1. Biology 162 Computational Genetics Todd Vision Fall 2004 31 Aug 2004
Pairwise alignment
Biology 162 Computational Genetics
Todd Vision Fall 2004
31 Aug 2004

2. Preview General concepts in alignment How to read a dotplot
Scoring matrices and gap penalties
Basic dynamic programming algorithms
Needleman-Wunsch
Smith-Waterman
Using more realistic gap penalties

3. Homology
Two sequences are homologous if they are descended from a common ancestral sequence.
Homology is either all or nothing
Only similarity can be quantitative
An alignment is a model of positional homology between nucleotide or amino acid residues

4. Some applications of sequence alignment
Sequence/genome assembly
Locating exons within genomic sequences
Functional annotation by homology search against a database
Identification of conserved signatures/motifs/domains
Molecular evolution and phylogenetics
Structural homology modeling

5. Alignments classified by
Span
Global, encompassing full-length sequences
Local, restricted to conserved segments
Number of sequences
Pairwise, involving only two sequences
Multiple, involving more than two
Algorithm
Optimality guarantee
Heuristic

6. Amino acids versus DNA
DNA sequences give much worse alignments than amino acid sequences
Fewer letters
Less realistic scoring matrices
Some applications can align codons
How large would that scoring matrix be?
If that’s not possible
Use aa alignment to guide DNA alignment of coding sequences
Use conceptual translations (6 potential coding frames) for database searches

7. Dotplots: phage l cI vs. P22 c2 repressorB A
Window size
Stringency

8. Internal repeats: human LDL protein
Window size = 23 bp
Stringency = 7 bp

9. Inversions

10. Hanging ends y y x x
Overlap
Nesting x y

11. Percent amino acid identity
Twilight Zone
100 90 80 70 60 50 40 30 20 10
Percent amino acid identity

12. Scoring an alignment Possible relationships at a position
Match (identity)
Mismatch (substitution)
Gap (insertion/deletion, or indel)
A scoring matrix is used for matches and mismatches
Typically binary for nucleic acids
PAM, BLOSUM, & others for amino acids
Gap penalties must be “tacked on”
The alignment score is the sum of the scores at each position in the alignment, including gaps

13. LOD scores
Let pab be the expected frequency of aligned residue pair a and b among all aligned residues
Let qa be the frequency of individual amino acid a

14. Point Accepted Mutation (PAM) matrices
Trained on alignments of closely related proteins
PAM1 implies 1 substitution per 100 amino acids
PAM250 = (PAM1)250
Training set strongly biased toward globular proteins (more suitable matrices are available for more specific protein classes)

16. Choosing the right PAM matrix
Low PAM values discriminate among amino acids more dramatically
As the exponent increases, values within a row converge on amino acid frequencies
Choice of matrix typically depends on observed % identity
Classic chicken and egg problem
PAM250 corresponds to 20% identity
Assumes substitution rate is equal among sites (Poisson model), which we know to be false

17. BLOSUM scoring matrices
Trained on ungapped alignments (blocks) of divergent sequences to capture ‘long-term’ substitution patterns
Named BLOSUMx, where x (from 0 to 100) is the minimum percent identity of the sequences in the alignment. (The smaller the value of x, the more divergent the sequences).
Note that numbers have opposite meanings for PAM and BLOSUM!
BLOSUM62 is in wide use (eg it is the default in BLAST)

18. BLOSUM62 BLOSUM62 A R N D C Q E G H I L K M F P S T W Y V B Z X **
BLOSUM62

19. Gap penalties Naïve score Affine scores
Each gap position receives independent penalty of d
Affine scores
Score depends on length of contiguous gap
Gap opening penalty d
Gap extension penalty e

20. Dynamic programming
A problem solving technique that employs recursion to solve a larger problem by solving a nested set of similar subproblems

21. Application to pairwise alignment
Imagine
We know the score for the first i-1 and j-1 residues of sequences x and y
i-1 and j-1 are aligned in the optimal alignment
There are three possibilities for the next position in the alignment
A gap in sequence x
A gap in sequence y
A match or mismatch between i and j
The maximum scoring alignment among these has to be in the optimal global alignment

22. Overview of algorithm
We can use this fact to recursively fill out a matrix containing the score F(i,j) of the optimal alignment for every pair of residues i and j
We also store a pointer to one of three previously filled out cells in the matrix, forming a path graph
The optimal global alignment must be a path within the path graph
It can be found by performing a traceback from the final cell in the recursion

23. Path Graph Diagonal moves represent matches and mismatches
Horizontal and vertical moves represent gaps (indels)

24. Needleman-Wunsch recursion
xi, yj match
yj aligned to gap
xi aligned to gap
Let s(C,C)=1, s(C,G)=s(G,C)=-2, and d=-1 y ?C ?-
A G A C 3 2 ?- ?G
A G A C 3 2
A C 3 3 x A C 3
x: AC
y: AC

25. Needleman-Wunsch c g t g c g t c t g t g a Initialize F(0,0) = 0
Use pointers to remember path
Match=+1, Mismatch=-1, Gap=-2
arbitrary order of precedence:  , , 
Needleman-Wunsch
c g t g c g t c t
g t g a
 -2
 -4
 -6
 -8
 -10
 -12
 -14
-2
 -4
 -6
 -8
 -10
 -12
 -14

26. Needleman-Wunsch: completed path graph
c g t g c g t c t
g t g a
-2
-4
-6
-8
-10
-12
-14
-2
+1
-1
-3
-5
-7
-9
-11
-4
-1
 0
-8
-6
-3
-1
 0
-8
-5
-2
-10
-7
+2
-12
-9
 0
-14
-11
-3

27. Needleman-Wunsch: traceback
c g t g c g t c t
g t g a
-2
-4
-6
-8
-10
-12
-14
-2
+1
-1
-3
-5
-7
-9
-11
-4
-1
 0
-8
-6
-3
-1
 0
-8
-5
-2
-10
-7
+2
-12
-9
 0
-14
-11
-3
cgtgcg-t
| || | |
c-tgtgat
optimal global alignment:

28. Complexity of algorithm
For sequences of length m and n
We consider 3 options at each cell
We store mn scores and pointers
We trace back no more than m+n steps
3mn +m+n in time, 3mn in memory
O(mn) in both time and memory
If m=n, O(n2)

29. Smith-Waterman algorithm
Local pairwise alignment
Cells with negative scores are set to zero
Traceback from highest scoring cell
Stop when 0 is encountered
Also O(nm)

30. Smith-Waterman recursion
xi, yj match
yj aligned to gap
xi aligned to gap
score ≤ 0

31. Smith-Waterman algorithm
c g t g c g t c t
g t g a
+1
+2
+3
+1
+1
cgtgcgt
|||
ctgtgat
optimal local alignment:

32. Guaranteeing a local alignment
Use of SW algorithm alone does not guarantee “local” behavior
Sensitive to the scoring function (should be negative for random sequences)
Use of LOD scores help ensure this
Gap penalties must also be chosen carefully
If it is cheaper to insert a gap than to tolerate a mismatch, then gaps will be inserted where no alignment is possible

33. More realistic gap penalties
General gap function g(g)
Requires O(n3) operations

34. Affine gap penalties Gap score: g(g)=-d-(g-1)e Can be done in O(mn)
We need to keep track of three scores (and pointers) at each cell

35. A theme with variations
Overlapping or nested sequences
Do not penalize hanging ends
Repeated sequences
Asymmetric algorithm can find multiple local alignments of x in y or y in x
The basic idea admits many variations

36. Things to keep in mind about pairwise alignments
There may be multiple optima
Optimality is only guaranteed with respect to the scoring function – the alignment may still be biologically wrong!
O(mn) is still too big when n is the size of a major sequence database

37. Summary
Dotplots are an excellent visual tool to decide whether and what kind of alignment is appropriate
PAM and BLOSUM series matrices provide empirical LOD values for scoring alignments
Different flavors of alignment are produced by variants on a basic dynamic programming algorithm
Needleman-Wunsch for global alignments
Smith-Waterman for local alignments
Affine gap penalties balance biological realism with computational feasibility

38. Reading assignment
Nicholas et al. (2002) Strategies for multiple sequence alignment. Biotechniques 32, (handout)