Table Of ContentLecture Notes in Bioinformatics 3678
EditedbyS.Istrail,P.Pevzner,andM.Waterman
EditorialBoard: A.Apostolico S.Brunak M.Gelfand
T.Lengauer S.Miyano G.Myers M.-F.Sagot D.Sankoff
R.Shamir T.Speed M.Vingron W.Wong
Subseries of Lecture Notes in Computer Science
Aoife McLysaght Daniel H. Huson (Eds.)
Comparative
Genomics
RECOMB 2005 International Workshop, RCG 2005
Dublin, Ireland, September 18-20, 2005
Proceedings
1 3
SeriesEditors
SorinIstrail,CeleraGenomics,AppliedBiosystems,Rockville,MD,USA
PavelPevzner,UniversityofCalifornia,SanDiego,CA,USA
MichaelWaterman,UniversityofSouthernCalifornia,LosAngeles,CA,USA
VolumeEditors
AoifeMcLysaght
UniversityofDublin,SmurfitInstituteofGenetics,TrinityCollege,Irland
E-mail:[email protected]
DanielH.Huson
TübingenUniversity,CenterforBioinformatics(ZBIT)
72076Tübingen,Germany
E-mail:[email protected]
LibraryofCongressControlNumber:2005932241
CRSubjectClassification(1998):F.2,G.3,E.1,H.2.8,J.3
ISSN 0302-9743
ISBN-10 3-540-28932-1SpringerBerlinHeidelbergNewYork
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Preface
The complexity of genome evolutionposes many exciting challenges to develop-
ersofmathematicalmodels andalgorithms,who haverecourseto a spectrumof
algorithmic,statisticalandmathematicaltechniques,rangingfromexact,heuris-
tic, fixed-parameterandapproximationalgorithmsfor problems basedonparsi-
mony models to Monte CarloMarkovChain algorithmsfor Bayesiananalysisof
problems based on probabilistic models.
The annual RECOMB Satellite Workshop on Comparative Genomics
(RECOMBComparativeGenomics)isaforumonallaspectsandcomponentsof
thisfield,rangingfromnewquantitativediscoveriesaboutgenomestructureand
process to theorems on the complexity of computational problems inspired by
genome comparison. The informal steering committee for this meeting consists
of David Sankoff, Jens Lagergrenand Aoife McLysaght.
Thisvolumecontainsthepaperspresentedatthe3rdRECOMBComparative
Genomicsmeeting,whichwasheldinDublin,Ireland,onSeptember18–20,2005.
The first two meetings of this series were held in Minneapolis, USA (2003) and
Bertinoro, Italy (2004).
This year, 21 papers were submitted, of which the Program Committee se-
lected14forpresentationatthe meetingandinclusioninthisproceedings.Each
submission was refereed by at least three members of the Program Committee.
Aftercompletionofthereferees’reports,anextensiveWeb-baseddiscussiontook
placeformakingdecisions.TheRECOMBComparativeGenomics2005Program
Committee consisted of the following 27 members: Vineet Bafna, Anne Berg-
eron, Mathieu Blanchette, Avril Coghlan, Dannie Durand, Nadia El-Mabrouk,
NiklasEriksen,AaronHalpern,RoseHoberman,DanielHuson,JensLagergren,
Giuseppe Lancia, Emmanuelle Lerat, Aoife McLysaght, Istvan Miklos, Bernard
Moret,PavelPevzner,BenRaphael,Marie-FranceSagot,DavidSankoff,Cathal
Seoighe, Beth Shapiro, Igor Sharakhov, Mike Steel, Jens Stoye, Glenn Tesler
andLouxinZhan.We wouldliketothank the ProgramCommittee members for
their dedication and hard work.
RECOMBComparativeGenomics 2005hadseveralinvitedspeakers,includ-
ing:Anne Bergeron(Universit´eduQu´ebec`a Montreal,Canada),LaurentDuret
(Laboratoire de Biometrie et Biologie Evolutive, Universit´e Claude Bernard,
Lyon, France), Eddie Holmes (Department of Biology, Pennsylvania State Uni-
versity,USA),JeffreyLawrence(DepartmentofBiologicalSciences,Universityof
Pittsburgh, USA), Stephan Schuster (Department of Biochemistry and Molecu-
lar Biology,Pennsylvania State University, USA), Ken Wolfe (Genetics Depart-
ment, Trinity College Dublin, Ireland) and Sophia Yancopoulos (Institute for
Medical Research, New York, USA).
In addition to the invited talks and the contributed talks, an important in-
gredient of the program was the lively poster session.
VI Preface
RECOMBComparativeGenomics 2005wouldliketo thankScience Founda-
tion Ireland (SFI) and Hewlett-Packard for providing financial support for the
conference.WewouldliketothanktheUniversityofDublin,TrinityCollege,for
hosting the meeting. We would like to thank Nadia Browne for administrative
support.
In closing, we would like to thank all the people who submitted papers and
posters and those who attended RECOMB Comparative Genomics 2005 with
enthusiasm.
September 2005 Aoife McLysaght and Daniel Huson
Table of Contents
Lower Bounds for Maximum Parsimony with Gene Order Data
Abraham Bachrach, Kevin Chen, Chris Harrelson, Radu Mihaescu,
Satish Rao, Apurva Shah ....................................... 1
Genes Order and Phylogenetic Reconstruction: Application to
γ-Proteobacteria
Guillaume Blin, Cedric Chauve, Guillaume Fertin.................. 11
Maximizing Synteny Blocks to Identify Ancestral Homologs
Guillaume Bourque, Yasmine Yacef, Nadia El-Mabrouk ............. 21
An Expectation-Maximization Algorithm for Analysis of Evolution of
Exon-Intron Structure of Eukaryotic Genes
Liran Carmel, Igor B. Rogozin, Yuri I. Wolf, Eugene V. Koonin..... 35
Likely Scenarios of Intron Evolution
Miklo´s Csu˝ro¨s ................................................. 47
OMA, a Comprehensive, Automated Project for the Identification
of Orthologs from Complete Genome Data: Introduction and First
Achievements
Christophe Dessimoz, Gina Cannarozzi, Manuel Gil,
Daniel Margadant, Alexander Roth, Adrian Schneider,
Gaston H. Gonnet ............................................. 61
The Incompatible Desiderata of Gene Cluster Properties
Rose Hoberman, Dannie Durand ................................. 73
The String Barcoding Problem is NP-Hard
Marcello Dalpasso, Giuseppe Lancia, Romeo Rizzi.................. 88
A Partial Solution to the C-Value Paradox
Jeffrey M. Marcus ............................................. 97
Individual Gene Cluster Statistics in Noisy Maps
Narayanan Raghupathy, Dannie Durand .......................... 106
Power Boosts for Cluster Tests
David Sankoff, Lani Haque...................................... 121
Reversals of Fortune
David Sankoff, Chungfang Zheng, Aleksander Lenert ............... 131
VIII Table of Contents
Very Low Power to Detect Asymmetric Divergence of Duplicated Genes
Cathal Seoighe, Konrad Scheffler ................................ 142
A Framework for Orthology Assignment from Gene RearrangementData
Krister M. Swenson, Nicholas D. Pattengale, Bernard M.E. Moret ... 153
Author Index................................................... 167
Lower Bounds for Maximum Parsimony with
Gene Order Data
Abraham Bachrach, Kevin Chen, Chris Harrelson, Radu Mihaescu,
Satish Rao, and Apurva Shah
Department of Computer Science,
UC Berkeley
Abstract. In this paper, we study lower bound techniques for branch-
and-boundalgorithmsformaximumparsimony,withafocusongeneor-
derdata.WegiveasimpleO(n3)timedynamicprogrammingalgorithm
for computing the maximum circular ordering lower bound, where n is
the number of leaves. The well-known gene order phylogeny program,
GRAPPA, currently implements two heuristic approximations to this
lowerbounds.Ourexperimentsshowasignificantimprovementoverboth
these methods in practice. Next,we show that the linear programming-
based lower bound of Tang and Moret (Tang and Moret, 2005) can be
greatly simplified, allowing us to solve the LP in O∗n3) time in the
worst case, and in O∗(n2.5) time amortized over all binary trees. Fi-
nally,weformalizetheproblemofcomputingthecircularorderinglower
bound, when the tree topologies are generated bottom-up, as a Path-
Constrained Traveling Salesman Problem, and give a polynomial-time
3-approximation algorithm forit.Thisisaspecial caseof themoregen-
eral Precedence-Constrained Travelling Salesman Problem and has not
previously been studied, tothe best of our knowledge.
1 Introduction
Currently,themostaccuratemethodsforphylogeneticreconstructionfromgene
order data are based on branch-and-bound search for the most parsimonious
tree under various distance measures. These include GRAPPA [1], BP-Analysis
[2], and the closely-related MGR [3]. Since branch-and-bound for this problem
is potentially a super-exponential-time process, computing good pruning lower
boundsisveryimportant.However,scoringaparticularpartialorfulltreetopol-
ogy is a hard computational problem for many metrics, in particular for gene
order data.
There has been a good deal of recent work on designing good lower bounds
for various distance measures. These techniques are divided between those spe-
cially designed for specific distance measures [4–6] and those that hold for arbi-
trarymetrics[7–9].Ourlowerboundsfallintothelattercategory.Lowerbounds
that hold for arbitrarymetrics are particularly appealing in the context of gene
order phylogeny, because an important direction for the field is to extend cur-
rent methods to use more realistic metrics than the breakpoint or inversiondis-
tances currently used. There is a growing body of algorithmic work on various
A.McLysaghtetal.(Eds.):RECOMB2005WsonComparativeGenomics,LNBI3678,pp.1–10,2005.
(cid:3)c Springer-VerlagBerlinHeidelberg2005
2 A. Bachrach et al.
distance measures, including transpositions,chromosome fusions/fissions,inser-
tions/deletions and various combinations of these (see [10] for a comprehensive
survey) and our lower bounds apply to all of them. One notable exception to
this is the tandem duplication and random loss model [11], which is well-suited
to animal mitochondrial genomes, but is asymmetric and therefore does not fit
into the standard metric parsimony framework.
Inthispaper,wegiveefficientimplementationsoftwolowerbounds.Thefirst
is a simple dynamic programming algorithm to compute the maximum circular
ordering lower bound in O(n3) time and O(n2) space. Since the exact running
time of the algorithm often depends on the choice of root, we also provide an
algorithm to compute the optimal root for a given un-rooted tree topology in
O(n2) time. Next, we greatly simplify the LP-based lower bound of [9] and
show how to implement it in O∗(n3) time1 in the worst case and O∗(n2.5) time
amortizedoverallbinarytrees.Finally,westudytheproblemoflowerbounding
the tree score when the only a partial topology has been constructed so far
and rephrase this as a Path-Constrained Travelling Salesman Problem. This is
a special case of the Precedence-Constrained Travelling Salesman Problem [12],
in which we are given a partial order graph on a subset of the cities and asked
to return a min cost tour that respects the partial ordering. Our version of the
problem is simply the case where the partial order graph is a directed path. To
ourknowledge,consideringtheeffectofarestrictedpartialorderonthisproblem
has not been previously studied, and we give a simple and fast algorithm that
computes a 3-approximation for the case of a line. The solution can then be
transformed into a lower bound by dividing the score by 3.
Finally, we have implemented our dynamic programming lower bound and
show that it gives better results on the benchmark Campanulaceae data set.
2 The Circular Ordering Lower Bound
Given a rooted binary tree in which one of each pair of children is designated
the left child and the other the right child, consider the left-to-right ordering of
the leaves, π, induced by some depth-first search of the tree. For a given metric
d(·)onpairsofleaves,say(cid:2)the inversiondistance,wedefine the circularordering
lowerboundtobeC(π)= n d(π(i),π(i+1)),wherewedefineπ(n+1)=π(1)
i=1
for notational convenience. By repeatedly invoking the triangle inequality, it is
easy to see that C(π) is a lower bound on the cost of the tree, and the bound is
2
tight if the distance d(·) is the shortest path metric induced by the tree.
Thesametreetopologycaninducemorethanoneleaforderingπbyswapping
left child and right children at internal nodes of the tree, and some leaf order-
ings may produce a higher lower bound that others. A brute-force exponential
timealgorithmforcomputingthemaximumcircularorderingistoenumerateall
possible combinationsof swapsatinternalnodes.This method has been consid-
ered too expensive to work well in practice [13]. Two heuristic approximations
1 The notation O∗(f(n)) omits factors that are logarithmic in n.
Lower Bounds for Maximum Parsimony with Gene OrderData 3
are implemented in GRAPPA. The first is the Swap-as-you-go heuristic [7], in
which a DFS traversal of the tree is performed, and a swap performed at each
internal node when it is visited as long as it improves the lower bound. This
heuristic has the attribute of running in linear time.
The second heuristic does a similar traversal,but when deciding whether to
swap the left and right children of an internal node, the algorithm tries both
of them, and keeps the one which gives the better lower bound for the current
subproblem. This latter approach runs in O(n4) time.
In this section, we show that, in fact, the maximum cicular ordering for a
given tree can be computed in O(n3) time by a straightforward dynamic pro-
gramming algorithm. We first note that the choice of the tree’s root does not
affecttheparsimonyscoreorthemaximumcircularorderinglowerbound.Since
the branch-and-boundalgorithmsearchesover unrooted topologies,for the pre-
sentation of the algorithm we assume an arbitrarily chosen root. On the other
hand,theexactrunningtimeofouralgorithmwilldependonthepositionofthe
root,sowe also considerthe problemofoptimalrootplacementafter givingthe
description of the algorithm.
At each internal node, v, let S be the set of leaves in the subtree rooted at
v
v. The dynamic programming algorithm constructs a table M which contains,
v
for each pair of leaves A,B ∈ S , the maximum score attainable by a linear
v
orderingof the vertices in S that begins with A and ends with B, if one exists.
v
Note that such an ordering exists if and only if A and B are leaves in subtrees
rooted at different children of v.
Letthe childrenofv bel andr. Weinductively assumethatthe tablesM(r)
andM(l)havealreadybeenconstructed.Letll andlr be l’schildrenandrl and
rr be r’s children, and let us assume that the subtrees rooted at ll, lr, rl and
rr have a,b,c and d leaves respectively (if r or l are leaves, then this step may
be omitted). Intuitively, we could construct M(v) by considering all possible
quartets of leaves A∈ S ,B ∈ S ,C ∈ S and D ∈ S . We will then perform
ll lr rl rr
O(abcd) operations at node v, which would lead to a running time of O(n4) for
the whole tree.
We can do better than this naive implementation in the following way. Let
A∈S and C ∈S . Let
ll rl
δ(A,C)= max[M (A,B)+d(B,C)]. (1)
l
B∈Slr
So δ(A,C) is the highestscoreattainable by alinear orderingof the leavesinS
l
which also takes a final step to C. Now for D ∈S we obtain
rr
M (A,D)= max[δ(A,C)+M (C,D)]. (2)
v r
C∈Srl
The maximum circular ordering lower bound is given at the root by the
expression
max [M (A,D)+d(A,D)]
v
A∈Sl,D∈Sr
