pairwise sequence alignments
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August 2006 Page 1
Pairwise sequence alignments
Etienne de Villiers
Adapted with permission of Swiss EMBnet node and SIB
August 2006 Page 2
Outline
•Introduction
•Definitions
•Biological context of pairwise alignments
•Computing of pairwise alignments
•Some programs
August 2006 Page 3
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
August 2006 Page 4
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 GFVVVDCFATWCGPCKAIAPTVEKFAQTY G ++VD +A WCGPCK IAP +++ A Y ??? GAILVDFWAEWCGPCKMIAPILDEIADEY
THIO_EMENI GFVVVDCFATWCGPCKAIAPTVEKFAQTY G ++VD +A WCGPCK IAP +++ A Y ??? GAILVDFWAEWCGPCKMIAPILDEIADEY
THIO_EMENISwissProt
ExtrapolateExtrapolate
???
August 2006 Page 5
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 proteinsNature keeps re-using domains
• Alignments try to tell the evolutionnary story of the proteinsRelationships
Same Sequence
Same 3D Fold
Same Origin Same Function
August 2006 Page 6
Example: An alignment - textual view
• Two similar regions of the Drosophila melanogaster Slit and Notch proteins
970 980 990 1000 1010 1020 SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC ..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. :NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC 740 750 760 770 780 790
970 980 990 1000 1010 1020 SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC ..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. :NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC 740 750 760 770 780 790
August 2006 Page 7
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
Uro
kinase
-Typ
e p
lasm
inog
en
Activ
ato
r
URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html
August 2006 Page 8
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.
SimilarityProportion 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.
August 2006 Page 9
Matches
Definition example The set of all globins and a test to identify them
True positives
True negatives
False positives
False negatives
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
G
G
G
G
G
G
G
X
XX
XX
August 2006 Page 10
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).
August 2006 Page 11
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.
True positives
True negatives
False positives
False negatives
Greater sensitivity
Less selectivity
Less sensitivity
Greater selectivity
August 2006 Page 12
Pairwise sequence alignment Concept of a sequence alignment
• Pairwise Alignment:Explicit mapping between the residues of 2
sequences
– Tolerant to errors (mismatches, insertion / deletions or indels)
– Evaluation of the alignment in a biological concept (significance)
Seq A GARFIELDTHELASTFA-TCAT||||||||||| || ||||
Seq B GARFIELDTHEVERYFASTCAT
Seq A GARFIELDTHELASTFA-TCAT||||||||||| || ||||
Seq B GARFIELDTHEVERYFASTCAT
errors / mismatches insertion
deletion
August 2006 Page 13
Pairwise sequence alignment
Number of alignments• There are many ways to align two sequences• Consider the sequence fragments below: a simple
alignment shows some conserved portions
but also:
CGATGCAGACGTCA ||||||||CGATGCAAGACGTCA
CGATGCAGACGTCA ||||||||CGATGCAAGACGTCA
CGATGCAGACGTCA||||||||CGATGCAAGACGTCA
CGATGCAGACGTCA||||||||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)
August 2006 Page 14
Alignment 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:
is better than:
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
• We can express this notion more rigorously, by using ascoring system
August 2006 Page 15
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.
Score: 12
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
Score: 5
August 2006 Page 16
Introducing biological information
Importance of the scoring systemdiscrimination of significant biological alignments
• Based on physico-chemical properties of amino-acidsHydrophobicity, acid / base, sterical properties, ...Scoring system scales are arbitrary
• Based on biological sequence informationSubstitutions observed in structural or evolutionary
alignments of well studied protein familiesScoring 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 amino-acid by another
August 2006 Page 17
Substitution matrices (log-odds matrices)
Example matrix
PAM250From: A. D. Baxevanis, "Bioinformatics"
(Leu, Ile): 2
(Leu, Cys): -6...
• 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
chancebyexpected
observedlog
chancebyexpected
observedlog
• For a set of well known proteins:• Align the sequences• Count the mutations at each position• For each substitution set the score to
the log-odd ratio
August 2006 Page 18
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 familiesOld standard matrix:PAM250
August 2006 Page 19
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 databaseStandard matrix: BLOSUM62
August 2006 Page 20
Matrix choice
Limitations• Substitution matrices do not take into account long range
interactions between residues.
• They assume that identical residues are equal ( whereas in real life 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.
August 2006 Page 21
Alignment score Amino acid substitution matrices
• Example: PAM250• Most used: Blosum62
Raw score of an alignment
TPEA¦| |APGA
TPEA¦| |APGA
Score = 1 = 9+ 6 + 0 + 2
August 2006 Page 22
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|||||||||GCATGCATGGGCAACTGCAT
GCATGCATGCAACTGCAT|||||||||GCATGCATGGGCAACTGCAT
can be improved by inserting a gap
GCATGCATG--CAACTGCAT||||||||| |||||||||GCATGCATGGGCAACTGCAT
GCATGCATG--CAACTGCAT||||||||| |||||||||GCATGCATGGGCAACTGCAT
August 2006 Page 23
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|||||| |||||||CGATGC------AGCATCG
CGATGCAGCAGCAGCATCG|||||| |||||||CGATGC------AGCATCG
CGATGCAGCAGCAGCATCG|| || |||| || || |CG-TG-AGCA-CA--AT-G
CGATGCAGCAGCAGCATCG|| || |||| || || |CG-TG-AGCA-CA--AT-G
gap opening
Gap opening penalty• Counted each time a gap is opened in an alignment
(some programs include the first extension into this penalty)
gap extension
Gap extension penalty• Counted for each extension of a gap in an alignment
August 2006 Page 24
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|||||| |||||||CGATGC------AGCATCG
CGATGCAGCAGCAGCATCG|||||| |||||||CGATGC------AGCATCG
CGATGCAGCAGCAGCATCG|| || |||| || || |CG-TG-AGCA-CA--AT-G
CGATGCAGCAGCAGCATCG|| || |||| || || |CG-TG-AGCA-CA--AT-G
gap opening
13 x 1 - 10 - 6 x 1 = -3
gap extension
13 x 1 - 5 x 10 - 6 x 1 = -43
August 2006 Page 25
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 systemAllows the comparison of different alignmentsUnits: expressed in bits
August 2006 Page 26
...
Statistical evaluation of results
Distribution of alignment scores - Extreme Value Distribution
• Random sequences and alignment scoresSequence alignment scores between random
sequences are distributed following an extreme value distribution (EVD).
score
ob
s
AlaVal...Trp
Random sequences Pairwise alignments Score distribution
low score
low score
low score
low score
high score
high score due to "luck"
August 2006 Page 27
score y: our alignment is very improbable to obtain with random sequences
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.
scorescore x: our alignment has a great probability of being the result of random sequence similarity
Thresholdsignificant alignment
August 2006 Page 28
Statistical evaluation of results
Statistics derived from the scores• 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-valueNumber of matches with this score one can expect to
find by chance in a database of this sizeThe 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 = p x N
100%
0%
N
0
August 2006 Page 29
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
Uro
kinase
-Typ
e p
lasm
inog
en
Activ
ato
r
August 2006 Page 30
Reading a DotplotAs simple as projecting the diagonals onto the axis.
Tissue-Type plasminogen Activator
Uro
kinase
-Typ
e p
lasm
inog
en
Activ
ato
r
Tissue-Type plasminogen Activator
A A’ B DC
Urokinase-Type plasminogen ActivatorA CB D
August 2006 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.Between 2 different sequences orInside the same sequence (ssDNA repeats, RNA stem loops, etc)
It does not provide an alignment.
August 2006 Page 32
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.
Alignment types• Global Alignment between the complete sequence A and the
complete sequence B• Local Alignment between a sub-sequence of A an a sub-
sequence of B
Computer implementation (Algorithms)• Dynamic programing• Global Needleman-Wunsch• Local Smith-Waterman
August 2006 Page 33
Global alignment (Needleman-Wunsch)
Example Global alignments are very sensitive to gap penaltiesGlobal alignments do not take into account the modular
nature of proteinsTissue-Type plasminogen Activator
Uro
kinase
-Typ
e p
lasm
inog
en
Activ
ato
r
Global alignment:
August 2006 Page 34
Local alignment (Smith-Waterman)
Example Local alignments are more sensitive to the modular nature
of proteinsThey can be used to search databases
Tissue-Type plasminogen Activator
Uro
kinase
-Typ
e p
lasm
inog
en
Activ
ato
r
Local alignments:
August 2006 Page 35
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)
August 2006 Page 36
Acknowledgments & References
Laurent Falquet, Lorenza Bordoli ,Volker Flegel, Frédérique Galisson
References• Ian Korf, Mark Yandell & Joseph Bedell, BLAST,
O’Reilly• David W. Mount, Bioinformatics, Cold Spring Harbor
Laboratory Press• Jean-Michel Claverie & Cedric Notredame,
Bioinformatics for Dummies, Wiley Publishing
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