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Pairwise sequence alignments Etienne de Villiers Adapted with permission of Swiss EMBnet node and SIB August 2006 Page 1 Outline • Introduction • Definitions • Biological context of pairwise alignments • Computing of pairwise alignments • Some programs August 2006 Page 2 Importance of pairwise alignments 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 August 2006 Page 3 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 Extrapolate ??? August 2006 THIO_EMENI SwissProt Page 4 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 Origin Same Function Same 3D Fold August 2006 Page 5 Example: An alignment - textual view • 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 August 2006 Page 6 Example: An alignment - graphical view • Comparing the tissue-type and urokinase type plasminogen activators. Displayed using a diagonal plot or Dotplot. Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html August 2006 Page 7 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. August 2006 Page 8 Definition example The set of all globins and a test to identify them Consider: • a set S (say, globins: G) • a test t that tries to detect members of S (for example, through a pairwise comparison with another globin). Globins G True positives True negatives G G G G G False positives G G X False negatives X X X X Matches August 2006 Page 9 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). August 2006 Page 10 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 Greater sensitivity Less selectivity True negatives False positives False negatives Less sensitivity Greater selectivity August 2006 Page 11 Pairwise sequence alignment Concept of a sequence alignment • Pairwise Alignment: Explicit mapping between the residues of 2 sequences deletion Seq A GARFIELDTHELASTFA-TCAT ||||||||||| || |||| Seq B GARFIELDTHEVERYFASTCAT errors / mismatches insertion – Tolerant to errors (mismatches, insertion / deletions or indels) – Evaluation of the alignment in a biological concept (significance) August 2006 Page 12 Pairwise sequence alignment Number of alignments • There are many ways to align two sequences • Consider the sequence fragments below: a simple alignment shows some conserved portions CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA but also: CGATGCAGACGTCA |||||||| CGATGCAAGACGTCA • Number of possible alignments for 2 sequences of length 1000 residues: more than 10600 gapped alignments (Avogadro 1024, estimated number of atoms in the universe 1080) August 2006 Page 13 Alignment 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: CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA is better than: ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG • We can express this notion more rigorously, by using a scoring system August 2006 Page 14 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. CGAGGCACAACGTCA ||| ||| |||||| CGATGCAAGACGTCA Score: 12 ATTGGACAGCAATCAGG | || | | ACGATGCAAGACGTCAG Score: 5 August 2006 Page 15 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 aminoacid by another August 2006 Page 16 Substitution matrices (log-odds matrices) Example matrix (Leu, Ile): 2 (Leu, Cys): -6 ... • 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 observed log expected by chance • 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 PAM250 From: August 2006 A. D. Baxevanis, "Bioinformatics" Page 17 Matrix choice Different kind of matrices • PAM series (Dayhoff M., 1968, 1972, 1978) Percent Accepted Mutation. A unit introduced by Dayhoff et al. to quantify the amount of evolutionary change in a protein sequence. 1.0 PAM unit, is the amount of evolution which will change, on average, 1% of amino acids in a protein sequence. A PAM(x) substitution matrix is a look-up table in which scores for each amino acid substitution have been calculated based on the frequency of that substitution in closely related proteins that have experienced a certain amount (x) of evolutionary divergence. Based on 1572 protein sequences from 71 families Old standard matrix: PAM250 August 2006 Page 18 Matrix choice Different kind of matrices • BLOSUM series (Henikoff S. & Henikoff JG., PNAS, 1992) Blocks Substitution Matrix. A substitution matrix in which scores for each position are derived from observations of the frequencies of substitutions in blocks of local alignments in related proteins. Each matrix is tailored to a particular evolutionary distance. In the BLOSUM62 matrix, for example, the alignment from which scores were derived was created using sequences sharing no more than 62% identity. Sequences more identical than 62% are represented by a single sequence in the alignment so as to avoid overweighting closely related family members. Based on alignments in the BLOCKS database Standard matrix: BLOSUM62 August 2006 Page 19 Matrix choice Limitations • Substitution matrices do not take into account long range interactions between residues. • They assume that identical residues are equal ( whereas in real life 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. August 2006 Page 20 Alignment score Amino acid substitution matrices • Example: • Most used: PAM250 Blosum62 Raw score of an alignment TPEA ¦| | APGA Score = 1 + 6 + 0 + 2 = 9 August 2006 Page 21 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 can be improved by inserting a gap GCATGCATG--CAACTGCAT ||||||||| ||||||||| GCATGCATGGGCAACTGCAT August 2006 Page 22 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 gap opening CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G gap extension Gap opening penalty • Counted each time a gap is opened in an alignment (some programs include the first extension into this penalty) Gap extension penalty • Counted for each extension of a gap in an alignment August 2006 Page 23 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 gap opening gap extension 13 x 1 - 10 - 6 x 1 = 3 August 2006 CGATGCAGCAGCAGCATCG || || |||| || || | CG-TG-AGCA-CA--AT-G 13 x 1 - 5 x 10 - 6 x 1 = 43 Page 24 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 • It is possible that a "bad" long alignment gets a better raw score than a very good short alignment. We need a normalised score to compare alignments ! We need to evaluate the biological meaning of the score (p-value, e-value). • Normalised score Is independent of the scoring system Allows the comparison of different alignments Units: expressed in bits August 2006 Page 25 Statistical evaluation of results Distribution of alignment scores - Extreme Value Distribution • Random sequences and alignment scores Sequence alignment scores between random sequences are distributed following an extreme value distribution (EVD). Pairwise alignments Score distribution low score Ala Val ... Trp low score obs Random sequences low score low score score high score high score due to "luck" ... August 2006 Page 26 Statistical evaluation of results Distribution of alignment scores - Extreme Value Distribution • High scoring random alignments have a low probability. • The EVD allows us to compute the probability with which our biological alignment could be due to randomness (to chance). • Caveat: finding the threshold of significant alignments. Threshold significant alignment score score x: our alignment has a great probability of being the result of random sequence similarity August 2006 score y: our alignment is very improbable to obtain with random sequences Page 27 Statistical evaluation of results Statistics derived from the scores 100% 0% N 0 • 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 • Relationship between e-value and p-value: In a database containing N sequences e=pxN August 2006 Page 28 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 similarity stands out as a diagonal. Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator August 2006 Page 29 Reading a Dotplot As simple as projecting the diagonals onto the axis. Tissue-Type plasminogen Activator Urokinase-Type plasminogen Activator Tissue-Type plasminogen Activator A’ A A B B C C D D Urokinase-Type plasminogen Activator August 2006 Page 30 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. Between 2 different sequences or Inside the same sequence (ssDNA repeats, RNA stem loops, etc) It does not provide an alignment. August 2006 Page 31 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. Alignment types • Global • Local Alignment between the complete sequence A and the complete sequence B Alignment between a sub-sequence of A an a subsequence of B Computer implementation (Algorithms) • Dynamic programing • Global Needleman-Wunsch • Local Smith-Waterman August 2006 Page 32 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: August 2006 Page 33 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: August 2006 Page 34 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) August 2006 Page 35 Acknowledgments & References Laurent Falquet, Lorenza Bordoli ,Volker Flegel, Frédérique Galisson References • Ian Korf, Mark Yandell & Joseph Bedell, BLAST, O’Reilly • David W. Mount, Bioinformatics, Cold Spring Harbor Laboratory Press • Jean-Michel Claverie & Cedric Notredame, Bioinformatics for Dummies, Wiley Publishing August 2006 Page 36