Algorithms in Bioinformatics: First International Workshop, WABI 2001 Århus Denmark, August 28–31, 2001 Proceedings

311 Pages·2001·5.485 MB·English

by  István Miklós, Zoltán Toroczkai (auth.), Olivier Gascuel, Bernard M. E. Moret (eds.)

Preface
Wearevery pleased to present the proceedings oftheFirst Workshop on Bioin-
formatics (WABI 2001), which took place in Aarhus on August 28{31, 2001,
under the auspices of the European Association for Theoretical Computer Sci-
ence (EATCS) and the Danish Center for Basic Research in Computer Science
(BRICS).
TheWorkshoponAlgorithmsinBioinformaticscoversresearchonallaspects
of algorithmic work in bioinformatics. The emphasis is on discrete algorithms
that address important problems in molecular biology. These are founded on
sound models, are computationally e(cid:14)cient, and have been implemented and
tested insimulationsandonrealdatasets. The goalistopresent recent research
results, includingsigni(cid:12)cantwork-in-progress,and toidentifyandexplore direc-
tions of future research. Speci(cid:12)c topics of interest include, but are not limited
to:
{ Exactandapproximatealgorithmsforgenomics,sequence analysis,geneand
signal recognition, alignment, molecular evolution, structure determination
or prediction, gene expression and gene networks, proteomics, functional
genomics, and drug design.
{ Methods, software and dataset repositories for development and testing of
such algorithmsand their underlying models.
{ High-performanceapproachestocomputationallyhardproblemsinbioinfor-
matics, particularly optimization problems.
A major goal of the workshop is to bring together researchers spanning the
rangefromabstractalgorithmdesigntobiologicaldatasetanalysis,toencourage
dialogue between application specialists and algorithm designers, mediated by
algorithmengineersandhigh-performancecomputingspecialists.Webelievethat
such adialogueisnecessary forthe progress ofcomputationalbiology,inasmuch
as application specialists cannot analyze their datasets without fast and robust
algorithmsand,conversely,algorithmdesignerscannotproduceusefulalgorithms
without being aware of the problems faced by biologists. Part of this mix was
achieved automatically this year by colocating into a single large conference,
ALGO 2001, three workshops: WABI 2001, the 5th Workshop on Algorithm
Engineering(WAE2001),andthe9thEuropeanSymposiumonAlgorithms(ESA
2001), andsharing keynote addresses amongthe three workshops.ESA attracts
algorithmdesigners, mostly with a theoretical leaning, while WAE is explicitly
targeted at algorithmengineers and algorithmexperimentalists.
These proceedings reflect such a mix. We received over 50 submissions in
response to our call and were able to accept 23 of them, ranging from mathe-
maticaltools through to experimental studies of approximationalgorithms and
reportsonsigni(cid:12)cantcomputationalanalyses.Numerousbiologicalproblemsare
dealt with, including genetic mapping,sequence alignmentand sequence analy-
sis, phylogeny,comparative genomics, and protein structure.
VI Preface
We were also fortunate to attract Dr. Gene Myers, Vice-President for Infor-
matics Research at Celera Genomics, and Prof. Jotun Hein, Aarhus University,
to address the joint workshops, joining (cid:12)ve other distinguished speakers (Profs.
Herbert Edelsbrunner and Lars Arge from Duke University, Prof. Susanne Al-
bers from Dortmund University, Prof. Uri Zwick from Tel Aviv University, and
Dr. Andrei Broder from Alta Vista). The quality of the submissions and the
interest expressed inthe workshopispromising{plansfornextyear’sworkshop
are under way.
We would like to thank all the authors for submitting their work to the
workshop and all the presenters and attendees for their participation. We were
particularly fortunate in enlisting the help of a very distinguished panel of re-
searchers for our program committee, which undoubtedly accounts for the large
number of submissions and the high quality of the presentations. Our heartfelt
thanks go to all:
Craig Benham (Mt Sinai School of Medicine, New York, USA)
MikhailGelfand (Integrated Genomics, Moscow, Russia)
Ra(cid:11)aele Giancarlo(U. di Palermo, Italy)
Michael Hallett (McGill U., Canada)
Jotun Hein (Aarhus U., Denmark)
Michael Hendy (Massey U., New Zealand)
Inge Jonassen (Bergen U., Norway)
Junhyong Kim (Yale U., New Haven, USA)
Jens Lagergren (KTH Stockholm, Sweden)
Edward Marcotte (U. Texas Austin, USA)
Satoru Miyano (Tokyo U., Japan)
Gene Myers (Celera Genomics, USA)
Marie-France Sagot (Institut Pasteur, France)
David Sanko(cid:11) (U. Montreal, Canada)
Thomas Schiex (INRA Toulouse,France)
Joao Setubal (U. Campinas, Sao Paolo,Brazil)
Ron Shamir (Tel Aviv U., Israel)
Lisa Vawter (GlaxoSmithKline,USA)
Martin Vingron (Max Planck Inst. Berlin, Germany)
Tandy Warnow (U. Texas Austin, USA)
In addition,theopinion ofseveral other researchers was solicited.These subref-
erees include TimBeissbarth, Vincent Berry, Benny Chor, Eivind Coward, Ing-
var Eidhammer, Thomas Faraut, Nicolas Galtier, Michel Goulard, Jacques van
Helden,AnjavonHeydebreck, InaKoch,ChaimLinhart,Hannes Luz,Vsevolod
Yu, Michal Ozery, Itsik Pe’er, Sven Rahmann, Katja Rateitschak, Eric Rivals,
Mikhail A. Roytberg, Roded Sharan, Jens Stoye, Dekel Tsur, and Jian Zhang.
We thank them all.
Lastly, we thank Prof. Erik Meineche-Schmidt, BRICS codirector, who
startedtheentireenterprisebycallingononeofus(BernardMoret)tosetupthe
workshopandwho ledthe teamofcommittee chairs andorganizers through the
Preface VII
setup, development, and actual events of the three combined workshops, with
the assistance of Prof. Gerth Br(cid:28)dal.
We hope that you will consider contributing to WABI 2002, through a sub-
mission or by participating in the workshop.
June 2001 Olivier Gascuel and Bernard M.E. Moret
Table of Contents
An Improved Model for Statistical Alignment.......................... 1
Istva´n Mikl´os, Zolt´an Toroczkai
Improving Profile-Profile Alignments via Log Average Scoring ........... 11
Niklas von O¨hsen, Ralf Zimmer
False Positives in Genomic Map Assembly and Sequence Validation ...... 27
Thomas Anantharaman, Bud Mishra
Boosting EM for Radiation Hybrid and Genetic Mapping ............... 41
Thomas Schiex, Patrick Chabrier, Martin Bouchez, Denis Milan
Placing Probes along the Genome Using Pairwise Distance Data ......... 52
Will Casey, Bud Mishra, Mike Wigler
ComparingaHiddenMarkovModelandaStochasticContext-FreeGrammar 69
Arun Jagota, Rune B. Lyngsø, Christian N.S. Pedersen
Assessing the Statistical Significance of OverrepresentedOligonucleotides . 85
Alain Denise, Mireille R´egnier, Mathias Vandenbogaert
Pattern Matching and Pattern Discovery Algorithms for Protein Topologies 98
Juris V¯ıksna, David Gilbert
Computing Linking Numbers of a Filtration........................... 112
Herbert Edelsbrunner, Afra Zomorodian
Side Chain-Positioning as an Integer Programming Problem............. 128
Olivia Eriksson, Yishao Zhou, Arne Elofsson
A Chemical-Distance-Based Test for Positive Darwinian Selection ........ 142
Tal Pupko, Roded Sharan, Masami Hasegawa, Ron Shamir, Dan Graur
FindingaMaximumCompatibleTreeforaBoundedNumberofTreeswith
Bounded Degree Is Solvable in PolynomialTime ....................... 156
Ganeshkumar Ganapathysaravanabavan, Tandy Warnow
Experiments in Computing Sequences of Reversals .................... 164
Anne Bergeron, Franc¸ois Strasbourg
Exact-IEBP:A New Technique for Estimating Evolutionary Distances
between Whole Genomes............................................ 175
Li-San Wang
Finding an Optimal Inversion Median: Experimental Results ............ 189
Adam C. Siepel, Bernard M.E. Moret
X Table of Contents
Analytic Solutions for Three-Taxon MLMC Trees with Variable Rates
Across Sites ....................................................... 204
Benny Chor, Michael Hendy, David Penny
The Performance of Phylogenetic Methods on Trees of Bounded Diameter. 214
Luay Nakhleh, Usman Roshan, Katherine St. John, Jerry Sun,
Tandy Warnow
(1+ε)-Approximation of Sorting by Reversals and Transpositions ........ 227
Niklas Eriksen
On the Practical Solution of the Reversal Median Problem .............. 238
Alberto Caprara
Algorithms for Finding Gene Clusters ................................ 252
Steffen Heber, Jens Stoye
Determination of Binding Amino Acids Based on Random Peptide Array
Screening Data .................................................... 264
Peter J. van der Veen, L.F.A. Wessels, J.W. Slootstra, R.H. Meloen,
M.J.T. Reinders, J. Hellendoorn
A Simple Hyper-Geometric Approach for Discovering Putative
Transcription Factor Binding Sites ................................... 278
Yoseph Barash, Gill Bejerano, Nir Friedman
Comparing Assemblies Using Fragments and Mate-Pairs ................ 294
Daniel H. Huson, Aaron L. Halpern, Zhongwu Lai, Eugene W. Myers,
Knut Reinert, Granger G. Sutton
Author Index.................................................... 307
An Improved Model for Statistical Alignment
Istva´nMiklo´s1andZolta´nToroczkai2
1 DepartmentofPlantTaxonomyandEcology
Eo¨tvo¨sUniversity,Ludovikate´r2,H-1083Budapest,Hungary
[email protected]
2 TheoreticalDivisionandCenterforNonlinearStudies
LosAlamosNationalLaboratory,LosAlamos,NM87545,USA
[email protected]
Abstract. Thestatisticalapproachtomolecularsequenceevolutioninvolvesthe
stochasticmodelingofthesubstitution,insertionanddeletionprocesses.Substi-
tutionhasbeenmodeledinareliablewayformorethanthreedecadesbyusing
finite Markov-processes. Insertion and deletion, however, seem tobe more dif-
ficulttomodel,andtherecentapproaches cannotacceptablydealwithmultiple
insertionsanddeletions.Anewmethodbasedonageneratingfunctionapproach
isintroducedtodescribethemultipleinsertionprocess.Thepresentedalgorithm
computes the approximate jointprobability of two sequences inO(l3)running
timewherelisthegeometricmeanofthesequencelengths.
1 Introduction
Thetraditionalsequenceanalysis[1]needsproperevolutionaryparameters.Thesepa-
rametersdependontheactualdivergencetime,whichisusuallyunknownaswell.An-
other major problem is that the evolutionary parameters cannot be estimated from a
single alignment.Incorrectlydeterminedparametersmightcause unrecognizablebias
inthesequencealignment.
Onewaytobreakthisviciouscircleisthemaximumlikelihoodparameterestima-
tion.InthepioneeringworkofBishopandThompson[2],anapproximatelikelihood
calculationwasintroduced.Severalyearslater,Thorne,Kishino,andFelsensteinwrote
alandmarkpaper[3],inwhichtheypresentedanimprovedmaximumlikelihoodalgo-
rithm,whichestimatestheevolutionarydistancebetweentwosequencesinvolvingall
possiblealignmentsinthelikelihoodcalculation.Their1991model(frequentlyreferred
to as the TKF91 model) considers only single insertions and deletions, but this con-
siderationis ratherunrealistic[4,5].Lateritwas furtherimprovedbyallowinglonger
insertionsanddeletions[4]inthemodel,whichisusuallycoinedastheTKF92model.
However,thismodelassumesthatsequencescontainunbreakablefragments,andonly
wholefragmentsareinsertedanddeleted.Asitwasshown[4],thefragmentmodelhas
aflaw:consideringunbreakablefragments,thereisnopossibleexplanationforoverlap-
pingdeletionswithascenarioofjusttwoevents.Thisproblemissolvablebyassuming
that the ancestral sequencewas fragmentedindependentlyon both branches immedi-
atelyafterthesplit,andsequencesevolvedsincethenaccordingtothefragmentmodel
[6].However,thisassumptiondoesnotsolvetheproblemcompletely:fragmentsdonot
O.GascuelandB.M.E.Moret(Eds.):WABI2001,LNCS2149,pp.1–10,2001.
(cid:1)c Springer-VerlagBerlinHeidelberg2001
2 Istva´nMiklo´sandZolta´nToroczkai
havebiologicalrealism. The lack ofthe biologicalrealism is revealedwhenwe want
togeneralizethissplitmodelformultiplesequencecomparison.Forexample,consider
that we have proteins from humans, gorillas and chimps. When we want to analyze
the three sequences simultaneously, two pairs of fragmentation are needed: one pair
at the gorilla-(humanand chimp)split and one at the human-chimpsplit. When only
sequences from gorillas and humans are compared, the fragmentation at the human-
chimpsplitisomitted.Thus,thedescriptionoftheevolutionoftwosequencesdepends
on the number of the introduced splits, and there is no sensible interpretation to this
dependence.
1.1 TheThorne–Kishino–FelsensteinModel
Since our model is related to the TKF91 model we describe it briefly. Most of the
definitionsandnotationsareintroducedinhere.
The TKF model is the fusion of two independent time-continuous Markov pro-
cesses,thesubstitutionandtheinsertion-deletionprocess.
The Substitution Process: Each character can be substituted independently for an-
other character dictated by one of the well-knownsubstitution processes [7],[8].The
substitutionprocessisdescribedbyasystemoflineardifferentialequations
dx(t)
=Q·x(t) (1)
dt
whereQistheratematrix.SinceQcontainstoomanyparameters,itisusuallysepa-
ratedintotwocomponents,Q0s,whereQ0iskeptconstantandisestimatedwithaless
rigorousmethodthanmaximumlikelihood[4].Thesolutionof(1)is
x(t)=eQ0stx(0) (2)
The Insertion-Deletion Process: The insertion-deletion process is traditionally de-
scribednotin termsofaminoacids ornucleotidesbut interms ofimaginarylinks.A
mortallinkisassociatedtotherightofeachcharacter,andadditionally,thereisanim-
mortallinkattheleftendofthesequence.Eachlinkcangivebirthtoamortallinkwith
birthrateλ.Thenewbornlinkalwaysappearsattherightsideofitsparent.Accompa-
nyingthebirthofamortallink,isthebirthofacharacterdrawnfromtheequilibrium
distribution.Onlymortallinks candieoutwithdeathrate µ, takingtheircharacterto
the left with them. Assuming independencebetween links, it is sufficient to describe
the fate of single mortal link and the immortal one. According to the possible histo-
riesoflinks(Figure 1),threetypesoffunctionsareconsidered.Letp(1)(t)denotethe
k
probabilitythataftertimet,amortallinkhassurvived,andhasexactlyk descendants
includingitself.Letp(2)(t)denotetheprobabilitythataftertimet,amortallinkdied,
k
butitleftexactlyk descendants.Letpk(t)denotetheprobabilitythataftertimet,the
immortallinkhasexactlykdescendants,includingitself.
AnImprovedModelforStatisticalAlignment 3
Time Immortal Mortal Mortal
0 o * *
t o*...* **...* −*...*
k p(t) p(1)(t) p(2)(t)
k k k
Fig.1.ThePossibleFatesofLinks.Thesecondcolumnshowsthefateoftheimmortal
link(o).After a time periodt it has k descendantsincludingitself. The thirdcolumn
describes the fate of a survived mortal link (*). It has k descendants including itself
after time t. The fourth column depicts the fate of a mortal link that died, but left k
descendantsaftertimet.
Calculating the Joint Probability of Two Sequences: The joint probabilityof two
sequencesAandBiscalculatedastheequilibriumprobabilityofsequenceAtimesthe
probabilitythat sequenceB evolvedfromA undertime2t,wheret is the divergence
time.
P(A,B)=P∞(A)P2t(B |A) (3)
Apossibletransitionisdescribedasanalignment.Theuppersequenceistheancestor;
thelowersequenceis thedescendant.Forexamplethefollowingalignmentdescribes
that the immortal link o has one descendant,the first mortal link * died out, and the
secondmortallinkhastwodescendantsincludingitself.
o - A* U* -
o G* - C* A*
Theprobabilityofanalignmentistheprobabilityoftheancestor,timestheprobability
ofthetransition.Forexample,theprobabilityoftheabovealignmentis
γ2π(A)π(U)p2(t)π(G)p(02)(t)p(21)(t)fUC(2t)π(A) (4)
where γn is the probabilitythat a sequencecontains n mortal links, π(X) is the fre-
quency of the character X, and fij(2t) is the probabilitythat a character i is of j at
time2t.Thejointprobabilityoftwosequencesisthesummationofthealignmentprob-
abilities.
2 The Model
OurmodeldiffersfromtheTKFmodelsintheinsertion-deletionprocess.TheTKF91
model assumes only single insertions and deletions, as illustrated in Figure 2. Long
insertions and deletions are allowed in the TKF92 model, as illustrated in Figure 3.
However,theselongindelsareconsideredasunbreakablefragmentsastheyhaveonly
onecommonmortallink.Thedeathofthemortallinkcausesthedeletionofeverychar-
acterinthelonginsertion.Thedistinctionfromthepreviousmodelisthatinourmodel
4 Istva´nMiklo´sandZolta´nToroczkai
λ λ
A* A*C* A*C*G*
µ µ
Fig.2. TheFlow-chartoftheTKF91Model.Eachlinkcangivebirthtoamortallink
withbirthrateλ>0.Mortallinksdiewithdeathrateµ>0.
λr(1−r)
λr
A* A*C* A*CG*
µ
µ
Fig.3.TheFlowchartoftheThorne–Kishino–FelsensteinFragmentModel.Alinkcan
give birth to a fragment of length k with birth rate λr(1 − r)k−1, with λ > 0 and
0<r <1.Fragmentsareunbreakablesothatonlywholefragmentscandiewithdeath
rateµ>0.
λr(1−r)
λr λr
A* A*C* A*C*G*
µ µ
Fig.4.TheFlowchartofOurModel.Eachlinkcangivebirthtokmortallinkswithbirth
rateλr(1−r)k−1,withλ>0and0<r<1.Eachnewbornlinkcandieindependently
withdeathrateµ>0.
everycharacterhasitsownmortallinkinthelonginsertions,asillustratedinFigure 4.
Thus,thismodelallowslonginsertionswithoutconsideringunbreakablefragments.It
is possiblethatalongfragmentis insertedintothesequencefirst andsomeofthein-
sertedlinksdieandsomeofthemsurviveafterthen.Alinkgivesbirthtoablockofk
mortallinkswithrateλk,where
λk =λr(1−r)k−1, k =1,2,..., λ>0, 0<r <1 (5)
Onlymortallinkscandiewithrateµ>0.
AnImprovedModelforStatisticalAlignment 5
2.1 CalculatingtheGeneratingFunctions
The Master Equation: First, the probabilities of the possible fates of the immortal
link is computed. Collecting the gain and loss terms for this birth-death process, the
followingMasterequationisobtained:
 
dp n(cid:1)−1 (cid:1)∞
dtn = (n−j)λjpn−j +nµpn+1−n λj +(n−1)µpn (6)
j=1 j=1
(cid:6) (cid:6) (cid:6)
Using ∞j=1λj =λand nj=−11(n−j)λjpn−j = nk=−11kλn−kpk,wehave:
dp n(cid:1)−1
dtn =λr k(1−r)n−k−1pk+nµpn+1−(nλ+(n−1)µ)pn (7)
k=1
Duetotheimmortallink,wehave∀t, p0(t)=0.Forn=1,thesumin(7)isvoid.The
initialconditionsaregivenby:
pn(0)=δn,1 (8)
Next,weintroducethegeneratingfunction[9]:
(cid:1)∞
P(ξ;t)= ξnpn(t) (9)
n=0
Multiplying(7)byξn,thensummingovern,weobtainalinearPDEforthegenerating
function: (cid:7) (cid:8)
∂P λξ ∂P µ
−(1−ξ) µ− =−(1−ξ) P (10)
∂t 1−ξ(1−r) ∂ξ ξ
withinitialconditionP(ξ;0)=ξ.
SolutiontothePDEfortheGeneratingFunction:WeusethemethodofLagrange:
dt dξ dP
= (cid:9) (cid:10) = (11)
1 −(1−ξ) µ− λξ −(1−ξ)µξP
1−ξ(1−r)
The two equalities define two, one-parameter families of surfaces, namely v(t;ξ;P)
andw(t;ξ;P).Afterintegratingthefirstandthesecondequalitiesin(11)thefollowing
familiesofsurfacesareobtained:
(1−ξ)r
v(ξ;t)= (µ−aξ)λ/ae−t(µr−λ) =c1 (12)
(µ−aξ)r
w(ξ;t;P)=P ξ =c2 (13)
witha≡λ+µ(1−r)>0.Thegeneralformofthesolutionisanarbitraryfunctionof
w =g(v).Thismeans:
(cid:7) (cid:8)
(1−ξ)r
P(ξ;t)=ξ(µ−aξ)−λ/ag e−t(µr−λ) (14)
(µ−aξ)λ/a