1. Developing Pairwise Sequence Alignment Algorithms
Dr. Nancy Warter-Perez

2. Developing Pairwise Sequence Alignment Algorithms
Outline
Overview of global and local alignment
References for sequence alignment algorithms
Discussion of Needleman-Wunsch iterative approach to global alignment
Discussion of Smith-Waterman recursive approach to local alignment
Discussion of how LCS Algorithm can be extended for
Global alignment (Needleman-Wunsch)
Local alignment (Smith-Waterman)
Group assignments for project
Developing Pairwise Sequence Alignment Algorithms

3. Overview of Pairwise Sequence Alignment
Dynamic Programming
Applied to optimization problems
Useful when
Problem can be recursively divided into sub-problems
Sub-problems are not independent
Needleman-Wunsch is a global alignment technique that uses an iterative algorithm and no gap penalty (could extend to fixed gap penalty).
Smith-Waterman is a local alignment technique that uses a recursive algorithm and can use alternative gap penalties (such as affine). Smith-Waterman’s algorithm is an extension of Longest Common Substring (LCS) problem and can be generalized to solve both local and global alignment.
Note: Needleman-Wunsch is usually used to refer to global alignment regardless of the algorithm used.
Developing Pairwise Sequence Alignment Algorithms

4. Developing Pairwise Sequence Alignment Algorithms
References
An Introduction to Bioinformatics Algorithms (Computational Molecular Biology) Neil C. Jones, Pavel Pevzner
Computational Molecular Biology – An Algorithmic Approach, Pavel Pevzner
Introduction to Computational Biology – Maps, sequences, and genomes, Michael Waterman
Algorithms on Strings, Trees, and Sequences – Computer Science and Computational Biology, Dan Gusfield
Developing Pairwise Sequence Alignment Algorithms

5. Developing Pairwise Sequence Alignment Algorithms
Classic Papers
Needleman, S.B. and Wunsch, C.D. A General Method Applicable to the Search for Similarities in Amino Acid Sequence of Two Proteins. J. Mol. Biol., 48, pp , (
Smith, T.F. and Waterman, M.S. Identification of Common Molecular Subsequences. J. Mol. Biol., 147, pp , 1981.(
Developing Pairwise Sequence Alignment Algorithms

6. Why search sequence databases?
I have just sequenced something. What is known about the thing I sequenced?
I have a unique sequence. Is there similarity to another gene that has a known function?
I found a new protein sequence in a lower organism. Is it similar to a protein from another species?
Developing Pairwise Sequence Alignment Algorithms

7. Global Alignment Method
Output:
An alignment of two sequences is represented by three lines
The first line shows the first sequence
The third line shows the second sequence.
The second line has a row of symbols.
The symbol is a vertical bar wherever characters in
the two sequences match, and a space where ever they do not.
Dots (or dashes) may be inserted in either sequence to represent gaps.
Developing Pairwise Sequence Alignment Algorithms

8. Global Alignment Method (cont. 1)
For example, the two hypothetical sequences
abcdefghajklm
abbdhijk
could be aligned like this
|| | | ||
abbd...hijk
As shown, there are 6 matches,
2 mismatches, and one gap of length 3.
Developing Pairwise Sequence Alignment Algorithms

9. Global Alignment Method (cont. 2)
The alignment can be scored according to a payoff matrix for
fixed scoring. You can also use PAM or BLOSUM.
$payoff = {match => $match,
mismatch => $mismatch,
gap_open => $gap_open,
gap_extend => $gap_extend};
For correct operation, an algorithm is created such that the
match must be positive and the other payoff entities must be negative.
Developing Pairwise Sequence Alignment Algorithms

10. Global Alignment Method (cont. 3)
Example
Given the payoff matrix
$payoff = {match => 4,
mismatch => -3,
gap_open => -2,
gap_extend => -1};
What is the alignment and what is the alignment score for the
Following two sequences?
Sequence 1: abcdefghajklm
Sequence 2: abbdhijk
Developing Pairwise Sequence Alignment Algorithms

11. Global Alignment Method (cont. 4)
The sequences
abcdefghajklm
abbdhijk
are aligned and scored like this
a b c d e f g h a j k l m
| | | | | |
a b b d h i j k
match
mismatch
gap_open
gap_extend
for a total score of = 13.
Developing Pairwise Sequence Alignment Algorithms

12. Global Alignment Method (cont. 5)
The algorithm should guarantee that no other
alignment of these two sequences has a
higher score under this payoff matrix.
Developing Pairwise Sequence Alignment Algorithms

13. Three steps in Dynamic Programming
1. Initialization
2. Matrix fill or scoring
3. Traceback and alignment
Developing Pairwise Sequence Alignment Algorithms

14. Developing Pairwise Sequence Alignment Algorithms
Ends-Free Global Alignment with Fixed Scoring
Two sequences will be aligned.
GGATCGA (sequence #1 = V)
GAATTCAGTTA (sequence #2 = W)
A simple fixed scoring scheme will be used
(vi, wj) = 1 if the residue at position i of sequence #1 (vi) is the
same as the residue at position j of the sequence #2 (wj) – called
match score
(vi, wj) = 0 if vi ≠ wj – called mismatch score
(vi, -) = (-, wj) = 0 – called gap penalty
Developing Pairwise Sequence Alignment Algorithms

15. Developing Pairwise Sequence Alignment Algorithms
Matrix fill step: Each position Si,j is defined to be the
MAXIMUM score at position i,j
Si,j = MAXIMUM [
Si-1, j-1 + (vi, wj) (match or mismatch in the diagonal)
Si, j-1 + w (gap in sequence #1 = V)
Si-1, j + w (gap in sequence #2 = W)]
column
row
Developing Pairwise Sequence Alignment Algorithms

16. Developing Pairwise Sequence Alignment Algorithms
Initialization step: 1) Create Matrix with m + 1 columns
and n + 1 rows, where n = number of letters in sequence 1
and m = number of letters in sequence 2.
2) First column and first row will be filled with 0’s (for
ends-free alignment).
Developing Pairwise Sequence Alignment Algorithms

17. Developing Pairwise Sequence Alignment Algorithms
Scoring Step:
Fill in row by row:
Developing Pairwise Sequence Alignment Algorithms

18. Developing Pairwise Sequence Alignment Algorithms
Traceback Step:
Seq#1 G G A - T C - G - - A
| | | | | |
Seq#2 G A A T T C A G T T A
Developing Pairwise Sequence Alignment Algorithms

19. Global Alignment output file
Global: HBA_HUMAN vs HBB_HUMAN
Score:
HBA_HUMAN VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFP 44
|:| :|: | | |||| : | | ||| |: : :| |: :|
HBB_HUMAN VHLTPEEKSAVTALWGKV..NVDEVGGEALGRLLVVYPWTQRFFE 43
HBA_HUMAN HF.DLS.....HGSAQVKGHGKKVADALTNAVAHVDDMPNALSAL 83
| ||| |: :|| ||||| | :: :||:|:: : |
HBB_HUMAN SFGDLSTPDAVMGNPKVKAHGKKVLGAFSDGLAHLDNLKGTFATL 88
HBA_HUMAN SDLHAHKLRVDPVNFKLLSHCLLVTLAAHLPAEFTPAVHASLDKF 128
|:|| || ||| ||:|| : |: || | |||| | |: |
HBB_HUMAN SELHCDKLHVDPENFRLLGNVLVCVLAHHFGKEFTPPVQAAYQKV 133
HBA_HUMAN LASVSTVLTSKYR
:| |: | ||
HBB_HUMAN VAGVANALAHKYH
%id = %similarity = (88/139 *100)
Overall %id = 43.15; Overall %similarity = (88/146 *100)
Developing Pairwise Sequence Alignment Algorithms

20. Developing Pairwise Sequence Alignment Algorithms
LCS Problem (review)
Similarity score
si-1,j
si,j = max { si,j-1
si-1,j-1 + 1, if vi = wj
Developing Pairwise Sequence Alignment Algorithms

21. Extend LCS to Global Alignment
si-1,j + (vi, -)
si,j = max { si,j-1 + (-, wj)
si-1,j-1 + (vi, wj)
(vi, -) = (-, wj) = - = fixed gap penalty
(vi, wj) = score for match or mismatch – can be fixed, from PAM or BLOSUM
Developing Pairwise Sequence Alignment Algorithms

22. Global Alignment Alternatives
Ends-free alignment – don’t penalize gaps at the beginning or end
Initialize first row and column of S to 0
Search last row and column for maximum score
Regular global alignment – score end to end (penalize gaps at beginning and end)
Initialize first row and column of S with gap penalty
Alignment score is in the lower right corner of S
Developing Pairwise Sequence Alignment Algorithms

23. Historical Perspective: Needleman-Wunsch (1 of 3)
Match = 1
Mismatch = 0
Gap = 0
Developing Pairwise Sequence Alignment Algorithms

24. Historical Perspective: Needleman-Wunsch (2 of 3)
Developing Pairwise Sequence Alignment Algorithms

25. Historical Perspective: Needleman-Wunsch (3 of 3)
From page 446:
It is apparent that the above array operation can begin at any of a number of points along the borders of the array, which is equivalent to a comparison of N-terminal residues or C-terminal residues only. As long as the appropriate rules for pathways are followed, the maximum match will be the same. The cells of the array which contributed to the maximum match, may be determined by recording the origin of the number that was added to each cell when the array was operated upon.
Developing Pairwise Sequence Alignment Algorithms

26. Developing Pairwise Sequence Alignment Algorithms
Smith-Waterman Algorithm Advances in Applied Mathematics, 2: (1981)
The Smith-Waterman algorithm is a local alignment tool used to obtain sensitive pairwise similarity alignments.
Smith-Waterman algorithm uses dynamic programming.
It selects the optimal path as the highest ranked alignment.
Smith-Waterman algorithm is useful for finding local areas of similarity between sequences that are too dissimilar for global alignment.
The S-W algorithm uses a lot of computer memory.
BLAST and FASTA are other search algorithms that use some aspects of S-W.
Developing Pairwise Sequence Alignment Algorithms

27. Smith-Waterman (cont. 1)
a. It searches for sequence matches.
b. Assigns a score to each pair of amino acids
-uses similarity scores
-uses positive scores for related residues
-uses negative scores for substitutions and gaps
c. Initializes edges of the matrix with zeros
d. As the scores are summed in the matrix, any sum below 0 is
recorded as a zero.
e. Begins backtracing at the maximum value found
anywhere in the matrix.
f. Continues the backtrace until the score falls to 0.
Developing Pairwise Sequence Alignment Algorithms

28. Developing Pairwise Sequence Alignment Algorithms
Smith-Waterman (cont. 2)
H E A G A W G H E E
Put zeros on
borders. Assign initial scores
based on a scoring
matrix. Calculate new scores based on
adjacent cell scores.
If sum is less than
zero or equal to zero
begin new scoring
with next cell. P A W H E
This example uses the BLOSUM45 Scoring Matrix with a gap
penalty of -8.
Developing Pairwise Sequence Alignment Algorithms

29. Developing Pairwise Sequence Alignment Algorithms
Smith-Waterman (cont. 3)
H E A G A W G H E E P A W H E
Begin backtrace at the
maximum value found
anywhere on the matrix.
Continue the backtrace
until score falls to zero
AWGHE
|| ||
AW-HE
Path Score=28
Developing Pairwise Sequence Alignment Algorithms

30. Calculation of similarity score and percent similarity
A W G H E
A W - H E
Blosum45 SCORES
GAP PENALTY (novel)
% SIMILARITY =
NUMBER OF POS. SCORES
DIVIDED BY NUMBER OF AAs
IN REGION x 100
Similarity Score= 28
% SIMILARITY = 4/5 x 100
= 80%
Developing Pairwise Sequence Alignment Algorithms

31. Extend LCS to Local Alignment
0 (no negative scores)
si-1,j + (vi, -)
si,j = max { si,j-1 + (-, wj)
si-1,j-1 + (vi, wj)
(vi, -) = (-, wj) = - = fixed gap penalty
(vi, wj) = score for match or mismatch – can be fixed, from PAM or BLOSUM
Developing Pairwise Sequence Alignment Algorithms

32. Historical Perspective: Smith-Waterman (1 of 3)
Algorithm
The two molecular sequences will be A=a1a an, and B=b1b bm. A similarity s(a,b) is given between sequence elements a and b. Deletions of length k are given weight Wk. To find pairs of segments with high degrees of similarity, we set up a matrix H . First set
Hk0 = Hol = 0 for 0 <= k <= n and 0 <= l <= m.
Preliminary values of H have the interpretation that H i j is the maximum similarity of two segments ending in ai and bj. respectively. These values are obtained from the relationship
Hij=max{Hi-1,j-1 + s(ai,bj), max {Hi-k,j – Wk}, max{Hi,j-l - Wl }, 0} ( 1 ) k >= l >= 1
1 <= i <= n and 1 <= j <= m.
Developing Pairwise Sequence Alignment Algorithms

33. Historical Perspective: Smith-Waterman (2 of 3)
The formula for Hij follows by considering the possibilities for ending the segments at any ai and bj.
If ai and bj are associated, the similarity is
Hi-l,j-l + s(ai,bj).
(2) If ai is at the end of a deletion of length k, the similarity is
Hi – k, j - Wk .
(3) If bj is at the end of a deletion of length 1, the similarity is
Hi,j-l - Wl. (typo in paper)
(4) Finally, a zero is included to prevent calculated negative similarity, indicating no similarity up to ai and bj.
Developing Pairwise Sequence Alignment Algorithms

34. Historical Perspective: Smith-Waterman (3 of 3)
The pair of segments with maximum similarity is found by first locating the maximum element of H. The other matrix elements leading to this maximum value are than sequentially determined with a traceback procedure ending with an element of H equal to zero. This procedure identifies the segments as well as produces the corresponding alignment. The pair of segments with the next best similarity is found by applying the traceback procedure to the second largest element of H not associated with the first traceback.
Developing Pairwise Sequence Alignment Algorithms

35. The E value (false positive expectation value)
The Expect value (E) is a parameter that describes the number of “hits” one can "expect" to see just by chance when searching a database of a particular size. It decreases exponentially as the Similarity Score (S) increases (inverse relationship). The higher the Similarity Score, the lower the E value. Essentially, the E value describes the random background noise that exists for matches between two sequences. The E value is used as a convenient way to create a significance threshold for reporting results. When the E value is increased from the default value of 10 prior to a sequence search, a larger list with more low-similarity scoring hits can be reported. An E value of 1 assigned to a hit can be interpreted as meaning that in a database of the current size you might expect to see 1 match with a similar score simply by chance.
Developing Pairwise Sequence Alignment Algorithms

36. E value (Karlin-Altschul statistics)
E = K•m•n•e-λS
Where K is constant, m is the length of the query sequence, n is the length of the database sequence, λ is the decay constant, S is the similarity score.
If S increases, E decreases exponentially.
If the decay constant increases, E decreases exponentially
If m•n increases the “search space” increases and there is a greater chance for a random “hit”, E increases. Larger database will increase E. However, larger query sequence often decreases E. Why???
Developing Pairwise Sequence Alignment Algorithms

37. Project Teams and Presentation Assignments
Base Project (Global Alignment):
Larry and Darnell
Extension 1 (Ends-Free Global Alignment):
Steven and Charlie
Extension 2 (Local Alignment):
Olivera and Natalia
Extension 3 (Local Alignment – all):
Brittany and Alana
Extension 4 (Database):
Nathaniel and Anna U.
Extension 5 (Space Efficient Algorithm):
David and Shilpa
Extension 6 (Affine Gap Penalty):
Rachel and Anna P.
Extension 7 (Hirschberg’s Algorithm):
Wendy and Andrew
Developing Pairwise Sequence Alignment Algorithms

38. Developing Pairwise Sequence Alignment Algorithms
Workshop
Meet with your group and develop for the overall structure of your program
High-level algorithm
Identify the modules, functions (including parameters), and global variables
Determine who is responsible for each module
Devise a development timeline and a testing strategy
Developing Pairwise Sequence Alignment Algorithms