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 • 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 Si,j + Si-1,j-1 Si,j = Max Si,j + Max {Si-1,0 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. – extend all matches to seek high-scoring segment pairs BLAST quickly scans each sequence in a database of protein sequences for ungapped regions showing high similarity, which are called high-scoring segment pairs (HSP), using the tables of similar peptides. The word hits are extended in either direction in an attempt to generate an alignment with a score exceeding the threshold of S, and as far as the cumulative alignment score can be increased. • Return: segment pairs (HSPs) scoring at least S Compiling list of words… •Given: – query sequence: QLNFSAGW – word length w = 3 – word score threshold T = 8 • Step 1: determine all words of length w in query sequence QLN LNF NFS FSA SAG AGW Compiling list of words (Ctd)… • Step 2: determine all words that score at least T when compared to a word in the query sequence: words from query words w/ T=8 sequence QLN QLN=11, QMD=9, HLN=8, ZLN=9,… LNF LNF=9, LBF=8, LBY=7, FNW=7,… NFS NFS=12, AFS=8, NYS=8, DFT=10,… … SAG none ... Scanning the Database • Search all sequences in the database for all occurrences of query words that • Remember hits Extending Hits • Extend hits in both directions (without allowing gaps) • Terminate extension in one direction when score falls certain distance below best score for shorter extensions • return segment pairs scoring at least S Sensitivity versus Running Time • the main parameter controlling the sensitivity vs. running-time trade-off is T (threshold for what becomes a query word) – small T: greater sensitivity, more hits to expand –large T: lower sensitivity, fewer hits to expand BLAST Notes • may fail to find all HSPs – may miss seeds if T is too stringent – extension is greedy • empirically, 10 to 50 times faster than Smith- Waterman • is a heuristic local alignment technique • large impact: – NCBI’s BLAST server handles more than 50,000 queries a day – most used bioinformatics program BLAST flavours • blastp compares an amino acid query sequence against a protein sequence database • blastn compares a nucleotide query sequence against a nucleotide sequence database • blastx compares the six-frame conceptual protein translation products of a nucleotide query sequence against a protein sequence database • tblastn compares a protein query sequence against a nucleotide sequence database translated in six reading frames • tblastx compares the six-frame translations of a nucleotide query sequence against the six-frame translations of a nucleotide sequence database. More Recent BLAST Extensions • the two-hit method • gapped BLAST • PSI-BLAST all are aimed at increasing sensitivity while limiting run-time • Altschul et al., Nucleic Acids Research 1997 The Two-Hit Method • extension step typically accounts for 90% of BLAST’s execution time • key idea: do extension only when there are two hits on the same diagonal within distance A of each other • to maintain sensitivity, lower T parameter – more single hits found – but only small fraction have associated 2nd hit The Two-Hit Method Figure from: Altschul et al. Nucleic Acids Research 25, 1997 Gapped BLAST • Start gapped alignment only if two-hit extension has a sufficiently high score • find length-11 segment with highest score; use central pair in this segment as seed • run DP process both forward & backward from seed • prune cells when local alignment score falls a certain distance below best score yet Gapped BLAST The black parts in the figure are the parts that are covered by Dynamic Programming starting in two directions from the seed: the best alignment found in both directions are then combined in the final optimal gapped alignment. Figure from: Altschul et al. Nucleic Acids Research 25, 1997 BLAST usage • BLAST produces a list of Q sequences that score higher than the specified threshold (putative homologs) Pos. • But there is always the T problem of false positives and false negatives DB Neg. • As a trick to find more sequences, you can use database sequences found as a query for a new BLAST search or use See “Primer of Genome Science” P. 86-87 PSI-BLAST box “Searching Sequence Databases Using BLAST” PSI-BLAST PSI (Position Specific Iterated) BLAST basic idea: 1. Carry out gapped-BLAST using the query sequence to find first hits Query sequence is first scanned for the presence of so-called low-complexity regions (Wooton and Federhen, 1996), i.e. regions with a biased composition likely to lead to spurious hits are excluded from alignment. 2. use results from (gapped) BLAST query to construct a profile matrix (PSSM), containing information about the query sequence and hits found The program takes significant local alignments found (E-value better than threshold), constructs a (master-slave) multiple alignment and abstracts a position specific scoring matrix (PSSM) from this alignment. 3. search database with PSSM (containing improved information from multiple sequence segments) instead of single query sequence 4. Iterate preceding two steps Rescan the database in a subsequent round to find more homologous sequences. Iteration continues until user decides to stop or search has converged (no more hits found) PSI-BLAST iteration Q xxxxxxxxxxxxxxxxx Query sequence Low- complexity Gapped BLAST search region Q xxxxxxxxxxxxxxxxx Query sequence Database hits make PSSM make new A C PSSM D . . Y Pi PSSM Px Gapped BLAST search A C D . . Y Pi PSSM Px Database hits A Profile Matrix (Position Specific Scoring Matrix – PSSM) PSI BLAST • Searching with a Profile • aligning profile matrix to a simple sequence – like aligning two sequences – except score for aligning a character with a matrix position is given by the matrix itself – not a substitution matrix PSI BLAST: Constructing the Profile Matrix Remember that only local fragments are fished out of the database by BLAST! These can cover only part of the query sequence. Figure from: Altschul et al. Nucleic Acids Research 25, 1997 PSI-BLAST output example Normalised sequence similarity The p-value is defined as the probability of seeing at least one unrelated score S greater than or equal to a given score x in a database search over n sequences. This probability follows the Poisson distribution (Waterman and Vingron, 1994): P(x, n) = 1 – e-n⋅P(S≥ x), where n is the number of sequences in the database Depending on x and n (fixed) Normalised sequence similarity Statistical significance The E-value is defined as the expected number of non- homologous sequences with score greater than or equal to a score x in a database of n sequences: E(x, n) = n⋅P(S ≥ x) if E-value = 0.01, then the expected number of random hits with score S ≥ x is 0.01, which means that this E- value is expected by chance only once in 100 independent searches over the database. if the E-value of a hit is 5, then five fortuitous hits with S ≥ x are expected within a single database search, which renders the hit not significant. Normalised sequence similarity Statistical significance • Database searching is commonly performed using an E-value in between 0.1 and 0.001. • Low E-values decrease the number of false positives in a database search, but increase the number of false negatives, thereby lowering the sensitivity of the search. Functional annotation by BLAST local search Serious problem: multi-domain proteins See “Primer of Genome Science” Pp. 105-108: “Functional Annotation and Gene Family Clusters” Homology-derived Secondary Structure of Proteins (HSSP) Sander & Schneider, 1991 Literature: Read the following pages in Gibson and Muse’s “Primer of Genome Science” Pp. 25-26 box “GenBank Files” Pp. 72-75 box “Pairwise Sequence Alignment” Pp. 86-87 box “Searching Sequence Databases Using BLAST” Pp. 105-108: “Functional Annotation and Gene Family Clusters” P. 114 box “Phylogenetics”