTGATACGCCGTATAGTCTATCT ACGTCTGAT ATAGTCTATCT ACGTCTGATACGCCGTATAGTCTATCT AC-T-TGA--CG-CGT-TA-TCTATCT
We can achieve this by penalizing more for a new gap, than for extending an existing gap  
Intro to Bioinformatics – Sequence Alignment

13. Scoring a Sequence Alignment (2)
Given
Match/mismatch score: +1/+0
Gap origination/length penalty: –2/–1
Sequences ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT 
Matches: 18 × (+1)
Mismatches: 2 × 0
Origination: 2 × (–2)
Length: 7 × (–1)
Caution: Sometime “gap extension” used instead of “gap length” …
Score = +7
Intro to Bioinformatics – Sequence Alignment

14. How can we find an optimal alignment?
Finding the alignment is computationally hard: ACGTCTGATACGCCGTATAGTCTATCT CTGAT---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
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
Intro to Bioinformatics – Sequence Alignment

16. Dynamic Programming Example
Solving Fibonacci number f(n) = f(n-1) + f(n-2) recursively takes exponential time
Because many numbers are recalculated
Solving it using dynamic programming only takes a linear time
Use an array f[] to store the numbers
f[0] = 1;
f[1] = 1;
for (i = 2; i <= n; i++)
f[i] = f[i – 1] + f[i – 2];
Intro to Bioinformatics – Sequence Alignment

17. Global Sequence Alignment
Needleman-Wunsch algorithm
Suppose we are aligning: a with a …
Di,j = max{ Di-1,j + d(Ai, –), Di,j-1 + d(–, Bj), Di-1,j-1 + d(Ai, Bj) } B
i-1
j-1 j i A
Seq1
Seq2
Intro to Bioinformatics – Sequence Alignment

18. Dynamic Programming (DP) Concept
Suppose we are aligning: CACGA
CGA
Intro to Bioinformatics – Sequence Alignment

19. DP – Recursion Perspective
Suppose we are aligning: ACTCG ACAGTAG
Last position choices:
G +1 ACTC G ACAGTA G -1 ACTC - ACAGTAG ACTCG G ACAGTA
Intro to Bioinformatics – Sequence Alignment

20. What is the optimal alignment?
ACTCG ACAGTAG
Match: +1
Mismatch: 0
Gap: –1
Intro to Bioinformatics – Sequence Alignment

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

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

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

24. Needleman-Wunsch: Step 2 (cont’d)
Fill out the rest of the table likewise…
The optimal alignment score is calculated in the lower-right corner
Intro to Bioinformatics – Sequence Alignment

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

26. 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
Score = +2
Intro to Bioinformatics – Sequence Alignment

27. Algorithm Analysis Brute force approach Dynamic programming
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
Intro to Bioinformatics – Sequence Alignment

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

29. Practice Problem
Find an optimal alignment for these two sequences: GCGGTT GCGT
GCGGTT GCG-T-
Score = +2
Intro to Bioinformatics – Sequence Alignment

30. Semi-global alignment
Suppose we are aligning: GCG GGCG
Which do you prefer? G-CG -GCG GGCG GGCG
Semi-global alignment allows gaps at the ends for free.
Terminal gaps are usually the result of incomplete data acquisition  no biologically significant
Intro to Bioinformatics – Sequence Alignment

31. Semi-global alignment
Semi-global alignment allows gaps at the ends for free.
Initialize first row and column to all 0’s
Allow free horizontal/vertical moves in last row and column
Intro to Bioinformatics – Sequence Alignment

32. 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
CGATG AAATGGA
This is achieved by allowing a 4th alternative at each position in the table: zero.
Intro to Bioinformatics – Sequence Alignment

33. Local Sequence Alignment
Why local sequence alignment?
Subsequence comparison between a DNA sequence and a genome
Protein function domains
Exons matching
Smith-Waterman algorithm
Initialization: D1,j = , Di,1 = 
Di,j = max{
Di-1,j + d(Ai, –),
Di,j-1 + d(–,Bj),
Di-1,j-1 + d(Ai,Bj),
0 }
Intro to Bioinformatics – Sequence Alignment

34. Local alignment Score: Match = 1, Mismatch = -1, Gap = -11 2 3
CGATG AAATGGA
Intro to Bioinformatics – Sequence Alignment

35. Local alignment Another example
Intro to Bioinformatics – Sequence Alignment

36. More Example Align Global Alignment: ATGGCCTC ACGGC-TC ATGGCCTC
Mismatch  = -3
Gap  = -4 -- A C G T -- A T G C -4 -8
-12
-16
-20
-24
-28 -4 -8
-12
-16
-20
-24
-28
-32 -7
-11
-15
-19
-23 -2 -6
-10
-14
-18 -1 -5 -9
-13
-17 -4 -8
-12 1 -3
-27
-22
-21
-16 1 -3
Global
Alignment:
ATGGCCTC
ACGGC-TC
Intro to Bioinformatics – Sequence Alignment

37. More Example Local Alignment: ATGGCCTC ACGG CTC or ACGGC TC -- A C G T1 2 3 1
Intro to Bioinformatics – Sequence Alignment

38. 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
Intro to Bioinformatics – Sequence Alignment

39. Scoring Matrices for Protein Sequence
PAM 250
Intro to Bioinformatics – Sequence Alignment

40. Scoring Matrices for Protein Sequence
PAM (Percent Accepted Mutations)
1 PAM unit can be thought of as the amount of time in which an “average” protein mutates 1 out of every 100 amino acids.
Perform multiple sequence alignment on a “family” of proteins that are at least 85% similar. Find the frequency of amino acid i and j are aligned to each other and normalize it.
Entry mij in PAM1 represents the probability of amino acid i substituted by amino acid j in 1 PAM unit
PAM 2 = PAM 1 × PAM 1
PAM n = (PAM 1)n, e.g., PAM 250 = (PAM 1)250
Questions
Why are values in a PAM matrix integers? Shouldn’t a probability be between 0 and 1?
Why is PAM250 possible? Shouldn’t a probability be less than or equal to 100%?
Intro to Bioinformatics – Sequence Alignment

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

42. Using Protein Scoring Matrices
Divergence
BLOSUM 80 BLOSUM 62 BLOSUM 45
PAM 1 PAM 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
Intro to Bioinformatics – Sequence Alignment

43. Multiple Sequence Alignment
Why multiple sequence alignment (MSA)
Two sequences might not look very similar.
But, some “similarity” emerges with more sequences, however.
Is dynamic programming still applicable?
CLUSTALW
One of most popular tools for MSA
Heuristic-based approach
Basic
1) Calculate the distance matrix based on pairwise alignments
2) Construct a guide tree
NJ (unrooted tree)  Mid-point (rooted tree)
3) Progressive alignment using the guide tree