1. ©CMBI 2001 Alignment Most alignment programs create an alignment that represents what happened during evolution at the DNA level. To carry over information from a well studied to a newly determined sequence, we need an alignment that represents the protein structures of today.

2. ©CMBI 2001 The amino acids Most information that enters the alignment procedure comes from the physicochemical properties of the amino acids. Example: which is the better alignment (left or right)? CPISRTWASIFRCW CPISRT---LFRCW CPISRTL---FRCW

3. ©CMBI 2001 A difficult alignment problem AYAYAYAYSY LGLPLPLPLP So, in an alignment of more than 2 sequences you can find more information than from just the 2 sequences you are interested in. How do we make these multi- sequence alignmnets? AGAPAPAPSP

4. ©CMBI 2001 A difficult alignment problem solved AYAYAYAYSY AGAPAPAPSP LGLPLPLPLP

5. ©CMBI 2001 Alignment order MIESAYTDSW QFEKSYVTDY -MIESAYTDSW QFEKSYVTDY-

6. ©CMBI 2001 Alignment order MIESAYTDSW QFEKSYVTDY QWERTYASNF -MIESAYTDSW QFEKSYVTDY- QWERTYASNF-

7. ©CMBI 2001 Conclusion Align first the sequences that look very much like each other. So you ‘build up information’ while generating those alignments that most likely are correct.

8. ©CMBI 2001 Alignment order In order to know which sequences look most like each other, you need to do all pairwise alignments first. This is exactly what CLUSTAL does. CLUSTAL builds a tree while doing the build-up of the multiple sequence alignment.

9. ©CMBI 2001 MSA and trees Take, for example, the three sequences: 1 ASWTFGHK 2 GTWSFANR 3 ATWAFADR and you see immediately that 2 and 3 are close, while 1 is further away. So the tree will look roughly like: 3 2 1

10. ©CMBI 2001 Aligning sequences; start with distances D E Matrix of pair-wise distances between five sequences. 10 8 7 D and E are the closest pair. Take them, and collapse the matrix by one row/column.

11. ©CMBI 2001 Aligning sequences D E A B

12. ©CMBI 2001 Aligning sequences D E C A B

13. ©CMBI 2001 Aligning sequences D E C A B

14. ©CMBI 2001 Back to the alignment 1 ASWTFGHK 2 GTWSFANR 3 ATWAFADR Actually I cheated. 1 is closer to 3 than to 2 because of the A at position 1. How can we express this in the tree? For example: 3 2 1 3 2 1 I will call this tree-flipping

15. ©CMBI 2001 Can we generalize tree-flipping? To generalize tree flipping, sequences must be placed ‘distance- correct’ in 1 dimension: 2 3 1 And then connect them, as we did before: So, now most info sits in the horizontal dimension. Can we use the vertical dimension usefully?

16. ©CMBI 2001 The problem is actually bigger 1 ASWTFGHK 2 GTWSFANR 3 ATWAFADR d(i,j) is the distance between sequences i and j. d(1,2)=6; d(1,3)=5; d(2,3)=3. 1 3 2 So a perfect representation would be: But what if a 4th sequence is added with d(1,4)=4, d(2,4)=5, d(3,4)=4? Where would that sequence sit?

17. ©CMBI 2001 So, nice tree, but what did we actually do? 1)We determined a distance measure 2)We measured all pair-wise distances 3)We reduced the dimensionality of the space of the problem 4)We used an algorithm to visualize In a way, we projected the hyperspace in which we can perfectly describe all pair-wise distances onto a 1-dimensional line. What does this sentence mean?

18. ©CMBI 2001 Projection Fuller projection; Unfolded Dymaxion map Gnomonic projection: Correct distances Political projection Source: Wikepedia Mercator projection

19. ©CMBI 2001 Back to sequences: ASASDFDFGHKMGHS 1 ASASDFDFRRRLRHS 2 ASASDFDFRRRLRIT 5 ASLPDFLPGHSIGHS 3 ASLPDFLPGHSIGIT 6 ASLPDFLPRRRVRIT 3 The more dimensions we retain, the less information we loose. The three is now in 3D…

20. ©CMBI 2001 Projection to visualize clusters We want to reduce the dimensionality with minimal distortion of the pair-wise distances. One way is Eigenvector determination, or PCA.

21. ©CMBI 2001 PCA to the rescue Now we have made the data one-dimensional, while the second, vertical, dimension is noise. If we did this correctly, we kept as much data as possible.

22. ©CMBI 2001 Back to sequences: In we have N sequences, we can only draw their distance matrix in an N-1 dimensional space. By the time it is a tree, how many dimensions, and how much information have we lost? Perhaps we should cluster in a different way?

23. ©CMBI 2001 Cluster on critical residues? QWERTYAKDFGRGH AWTRTYAKDFGRPM SWTRTNMKDTHRKC QWGRTNMKDTHRVW Gray = conserved Red = variable Green = correlated

24. ©CMBI 2001 Conclusions from correlated residues

25. ©CMBI 2001 Other algorithms Multi-sequence alignment can also be done with an iterative ‘profile’ alignment. A) Make an alignment of few, well-aligned sequences B) Align all sequences using this profile

26. ©CMBI 2001 1. What is a profile? Normally, we use a PAM-like matrix to determine the score for each possible match in an alignment. This assumes that all matches between I E are the same. But the aren’t.

27. ©CMBI 2001 2. What is a profile? QWERTYIPASEF At 1, E and I are QWEKSFIPGSEY both OK. NWERTMVPVSEM QFEKTYLPSSEY At 2, I is OK, NFIKTLMPATEF but E surely not. QYIRSLIPAGEM NYIQSLIPSTEL At 3, E is OK, QFIRSLFPSSEI but I surely not. 1 2 3

28. ©CMBI 2001 3. What is a profile? The knowledge about which residue types are good at a certain position in the multiple sequence alignment can be expressed in a profile. A profile holds for each position 20 scores for the 20 residue types, and sometimes also two values for position specific gap open and gap elongation penalties.

29. ©CMBI 2001 Conserved, variable, or in-between QWERTYASDFGRGH QWERTYASDTHRPM QWERTNMKDFGRKC QWERTNMKDTHRVW Gray = conserved Black = variable Green = correlated mutations

30. ©CMBI 2001 Correlated mutations determine the tree shape 1 AGASDFDFGHKM 2 AGASDFDFRRRL 3 AGLPDFMNGHSI 4 AGLPDFMNRRRV

31. ©CMBI 2001 Correlation = Information 1, 2 and 5 bind calcium; 3 and 4 don’t. Which residues bind calcium? 123456789012345 1 ASDFNTDEKLRTTFI 2 ASDFSTDEKLKTTFI 3 LSFFTTDTRLATIYI 4 LSHFLTNLRLATIYI 5 ASDFTTDEKLALTFI Red has correct correlation, but wrong residue type. Brown has correct type, but wrong correlation. Green can be calcium-binders.