Page 1 August 2006 Pairwise sequence alignments Etienne de Villiers Adapted with permission of Swiss...

August 2006

Pairwise sequence alignments

Etienne de Villiers

Adapted with permission of Swiss EMBnet node and SIB

August 2006

Outline

•Introduction

•Definitions

•Biological context of pairwise alignments

•Computing of pairwise alignments

•Some programs

August 2006

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

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

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

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

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

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

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

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

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

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

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

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


ATTGGACAGCAATCAGG| || | |ACGATGCAAGACGTCAG


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

August 2006

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

August 2006

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

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

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

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

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

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

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

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|| || |||| || || |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

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

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

gap extension

13 x 1 - 5 x 10 - 6 x 1 = -43

August 2006

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

...


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

score y: our alignment is very improbable to obtain with 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 has a great probability of being the result of random sequence similarity

Thresholdsignificant alignment

August 2006


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

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

Reading a DotplotAs simple as projecting the diagonals onto the axis.


Uro

kinase

-Typ

e p

lasm

inog

en

Activ

ato

r


A A’ B DC

Urokinase-Type plasminogen ActivatorA CB D

August 2006

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

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

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

Local alignment (Smith-Waterman)

Example Local alignments are more sensitive to the modular nature

of proteinsThey can be used to search databases


Uro

kinase

-Typ

e p

lasm

inog

en

Activ

ato

r

Local alignments:

August 2006

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

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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