1. Page 1 march 2003 Pairwise sequence alignments Volker Flegel

2. Page 2 march 2003 Goal Sequence comparison through pairwise alignments Goal of pairwise comparison is to find conserved regions (if any) between two sequences Extrapolate information about our sequence using the known characteristics of the other sequence THIO_EMENI GFVVVDCFATWCGPCKAIAPTVEKFAQTY G ++VD +A WCGPCK IAP +++ A Y ??? GAILVDFWAEWCGPCKMIAPILDEIADEY THIO_EMENI GFVVVDCFATWCGPCKAIAPTVEKFAQTY G ++VD +A WCGPCK IAP +++ A Y ??? GAILVDFWAEWCGPCKMIAPILDEIADEY THIO_EMENI SwissProt Extrapolate ???

3. Page 3 march 2003 Do alignments make sense ? Evolution of sequences Sequences evolve through mutation and selection  Selective pressure is different for each residue position in a protein (i.e. conservation of active site, structure, charge, etc.) Modular nature of proteins  Nature keeps re-using domains Alignments try to tell the evolutionnary story of the proteins Relationships Same Sequence Same 3D Fold Same OriginSame Function

4. Page 4 march 2003 Example: An alignment Two similar regions of the Drosophila melanogaster Slit and Notch proteins 970 980 990 1000 1010 1020 SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC..:.: :. :.:...:.:.. : :.. : ::... :.: ::..:. :. :. : NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC 740 750 760 770 780 790 970 980 990 1000 1010 1020 SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC..:.: :. :.:...:.:.. : :.. : ::... :.: ::..:. :. :. : NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC 740 750 760 770 780 790

5. Page 5 march 2003 Example: A diagonal plot Comparing the tissue-type and urokinase type plasminogen activators Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator URL:www.isrec.isb-sib.ch/java/dotlet/Dotlet.html

6. Page 6 march 2003 Relationships to other techniques Sequence analysis tools depending on pairwise comparison Multiple alignments Profile and HMM making (used to search for protein families and domains) 3D protein structure prediction Phylogenetic analysis Construction of certain substitution matrices Similarity searches in a database

7. Page 7 march 2003 Some definitions Identity Proportion of pairs of identical residues between two aligned sequences. Generally expressed as a percentage. This value strongly depends on how the two sequences are aligned. Similarity Proportion of pairs of similar residues between two aligned sequences. If two residues are similar is determined by a substitution matrix. This value also depends strongly on how the two sequences are aligned, as well as on the substitution matrix used. Homology Two sequences are homologous if and only if they have a common ancestor. There is no such thing as a level of homology ! (It's either yes or no) Homologous sequences do not necessarily serve the same function...... Nor are they always highly similar: structure may be conserved while sequence is not.

8. Page 8 march 2003 More definitions Consider a set S (say, globins) and a test t that tries to detect members of S (for example, through a pairwise comparison with another globin). True positive A protein is a true positive if it belongs to S and is detected by t. True negative A protein is a true negative if it does not belong to S and is not detected by t. False positive A protein is a false positive if it does not belong to S and is (incorrectly) detected by t. False negative A protein is a false negative if it belongs to S and is not detected by t (but should be).

9. Page 9 march 2003 Definition example The set of all globins and a test to identify them Globins Matches True positives True negatives False positives False negatives

10. Page 10 march 2003 Even more definitions Sensitivity Ability of a method to detect positives, irrespective of how many false positives are reported. Selectivity Ability of a method to reject negatives, irrespective of how many false negatives are rejected. True positives True negatives False positives False negatives Greater sensitivity Less selectivity Less sensitivity Greater selectivity

11. Page 11 march 2003 Pairwise sequence alignments Concept of sequence alignment Pairwise Alignment:  Explicit mapping between the residues of 2 sequences – Tolerant to errors (mismatches, insertion / deletions or indels) – Evaluation of the alignment in a biological concept (significance) Seq A GARFIELDTHELASTFA-TCAT ||||||||||| || |||| Seq B GARFIELDTHEVERYFASTCAT Seq A GARFIELDTHELASTFA-TCAT ||||||||||| || |||| Seq B GARFIELDTHEVERYFASTCAT errors / mismatchesinsertion deletion

12. Page 12 march 2003 Alignements Number of alignments There are many ways to align two sequences Consider the sequence fragments below: a simple alignment shows some conserved portions but also: CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA Number of possible alignments for 2 sequences of length 1000 residues:  more than 10 600 gapped alignments (Avogadro 10 24, estimated number of atoms in the universe 10 80 )

13. Page 13 march 2003 Alignement evaluation What is a good alignment ? We need a way to evaluate the biological meaning of a given alignment Intuitively we "know" that the following alignment: is better than: CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG We can express this notion more rigorously, by using a scoring system.

14. Page 14 march 2003 Scoring system Simple alignment scores A simple way (but not the best) to score an alignment is to count 1 for each match and 0 for each mismatch.  Score: 12 CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG  Score: 5

15. Page 15 march 2003 Introducing biological information Importance of the scoring system  discrimination of significant biological alignments Based on physico-chemical properties of amino-acids  Hydrophobicity, acid / base, sterical properties,...  Scoring system scales are arbitrary Based on biological sequence information  Substitutions observed in structural or evolutionary alignments of well studied protein families  Scoring systems have a probabilistic foundation Substitution matrices In proteins some mismatches are more acceptable than others Substitution matrices give a score for each substitution of one amino- acid by another

16. Page 16 march 2003 Substitution matrices (log-odds matrices) Example matrix PAM250 From:A. D. Baxevanis, "Bioinformatics" (Leu, Ile):2 (Leu, Cys):-6... Positive score: the amino acids are similar, mutations from one into the other occur more often then expected by chance during evolution Negative score: the amino acids are dissimilar, the mutation from one into the other occurs less often then expected by chance during evolution For a set of well known proteins: Align the sequences Count the mutations at each position For each substitution set the score to the log-odd ratio

17. Page 17 march 2003 Matrix choice Different kind of matrices PAM series(M. Dayhoff, 1968, 1972, 1978)  Based on 1572 protein sequences from 71 families  Old standard matrix:PAM250 BLOSUM series  Based on alignments in the BLOCKS database  Standard matrix:BLOSUM62 Limitations Substitution matrices do not take into account long range interactions between residues. They assume that identical residues are equal (a residue at the active site has other evolutionary constraints than the same residue outside of the active site) They assume evolution rate to be constant.

18. Page 18 march 2003 Alignment score Amino acid substitution matrices Example: PAM250 Most used: Blosum62 Raw score of an alignment TPEA ¦| | APGA TPEA ¦| | APGA Score = 1= 9 It is possible that a good long alignment gets a better raw score than a very good short alignment.  We need a normalised score to compare alignments ! (p-value, e-value) +6+0+2

19. Page 19 march 2003 Gaps Insertions or deletions Proteins often contain regions where residues have been inserted or deleted during evolution There are constraints on where these insertions and deletions can happen (between structural or functional elements like: alpha helices, active site, etc.) Gaps in alignments GCATGCATGCAACTGCAT ||||||||| GCATGCATGGGCAACTGCAT GCATGCATGCAACTGCAT ||||||||| GCATGCATGGGCAACTGCAT can be improved by inserting a gap GCATGCATG--CAACTGCAT ||||||||| GCATGCATGGGCAACTGCAT GCATGCATG--CAACTGCAT ||||||||| GCATGCATGGGCAACTGCAT

20. Page 20 march 2003 Gap opening and extension penalties Costs of gaps in alignments We want to simulate as closely as possible the evolutionary mechanisms involved in gap occurence. Example Two alignments with identical number of gaps but very different gap distribution. We may prefer one large gap to several small ones (e.g. poorly conserved loops between well-conserved helices) CGATGCAGCAGCAGCATCG |||||| ||||||| CGATGC------AGCATCG CGATGCAGCAGCAGCATCG |||||| ||||||| CGATGC------AGCATCG CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G gap opening Gap opening penalty Counted each time a gap is opened in an alignment (some programs include the first extension into this penalty) gap extension Gap extension penalty Counted for each extension of a gap in an alignment

21. Page 21 march 2003 Gap opening and extension penalties Example With a match score of 1 and a mismatch score of 0 With an opening penalty of 10 and extension penalty of 1, we have the following score: CGATGCAGCAGCAGCATCG |||||| ||||||| CGATGC------AGCATCG CGATGCAGCAGCAGCATCG |||||| ||||||| CGATGC------AGCATCG CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G gap opening 13 x 1 - 10 - 6 x 1 = - 3 gap extension 13 x 1 - 5 x 10 - 6 x 1 = - 43

22. Page 22 march 2003 Statistical evaluation of results Alignments are evaluated according to their score Raw score  It's the sum of the amino acid substitution scores and gap penalties (gap opening and gap extension)  Depends on the scoring system (substitution matrix, etc.)  Different alignments should not be compared based only on the raw score Normalised score  Is independent of the scoring system  Enables us to compare different alignments  Units: expressed in bits

23. Page 23 march 2003 Statistical evaluation of results Statistics derived from the scores p-value  Probability that an alignment with this score occurs by chance in a database of this size  The closer the p-value is towards 0, the better the alignment e-value  Number of matches with this score one can expect to find by chance in a database of this size  The closer the e-value is towards 0, the better the alignment

24. Page 24 march 2003 Diagonal plots or Dotplot Concept of a Dotplot Produces a graphical representation of similarity regions. The horizontal and vertical dimensions correspond to the compared sequences. A region of of similarity stands out as a diagonal. Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator

25. Page 25 march 2003 Dotplot construction Simple example A dot is placed at each position where two residues match.  The colour of the dot can be chosen according to the substitution value in the substitution matrix THEFA-TCAT ||||| |||| THEFASTCAT THEFA-TCAT ||||| |||| THEFASTCAT Note This method produces dotplots with too much noise to be useful  The noise can be reduced by calculating a score using a window of residues  The score is compared to a threshold or stringency

26. Page 26 march 2003 Dotplot construction Window example Each window of the first sequence is aligned (without gaps) to each window of the 2nd sequence A colour is set into a rectangular array according to the score of the aligned windows THE ||| THE ||| THE Score: 23 THE HEF THE HEF Score: -5 CAT THE CAT THE Score: -4 HEF THE HEF THE Score: -5

27. Page 27 march 2003 Dotplot limitations  It's a visual aid. The human eye can rapidly identify similar regions in sequences.  It's a good way to explore sequence organisation.  It does not provide an alignment. Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator

28. Page 28 march 2003 Relationship between alignment and dotplot An alignment can be seen as a path through the dotplot diagramm. Creating an alignment Seq B A-CA-CA | || | Seq A ACCAAC- Seq B A-CA-CA | || | Seq A ACCAAC- Seq B ACA--CA | Seq A A-CCAAC Seq B ACA--CA | Seq A A-CCAAC

29. Page 29 march 2003 Finding an alignment Alignment algorithms An alignment program tries to find the best alignment between two sequences given the scoring system. This can be seen as trying to find a path through the dotplot diagram including all (or the most visible) diagonals. Alignement types GlobalAlignment between the complete sequence A and the complete sequence B LocalAlignment between a sub-sequence of A an a sub- sequence of B Computer implementation (Algorithms) Dynamic programing GlobalNeedleman-Wunsch LocalSmith-Waterman

30. Page 30 march 2003 Global alignment (Needleman-Wunsch) Example  Global alignments are very sensitive to gap penalties  Global alignments do not take into account the modular nature of proteins Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator Global alignment:

31. Page 31 march 2003 Local alignment (Smith-Waterman) Example  Local alignments are more sensitive to the modular nature of proteins  They can be used to search databases Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator Local alignments:

32. Page 32 march 2003 Optimal alignment extension How to extend optimaly an optimal alignment An optimal alignment up to positions i and j can be extended in 3 ways. Keeping the best of the 3 guarantees an extended optimal alignment. Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j We have the optimal alignment extended from i and j by one residue. Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j a i+1 b j+1 a i+1 b j+1 Score = Score ij + Subst ij Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j a i+1 - a i+1 - Score = Score ij - gap Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j Seq A a 1 a 2 a 3... a i-1 a i Seq B b 1 b 2 b 3... b j-1 b j - b j+1 - b j+1 Score = Score ij - gap

33. Page 33 march 2003 Exact algorithms Simple example (Needleman-Wunsch) Scoring system:  Match score:2  Mismatch score:-1  Gap penalty:-2 Note We have to keep track of the origin of the score for each element in the matrix.  This allows to build the alignment by traceback when the matrix has been completely filled out. Computation time is proportional to the size of sequences (n x m). 0 - 2 2 + 2 F (i- 1,j) F (i,j) s (xi,yj) F (i-1,j- 1) -d F (i,j- 1) -d F(i,j):score at position i, j s(x i,y j ):match or mismatch score (or substitution matrix value) for residues x i and y j d:gap penalty (positive value) GA-TTA || GAATTC GA-TTA || GAATTC

34. Page 34 march 2003 Algorithms for pairwise alignments Web resources LALIGN - pairwise sequence alignment: www.ch.embnet.org/software/LALIGN_form.html PRSS - alignment score evaluation: www.ch.embnet.org/software/PRSS_form.html Concluding remarks Substitution matrices and gap penalties introduce biological information into the alignment algorithms. It is not because two sequences can be aligned that they share a common biological history. The relevance of the alignment must be assessed with a statistical score. There are many ways to align two sequences. Do not blindly trust your alignment to be the only truth. Especially gapped regions may be quite variable. Sequences sharing less than 20% similarity are difficult to align:  You enter the Twilight Zone (Doolittle, 1986)  Alignments may appear plausible to the eye but are no longer statistically significant.  Other methods are needed to explore these sequences (i.e: profiles)