1. COFFEE: an objective function for multiple sequence alignments
Wang Yi
Computational Genomics Group
Bioinformatics Institute

2. Why MSA
Multiple Sequence Alignments (MSA) are among the most important tools for analyzing biological sequences
Useful for:
Structure prediction
Phylogenetic analysis
Function prediction
Polymerase Chain Reaction (PCR) primer design
And more…

3. What is COFFEE
Consistency based Objective Function For alignmEnt Evaluation
The COFFEE score reflects the level of consistency between a MSA and a library containing pairwise alignments of the same group of sequences

4. What is consistency? Why study consistency between MSA and pairwise alignment?

5. Why pairwise alignments
MSA, unlike pairwise alignment, cannot guarantee optimality yet
Pairwise alignments use dynamic programming to obtain optimal result
While it is too expensive for MSA to adopt the same algorithm
People try to exploit the optimality of pairwise alignment by progressively combine them into MSA

6. Pairwise alignments to MSA
ClustalW is a widely recognized package among such attempts
ClustalW generates a guide tree according to the distances between each pair of sequences
Then it aligns all these sequences progressively, from the closest branches to the most distant ones

7. Problem with ClustalW
Mistakes made at the beginning of this procedure are never corrected
This problem stems from not considering the consistency between close pair and distant ones

8. Two solutions To solve this problem, we can do either:
Check the consistency between one pairwise alignment and the rest of the library before the progressive alignment
Or: after obtaining a MSA, check the consistency between each pair of residues with its counterpart in pairwise alignment library

9. Consistency Vs Consistency
These two kinds of consistency are actually closely related:
To increase the consistency between pairs will decrease the chance of inconsistency between a pair with its origin in the library
T-COFFEE takes the first approach while COFFEE calculates the latter

10. A simple example Suppose we have four sequences:
SeqA: THE LAST FAT CAT
SeqB: THE FAST CAT
SeqC: THE VERY FAST CAT
SeqD: THE FAT CAT
We make a pairwise alignment library of these sequences:

11. Compare the consistency
SeqA THE LAST FAT CAT SeqB THE FAST CAT ---
SeqA THE LAST FA-T CAT SeqC THE VERY FAST CAT
SeqA THE LAST FAT CAT SeqD THE ---- FAT CAT
SeqB THE ---- FAST CAT SeqC THE VERY FAST CAT
SeqB THE FAST CAT SeqD THE FA-T CAT
SeqC THE VERY FAST CAT SeqD THE ---- FA-T CAT
SeqA THE LAST FA-T CAT SeqB THE FAST CA-T --- SeqC THE VERY FAST CAT SeqD THE ---- FA-T CAT
Or SeqA THE LAST FA-T CAT SeqB THE ---- FAST CAT SeqC THE VERY FAST CAT SeqD THE ---- FA-T CAT

12. How COFFEE works
Create a library of pairwise alignment for each possible pairs of sequences
Compare each pair of aligned residues in the MSA to its counterpart in the library
The overall consistency score is equal to the number of pairs that occur in both MSA and the library, divided by the total number of pairs in MSA.

13. How COFFEE works
To decrease the amount of noise produced by inaccurate pairwise alignments in the library, we set a weight for each of them
The weight equals the percent identity between the alignment
For example: SeqA THE LAST FAT CAT SeqB THE FAST CAT ---
The weight is 8/13*100%=61.5%

14. The idea of weight
The lower the weight (the more mismatches in the pairwise alignment), the more distant these two sequences are, and the less necessary we need to keep such pair in MSA.
Therefore, with weight taken into mind we can keep the consistency only when it’s necessary

15. COFFEE Score
Aij is the pairwise projection of sequences i and j obtained from a MSA
Len(Aij) is the length of Aij
Wij is the weight of pairwise alignment on sequences i and j in the library
Score(Aij) is the number of aligned pairs of residues that are shared between Aij and the library

16. Features of COFFEE
There is no gap penalty, since they are already contained in the library
The score is normalized by the value of maximum score, thus it’s between 0 and 1
The cost of substitution is made position dependent, i.e., we tolerate mismatch that already occurred in the library

17. Comments on COFFEE

18. Position-specific issue
The current objective function is not position-specific enough
It applies general weights in the whole pairwise alignments instead of functional parts
Even very close alignment has non-functional parts, which contain more mismatches

19. Distant and close alignments
A close alignment example:
THE –FIRST GULF WAR IS FOR JUSTICE ||| || |||| ||| || ||| | THE THIRD- GULF WAR IS FOR ---OIL–
A distant alignment example:
GO ATTACK THIS WEAK BUT EVIL IRAQ || |||| DUN TOUCH THE ARMED AND EVIL NKOREA

20. Position-specific issue
The current score function places the same weight to such non-important section
It does reduce the amount of noise produced by inaccurate alignment of distant sequences
However it fails to do so in close ones
Nonetheless, it gives lower weight to functional part in distant sequences

21. Revision of COFFEE
Score(Aijl) = 1 when the pair at position l in sequence i and j occurs with that in library, otherwise it is 0
W(Aijl) = 1 when the pair at position l in sequence i and j in the library are identical, otherwise it’s k (0<=k<1)

22. Features of the revision
Dispose of the idea as to adopt overall weight
Instead we check the identity of each pair of residues
The value of k depends on how we evaluate mismatch
It could be set according to substitution matrix

23. Alternative alignment
Although pairwise alignment is optimal, it depends on its constraints, such as penalty
Different constraints generate alignments of various purpose
Instead of only one alignment of each possible pair of sequences in the library, we could add its alternative alignment(s) so as to include more information

24. Alternative alignment
When using library with alternative alignments, we have to apply the revision of COFFEE introduced previously
Otherwise pairs from different alignments can use only one weight from them
However, till now scientists used to weigh different alignments of the same constraint
How to weigh alignments of different constraints is yet a new challenge

25. Conclusion
COFFEE evaluates the consistency of each pairwise projection with its pairwise alignment
COFFEE can be used in iterative MSA algorithm at a judging point
COFFEE is not position-specific enough to filter noise due to inaccurate alignments, which leads to a revision provided by our group
Alternative pairwise alignments could be added to the library to include more information between sequences

26. Thanks for your attention!
Feb 20th, 2003