page 1 march 2003 pairwise sequence alignments volker flegel

march 2003

Pairwise sequence alignments

Volker Flegel

march 2003

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

???

march 2003

Do alignments make sense ?Evolution of sequences

• Sequences evolve through mutation and selectionSelective 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

march 2003

Example: An alignment

• 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

march 2003

Example: A diagonal plot

• Comparing the tissue-type and urokinase type plasminogen activators

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

march 2003

Relationships to other techniques

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

march 2003

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.

march 2003

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).

march 2003

Definition example

The set of all globins and a test to identify them

Globins

Matches

True positives

True negatives

False positives

False negatives

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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.

True positives

True negatives

False positives

False negatives

Greater sensitivity

Less selectivity

Less sensitivity

Greater selectivity

march 2003

Pairwise sequence alignments

Concept of 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

march 2003

Alignements

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)

march 2003

Alignement evaluationWhat 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 a scoring system.

march 2003

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

march 2003

Introducing biological informationImportance of the scoring system

discrimination 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

march 2003

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

march 2003

Matrix choice

Different kind of matrices• PAM series (M. Dayhoff, 1968, 1972, 1978)

Based on 1572 protein sequences from 71 familiesOld standard matrix:PAM250

• BLOSUM seriesBased on alignments in the BLOCKS databaseStandard matrix: BLOSUM62

Limitations• Substitution matrices do not take into account long range

interactions between residues.• They assume that identical residues are equal (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.

march 2003

Alignment score

Amino acid substitution matrices • Example: PAM250• Most used: Blosum62

Raw score of an alignment

TPEA¦| |APGA

TPEA¦| |APGA

Score = 1 = 9

• It is possible that a good long alignment gets a better raw score than a very good short alignment.

We need a normalised score to compare alignments ! (p-value, e-value)

+ 6 + 0 + 2

march 2003

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

march 2003

Gap opening and extension penaltiesCosts 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

march 2003

Gap opening and extension penaltiesExample

• 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

march 2003

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

• Normalised score Is independent of the scoring systemEnables us to compare different alignmentsUnits: expressed in bits

march 2003

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

march 2003

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 of similarity stands out as a diagonal.


Uro

kinase

-Typ

e p

lasm

inog

en

Activ

ato

r

march 2003

Dotplot constructionSimple 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 matrixT H E F A T C A T

T

H

E

F

A

S

T

C

A

T

THEFA-TCAT||||| ||||THEFASTCAT

THEFA-TCAT||||| ||||THEFASTCAT

Note• This method produces dotplots with too much noise to be

usefulThe noise can be reduced by calculating a score using a

window of residuesThe score is compared to a threshold or stringency

march 2003

Dotplot constructionWindow 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

T H E F A T C A T

T

H

E

F

A

S

T

C

A

T

THE|||THE

THE|||THE

Score: 23

THE

HEF

THE

HEF

Score: -5

CAT

THE

CAT

THE

Score: -4

HEF

THE

HEF

THE

Score: -5

march 2003

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.


Uro

kinase

-Typ

e p

lasm

inog

en

Activ

ato

r

march 2003

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

march 2003

Finding an alignmentAlignment 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

march 2003

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:

march 2003

Local alignment (Smith-Waterman)

Example Local alignments are more sensitive to the modular nature

of proteinsThey can be used to search databasesTissue-Type plasminogen Activator

Uro

kinase

-Typ

e p

lasm

inog

en

Activ

ato

r

Local alignments:

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Optimal alignment extensionHow 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+1

Score = Scoreij + Substij





ai+1

-

ai+1

-Score = Scoreij - gap





-

bj+1

-

bj+1

Score = 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 completely filled out.• Computation time is proportional to the size of sequences (n

x m).

G A T T A

0 -2 -4 -6 -8 -10

G -2

A -4

A -6

T -8

T -10

C -12

G A T T A

0 -2 -4 -6 -8 -10

G -2 2 0 -2 -4 -6

A -4 0 4

A -6

T -8

T -10

C -12

0 - 2

0 - 2

2 + 2

G A T T A

0 -2 -4 -6 -8 -10

G -2 2 0 -2 -4 -6

A -4 0 4 2 0 -2

A -6 -2 2 3 1 2

T -8 -4 0 4 5 3

T -10 -6 -2 2 6 4

C -12 -8 -4 0 4 5

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 yj

d:gap penalty (positive value)

GA-TTA|| ||GAATTC

GA-TTA|| ||GAATTC

march 2003

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)

page 1 march 2003 pairwise sequence alignments volker flegel

Documents

aligned sequences

homologous sequences

sequence thio

database slide

goal sequence comparison

alignments volker flegel

originsame function

domains alignments