Alignment principles and homology searching using (PSI-)BLAST Jaap Heringa Centre for Integrative Bioinformatics VU (IBIVU) http://ibivu.cs.vu.nl Bioinformatics “Nothing in Biology makes sense except in the light of evolution” (Theodosius Dobzhansky (1900-1975)) “Nothing in bioinformatics makes sense except in the light of Biology” Evolution Four requirements: • Template structure providing stability (DNA) • Copying mechanism (meiosis) • Mechanism providing variation (mutations; insertions and deletions; crossing-over; etc.) • Selection (enzyme specificity, activity, etc.) Evolution Ancestral sequence: ABCD ACCD (B C) ABD (C ø) mutation deletion ACCD or ACCD Pairwise Alignment AB─D A─BD See “Primer of Genome Science” P. 114 – box “Phylogenetics” Evolution Ancestral sequence: ABCD ACCD (B C) ABD (C ø) mutation deletion ACCD or ACCD Pairwise Alignment AB─D A─BD See “Primer of Genome Science” P. 114 – true alignment box “Phylogenetics” Comparing two sequences •We want to be able to choose the best alignment between two sequences. •Alignment assumes divergent evolution (common ancestry) as opposed to convergent evolution •The first sequence to be compared is assigned to the horizontal axis and the second is assigned to the vertical axis. See “Primer of Genome Science” P. 72-75 box “Pairwise Sequence Alignment” MTSAVLPAAYDRKHTSIIFQTSWQ M T S A V L P A A Y D R K H T T S W Q All possible alignments between the two sequences can be represented as a path through the search matrix MTSAVLPAAYDRKHTSIIFQTSWQ M T S A V L P A A Y Corresponds D to stretch R “SIIFQ” in K horizontal H sequence T (indel) T S W Q All possible alignments between the two sequences can be represented as a path through the search matrix A protein sequence alignment MSTGAVLIY--TSILIKECHAMPAGNE----- ---GGILLFHRTHELIKESHAMANDEGGSNNS A DNA sequence alignment attcgttggcaaatcgcccctatccggccttaa attt---ggcggatcg-cctctacgggcc---- Sequence alignment History 1970 Needleman-Wunsch global pair-wise alignment 1981 Smith-Waterman local pair-wise alignment 1984 Hogeweg-Hesper progressive multiple alignment 1989 Lipman-Altschul-Kececioglu simultaneous multiple alignment 1994 Hidden Markov Models (HMM) for multiple alignment 1996 Iterative strategies for progressive multiple alignment revived 1997 PSI-Blast (PSSM) Pair-wise alignment T D W V T A L K T D W L - - I K Combinatorial explosion - 1 gap in 1 sequence: n+1 possibilities - 2 gaps in 1 sequence: (n+1)n - 3 gaps in 1 sequence: (n+1)n(n-1), etc. 2n (2n)! 22n = ~ n (n!)2 √πn 2 sequences of 300 a.a.: ~1088 alignments 2 sequences of 1000 a.a.: ~10600 alignments! Dynamic programming Scoring alignments gp(k) is gap of s(ai,bj) Nk • gp(k) size k, Nk is the Sa,b = ∑l + ∑k number of gaps of length k gp(k) = -Popen -k⋅Pextension affine gap penalties Popen and Pextension are the penalties for gap initialisation and extension, respectively s(ai,bj) describes the likelihood of a given ∑l residue match in the alignment Amino acid exchange matrices How do we get one? First systematic method to derive amino 20×20 acid exchange matrices by Margaret Dayhoff et al. (1978) – Atlas of Protein Structure. There are now various matrix series (PAM, BLOSUM) corresponding to different evolutionary speeds or time since divergence And how do we get associated gap penalties? Gap-opening Gap-extension penalty penalty Formalisms are available for exchange matrices but for gap penalties no formal theory exists yet. Most researchers use recommended gap penalty values provided by experts Dynamic programming Scoring alignments T D W V T A L K T D W L - - I K 20×20 Gap is 2 positions long 10 1 Amino Acid Affine gap penalties Exchange Matrix (Popen, Pextension) Score: s(T,T)+s(D,D)+s(W,W)+s(V,L) -Popen -2Pext + +s(L,I)+s(K,K) A 2 R -2 6 N 0 0 2 PAM250 matrix D 0 -1 2 4 C -2 -4 -4 -5 12 Q 0 1 1 2 -5 4 amino acid E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 5 exchange matrix H -1 2 2 1 -3 3 1 -2 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 (log odds) L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 Positive exchange values K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 denote mutations that are M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 more likely than randomly F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 expected, while negative P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6 numbers correspond to S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 avoided mutations compared T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 to the randomly expected W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 situation Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 B 0 -1 2 3 -4 1 2 0 1 -2 -3 1 -2 -5 -1 0 0 -5 -3 -2 2 Z 0 0 1 3 -5 3 3 -1 2 -2 -3 0 -2 -5 0 0 -1 -6 -4 -2 2 3 A R N D C Q E G H I L K M F P S T W Y V B Z Pairwise sequence alignment needs sense of evolution Global dynamic programming MDAGSTVILCFVG M D Evolution A A S T I L C G Amino Acid Exchange S Matrix Search matrix MDAGSTVILCFVG- Gap penalties MDAAST-ILC--GS (open,extension) Alignment Pairwise sequence alignment Global dynamic programming MDAGSTVILCFVG M Evolution D A A S T I L C Amino Acid Exchange G S Matrix Search matrix MDAGSTVILCFVG- Gap penalties MDAAST-ILC--GS (open,extension) Global dynamic programming j-1 i-1 Max{S0<x<i-1, j-1 - Pi - (i-x-1)Px} S Si,j = si,j + Max i-1,j-1 Max{Si-1, 0<y<j-1 - Pi - (j-y-1)Px} Global dynamic programming Global dynamic programming Pairwise alignment • Global alignment: all gaps are penalised • Semi-global alignment: N- and C-terminal gaps (end-gaps) are not penalised End-gaps MSTGAVLIY--TS----- ---GGILLFHRTSGTSNS End-gaps Local dynamic programming (Smith & Waterman, 1981) LCFVMLAGSTVIVGTR E D Negative A numbers S T I L C Amino Acid G S Exchange Matrix Search matrix Gap penalties (open, AGSTVIVG extension) A-STILCG This is a local alignment (only part of the sequences aligned) Local dynamic programming (Smith & Waterman, 1981) j-1 i-1 Si,j + Max{S0<x<i-1,j-1 -Pi -(i-x-1)Px} Si,j + Si-1,j-1 Si,j = Max Si,j + Max {Si-1,0<y<j-1 -Pi -(j-y-1)Px} 0 Local dynamic programming Multiple sequence alignment (MSA) of 12 * Flavodoxin + cheY sequence Progressive multiple alignment - general principle 1 All- 2 Score 1-2 against- 1 Score 1-3 all 3 pairwise 4 Score 4-5 alignment 5 Scores Similarity 5×5 matrix Scores to distances Iteration possibilities Guide tree Multiple alignment Sequence database (or homology) searching -available techniques DP too slow • Dynamic Programming (DP) for repeated database •FASTA searches • BLAST and PSI-BLAST Fast heuristics •QUEST This lecture •HMMER Hidden Markov modelling •SAM-T99 (more recent, slow) Homology Searching Motivation •If you have an unknown gene, you can try and find a homologous sequence (an ortholog or a paralog) in an annotated sequence database, i.e. a database containing sequences for which the functions are known •You then transfer the information from a putatively homologous database sequence to the query sequence This transfer of information based on homology has arguably produced more knowledge about genes than any other technique See “Primer of Genome Science” Pp. 25-26 box “GenBank Files” Heuristic Alignment Motivation •dynamic programming has performance O(mn), where m and n are the sequence lengths, which is too slow for large databases with high query traffic •heuristic methods do fast approximation to dynamic programming – FASTA [Pearson & Lipman, 1988] – BLAST [Altschul et al., 1990] Heuristic Alignment Motivation • consider the task of searching SWISS-PROT against a query sequence: – say our query sequence is 362 amino-acids long – SWISS-PROT release 38 contains 29,085,265 amino acids • finding local alignments via dynamic programming would entail O(1010) matrix operations • many servers handle thousands of such queries a day (NCBI > 50,000) BLAST • Basic Local Alignment Search Tool • BLAST heuristically finds high scoring segment pairs (HSPs): – identical length segments each time from 2 sequences (query and database sequence) with statistically significant match scores – i.e. ungapped local alignments • key tradeoff: sensitivity vs. speed • Sensitivity = number of significant matches detected/ number of significant matches in DB BLAST Overview • Given: query sequence q, word length w, word score threshold T, segment score threshold S – compile a list of “words” that score at least T when compared to words from q To gain speed, BLAST generates all words (tripeptides) from a query sequence and for each of those the derivation of a table of similar tripeptides: the number of tripeptides is only a fraction of total number possible. – scan database for matches to words in list The initial search is done for each tripeptide that can be found in the table of similar tripeptides for each query tripeptide, and scores at least the threshold value T when compared to the query tripeptide using a substitution matrix for scoring.