1. Needleman-Wunsch with affine gaps
Gap scores: g(g)=-d-(g-1)e where d=2, e=1
Precedence: M, Ix, Iy
PAM 250 A C D 2 -2 12 -5 4
Align the sequences: CA and DC

2. Multiple sequence alignment
Biology 162 Computational Genetics
Todd Vision
2 Sep 2004

3. Preview How to score a multiple alignment
Sum of pairs scores
Weighting
Generalizing pairwise alignment algorithms
Full dynamic programming
Carillo-Lipman
Practical methods
Progressive
Iterative
Stochastic
Probabilistic
Some final thoughts

4. Multiple sequence alignment (MSA)

5. Mind the gaps
Trivial
Difficult

6. Natural score Tree score
Even with a known tree, finding an MSA to optimize the tree score is NP-hard A
SAE B E
SBD
SDE D
SCD C

7. Star-tree scores Assume an unresolved phylogeny Sum-of-pairs ()
Entropy
Consistency
Weighs agreement with external evidence

8. Entropy as used in a sequence logo

9. SP scores: pros and cons
Easy, intuitive, work OK
Cons
Substitution scores based on pairs of residues
Inconsistent behavior with k
One mismatch matters more when k is large than when k is small
Gap penalties undefined for s(-,-)

10. Natural gap penalties
Gap costs in multiple alignment should be equal to sum of gap costs in induced pairwise alignments
Computationally prohibitive to compute for most algorithms
Instead, quasi-natural gap costs are computed
They are almost always identical

11. Weighted SP scores
Scores are not independent due to (unaccounted for) shared ancestry
To correct this, sum-of-pairs scores from related sequences can be down-weighted
Variety of weighting schemes exist
Tree-based weighting is simplest
Assign weights proportional to sum of branch lengths on a phylogenetic tree
Obviously requires a tree (but we have an approximate tree in some algorithms)

12. Full dynamic programming
We have k sequences of length n
Recursion equations are similar to pairwise case
We can use a simple extension of pairwise scoring
As before, we can guarantee an optimal alignment
The problem is we must fill out a k-dimensional hypercube
Time and space grow exponentially in k
At least O(k22knk)
Computationally prohibitive even for a moderate number of short sequences

13. Carillo-Lipman algorithm
Reduce volume of hypercube that is searched
Upper bound on score
Score of optimal MSA is less than or equal to sum of scores of optimal pairwise alignments
Lower bound on score
Score of optimal MSA must be greater or equal to score of heuristic MSA
Projections in each dimension defined by optimal pairwise alignments and induced heuristic alignments
Optimum path is bounded by projections in all dimensions

14. Carillo-Lipman algorithm

15. Carillo-Lipman algorithm
Only works for SP scoring function
Implemented in MSA software
Can still only tackle small cases (eg 15 sequences of length 300)

16. Practical global alignment methods
Progressive
Uses a guide tree to reduce the problem to multiple pairwise alignments
Iterative
Initialized with a fast multiple alignment
Sequences are randomly partitioned and pairwise aligned until convergence
Stochastic
Genetic algorithms as an example
Probabilistic
Hidden Markov models

17. Progressive Alignment
Fast, but no guarantee of finding the optimum
Implementations: Feng-Doolittle, ClustalW, Pileup
Steps
Compute all k(k-1)/2 pairwise alignments
Use alignment scores to construct guide tree
Perform pairwise alignments beginning at the leaves of the guide tree and working toward the root

18. Pairwise score matrix S12 S13 S14 S15 S23 S24 S25 S34 S35 S45
Sequence 1
Sequence 2
Sequence 3
Sequence 4
Sequence 5
S12
S13
S14
S15
S23
S24
S25
S34
S35
S45

19. Guide Tree Sequence 1 Sequence 2 Sequence 3 Sequence 4 Sequence 5 2 4

20. New Problem How to align a sequence to an alignment?
Or two alignments to each other?
Feng-Doolittle solution
Choose highest scoring pair of sequences between the two groups to guide the alignment
ClustalW solution
Profile alignment: compute generalized sum of pairs score

21. Profiles Profile II Profile I 1 2 3 4 1 2 3 4 ---------- ----------
a w w w w
pos c w w w w
g w w w w
t w w w w S
Profile I
a w w w w
pos c w w w w
g w w w w
t w w w w S

22. ClustalW- ad hoc improvements
Variable substitution matrix
Encourage gaps preferentially in structural loops
Residue-specific gap penalties
Reduced penalties in hydrophilic regions
Reduced gap penalties in positions already containing gaps
Increased gap opening penalties in flanking sequence of gap

23. Progressive alignment: major weakness
Errors introduced in the alignment of subgroups are propagated through all subsequent steps
There is no provision for correcting such errors once they happen
Local optimum versus global optimum

24. Iterative alignment
Again capitalizes on the ease of pairwise alignment between groups of sequences
Allows for gaps to be removed and positions to be shifted in each iteration
Some algorithms guarantee convergence given long enough
Can be several orders of magnitude slower than progressive methods
Most successful implementation: PRRN

25. Iterative alignment ACGATAGACAT ACG-TACAGAT ACGATAGACAT ACGATAGACAT
CGA-TAGAGAC
CGA-TACAGAC
ACGATAGACAT
ACG-TACAGAT
-CGATAGAGAC
-CGATACAGAC
CGA-TAGAGAC
CGA-TACAGAC

26. T-COFFEE Uses consistency as an objective function
Evaluates consistency with pairs of residues found in optimal local alignments and heuristic global alignment
The consistency function can also incorporate extraneous information (such as structural constraints)
Among the most successful of approaches when % identity is moderate to good

27. Dialign A multiple local alignment algorithm
Informally, it works by chaining together ungapped segments from dotplots
Does not explicitly score gaps at all
May contain unaligned regions flanked by aligned regions

28. Stochastic methods Genetic algorithms (eg SAGA)
Initalize with population of heuristic alignments
Evaluate ‘fitness’ of individual alignments
Can employ computationally intensive scoring functions
Create new generation of alignments
Select parents according to fitness
‘Cross-over’ attributes of parents
Apply mutation to perturb progeny alignments
Return to ‘evaluate fitness’ step
Stopping rule

29. Probabilistic methods
Hidden Markov Models
Models that generate MSAs
Many parameters to fit
Probability of each residue in each column
Probability of entering gap states between columns
Perform poorly on unaligned sequences
But are commonly used in signature databases
Perform well for finding matches to already aligned sequences
Efficient algorithms exist for aligning sequences to HMMs

30. Hidden Markov model

31. How do you know when you’ve got the right answer?
Short answer: you don’t.
Structural superposition typically used to evaluate methodologies
BAliBASE: database of curated reference alignments

32. Comparison of test and reference alignments
Modified SP score
Frequency with which pairs of residues aligned in test are aligned in reference
Column score
Frequency with which entire columns of residues are aligned in both test and reference

33. Be skeptical! MSA is a hard problem
Computationally
Biologically
There is no ‘one size fits all’ algorithm
No two algorithms need agree

34. The future of MSA
Chances are your new sequence matches something already in the database
It may soon be a rarity to generate an MSA from scratch
Signature databases currently allow local alignment of a query to a pre-existing local multiple alignment (eg InterProScan)

35. Summary Challenges in MSA How MSA is achieved in practice
Even bounded dynamic programming is impractical
Appropriate scoring is not obvious
How MSA is achieved in practice
Fastest
Progressive pairwise alignment
Slower
Iterative alignment
Stochastic alignment
Automated MSAs require manual scrutiny

36. Reading Assignment
Pertsemlidis A, Fondon JW (2002) Having a BLAST with bioinformatics (and avoiding BLASTphemy), 10 pgs.

37. Reading Assignment
Gusfield D (1997) pgs in Algorithms on Strings, Trees and Sequences.
Durbin et al. (1998) pgs. 36, in Biological Sequence Analysis.