1. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology Bioinformatics Algorithms and Data Structures CLUSTAL W Algorithm Lecturer: Dr. Rose Slides by: Dr. Rose March 29, 2007

2. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. Q: What is a guide tree? –The most closely related sequences are aligned first. –The more distant related sequences are gradually added.

5. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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 User selectable: –Fast approximate alignment –Full dynamic programming

16. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology CLUSTAL W Algorithm Basic method: 1.Distance matrix is calculated Distances are pairwise alignment scores Gives divergence of each pair of sequences 2.Guide tree built from distance matrix 3.Progressive alignment according to guide tree Branching order of tree specifies alignment order Alignment progresses from leaves to root.

17. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology CLUSTAL W Algorithm Distance matrix/pairwise alignments phase –Full DP alignment Alignment uses: 1.gap opening penalties 2.gap extension penalties 3.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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology NJ Algorithm NJ example from: http://www.icp.ucl.ac.be/~opperd/private/neighbor.html 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology NJ Algorithm Step 2: continued M(ij)=d(ij) - [r(i) + r(j)]/(N-2) Distance matrixAverage divergence matrix

29. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology NJ Algorithm The tree after U is added.

31. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology NJ Algorithm Now N = N-1 = 5 Repeat steps 1 through 4 Stop when N = 2

33. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology CLUSTAL W Algorithm Example: 1.A & B are aligned 2.C is aligned with the result of (1) 3.D & E are aligned 4.The results of (2) and (3) are aligned 5.F is aligned with the result of (4)

37. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology 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. UNIVERSITY OF SOUTH CAROLINA College of Engineering & Information Technology The End