Alignment principles and homology searching using (PSI-)BLAST

Jaap HeringaCentre for Integrative Bioinformatics VU (IBIVU)

http://ibivu.cs.vu.nl

“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”

Bioinformatics

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)

ACCD or ACCD Pairwise Alignment AB─D A─BD

mutation deletion

See “Primer of Genome Science” P. 114 – box “Phylogenetics”

Evolution Ancestral sequence: ABCD

ACCD (B C) ABD (C ø)

ACCD or ACCD Pairwise Alignment AB─D A─BD

true alignment

mutation deletion

See “Primer of Genome Science” P. 114 – 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”

MTSAVLPAAYDRKHTSIIFQTSWQMTSAVLPAAYDRKHTTSWQ

All possible alignments between the two sequences can be represented as a path through the search matrix

MTSAVLPAAYDRKHTSIIFQTSWQMTSAVLPAAYDRKHTTSWQ

All possible alignments between the two sequences can be represented as a path through the search matrix

Corresponds to stretch “SIIFQ” in horizontal sequence (indel)

A protein sequence alignmentMSTGAVLIY--TSILIKECHAMPAGNE--------GGILLFHRTHELIKESHAMANDEGGSNNS

A DNA sequence alignmentattcgttggcaaatcgcccctatccggccttaaattt---ggcggatcg-cctctacgggcc----

Sequence alignmentHistory

1970 Needleman-Wunsch global pair-wise alignment

1981 Smith-Waterman local pair- wise alignment1984 Hogeweg-Hesper progressive multiple

alignment1989 Lipman-Altschul-Kececioglu simultaneous

multiple alignment 1994 Hidden Markov Models (HMM) for

multiple alignment1996 Iterative strategies for progressive multiple

alignment revived 1997 PSI-Blast (PSSM)

Pair-wise alignment

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 n 2 sequences of 300 a.a.: ~1088 alignments 2 sequences of 1000 a.a.: ~10600 alignments!

T D W V T A L KT D W L - - I K

Dynamic programmingScoring alignments

Sa,b = +

gp(k) = -Popen -kPextension affine gap penalties

Popen and Pextension are the penalties for gap initialisation and extension, respectively

li jbas ),( )(kgpN

kk

li jbas ),( describes the likelihood of a given

residue match in the alignment

gp(k) is gap of size k, Nk is the number of gaps of length k

Amino acid exchange matrices

How do we get one?

And how do we get associated gap penalties?

2020

Gap-opening penalty

Gap-extension penalty

First systematic method to derive amino 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

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 programmingScoring alignments

10 1Amino Acid Exchange

MatrixAffine gap penalties (Popen, Pextension)

2020

Score: s(T,T)+s(D,D)+s(W,W)+s(V,L) -Popen -2Pext + +s(L,I)+s(K,K)

T D W V T A L KT D W L - - I K

Gap is 2 positions long

A 2

R -2 6

N 0 0 2

D 0 -1 2 4

C -2 -4 -4 -5 12

Q 0 1 1 2 -5 4

E 0 -1 1 3 -5 2 4

G 1 -3 0 1 -3 -1 0 5

H -1 2 2 1 -3 3 1 -2 6

I -1 -2 -2 -2 -2 -2 -2 -3 -2 5

L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6

K -1 3 1 0 -5 1 0 -2 0 -2 -3 5

M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6

F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9

P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6

S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2

T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3

W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17

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

PAM250 matrix

amino acid exchange matrix (log odds)

Positive exchange values denote mutations that are more likely than randomly expected, while negative numbers correspond to avoided mutations compared to the randomly expected situation

Pairwise sequence alignment needs sense of evolution

Global dynamic programmingMDAGSTVILCFVG

MDAASTILCGS Amino Acid

Exchange Matrix

Gap penalties (open,extension)

Search matrix

MDAGSTVILCFVG-MDAAST-ILC--GS

Evolution

Alignment

Global dynamic programming

i-1

j-1

Si,j = si,j + Max Max{S0<x<i-1, j-1 - Pi - (i-x-1)Px}Si-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

MSTGAVLIY--TS--------GGILLFHRTSGTSNS

End-gaps

End-gaps

Local dynamic programming (Smith & Waterman, 1981)

LCFVMLAGSTVIVGTREDASTILCGS

Amino AcidExchange Matrix

Gap penalties (open, extension)

Search matrix

Negativenumbers

AGSTVIVGA-STILCG

This is a local alignment (only part of the sequences aligned)

Local dynamic programming (Smith & Waterman, 1981)

i-1

j-1

Si,j = Max Si,j + Max{S0<x<i-1,j-1 - Pi - (i-x-1)Px}Si,j + Si-1,j-1

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

1213

45

Guide tree Multiple alignment

Score 1-2Score 1-3

Score 4-5

Scores Similaritymatrix5×5

Scores to distances Iteration possibilities

All-against-all pairwise alignment

Sequence database (or homology) searching-available techniques

• Dynamic Programming (DP)

• FASTA• BLAST and PSI-BLAST• QUEST

• HMMER• SAM-T99

Fast heuristics

Hidden Markov modelling (more recent, slow)

DP too slow for repeated database searches

This lecture

•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 sequenceThis transfer of information based on homology has arguably produced more knowledge about genes than any other technique

Homology Searching Motivation

See “Primer of Genome Science” Pp. 25-26 box “GenBank Files”

•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

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 qTo 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 listThe 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 pairsBLAST 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=8sequenceQLN 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

sequences that score higher than the specified threshold (putative homologs)

• But there is always the problem of false positives and false negatives

• As a trick to find more sequences, you can use database sequences found as a query for a new BLAST search or use PSI-BLAST

Q

Pos.

Neg.DB

T

See “Primer of Genome Science” P. 86-87 box “Searching Sequence Databases Using BLAST”

PSI-BLASTPSI (Position Specific Iterated) BLAST

basic idea:1. Carry out gapped-BLAST using the query sequence to find first

hitsQuery 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 foundThe 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 stepsRescan 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

ACD..Y

PiPx

Query sequence

PSSM

Q Query sequenceGapped BLAST search

Database hits

Gapped BLAST searchACD..Y

PiPx

PSSM

Database hits

xxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxx

make new PSSM

make PSSM

Low-complexity region

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 similarityThe 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-nP(S x),

where n is the number of sequences in the databaseDepending on x and n (fixed)

Normalised sequence similarityStatistical 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) = nP(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 similarityStatistical 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.

See “Primer of Genome Science” Pp. 105-108: “Functional Annotation and Gene Family Clusters”

Functional annotation by BLAST local search

Serious problem: multi-domain proteins

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. 86-87 box “Searching Sequence Databases Using BLAST”

Pp. 72-75 box “Pairwise Sequence Alignment”

P. 114 box “Phylogenetics”

Pp. 105-108: “Functional Annotation and Gene Family Clusters”