Bioinformatics Algorithms and Data Structures

1. Bioinformatics Algorithms and Data Structures CLUSTAL W Algorithm Lecturer: Dr. Rose Slides by: Dr. Rose April 3, 2003

2. Multiple Sequence Alignment • CLUSTAL is an algorithm for aligning multiple sequences. • Reasons for computing multiple alignments: • Characterizing protein families • Detect homology between sequences and families of sequences • Predict secondary and tertiary structures of new sequences. • Needed for creating of phylogenetic trees.

3. Multiple Sequence Alignment • Recall: DP used for 2 sequence alignment • Guarantees optimal alignment relative to the scoring table that is used. • DP is only practical for small numbers of short sequences. • Impractical for: • large numbers of sequences • Very long sequences • i.e., more than 8 proteins of average length.

4. Progressive Algorithms • Progressive Approaches • Exploit idea that homologous sequences are related by evolution. • Multiple alignments can be built up from pairwise alignments. • The pairwise alignments follow branching in the guide tree. • The most closely related sequences are aligned first. • The more distant related sequences are gradually added.

5. Progressive Algorithms • Empirical observations: • For simple cases: • correctly align domains of known secondary and tertiary structures. • closely related sequences are less sensitive to parameter settings, i.e., gap penalties and weight matrix. • In all cases: • gaps are preserved, i.e., once a gap always a gap. • progressive alignment gives an idea of the variability at each position before more distant sequences are added.

6. Progressive Algorithms • Empirical observations: • For more complicated cases: • Progressive approach is less reliable for highly divergent sequences (less than 25-30% identity). • gives a good starting point for further manual/automatic refinement.

7. Problems with Progressive Algorithms • Local minimum problem • Recall this is a greedy algorithm approach • Sequences are added greedily: • Multiple alignments are built up from pairwise alignments. • The pairwise alignments follow branching in the initial guide tree. (more on this later) • No guarantee of a global optimum • Any misaligned regions made early on can not be corrected later on.

8. Problems with Progressive Algorithms • Sensitivity to alignment parameters • problematic also for iterative and stochastic algorithms. • Traditional parameters: • weight table • cost of opening a gap • cost of extending a gap • Expectation is one set of parameters works well over • all sequences in the set • all parts of each sequence

9. Problems with Progressive Algorithms • Sensitivity to alignment parameters continued • A single weight matrix choice will generally work for closely related sequences. • weight matrices give highest weight to identities • Any weight matrix will work ok if identities dominate • For divergent sequences: • Nonidentical residues are more significant • Scores to these residues are critical • Different weight matrices will be required for: • different evolutionary distances • Different classes of proteins

10. Problems with Progressive Algorithms • Sensitivity to alignment parameters continued • A range of gap penalty values will generally work for closely related sequences. • For divergent sequences: • The specific choice of gap penalty value becomes critical • For proteins gaps don’t occur randomly. • Recall our discussion of conserved secondary features • Gaps occur between alpha helices and beta strands rather than within them

11. CLUSTAL W Contributions • Dynamically vary gap penalties according to position & residue • Local gap opening penalty adjustment: • relative to observed relative frequency of gaps next to each of the 20 amino acid. • reduced for loop or random coil regions (as indicated by short stretches of hydrophilic residues) • reduced for gaps found in early alignments • increased within 8 residues of existing gaps (observation: gaps tend not to be closer than 8 residues)

12. CLUSTAL W Contributions • Weight matrices are chosen dynamically • PAM series and BLOSUM series are main series of amino acid weight matrices in use. • Choice of weight matrix is by estimation of divergence of sequences being aligned at each step. • Different weight matrices are appropriate depending on similarity of sequences

13. CLUSTAL W Contributions • Different weight matrices are appropriate depending on similarity of sequences: • For closely related sequences: • identities predominate • Only frequent conservative substitutions are scored high • For evolutionary divergent sequences: • Less weight should be given to identities • Weight matrix should be tuned to greater evolutionary distance

14. CLUSTAL W Contributions • Weighting of sequences: • corrects for unequal sampling across the evolutionary distance in the data set. • Downweights similar sequences • Upweights divergent sequences • Weight are calculated from the branch lengths of the initial guide tree.

15. CLUSTAL W Contributions • Neighbor-Joining method used to calculate guide tree • Less sensitive to unequal evolutionary rates in different branches. • Significance: branch lengths are used to derive sequence weights. • Accuracy of distance calculations for guide tree: • Tree constructed from pairwise distance matrix • Fast approximate alignment • Full dynamic programming • User selectable

16. CLUSTAL W Algorithm Basic method: • Distance matrix is calculated • Distances are pairwise alignment scores • Gives divergence of each pair of sequences • Guide tree built from distance matrix • Progressive alignment according to guide tree • Branching order of tree specifies alignment order • Alignment progresses from leaves to root.

17. CLUSTAL W Algorithm Distance matrix/pairwise alignments phase • Two choices: fast approximation or DP • Fast approximation: • Defn a k-tuple match is a run of identical residues, typically • 1 to 2 for proteins • 2 to 4 for nucleotide sequences • Scores are calculated as: (k-tuple matches) – fixed penalty per gap • Score is initially calculated as a percent identity score. • Distance = 1.0 – (score/100)

18. CLUSTAL W Algorithm Distance matrix/pairwise alignments phase • Full DP alignment • Alignment uses: • gap opening penalties • gap extension penalties • full amino acid weight matrix. • Scores are calculated as: (#identies)/(#residues), gaps not included • Score is initially calculated as a percent identity score. • Distance = 1.0 – (score/100)

19. NJ Algorithm Neighbor Joining to Calculate the Guide Tree Phase: • does not require a uniform molecular clock • the raw data are provided as a distance matrix • the initial tree is a star tree • distance matrix is modified • distance between node pairs is adjusted on the basis of their average divergence from all other nodes. • the least-distant pair of nodes are linked.

20. NJ Algorithm Neighbor Joining to Calculate the Guide Tree Phase: • When two nodes are linked: • Add their common ancestral node to the tree • delete the terminal nodes with their branches • the common ancestor is now a terminal node on a smaller tree • At each step, two terminal nodes are replaced by one new node • The process is complete when there are only two nodes separated by a single branch

21. NJ Algorithm • Advantages of Neighbor Joining • Fast. • Can be used on large datasets • Can support bootstrap analysis • Can handle lineages with largely different branch lengths (different molecular evolutionary rates) • Can be used with methods that use correction for multiple substitutions

22. NJ Algorithm • Disadvantages of Neighbor Joining • sequence information is reduced • Sequences are boiled down to distances • No secondary or tertiary features used • gives only one possible tree • strongly dependent on the model of evolution used

23. NJ Algorithm • NJ example from: http://www.icp.ucl.ac.be/~opperd/private/neighbor.html • Consider the following tree: • Notice that the branches for D and B are longer. • This expresses the idea that they have a faster molecular clock than the other OTUs.

24. NJ Algorithm The distance matrix for the tree is: Normally, we create the tree from the distances. In this example, we use to tree to derive the distances.

25. NJ Algorithm • We start with a star tree. • Notice that we have 6 operational taxonomic units (OTUs) • The start tree has a leaf for each OTU

26. NJ Algorithm Step 1: Calculate the net divergence for each OTU. The net divergence is the sum of distances from i to all other OTUs. • r(A) = 5+4+7+6+8=30 • r(B) = 42 • r(C) = 32 • r(D) = 38 • r(E) = 34 • r(F) = 44

27. NJ Algorithm Step 2: Calculate a new distance matrix based on average divergence: M(ij)=d(ij) - [r(i) + r(j)]/(N-2) Example: A,B M(AB)=d(AB) -[(r(A) + r(B)]/(N-2) = -13 • Recall: • r(A) =30 • r(B) = 42

28. NJ Algorithm Step 2: continued M(ij)=d(ij) - [r(i) + r(j)]/(N-2) Distance matrix Average divergence matrix

29. NJ Algorithm Step 3: choose two OTUs for which Mij is the smallest. • the possible choices are: A,B and D,E • arbitrarily choose A and B • form a new node called U, the parent of A & B. • calculate the branch length from U to A and B. S(AU) =d(AB) / 2 + [r(A)-r(B)] / 2(N-2) = 1 S(BU) =d(AB) -S(AU) = 4

30. NJ Algorithm • The tree after U is added.

31. NJ Algorithm Step 4: define distances from U to other terminal nodes: • d(CU) = d(AC) + d(BC) - d(AB) / 2 = 3 • d(DU) = d(AD) + d(BD) - d(AB) / 2 = 6 • d(EU) = d(AE) + d(BE) - d(AB) / 2 = 5 • d(FU) = d(AF) + d(BF) - d(AB) / 2 = 7 • Note: no change in paired distances {C,D,E,F}

32. NJ Algorithm • Now N = N-1 = 5 • Repeat steps 1 through 4 • Stop when N = 2

33. CLUSTAL W Algorithm • The final result of the tree produced by NJ is an unrooted tree. • The branch lengths are proportional to the estimated divergence. • A “mid-point” method is used to place the root: • The mid point is defined at the point where the means of the branch lengths on either side are equal.

34. CLUSTAL W Algorithm Basic Progressive Alignment Phase: • Use a series of pairwise alignments • The alignments follow the branching order of the guide tree • The alignments start from the leaves and progress towards the root • Full DP with a residue weight matrix is used • Gaps are preserved • Newly created gaps get full opening & extension penalties

35. CLUSTAL W Algorithm Basic Progressive Alignment Phase: • Each step involved two existing alignments or sequences • The score at a given position is the average of the pairwise weight matrix scores. Example: • aligning 2 alignments: with 3 and 4 sequences, respectively • The score at a given position is the average of the 3X4 comparisons. • The weight matrix has only positive scores • Each gap versus a residue is scored a zero, the worst value • This is the average linkage cluster distance metric

36. CLUSTAL W Algorithm Example: • A & B are aligned • C is aligned with the result of (1) • D & E are aligned • The results of (2) and (3) are aligned • F is aligned with the result of (4)

37. CLUSTAL W Algorithm Improvement to Progressive Alignment Phase: • Sequence weighting: • Calculated from the guide tree • Normalized so that largest weight is 1.0 • Closely related sequences receive lower weights • They over-represent their common information • A lower weight seeks to reduce this influence • Divergent sequences receive higher weights • Sequence weight impacts alignment scores: • each weight matrix value is multiplied by the weights of the two sequences.

38. CLUSTAL W Algorithm Improvement to Progressive Alignment Phase: • Two gap penalty types: • Gap opening (GOP) • Gap extension (GEP) • Actual assessed penalty depends on: • Weight matrix: GOP is scaled by the average score of mismatched residues • Similarity of sequences: % identity is used to • increase GOP for similar sequences • decrease GOP for divergent sequences

39. CLUSTAL W Algorithm • Actual assessed penalty depends on: continued • Length of sequences: the logarithm of the length of the shorter sequence is used to increase GOP with sequence length GOP = (GOP + log(min(N,M))) *(ave residue mismatch score) * (% identity scaling factor) • Difference in sequence lengths: GEP is increased to inhibit many long gaps in shorter sequences. GEP = GEP * (1.0 + |log(N/M)|)

40. CLUSTAL W Algorithm Improvement to Progressive Alignment Phase: • Position-specific gap penalties • Lowered GOP at existing gaps: • if a position already has gaps, GOP is reduced relative to the number of sequences with a gap at that position • GOP = GOP * 0.3 * (# sequences w/o gap)/(# sequences) • Increased GOP near existing gaps • New gap within 8 residues of an exisiting gap • GOP = GOP * (2 + ((8 – distance from gap) * 2) / 8)

41. CLUSTAL W Algorithm Improvement to Progressive Alignment Phase: • Position-specific gap penalties continued • Reduced GOP in hydrophilic stretches • 5 or more consecutive hydrophilic residues is a stretch  • Hydrophilic residues are: D,E,G,K,N,Q,P,R & S • GOP reduced by a third if there is no gap in a stretch • Residue specific penalty • GOP is modified if there is no gap and no hydrophilic stretch • There is an adjustment factor for each of the 20 residues • For mixtures, the factor is the average of all contributing residues

42. The End