Pairwise sequence alignments - BioinformaticsPairwise sequence alignment Concept of a sequence alignment •Pairwise Alignment: Explicit mapping between the residues of 2 sequences

VI, March 2005

Pairwise sequence alignments

Vassilios Ioannidis(From Volker Flegel©)

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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 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_EMENISwissProt

ExtrapolateExtrapolate

???

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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 3D Fold

Same Origin Same Function

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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 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

: .

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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-T

ype plasminogen A

ctivator

URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html

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Some definitions

IdentityProportion 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 wellas on the substitution matrix used.

HomologyTwo 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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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

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More definitionsConsider 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 positiveA protein is a true positive if it belongs to S and is detected by t.

True negativeA protein is a true negative if it does not belong to S and is not detected by t.

False positiveA protein is a false positive if it does not belong to S and is (incorrectly) detected by t.

False negativeA protein is a false negative if it belongs to S and is not detected by t (but should be).

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Even more definitions

SensitivityAbility of a method to detect positives,

irrespective of how many false positives are reported.

SelectivityAbility 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

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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

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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

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)

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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:

is better than:

CGAGGCACAACGTCA||| ||| ||||||CGATGCAAGACGTCA


ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG


• We can express this notion more rigorously, by using ascoring 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.

Score: 12





Score: 5

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Introducing biological information

Importance of the scoring systemdiscrimination 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 amino-acid by

another

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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 oftenthen expected by chance during evolution

• Negative score: the amino acids aredissimilar, the mutation from one into the otheroccurs less often then expected by chance duringevolution

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

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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 changein 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) substitutionmatrix is a look-up table in which scores for each amino acid substitution havebeen calculated based on the frequency of that substitution in closely relatedproteins 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 fromobservations of the frequencies of substitutions in blocks of local alignments inrelated proteins. Each matrix is tailored to a particular evolutionary distance. In theBLOSUM62 matrix, for example, the alignment from which scores were derivedwas created using sequences sharing no more than 62% identity. Sequences moreidentical than 62% are represented by a single sequence in the alignment so as toavoid 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 aresidue at the active site has other evolutionary constraints than the sameresidue outside of the active site)

• They assume evolution rate to be constant.

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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

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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|||||||||GCATGCATGGGCAACTGCAT

GCATGCATGCAACTGCAT|||||||||GCATGCATGGGCAACTGCAT

can be improved by inserting a gap

GCATGCATG--CAACTGCAT||||||||| |||||||||GCATGCATGGGCAACTGCAT

GCATGCATG--CAACTGCAT||||||||| |||||||||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 gapdistribution. We may prefer one large gap to several small ones(e.g. poorly conserved loops between well-conserved helices)

CGATGCAGCAGCAGCATCG|||||| |||||||CGATGC------AGCATCG


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

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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:





gap opening gap extension

13 x 1 - 10 - 6 x 1 = -3 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 shortalignment.

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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...


Distribution of alignment scores - Extreme Value Distribution• Random sequences and alignment scores

Sequence alignment scores between random sequences aredistributed following an extreme value distribution (EVD).

score

obs

AlaVal...Trp

Random sequences Pairwise alignments Score distribution

low score

low score

low score

low score

high score

high score due to "luck"

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score y: our alignment isvery improbable to obtainwith random sequences


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 hasa great probability ofbeing the result of randomsequence similarity

Thresholdsignificant alignment

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Statistics derived from the scores• p-value

Probability that an alignment with this score occurs by chance in adatabase 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 = p x N

100%

0%

N

0

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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.


Urokinase-T

ype plasminogen A

ctivator

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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 valuein 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 window ofresidues

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|||THE

THE|||THE

Score: 23

THE

HEF

THE

HEF

Score: -5

CAT

THE

CAT

THE

Score: -4

HEF

THE

HEF

THE

Score: -5

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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.


Urokinase-T

ype plasminogen A

ctivator

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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

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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 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

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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


Urokinase-T

ype plasminogen A

ctivator

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


Urokinase-T

ype plasminogen A

ctivator

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 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.





ai+1

bj+1

ai+1

bj+1Score = Scoreij + Substij





ai+1

-

ai+1

-Score = Scoreij - gap





-

bj+1

-

bj+1Score = Scoreij - gap

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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 in the matrix.

This allows to build the alignment by traceback when the matrix has been completelyfilled 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, js(xi,yj): match or mismatch score (or substitution matrix

value) for residues xi and yjd: gap penalty (positive value)

GA-TTA|| ||GAATTC

GA-TTA|| ||GAATTC

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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 beassessed with a statistical score.

• There are many ways to align two sequences.Do not blindly trust your alignment to be the only truth. Especially gappedregions 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)

Documents

Pairwise sequence alignments - BioinformaticsPairwise sequence alignment Concept of a sequence alignment •Pairwise Alignment: Explicit mapping between the residues of 2 sequences