Alignment principles and homology searching using (PSI-)BLAST

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Alignment principles and homology searching
using (PSI-)BLAST Jaap Heringa Centre for
Integrative Bioinformatics VU (IBIVU) http//ibivu
.cs.vu.nl
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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

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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.)

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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
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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
true alignment
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• 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
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MTSAVLPAAYDRKHTSIIFQTSWQ
MTSAVLPAAYDRKHTTSWQ
All possible alignments between the two sequences
can be represented as a path through the search
matrix
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MTSAVLPAAYDRKHTSIIFQTSWQ
Corresponds to stretch SIIFQ in horizontal
sequence (indel)
MTSAVLPAAYDRKHTTSWQ
All possible alignments between the two sequences
can be represented as a path through the search
matrix
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A protein sequence alignment MSTGAVLIY--TSILIKECHA
MPAGNE----- ---GGILLFHRTHELIKESHAMANDEGGSNNS A
DNA sequence alignment attcgttggcaaatcgcccctatccgg
ccttaa attt---ggcggatcg-cctctacgggcc----
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Sequence alignmentHistory
1970 Needleman-Wunsch global pair-wise
alignment 1981 Smith-Waterman local pair- wise
alignment 1984 Hogeweg-Hesper progressive
multiple alignment 1989 Lipman-Altschul-Kececiog
lu simultaneous multiple alignment 1994 Hidden
Markov Models (HMM) for multiple alignment 1996
Iterative strategies for progressive multiple
alignment revived 1997 PSI-Blast (PSSM)
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Pair-wise alignment
T D W V T A L K T D W L - - I K
Combinatorial explosion - 1 gap in 1 sequence
n1 possibilities - 2 gaps in 1 sequence (n1)n
- 3 gaps in 1 sequence (n1)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!
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Dynamic programmingScoring alignments
gp(k) is gap of size k, Nk is the number of gaps
of length k
Sa,b gp(k) -Popen -k?Pextension
affine gap penalties Popen and Pextension are
the penalties for gap initialisation and
extension, respectively
describes the likelihood of a given
residue match in the
alignment
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Amino acid exchange matrices
How do we get one? And how do we get
associated gap penalties?
20?20
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
Gap-extension penalty
Gap-opening 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
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Dynamic programmingScoring alignments
T D W V T A L K T D W L - - I K
Gap is 2 positions long
20?20
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Amino Acid Exchange Matrix
Affine gap penalties (Popen, Pextension)
Score s(T,T)s(D,D)s(W,W)s(V,L) -Popen -2Pext
s(L,I)s(K,K)
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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
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Pairwise sequence alignment needs sense of
evolution Global dynamic programming
MDAGSTVILCFVG
Evolution
M D A A S T I L C G S
Amino Acid Exchange Matrix
Search matrix
MDAGSTVILCFVG-
Gap penalties (open,extension)
MDAAST-ILC--GS
Alignment
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Pairwise sequence alignment Global dynamic
programming
MDAGSTVILCFVG
Evolution
M D A A S T I L C G S
Amino Acid Exchange Matrix
Search matrix
Gap penalties (open,extension)
MDAGSTVILCFVG-
MDAAST-ILC--GS
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Global dynamic programming
j-1
i-1
MaxS0ltxlti-1, j-1 - Pi - (i-x-1)Px Si-1,j-1 MaxS
i-1, 0ltyltj-1 - Pi - (j-y-1)Px
Si,j si,j Max
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Global dynamic programming
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Global dynamic programming
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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
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Local dynamic programming (Smith Waterman,
1981)
LCFVMLAGSTVIVGTR
E D A S T I L C G S
Negative numbers
Amino Acid Exchange Matrix
Search matrix
Gap penalties (open, extension)
AGSTVIVG A-STILCG
This is a local alignment (only part of the
sequences aligned)
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Local dynamic programming (Smith Waterman,
1981)
j-1
i-1
Si,j MaxS0ltxlti-1,j-1 - Pi - (i-x-1)Px Si,j
Si-1,j-1 Si,j Max Si-1,0ltyltj-1 - Pi -
(j-y-1)Px 0
Si,j Max
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Local dynamic programming
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Multiple sequence alignment (MSA) of 12
Flavodoxin cheY sequence
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Progressive multiple alignment - general
principle
1
All-against-all pairwise alignment
Score 1-2
2
1
Score 1-3
3
4
Score 4-5
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Scores
Similarity matrix
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Scores to distances
Iteration possibilities
Guide tree
Multiple alignment
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Sequence database (or homology)
searching-available techniques

• Dynamic Programming (DP)
• FASTA
• BLAST and PSI-BLAST
• QUEST
• HMMER
• SAM-T99

DP too slow for repeated database searches
Fast heuristics
This lecture
Hidden Markov modelling (more recent, slow)
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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
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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

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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 gt 50,000)

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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

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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

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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

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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/ T8
• sequence
• QLN QLN11, QMD9, HLN8, ZLN9,
• LNF LNF9, LBF8, LBY7, FNW7,
• NFS NFS12, AFS8, NYS8, DFT10,
• SAG none
• ...

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Scanning the Database

• Search all sequences in the database for all
  occurrences of query words that
• Remember hits

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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

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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

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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
• NCBIs BLAST server handles more than 50,000
  queries a day
• most used bioinformatics program

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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.

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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

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The Two-Hit Method

• extension step typically accounts for 90 of
  BLASTs 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

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The Two-Hit Method
Figure from Altschul et al. Nucleic Acids
Research 25, 1997
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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

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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
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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.
T
DB
Neg.
See Primer of Genome Science P. 86-87 box
Searching Sequence Databases Using BLAST
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PSI-BLASTPSI (Position Specific Iterated)
BLAST

• basic idea
• 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.
• 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)

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PSI-BLAST iteration
Query sequence
Q
xxxxxxxxxxxxxxxxx
Low-complexity region
Gapped BLAST search
Query sequence
Q
xxxxxxxxxxxxxxxxx
Database hits
make PSSM
make new PSSM
A C D . . Y
PSSM
Pi Px
Gapped BLAST search
A C D . . Y
PSSM
Pi Px
Database hits
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A Profile Matrix (Position Specific Scoring
Matrix PSSM)
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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

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PSI BLASTConstructing 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
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PSI-BLAST output example
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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)
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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)
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.
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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.

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Functional annotation by BLAST local
searchSerious problem multi-domain proteins
See Primer of Genome Science Pp. 105-108
Functional Annotation and Gene Family Clusters
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Homology-derived Secondary Structure of Proteins
(HSSP) Sander Schneider, 1991
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Literature Read the following pages in Gibson
and Muses 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