URL: www.isrec.isb-sib.ch/java/dotlet/Dotlet.html. VI - 2004. Page 8 ... This value strongly depends on how the two sequences are aligned. Similarity. Proportion of pairs of ..... The horizontal and vertical dimensions correspond to the compared ...
Pairwise sequence alignments
Volker Flegel Vassilios Ioannidis VI - 2004
Page 1
Outline
• Introduction • Definitions • Biological context of pairwise alignments • Computing of pairwise alignments • Some programs
VI - 2004
Page 2
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 3
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
???
VI - 2004
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
VI - 2004
Page 5
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
VI - 2004
Page 6
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
VI - 2004
Page 7
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.
VI - 2004
Page 8
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 9
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 VI - 2004
Page 10
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 VI - 2004
Page 11
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)
VI - 2004
Page 12
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)
VI - 2004
Page 13
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
VI - 2004
Page 14
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
VI - 2004
Page 15
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
VI - 2004
Page 16
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"
VI - 2004
Page 17
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 18
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 19
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.
VI - 2004
Page 20
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
VI - 2004
Page 21
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 VI - 2004
Page 22
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 VI - 2004
Page 23
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
VI - 2004
CGATGCAGCAGCAGCATCG CGATGCAGCAGCAGCATCG || || || || |||| |||| || || || || || CG-TG-AGCA-CA--AT-G CG-TG-AGCA-CA--AT-G
13 x 1 - 5 x 10 - 6 x 1 = -43
Page 24
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 25
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).
VI - 2004
...
score x ...
Ala Ala Val Val ... ... Tr p Tr p
Pairwise alignments
Score distribution
obs
Random sequences
score y score
Page 26
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
VI - 2004
Page 27
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
VI - 2004
Page 28
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
VI - 2004
Page 29
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 VI - 2004
Page 30
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
VI - 2004
Page 31
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
VI - 2004
Page 32
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-
VI - 2004
Page 33
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
VI - 2004
Page 34
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:
VI - 2004
Page 35
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: VI - 2004
Page 36
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. VI - 2004
Page 37
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). VI - 2004
Page 38
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) VI - 2004
Page 39
