Multiple Sequence Alignment Based on Compact Set

1
Multiple Sequence Alignment Based on Compact Set

• Department of Computer Science
• National Tsing Hua University
• Chuan Yi Tang

2
Multiple Sequence Alignment

• Given s set of sequences,the MSA problem is to
  find an alignment of the sequences such that some
  object function is minimized
• ie.(Sum of Pair Score)

3
MSA with SP-ScoreExact Algorithm and Heuristics

• k of Sequences n Sequences of length
• Exactly (using Dynamic Programming)
• O((2n)k)D.Snakoff, Simultaneous solution of RNA
  folding, alignment and Protosequence prolblems,
  SIAM J. Appl. Math.,(1985)
• Heuristics
• D.F.Feng,R.F.Doolittle, Progressive sequence
  alignment as a prerequisite to correct
  phylogenetic trees. J. Mol. Evol. 25, 351-360.,
  (1987)
• S.F.Altschul,D.J.Lipman, Trees,star and mutiple
  biological sequence aligment,SIAM J. Appl.
  Math.,(1989)
• D.J.lipman,S.F.Altschul, A tool for multiple
  sequences alignment,Proc.Nat.Acad. Sci.
  U.S.A.,(1989)
• S.C. Chan,A.K.C. Wang,D.K.Y. Chiu, A survey of
  multiples sequences comparison methods,Bull.Math
  Bio.,(1992)

4
MSA with SP-ScoreComplexity

• J Comput Biol 1994 Winter1(4)337-48
• On the complexity of multiple sequence
  alignment.
• Wang L. Jiang T.
• McMaster University, Hamilton, Ontario, Canada.
• We study the computational complexity of two
  popular problems in multiple sequence alignment
• 1. multiple alignment with SP-Score gt
  NP-complete(non-metric)
• 2. multiple tree alignment gt MAX SNP-hard
• Theoretical Computer Science259 (2001) 63-79
• The complexity with Multiple sequence alignment
  with SP-score that is a metric
• Paola Bonizzoni, Gianluca Della Vedoa
• 1. multiple alignment with SP-Score gt
  NP-complete(metric)

5
MSA with SP-ScoreApproximation

• Approximation Algorithm
• Performance ratio of 2-2/kD.Gusfilde,Efficient
  methods for multiple sequence alignment with
  guaranteed error bounds,Bull. Math Bio.,(1993)
• Performance ratio of 2-3/kP.Pevzner,Multiple
  alignment,communication cost,and graph
  matching,SIAM J. Appl. Math.,(1992)
• Performance ratio of 2-l/k(assembling l-way
  alignments,l k)V.Bafna,E.L.Lawler and
  Pevzner,Approximation algorithms for multiple
  sequences alignment,Theor. Comput. Sci.,(1997)
• Polynomial Time Approximation Scheme(PTAS)
• MSA within a constant band and allows only
  constant number of insertion and deletion gaps of
  arbitrary length per sequence on average M.
  Li,B. Ma. And L. Wang, Near optimal alignment
  within a band in polynomial time,STOC 2000.

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Compact Set Definition

• Let S be the set of n objects S1,S2,S3Sn and
  D(Si,Sj) denote the distance between Si and Sj in
  the distance matrix D.
• Consider any C which is a subset of S,if the
  distance between elements in C and not in C is
  larger than the longest distance in C , then C is
  called a compact set.
• Property
• The entire set S is a compact set.
• Each set consisting of a single object is also a
  compact set.

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Compact Set Example
11 Minimal border edge for compact set 3
S6
S5
10 Maximal inside edge for compact set 3
S1
S4
Compact Set 1
Distance Matrix
S2
S3
Compact Set 3
Compact Set 2
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Compact Set Example(cont)

• Compact Set is hierarchical

9
MSA Compact Set

• Consider 12 Protein sequences example
• S1 MAPSAPAKTAKALDAKKKVVKGKRTTHRRQVRTSVHFRRPVTLKTA
  RQARFPRKSAPKTSKMDHFRIIQHPLTTESAMKKIEEHNTLVFIVSNDAN
  KYQIKDAVHKLYNVQALKVNTLITPLQQKKAYVRLTADYDALDVANKIGV
  I
• S2 SSIIDYPLVTEKAMDEMDFQNKLQFIVDIDAAKPEIRDVVESEYDV
  TVVDVNTQITPEAEKKATVKLSAEDDAQDVASRIGVF
• S3 SWDVIKHPHVTEKAMNDMDFQNKLQFAVDDRASKGEVADAVEEQYD
  VTVEQVNTQNTMDGEKKAVVRLSEDDDAQEVASRIGVF
• S4 MAPKAKKEAPAPPKAEAKAKALKAKKAVLKGVHSHKKKKIRTSPTF
  RRPKTLRLRRQPKYPRKSAPRRNKLDHYAIIKFPLTTESAMKKIEDNNTL
  VFIVDVKANKHQIKQAVKKLYDIDVAKVNTLIRPDGEKKAYVRLAPDYDA
  LDVANKIGII
• S5 MAPSTKATAAKKAVVKGTNGKKALKVRTSASFRLPKTLKLARSPKY
  ATKAVPHYNRLDSYKVIEQPITSETAMKKVEDGNTLVFKVSLKANKYQIK
  KAVKELYEVDVLSVNTLVRPNGTKKAYVRLTADFDALDIANRIGYI
• S6 MDAFDVIKTPIVSEKTMKLIEEENRLVFYVERKATKEDIKEAIKQ
  LFNAEVAEVNTNITPKGQKKAYIKLKDEYNAGEVAASLGIY
• S7 MAPAKADPSKKSDPKAQAAKVAKAVKSGSTLKKKSQKIRTKVTFHR
  PKTLKKDRNPKYPRISAPGRNKLDQYGILKYPLTTESAMKKIEDNNTLVF
  IVDIKADKKKIKDAVKKMYDIQTKKVNTLIRPDGTKKAYVRLTPDYDALD
  VANKIGII
• S8 MAPSTKAASAKKAVVKGSNGSKALKVRTSTTFRLPKTLKLTRAPKY
  ARKAVPHYQRLDNYKVIVAPIASETAMKKVEDGNTLVFQVDIKANKHQIK
  QAVKDLYEVDVLAVNTLIRPNGTKKAYVRLTADHDALDIANKIGYI
• S9 MPPKSSTKAEPKASSAKTQVAKAKSAKKAVVKGTSSKTQRRIRTSV
  TFRRPKTLRLSRKPKYPRTSVPHAPRMDAYRTLVRPLNTESAMKKIEDNN
  TLLFIVDLKANKRQIADAVKKLYDVTPLRVNTLIRPDGKKKAFVRLTPEV
  DALDIANKIGFI
• S10 MAPKAKKEAPAPPKAEAKAKALKAKKAVLKGVHSHKKKKIRTSPT
  FRRPKTLRLRRQPKYPRKSAPRRNKLDHYAIIKFPLTTESAMKKIEDNNT
  LVFIVDVKANKHQIKQAVKKLYDIDVAKVNTLIRPDGEKKAYVRLAPDYD
  ALDVANKIGII
• S11 APSAKATAAKKAVVKGTNGKKALKVRTSATFRLPKTLKLARAPKY
  ASKAVPHYNRLDSYKVIEQPITSETAMKKVEDGNILVFQVSMKANKYQIK
  KAVKELYEVDVLKVNTLVRPNGTKKAYVRLTADYDALDIANRIGYI
• S12 MPAKAASAAASKKNSAPKSAVSKKVAKKGAPAAAAKPTKVVKVTK
  RKAYTRPQFRRPHTYRRPATVKPSSNVSAIKNKWDAFRIIRYPLTTDKAM
  KKIEENNTLTFIVDSRANKTEIKKAIRKLYQVKTVKVNTLIRPDGLKKAY
  IRLSASYDALDTANKMGLV

Original sequence
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MSA Compact Set(cont)
Original distance matrix
Original Compact Set Tree
Good MSA should Preserve Compact Set as well
11
MSA Compact Set(cont)

• S1 -----------------MAPSAPAKTAKALDAKKKVVKGKRTTHR
  RQVRTSVHFRRPVTLKTARQARFPRKSAPKTSKMDHFRIIQHPLTTESA
  
• S2 ---------------------------------------------
  ------------------------------------SSIIDYPLVTEKAM
  DEMDFQNKLQFIVDIDAAKPEIRDV
• S3 ---------------------------------------------
  -----------------------------------SWDVIKHPHVTEKAM
  NDMDFQNKLQFAVDDRASKGEV
• S4 --------MAPKAKKEAPAPPKAEAKAKALKAKKAVLKGVHSHKK
  KKIRTSPTFRRPKTLRLRRQPKYPRKSAPRRNKLDHYAIIKFPLTTES
• S5 ----------------------MAPSTKATAAKKAVVKGTNGKKA
  LKVRTSASFRLPKTLKLARSPKYATKAVPHYNRLDSYKVIEQPITSETAM
  KK
• S6 ---------------------------------------------
  ---------------------------------MDAFDVIKTPIVSEKTM
  KLIEEENRLVFYVERKATKEDIKEA
• S7 ----------MAPAKADPSKKSDPKAQAAKVAKAVKSGSTLKKK
  SQKIRTKVTFHRPKTLKKDRNPKYPRISAPGRNKLDQYGILKYPLTTE
• S8 ----------------------MAPSTKAASAKKAVVKGSNGSKA
  LKVRTSTTFRLPKTLKLTRAPKYARKAVPHYQRLDNYKVIVAPIASETAM
  KK
• S9 ------MPPKSSTKAEPKASSAKTQVAKAKSAKKAVVKGTSSKTQ
  RRIRTSVTFRRPKTLRLSRKPKYPRTSVPHAPRMDAYRTLVRPLN
• S10 --------MAPKAKKEAPAPPKAEAKAKALKAKKAVLKGVHSHK
  KKKIRTSPTFRRPKTLRLRRQPKYPRKSAPRRNKLDHYAIIKFPLTTE
• S11 -----------------------APSAKATAAKKAVVKGTNGK
  KALKVRTSATFRLPKTLKLARAPKYASKAVPHYNRLDSYKVIEQPITSET
  AMKK
• S12 MPAKAASAAASKKNSAPKSAVSKKVAKKGAPAAAAKPTKVVKVT
  KRKAYTRPQFRRPHTYRRPATVKPSSNVSAIKNKWDAFRIIRYP

MSA by MSA1
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MSA Compact Set(cont)

• S1 ------------MAPSAPAKTA-KALDAKKKVVKGK-RTTHR--
  R--QV--R---TSVHFRRPVTLKTARQARFPRKSAPK-TSKMDHFR-IIQ
  HPL
• S2 --------------------------------------------
  -------------------------------------------S--SIID
  YPLVTEKAMDEMDFQNKLQFIVDID- AAK
• S3 --------------------------------------------
  -------------------------------------------SW-DVIK
  HPHVTEKAMNDMDFQNKLQFAVD-DRA
• S4 MAPKA--KKEAPAPPKAEAK-A-KALKAKKAVLKGV-HSHKK--
  K--KI--R---TSPTFRRPKTLRLRRQPKYPRKSAPR-RNKLDHY-AIIK
  FP
• S5 -----------------MAPST-KATAAKKAVVKGT-NG--K--
  KALKV--R---TSASFRLPKTLKLARSPKYATKAVPH-YNRLDSYK-VIE
  QPITSET
• S6 --------------------------------------------
  -----------------------------------------MDAF-DVIK
  TPIVSEKTMKLIEEENRLVFYVER-KATK
• S7 MAP-A--KAD-PS-KKSDPK-A-QAAKVAKAVKSG--STLKK--
  KSQKI--R---TKVTFHRPKTLKKDRNPKYPRISAPG-RNKLDQY-GILK
  YP
• S8 -----------------MAPST-KAASAKKAVVKGS-NG--S--
  KALKV--R---TSTTFRLPKTLKLTRAPKYARKAVPH-YQRLDNYK-VIV
  APIASET
• S9 MPPKSSTKAE-PKASSAKTQVA-KAKSAKKAVVKGT-SS--K--
  TQRRI--R---TSVTFRRPKTLRLSRKPKYPRTSVPH-APRMDAYRTLVR
  
• S10 MAPKA--KKEAPAPPKAEAK-A-KALKAKKAVLKGV-HSHKK-
  -K--KI--R---TSPTFRRPKTLRLRRQPKYPRKSAPR-RNKLDHY-AII
  KF
• S11 ------------------APSA-KATAAKKAVVKGT-NG--K-
  -KALKV--R---TSATFRLPKTLKLARAPKYASKAVPH-YNRLDSYK-VI
  EQPITSET
• S12 ------MPAKAASAAASKKNSAPKSAVSKKVAKKGAPAAAAKP
  TKVVKVTKRKAYTRPQFRRPHTYRRPATVK-PSSNVSAIKNKWDAFR

MSA by MSA2
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MSA Compact Set(cont)
Compact Set Tree by MSA1
Distance Matrix by MSA1
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MSA Compact Set(cont)
Compact Set Tree by MSA2
Distance Matrix by MSA2
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Measure of Compact Set Preservation

• How can we measure the Compact Set Preservation
  in quantity?
• N1 of the original Compact Set relations
• N2 of the relations preserved after MSA
• Estimate by Compact Set Preservation

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Measure of Compact Set Preservation(cont)
Original Compact Set relations
1 2 4 1 2 5 1 3 4 1 3 5 2 3 4 2 3 5 1 2 3
4 5 1 4 5 2 4 5 3
Distance Matrix
N1 10
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Measure of Compact Set Preservation(cont)
The relations preserved after MSA
1 2 4 1 2 5 1 4 3 3 5 1 2 4 3 3 5 2 1 2 3 1 4
5 2 4 5 3 5 4

1 2 4 1 2 5 1 3 4 1 3 5 2 3 4 2 3 5 1 2 3
4 5 1 4 5 2 4 5 3
After MSA gt
Distance Matrix After MSA
N210-73 gt
Compact Set Tree after MSA
Estimate by Compact Set Preservation 3/10
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Why Pair Wise Compact Set?

• Evolutionary tree is the real judge
• Evolutionary tree has property to minimize the
  total evolutionary edges (say tree size) from
  pair wise distance which seems to be compact
• It is true in experiments

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Compact Set Relation Preserved Rate for
Evolutionary Tree
of relations preserved in Evolutionary Tree /
of Compact Set relations of Pair Wise Distance
More larger more better
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Compact Set Evaluation Algorithm

• Step1 Construct the original Compact Set Tree T
  and the Compact Set Tree after MSA T 1.
• Step2 Preorder Traversal T to generate the
  Compact Set relations after MSA R ,and mark the
  entry in the hash table H according to R.
• Step3 Preorder Traversal T to generate the
  Original Compact Set Relations R ,and check
  whether the marked entry in the hash table by R
  is a subset of the hash table H.
• Total Time Complexity O( ),where n is the
  number of sequences
• Reference
• 1. E. Dekel,J. Hu and W. Ouyang, An optimal
  algorithm for finding compact sets, Inform.
  Process. Lett. 44(1992) 285289

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Our Strategy for MSA

• Progressive alignment (Fei Feng and Doolittle
  1987 )
• with neighbor first( by using Minimal Spanning
  Tree(MST) Kruskal Merging Order)
• Set-to-Set align. Once a gap, always a gap.

Kruskal merging order tree
3
S3----ACAGACTCCA S4TTTAAAAGTC----
1
2
set1
S1
S2
S3
S4
S1---AACAGACTT-A- S2----ACAGACTT-AA S3----ACAGA
CTCCA- S4TTTAAAAGTC-----
S1AACAGACTTA- S2-ACAGACTTAA
set2
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Q Why do we use MST Kruskal Order?
A1It has similar structure with compact set
MST Order Merge Tree
Compact Tree
A2MST Kruskal order is obtained easily
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Score function
Match
Begin- gap
Gap-extended
---AACAGACTT-A- ----ACAGAC---AA ----ACAGACTCCA- TT
TAAAAGTC-C---
End-gap
Mismatch
Gap-open
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Strategy of set-to-set alignment

• Score(8, 8) Max

Score(7, 7) (a8ß8) Score(7, 8)
(a8G3) Score(8, 7) (G2ß8)
(a8ß8) (G,C)(G,-)(G,G)(-,C)(-,-)(-,G)
(-10)(-15)(10)(-15)(0)(-15) -45
Time Complexity of seta to setß alignment
(sasßlalß )(2388), Where sa,sß are the
number of sequences in seta and
setßrespectively, and la,lß are the length of
resulted sequences in seta and setß respectively.
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Time Complexity of our strategy

• The worst case happens in that the binary tree is
  balanced.
• Total set-to-set time complexity is bounded by
• where l is the length of the resulted sequences
  and n is the number of sequences.
• The worst case time complexity O(n2l2 )

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MSA Useful tools

• GCG (Genetics Computer Group) PileUp
• http//gcg.nhri.org.tw8003/gcg-bin/seqweb.cgi
• Clustalw
• http//clustalw.genome.ad.jp/

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Clustal W

• Pairwise alignment
• Calculate distance matrix
• Construct the unrooted Neighbor-Joining (NJ) tree
• Construct the rooted NJ tree
• rooted at mid-point
• Progressive alignment
• Align following the rooted NJ tree
• set-to-set alignment

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Experiment
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SP Score Result
Clustalw and our result are better than GCGs
More larger more better
30
Compact Set Relation Failure rate Result
of relation not preserved / of source compact
set relation
More smaller more better
31
Three-point Relative Scale Preserved Rate
For all three species A, B,C, we evaluate their
relative distance relation between original
distance matrix and the MSA distance are
identical or not.
32
I Believe Tree Only

• One might still not believe original pair wise
  distance is not a good judge
• One believes the true evolutionary tree only

33
Compact Set Relation Failure Rate
Take Protein 12 for example
of relations not preserved / of source
Compact Set relations
Distance
MSA_Method
More smaller more better
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Future Work

• Is our measurement and algorithms really good?
• Simulations and Web service
• Does Our MSA by set-to-set alignment satisfy some
  approximation property?
• Theoretical Proving
• How can we reduce the time?
• Hardwired Dynamic Programming
• exPARACEL http//www.paracel.com/