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Pairwise sequence alignments Volker Flegel Vassilios Ioannidis VI - 2004 Page 1 Outline • Introduction • Definitions • Biological context of pairwise alignments • Computing of pairwise alignments • Some programs VI - 2004 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 VI - 2004 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 THIO_EMENI ??? ??? GFVVVDCFATWCGPCKAIAPTVEKFAQTY GFVVVDCFATWCGPCKAIAPTVEKFAQTY GG ++VD ++VD +A +A WCGPCK WCGPCK IAP IAP +++ +++ AA YY GAILVDFWAEWCGPCKMIAPILDEIADEY GAILVDFWAEWCGPCKMIAPILDEIADEY Extrapolate Extrapolate ??? VI - 2004 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 VI - 2004 Page 5 Example: An alignment - textual view • Two similar regions of the Drosophila melanogaster Slit and Notch proteins 970 980 990 1000 1010 1020 970 980 990 1000 1010 1020 SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC ..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. : ..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. : NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC 740 750 760 770 780 790 740 750 760 770 780 790 VI - 2004 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 VI - 2004 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. VI - 2004 Page 8 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). VI - 2004 Page 9 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 G False positives G G True negatives X False negatives G G G G X X X X Matches VI - 2004 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. Greater sensitivity Less selectivity True positives True negatives Less sensitivity False positives Greater selectivity False negatives VI - 2004 Page 11 Pairwise sequence alignment Concept of a sequence alignment • Pairwise Alignment: ! Explicit mapping between the residues of 2 sequences deletion Seq Seq AAGARFIELDTHELASTFA-TCAT GARFIELDTHELASTFA-TCAT ||||||||||| || ||||||||||| || |||| |||| Seq B GARFIELDTHEVERYFASTCAT Seq B GARFIELDTHEVERYFASTCAT errors / mismatches insertion – Tolerant to errors (mismatches, insertion / deletions or indels) – Evaluation of the alignment in a biological concept (significance) VI - 2004 Page 12 Pairwise sequence alignement Number of alignments • There are many ways to align two sequences • Consider the sequence fragments below: a simple alignment shows some conserved portions CGATGCAGACGTCA CGATGCAGACGTCA |||||||| |||||||| CGATGCAAGACGTCA CGATGCAAGACGTCA but also: CGATGCAGACGTCA CGATGCAGACGTCA |||||||| |||||||| CGATGCAAGACGTCA 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) VI - 2004 Page 13 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: CGAGGCACAACGTCA CGAGGCACAACGTCA ||| ||| ||| ||| |||||| |||||| CGATGCAAGACGTCA CGATGCAAGACGTCA is better than: ATTGGACAGCAATCAGG ATTGGACAGCAATCAGG || || || || || ACGATGCAAGACGTCAG ACGATGCAAGACGTCAG • We can express this notion more rigorously, by using a scoring system VI - 2004 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 CGAGGCACAACGTCA ||| ||| ||| ||| |||||| |||||| CGATGCAAGACGTCA CGATGCAAGACGTCA !Score: 12 ATTGGACAGCAATCAGG ATTGGACAGCAATCAGG || || || || || ACGATGCAAGACGTCAG ACGATGCAAGACGTCAG !Score: 5 VI - 2004 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 VI - 2004 Page 16 Substitution matrices (log-odds matrices) • For a set of well known proteins: Example matrix (Leu, Ile): 2 (Leu, Cys): -6 ... • • • 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: A. D. Baxevanis, "Bioinformatics" VI - 2004 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 VI - 2004 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 over-weighting closely related family members. ! Based on alignments in the BLOCKS database ! Standard matrix: BLOSUM62 VI - 2004 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 reallife 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. VI - 2004 Page 20 Alignment score Amino acid substitution matrices • Example: • Most used: PAM250 Blosum62 Raw score of an alignment TPEA TPEA _| _| || APGA APGA Score = 1 + 6 + 0 + 2 = 9 VI - 2004 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 GCATGCATGCAACTGCAT ||||||||| ||||||||| GCATGCATGGGCAACTGCAT GCATGCATGGGCAACTGCAT can be improved by inserting a gap GCATGCATG--CAACTGCAT GCATGCATG--CAACTGCAT ||||||||| ||||||||| ||||||||| ||||||||| GCATGCATGGGCAACTGCAT GCATGCATGGGCAACTGCAT VI - 2004 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 CGATGCAGCAGCAGCATCG |||||| ||||||| |||||| ||||||| CGATGC------AGCATCG CGATGC------AGCATCG gap opening CGATGCAGCAGCAGCATCG CGATGCAGCAGCAGCATCG || || || || |||| |||| || || || || || CG-TG-AGCA-CA--AT-G 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 VI - 2004 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 CGATGCAGCAGCAGCATCG |||||| ||||||| |||||| ||||||| CGATGC------AGCATCG CGATGC------AGCATCG gap opening gap extension 13 x 1 - 10 - 6 x 1 = -3 VI - 2004 CGATGCAGCAGCAGCATCG CGATGCAGCAGCAGCATCG || || || || |||| |||| || || || || || CG-TG-AGCA-CA--AT-G 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 VI - 2004 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). VI - 2004 ... score x ... Ala Ala Val Val ... ... Tr p Tr p Pairwise alignments Score distribution obs Random sequences score y score 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 score y: our alignment is very improbable to obtain with random sequences VI - 2004 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 VI - 2004 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 VI - 2004 Page 29 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 THEFATCATTHEFASTCAT THEFA-TCAT THEFA-TCAT ||||| ||||| |||| |||| THEFASTCAT 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 VI - 2004 Page 30 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 THEFATCATTHEFASTCAT THE HEF THE CAT HEF THE CAT ||| ||| THE HEF THE THE HEF -5 Score: 23 -4 VI - 2004 Page 31 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 VI - 2004 Page 32 Creating an alignment Relationship between alignment and dotplot • An alignment can be seen as a path through the dotplot diagramm. Seq SeqBBBB Seq SeqAAAA ACA--CA A-CA-CA ACA--CA A-CA-CA || || || || A-CCAAC ACCAACA-CCAAC ACCAAC- VI - 2004 Page 33 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 • 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 VI - 2004 Page 34 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: VI - 2004 Page 35 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: VI - 2004 Page 36 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 Seq A A aa11 aa22 aa33 ... a ... aai-1 i-1 aii Seq Seq B B bb11 bb22 bb33 ... b ... bbj-1 j-1 bjj Seq Seq A A aa11 aa22 aa33 ... a ... aai-1 i-1 aii aai+1 i+1 Seq Seq B B bb11 bb22 bb33 ... b ... bbj-1 j-1 bjj bbj+1 j+1 Seq Seq A A aa11 aa22 aa33 ... a ... aai-1 i-1 aii aai+1 i+1 Seq Seq B B bb11 bb22 bb33 ... b ... bbj-1 j-1 bjj -- Seq Seq A A aa11 aa22 aa33 ... a ... aai-1 i-1 aii -- Seq Seq B B bb11 bb22 bb33 ... b ... bbj-1 j-1 bjj bbj+1 j+1 Score = Scoreij + Substi+1j+1 Score = Scoreij - gap Score = Scoreij - gap • We have the optimal alignment extended from i and j by one residue. VI - 2004 Page 37 Exact algorithms Simple example (Needleman-Wunsch) • Scoring system: ! Match score: ! Mismatch score: ! Gap penalty: 2 -1 -2 F(i-1,j- F(i,j- 1) s(xi,yj) 1) F(i- -d -d F(i,j) 1,j) F(i,j): score at position i, j s(x ,y ): match or mismatch score (or substitution matrix i j -10A 0-2-4-6-8-10 0-2-4-6-8-10 -220-2-4-6 -404 -40420-2 -6TA -8 -6-22312 GATTA GG A-4A-6T-8 C-12 GATTA GATTA0-2-4-6-8-10 G-2-220-2-4-6 AT T-10for C-12 T-8-40453 T-10-6-2264 C-12-8-4045 value) residues x and y i j d: gap penalty (positive value) 0-2 2+2 0-2 Note GA-TTA GA-TTA || || || || GAATTC GAATTC • 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). VI - 2004 Page 38 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) VI - 2004 Page 39