Trees, Stars, and Multiple Biological Sequence Alignment

1. Trees, Stars, and Multiple Biological Sequence Alignment Jesse Wolfgang CSE 497 February 19, 2004

2. Importance? • Molecular evolution (Dayhoff) • RNA folding (Trifonov, Bolshoi) • Gene regulation (Galas et al.) • Protein structure-function relationships(Wu, Kabat)

3. Introduction • Original sequence unknown • Must consider all possible transformations • Including insertions, deletions, and replacements • Choose the most likely set of transformations • With a given model of protein evolution

4. K-sequence: sequence of k characters • An alignment of the sequences is written as • Each is obtained from • Blanks are inserted in positions where some of the other sequences have a nonblank character • At least one must be nonblank for each • is the length of the aligned sequences Sequences and Alignments

5. D Q L F D N V QQ G L D - - Q – L F D N V Q - - - - - - Q G L - Alignments • Ex: sequences DQLF, DNVQ, QGL

6. A lattice of sequences with lengths n • Consists of -dimensional hypercubes • Cartesian product of strings of squares • Forms an -dimensional parallelepiped • A path between the sequences is a set of connected line segments (connected broken line) Lattices and Paths

7. Paths = 2n-1 = O(2n) 2 dimensions 3 dimensions 3 possible paths 7 possible paths

8. sublattice F L Q D D D - - N - - V - Q Q Q - - G L - L F - - Q D N V Q G L 3-dimensional parallelepiped Paths • Sequences DQLF, DNVQ, QGL

9. Note: • Where is the length of D B A B C D A B – D - B C D A B A B C D C D Paths and Sequence Length • Sequences: ABCD, ABD, BCD

10. Note: • Where is the length of D C B A I E F G H A B C D – - - - - - - - - - - E F G H - - - - - - - - - - - I J K J K Paths and Sequence Length • Sequences: ABCD, EFGH, IJK

11. denotes an alignment of and D Q L F F Q L Q G D Q D N V Q L G D Q – L F - Q G L - L Projections • Sequences DQLF, DNVQ, QGL

12. is a measure assigned to • Measure of the similarity among based upon a particular metric • For each measure there is at least one path with attaining a minimum value at , the optimal path Optimal Paths

13. Each vertex in L is an end corner of the sublattice • First: compute score of each of the possible paths for the cube that has a vertex at the original corner F L Q D Q D N V Q • Next: using this information, compute minimum score to reach the vertices of the adjacent cubes to the original corner G L Calculating Optimal Paths

14. Problems with This Algorithm • Calculates a weighted sum of its projected pairwise alignments • Called “Sum-of-the-Pairs” (SP) • Other methods fit biological intuition more closely

15. Tree-Alignment • Treat sequences as leaves of an evolutionary tree • Reconstruct ancestral sequences which minimize the cost of the tree • Must assign sequences to internal nodes • Align the given and reconstructed sequences • Star-alignment: only one internal node

16. Tree-Alignment • Many different methods for calculating tree alignments • Discuss version used by ClustalX

17. Tree-Alignment in ClustalX • Three main parts • Perform pairwise alignment on all sequences to calculate a distance matrix • Use distance matrix to calculate a guide tree • Sequences are progressively aligned using the branching order in the guide tree http://bimas.dcrt.nih.gov/clustalw/clustalw.html

18. Calculating Distance Matrix • Use standard dynamic programming to find the best alignment • Gap penalties for opening a gap and continuing a gap (possibly different) • Divide number of matches by total number of residues compared (excluding gaps) • Convert to distances by dividing by 100 and subtracting from 1 • Gives one entry in the n by n matrix

19. A T C GA T C C = 3/4 = .75/100 = 1-.0075 = .9925 A T C G A G G C = 1/4 = .25/100 = 1-.0025 = .9975 Calculating Distance Matrix • Ex: sequences ATCG, ATCC, AGGC, AGCC

20. Calculating Distance Matrix

21. Calculating a Guide Tree • Using Nearest-Neighbor method to group sequences • Results in an unrooted tree • Branch lengths proportional to estimated divergence • “Mid-point” method used to determine root • Means of the branch lengths to each side of the root are equal (or approximately equal)

22. ATCG = 1.8245 ATCT = 1.8245 AGGC = 1.3308 1/3 1 1.6599 GCAA = 1 .9975/2 .9975 .9925 .9925 Calculating a Guide Tree AGAA GCAA AGCC AGGC ATCG ATCT ATCG

23. ATCG = 1.4911 ATCT = 1.4911 1.4911 1 1 AGCC AGGC = 1.4986 .9975/2 .9975/2 GCAA = 1.4986 1.4986 ATCG AGAA .9925 .9925 ATCT ATCG AGGC GCAA Calculating a Guide Tree

24. Progressive Alignment • Perform a series of pairwise alignments • Slowly align larger and larger groups of sequences • Follow the branching order of the tree • From leaves to root

25. ATCT ATCG AGGC GCAA Progressive Alignment AGCC ATCG AGAA

26. A A C A A A C A C C A A A C A C A A C Traditional (SP) Tree-Alignment Star-Alignment Input seq Reconstructedseq Missmatches -- A, A, C A 6 1 2 Alignment Costs Traditional A, A, A, C, C A, A, A, C, C A, A, A, C, C

27. Alignment Inconsistencies • Different definitions of multiple alignments can yield different optimal alignments • Optimal tree-alignments minimize number of mutations from theorized common ancestors • SP-alignments maximize number of positions where aligned sequences agree • Sometimes makes more biological sense since certain regions of proteins more likely to mutate

28. Traditional (SP) Star-Alignment - A C C- A C C- T C TA T C T A C C -A C C -T C T -A T C T -- A C C - Alignment Inconsistencies • Ex: cost of 1 for aligning two different letters, cost of 2 for aligning a letter with a null • Sequences: ACC, ACC, TCT, ATCT Input sequences Reconstructedsequences

29. ClustalX Demo • Multiple sequence alignment program • For more information on ClustalX • http://www.at.embnet.org/embnet/progs/clustal/clustalx.htm