Download Pairwise sequence alignments

Pairwise sequence alignments
Volker Flegel
Vassilios Ioannidis
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Page 1
Outline
• Introduction
• Definitions
• Biological context of pairwise alignments
• Computing of pairwise alignments
• Some programs
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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
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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
THIO_EMENI
???
???
GFVVVDCFATWCGPCKAIAPTVEKFAQTY
GFVVVDCFATWCGPCKAIAPTVEKFAQTY
GG ++VD
++VD +A
+A WCGPCK
WCGPCK IAP
IAP +++
+++ AA YY
GAILVDFWAEWCGPCKMIAPILDEIADEY
GAILVDFWAEWCGPCKMIAPILDEIADEY
Extrapolate
Extrapolate
???
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THIO_EMENI
SwissProt
Page 4
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 proteins
! Nature keeps re-using domains
• Alignments try to tell the evolutionnary story of the proteins
Relationships
Same Sequence
Same Origin
Same Function
Same 3D Fold
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Example: An alignment
- textual view
• Two similar regions of the Drosophila melanogaster Slit and
Notch proteins
970
980
990
1000
1010
1020
970
980
990
1000
1010
1020
SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC
SLIT_DROME FSCQCAPGYTGARCETNIDDCLGEIKCQNNATCIDGVESYKCECQPGFSGEFCDTKIQFC
..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. :
..:.: :. :.: ...:.: .. : :.. : ::.. . :.: ::..:. :. :. :
NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC
NOTC_DROME YKCECPRGFYDAHCLSDVDECASN-PCVNEGRCEDGINEFICHCPPGYTGKRCELDIDEC
740
750
760
770
780
790
740
750
760
770
780
790
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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
Urokinase-Type plasminogen Activator
URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html
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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.
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 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.
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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).
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Definition example
The set of all globins and a test to identify them
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
True positives
G
False positives
G
G
True negatives
X
False negatives
G
G
G
G
X
X
X
X
Matches
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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.
Greater sensitivity
Less selectivity
True positives
True negatives
Less sensitivity
False positives
Greater selectivity
False negatives
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Pairwise sequence alignment
Concept of a sequence alignment
• Pairwise Alignment:
! Explicit mapping between the residues of 2 sequences
deletion
Seq
Seq AAGARFIELDTHELASTFA-TCAT
GARFIELDTHELASTFA-TCAT
|||||||||||
||
|||||||||||
|| ||||
||||
Seq
B
GARFIELDTHEVERYFASTCAT
Seq B GARFIELDTHEVERYFASTCAT
errors / mismatches
insertion
– Tolerant to errors (mismatches, insertion / deletions or indels)
– Evaluation of the alignment in a biological concept (significance)
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Pairwise sequence alignement
Number of alignments
• There are many ways to align two sequences
• Consider the sequence fragments below: a simple alignment
shows some conserved portions
CGATGCAGACGTCA
CGATGCAGACGTCA
||||||||
||||||||
CGATGCAAGACGTCA
CGATGCAAGACGTCA
but also:
CGATGCAGACGTCA
CGATGCAGACGTCA
||||||||
||||||||
CGATGCAAGACGTCA
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)
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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:
CGAGGCACAACGTCA
CGAGGCACAACGTCA
|||
||| |||
||| ||||||
||||||
CGATGCAAGACGTCA
CGATGCAAGACGTCA
is better than:
ATTGGACAGCAATCAGG
ATTGGACAGCAATCAGG
||
||
||
|| ||
ACGATGCAAGACGTCAG
ACGATGCAAGACGTCAG
• We can express this notion more rigorously, by using a
scoring system
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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.
CGAGGCACAACGTCA
CGAGGCACAACGTCA
|||
||| |||
||| ||||||
||||||
CGATGCAAGACGTCA
CGATGCAAGACGTCA
!Score: 12
ATTGGACAGCAATCAGG
ATTGGACAGCAATCAGG
||
||
||
|| ||
ACGATGCAAGACGTCAG
ACGATGCAAGACGTCAG
!Score: 5
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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 of
well 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 aminoacid by another
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Substitution matrices
(log-odds matrices)
• For a set of well known proteins:
Example matrix
(Leu, Ile): 2
(Leu, Cys): -6
...
•
•
•
Align the sequences
Count the mutations at each position
For each substitution set the score to the
log-odd ratio
&
#
observed
!!
log$$
expected
by
chance
%
"
• 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
PAM250
From:
A. D. Baxevanis, "Bioinformatics"
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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
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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
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Matrix choice
Limitations
• Substitution matrices do not take into account long range
interactions between residues.
• They assume that identical residues are equal (whereas in reallife
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.
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Alignment score
Amino acid substitution matrices
• Example:
• Most used:
PAM250
Blosum62
Raw score of an alignment
TPEA
TPEA
_|
_| ||
APGA
APGA
Score = 1 + 6 + 0 + 2 = 9
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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
GCATGCATGCAACTGCAT
|||||||||
|||||||||
GCATGCATGGGCAACTGCAT
GCATGCATGGGCAACTGCAT
can be improved by inserting a gap
GCATGCATG--CAACTGCAT
GCATGCATG--CAACTGCAT
|||||||||
||||||||| |||||||||
|||||||||
GCATGCATGGGCAACTGCAT
GCATGCATGGGCAACTGCAT
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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
CGATGCAGCAGCAGCATCG
||||||
|||||||
||||||
|||||||
CGATGC------AGCATCG
CGATGC------AGCATCG
gap opening
CGATGCAGCAGCAGCATCG
CGATGCAGCAGCAGCATCG
||
|| ||
|| ||||
|||| ||
|| ||
|| ||
CG-TG-AGCA-CA--AT-G
CG-TG-AGCA-CA--AT-G
gap extension
Gap opening penalty
• Counted each time a gap is opened in an alignment
(some programs include the first extension into this penalty)
Gap extension penalty
• Counted for each extension of a gap in an alignment
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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
CGATGCAGCAGCAGCATCG
||||||
|||||||
||||||
|||||||
CGATGC------AGCATCG
CGATGC------AGCATCG
gap opening
gap extension
13 x 1 - 10 - 6 x 1 = -3
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CGATGCAGCAGCAGCATCG
CGATGCAGCAGCAGCATCG
||
|| ||
|| ||||
|||| ||
|| ||
|| ||
CG-TG-AGCA-CA--AT-G
CG-TG-AGCA-CA--AT-G
13 x 1 - 5 x 10 - 6 x 1 = -43
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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
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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).
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...
score x
...
Ala
Ala
Val
Val
...
...
Tr
p
Tr
p
Pairwise alignments
Score distribution
obs
Random sequences
score y
score
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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.
Threshold
significant alignment
score
score x: our alignment
has a great probability
of being the result of
random sequence
similarity
score y: our alignment
is very improbable to
obtain with random
sequences
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Statistical evaluation of results
Statistics derived from the scores
100%
0%
N
0
• 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 by
chance 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=pxN
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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
Urokinase-Type plasminogen Activator
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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 substitution
value in the substitution matrix
THEFATCATTHEFASTCAT
THEFA-TCAT
THEFA-TCAT
|||||
||||| ||||
||||
THEFASTCAT
THEFASTCAT
Note
• This method produces dotplots with too much noise to be useful
! The noise can be reduced by calculating a score using a window
of residues
! The score is compared to a threshold or stringency
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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
HEF
THE
CAT
HEF
THE
CAT
|||
|||
THE
HEF
THE
THE
HEF
-5
Score: 23
-4
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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
Urokinase-Type plasminogen Activator
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Creating an alignment
Relationship between alignment and dotplot
• An alignment can be seen as a path through the dotplot diagramm.
Seq
SeqBBBB
Seq
SeqAAAA
ACA--CA
A-CA-CA
ACA--CA
A-CA-CA
|| ||
|| ||
A-CCAAC
ACCAACA-CCAAC
ACCAAC-
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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
• Local
Alignment between the complete sequence A and the
complete sequence B
Alignment between a sub-sequence of A an a subsequence of B
Computer implementation (Algorithms)
• Dynamic programing
• Global
Needleman-Wunsch
• Local
Smith-Waterman
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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
Urokinase-Type plasminogen Activator
Global alignment:
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Local alignment
(Smith-Waterman)
Example
! Local alignments are more sensitive to the modular nature of
proteins
! They can be used to search databases
Tissue-Type plasminogen Activator
Urokinase-Type plasminogen Activator
Local alignments:
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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
Seq A
A
aa11 aa22 aa33 ...
a
... aai-1
i-1 aii
Seq
Seq B
B
bb11 bb22 bb33 ...
b
... bbj-1
j-1 bjj
Seq
Seq A
A
aa11 aa22 aa33 ...
a
... aai-1
i-1 aii
aai+1
i+1
Seq
Seq B
B
bb11 bb22 bb33 ...
b
... bbj-1
j-1 bjj
bbj+1
j+1
Seq
Seq A
A
aa11 aa22 aa33 ...
a
... aai-1
i-1 aii
aai+1
i+1
Seq
Seq B
B
bb11 bb22 bb33 ...
b
... bbj-1
j-1 bjj
--
Seq
Seq A
A
aa11 aa22 aa33 ...
a
... aai-1
i-1 aii
--
Seq
Seq B
B
bb11 bb22 bb33 ...
b
... bbj-1
j-1 bjj
bbj+1
j+1
Score = Scoreij +
Substi+1j+1
Score = Scoreij - gap
Score = Scoreij - gap
• We have the optimal alignment extended from i and j by one residue.
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Exact algorithms
Simple example (Needleman-Wunsch)
• Scoring system:
! Match score:
! Mismatch score:
! Gap penalty:
2
-1
-2
F(i-1,j-
F(i,j-
1)
s(xi,yj)
1)
F(i-
-d
-d
F(i,j)
1,j)
F(i,j): score at position i, j
s(x ,y ): match or mismatch score (or substitution matrix
i j
-10A
0-2-4-6-8-10
0-2-4-6-8-10
-220-2-4-6
-404
-40420-2
-6TA
-8
-6-22312
GATTA
GG
A-4A-6T-8
C-12
GATTA
GATTA0-2-4-6-8-10
G-2-220-2-4-6
AT
T-10for
C-12
T-8-40453
T-10-6-2264
C-12-8-4045
value)
residues
x and
y
i
j
d: gap penalty (positive value)
0-2
2+2
0-2
Note
GA-TTA
GA-TTA
||
|| ||
||
GAATTC
GAATTC
• We have to keep track of the origin of the score for each element in
the 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).
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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)
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