Pairwise sequence alignments - Bioinformatics · Pairwise sequence alignments Volker Flegel...
Transcript of Pairwise sequence alignments - Bioinformatics · Pairwise sequence alignments Volker Flegel...
VI - 2004 Page 1
Pairwise sequence alignments
Volker FlegelVassilios Ioannidis
VI - 2004 Page 2
Outline
• Introduction
• Definitions
• Biological context of pairwise alignments
• Computing of pairwise alignments
• Some programs
VI - 2004 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
VI - 2004 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 knowncharacteristics 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_EMENI
SwissProt
ExtrapolateExtrapolate
???
VI - 2004 Page 5
Do alignments make sense ?
Evolution of sequences
• Sequences evolve through mutation and selection
! Selective pressure is different for each residue position in aprotein (i.e. conservation of active site, structure, charge,etc.)
• Modular nature of proteins
! Nature keeps re-using domains
• Alignments try to tell the evolutionnary story of the proteins
Relationships
Same Sequence
Same 3D Fold
Same Origin Same Function
VI - 2004 Page 6
Example: An alignment - textual view
• Two similar regions of the Drosophila melanogaster Slit andNotch 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
VI - 2004 Page 7
Example: An alignment - graphical view
• Comparing the tissue-type and urokinase type plasminogenactivators. Displayed using a diagonal plot or Dotplot.
Tissue-Type plasminogen Activator
Uro
kin
ase-T
ype p
lasm
inogen A
ctiv
ato
r
URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html
VI - 2004 Page 8
Some definitions
Identity
Proportion of pairs of identical residues between two alignedsequences.
Generally expressed as a percentage.
This value strongly depends on how the two sequences are aligned.
Similarity
Proportion 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 arealigned, as well as on the substitution matrix used.
Homology
Two sequences are homologous if and only if they have a commonancestor.
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.
VI - 2004 Page 9
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).
VI - 2004 Page 10
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
X
XX
X
VI - 2004 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
VI - 2004 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 AGARFIELDTHELASTFA-TCAT||||||||||| || ||||
Seq BGARFIELDTHEVERYFASTCAT
Seq AGARFIELDTHELASTFA-TCAT||||||||||| || ||||
Seq BGARFIELDTHEVERYFASTCAT
errors / mismatches insertion
deletion
VI - 2004 Page 13
Pairwise sequence alignement
Number of alignments
• There are many ways to align two sequences
• Consider the sequence fragments below: a simple alignmentshows 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)
VI - 2004 Page 14
Alignement 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 a
scoring system
VI - 2004 Page 15
Scoring system
Simple alignment scores
• A simple way (but not the best) to score an alignment is to count 1 foreach match and 0 for each mismatch.
!Score: 12
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG
!Score: 5
VI - 2004 Page 16
Introducing biological information
Importance of the scoring system
!discrimination of significant biological alignments
• Based on physico-chemical properties of amino-acids! Hydrophobicity, acid / base, sterical properties, ...
! Scoring system scales are arbitrary
• Based on biological sequence information
! Substitutions observed in structural or evolutionary alignments ofwell studied protein families
! Scoring 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
VI - 2004 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 aresimilar, mutations from one into the other occur
more often then expected by chance during
evolution
• Negative score: the amino acids aredissimilar, the mutation from one into the other
occurs less often then expected by chance during
evolution
!!"
#$$%
&
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
VI - 2004 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 families! Old standard matrix: PAM250
VI - 2004 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 database! Standard matrix: BLOSUM62
VI - 2004 Page 20
Matrix choice
Limitations
• Substitution matrices do not take into account long rangeinteractions between residues.
• They assume that identical residues are equal (whereas in reallifea residue at the active site has other evolutionary constraints thanthe same residue outside of the active site)
• They assume evolution rate to be constant.
VI - 2004 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
VI - 2004 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
VI - 2004 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 gapdistribution. 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
VI - 2004 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
VI - 2004 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 system
! Allows the comparison of different alignments! Units: expressed in bits
VI - 2004 Page 26
Statistical evaluation of results
Distribution of alignment scores - Extreme Value Distribution
• Random sequences and alignment scores! Sequence alignment scores between random sequences are
distributed following an extreme value distribution (EVD).
Ala
Val
...
Trp score
obsscore x
score y
......
Ala
Val
...
Trp
Random sequences Pairwise alignments Score distribution
VI - 2004 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 alignmenthas a great probability
of being the result of
random sequence
similarity
Threshold
significant alignment
VI - 2004 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-value
! Number of matches with this score one can expect to find bychance in a database of this size
! The 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
VI - 2004 Page 29
Diagonal plots or Dotplot
Concept of a Dotplot
• Produces a graphical representation of similarity regions.
• The horizontal and vertical dimensions correspond to thecompared sequences.
• A region of similarity stands out as a diagonal.
Tissue-Type plasminogen Activator
Uro
kin
ase-T
ype p
lasm
inogen A
ctiv
ato
r
VI - 2004 Page 30
Dotplot construction
Simple example
• A dot is placed at each position where two residues match.
! The colour of the dot can be chosen according to the substitutionvalue in the substitution matrix
THEFATCATTHEFASTCAT
THEFA-TCAT||||| ||||THEFASTCAT
THEFA-TCAT||||| ||||THEFASTCAT
Note
• This method produces dotplots with too much noise to be useful
! The noise can be reduced by calculating a score using a windowof residues
! The score is compared to a threshold or stringency
VI - 2004 Page 31
Dotplot construction
Window example
• Each window of the first sequence is aligned (without gaps) to each
window of the 2nd sequence• A colour is set into a rectangular array according to the score of the
aligned windows
THEFATCATTHEFASTCAT
THE|||THE
THE|||THE
Score: 23
THE
HEF
THE
HEF
Score: -5
CAT
THE
CAT
THE
Score: -4
HEF
THE
HEF
THE
Score: -5
VI - 2004 Page 32
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.! It does not provide an alignment.
Tissue-Type plasminogen Activator
Uro
kin
ase-T
ype p
lasm
inogen A
ctiv
ato
r
VI - 2004 Page 33
Relationship between alignment and dotplot
• An alignment can be seen as a path through the dotplot diagramm.
Creating an alignment
Seq B A-CA-CA| || |
Seq A ACCAAC-
Seq B A-CA-CA| || |
Seq A ACCAAC-
Seq B ACA--CA|
Seq A A-CCAAC
Seq B ACA--CA|
Seq A A-CCAAC
VI - 2004 Page 34
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.
Alignement 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
VI - 2004 Page 35
Global alignment (Needleman-Wunsch)
Example
! Global alignments are very sensitive to gap penalties! Global alignments do not take into account the modular nature of
proteins Tissue-Type plasminogen Activator
Uro
kin
ase-T
ype p
lasm
inogen A
ctiv
ato
r
Global alignment:
VI - 2004 Page 36
Local alignment (Smith-Waterman)
Example
! Local alignments are more sensitive to the modular nature ofproteins
! They can be used to search databases
Tissue-Type plasminogen Activator
Uro
kin
ase-T
ype p
lasm
inogen A
ctiv
ato
r
Local alignments:
VI - 2004 Page 37
Optimal alignment extension
How to extend optimaly an optimal alignment
• An optimal alignment up to positions i and j can be extended in 3 ways.
• Keeping the best of the 3 guarantees an extended optimal alignment.
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
• We have the optimal alignment extended from i and j by one residue.
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
ai+1
bj+1
ai+1
bj+1
Score = Scoreij +
Substi+1j+1
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
ai+1
-
ai+1
-Score = Scoreij - gap
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
Seq A a1 a2 a3 ... ai-1 ai
Seq B b1 b2 b3 ... bj-1 bj
-
bj+1
-
bj+1
Score = Scoreij - gap
VI - 2004 Page 38
Exact algorithms
Simple example (Needleman-Wunsch)
• Scoring system:! Match score: 2
! Mismatch score: -1
! Gap penalty: -2
Note
• We have to keep track of the origin of the score for each element inthe matrix.! This allows to build the alignment by traceback when the matrix has
been completely filled out.
• Computation time is proportional to the size of sequences (n x m).
GATTA0-2-4-6-8-10G-2A-4A-6T-8T-10C-12GATTA0-2-4-6-8-10G-220-2-4-6A-404A-6T-8T-10C-12
0 - 2
0 - 2
2 + 2
GATTA0-2-4-6-8-10G-220-2-4-6A-40420-2A-6-22312T-8-40453T-10-6-2264C-12-8-4045
F(i-
1,j)
F(i,j)
s(xi,yj)
F(i-1,j-
1)-d
F(i,j-
1)
-d
F(i,j): score at position i, j
s(xi,yj): match or mismatch score (or substitution matrix
value) for residues xi and yj
d: gap penalty (positive value)
GA-TTA|| ||GAATTC
GA-TTA|| ||GAATTC
VI - 2004 Page 39
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 alignmentmust 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)