Table Of ContentInteger Linear Programming in Computational
and Systems Biology
Integerlinearprogramming(ILP)isaversatilemodelingandoptimization
techniquethatisincreasinglyusedinnontraditionalwaysinbiology,with
thepotentialtotransformbiologicalcomputation.However,fewbiologists
know about it.This how-to and why-do text introduces ILP through the
lensofcomputationalandsystemsbiology.Itusesin-depthexamplesfrom
genomics,phylogenetics,RNAandproteinfolding,networkanalysis,can-
cer,ecology,co-evolution,DNAsequencingandsequenceanalysis,pedi-
greeandsiblinginference,haplotyping,clustering,andmoretoestablish
thepowerofILP.Thisbookaimstoteachthelogicofmodelingandsolving
problemswithILP,andtoteachthepractical“workflow”involvedinusing
ILPinbiology.
Written for a wide audience, with no biological or computational
prerequisites,thisbookisappropriateforbothentry-levelandadvanced
courses aimed at biological and computational students,and as a source
forspecialists.Numerousexercisesandaccompanyingsoftware(inPython
andPerl)demonstratetheconcepts.
Dan Gusfield is Distinguished Professor of Computer Science at the
University of California, Davis (UCD), and a fellow of the IEEE, the
ACM,and the International Society of Computational Biology (ISCB).
HispreviousbooksincludeTheStableMarriageProblem(withRobertW.
Irving)andAlgorithmsonStrings,TreesandSequences;andReCombina-
torics.HehasservedaschairofthecomputersciencedepartmentatUCD
(2000–2004), and was the founding editor-in-chief of The IEEE/ACM
TransactionsofComputationalBiologyandBioinformaticsuntilJanuary
2009.Hehasbeeninstrumentalinthedefinitionanddevelopmentofthe
intersectionbetweencomputerscienceandcomputationalbiology.
INTEGER LINEAR
PROGRAMMING IN
COMPUTATIONAL AND
SYSTEMS BIOLOGY
An Entry-Level Text and Course
DAN GUSFIELD
UniversityofCalifornia,Davis
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
OneLibertyPlaza,20thFloor,NewYork,NY10006,USA
477WilliamstownRoad,PortMelbourne,VIC3207,Australia
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CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitofeducation,
learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108421768
DOI:10.1017/9781108377737
©DanGusfield2019
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2019
PrintedandboundinGreatBritainbyClaysLtd,ElcografS.p.A.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Gusfield,Dan,author.
Title:Integerlinearprogrammingincomputationalandsystemsbiology:an
entry-leveltextandcourse/DanGusfield,UniversityofCalifornia,
Davis.
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversity
Press,2019.|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2018061722|ISBN9781108421768(hardback:alk.paper)
Subjects:LCSH:Computationalbiology–Mathematicalmodels.|Systems
biology–Mathematicalmodels.|Linearprogramming.
Classification:LCCQH324.2.G872019|DDC570.285–dc23
LCrecordavailableathttps://lccn.loc.gov/2018061722
ISBN978-1-108-42176-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
DedicatedtoDickKarp,mentorandrolemodeltomefor45yearsand
counting.ThankyouDickforallyourwisdom,support,andfriendship.
Contents
Introduction to the Book and Course pagexi
I.1 WhyIntegerProgramming? xi
I.2 AboutThisBookandCourse xii
I.3 TasksandSkills xiii
I.4 WhyLearnfromMe? xiv
I.5 TheOrganizationoftheBook xv
I.6 NoMath xvii
I.7 Acknowledgments xvii
Part I
1 A Flyover Introduction to Integer Linear Programming 3
1.1 LinearProgramming(LP)andItsUse 3
1.2 IntegerLinearProgramming(ILP) 11
1.3 ExpressibilityofIntegerLinearFormulations 14
2 Biological Networks,Graphs,and High-Density Subgraphs 15
2.1 BiologicalGraphsandNetworks 15
2.2 TheMaximum-CliqueProblemandItsSolutionUsingILP 29
2.3 BoundsandGurobiProgressReporting 44
3 Maximum Character Compatibility in Phylogenetics 49
3.1 BasicDefinitions 49
3.2 PhylogeneticTrees 50
3.3 PerfectPhylogenyandCancer 53
3.4 CharacterRemovalinthePerfect-PhylogenyModel 54
3.5 MinimumCharacterRemoval(MCR)intheStudyofCancer 60
4 Near Cliques,Dense Subgraphs,and Motifs in Biological Networks 65
4.1 NearCliques 65
4.2 InvertingtheNear-CliqueProblem 72
4.3 AShortInterruption:OurFirstILPIdioms 73
4.4 ReturntoNearCliques 75
vii
viii Contents
4.5 Finally:TheLargestHigh-DensitySubgraphProblem 77
4.6 MotifSearchingviaCliqueFinding 81
5 Convergent and Maximum Parsimony Problems in Phylogenetics 89
5.1 PhylogeneticsviaMaximumParsimony 90
5.2 ImprovingthePracticality 98
5.3 Software 101
5.4 ConcertedConvergentEvolution:CliquesAgain! 101
5.5 CatchingInfeasibilityErrorsUsingAnIISinGurobi 102
6 The RNA-Folding Problem 105
6.1 ACrudeFirstModelofRNAFolding 105
6.2 MoreComplexBiologicalEnhancements 114
6.3 FoldPredictionUsingaKnownRNAStructure 121
7 Protein Problems Solved By Integer Programming 122
7.1 TheProteinSide-ChainPositioningProblem 122
7.2 ProteinFoldingviatheHPModel 128
7.3 PredictingDomain-DomainInteractioninProteins 137
8 Tanglegrams and Coevolution 142
8.1 IntroductiontoCoevolution 142
8.2 Tree Drawings,SubtreeExchanges,andtheTanglegram
Problem 145
8.3 LogicforSolvingtheTanglegramProblem 147
8.4 AnILPFormulation 148
8.5 SoftwarefortheTanglegramProblem 153
8.6 TheIf-XORIdiomforBinaryVariables 154
9 Traveling Salesman Problems in Genomics 156
9.1 TheTravelingSalesmanProblem(TSP)inGenomics 156
9.2 TheTravelingSalesmanProblem(TSP) 157
9.3 TSProblemsinDNASequencingandAssembly 159
9.4 MarkerOrdering:ADifferentFragmentLayoutProblem 162
9.5 FindingSignalingPathwaysinCervicalCancer 169
(cid:2)
9.6 AnILPSolutiontotheTSTourProblemonG 169
9.7 EfficiencyandAlternativeFormulations 176
9.8 TheSubtour-EliminationApproachtoSolvingTSProblems 180
9.9 ExtendedModelingExercises 185
10 Integer Programming in Molecular Sequence Analysis 186
10.1 TheImportanceofSequenceAnalysis 186
10.2 TheStringSite-RemovalProblem(SSRP) 187
10.3 RepresentativeSequences 191
10.4 TheLongestCommon-Subsequence(LCS)Problem 196
10.5 OptimalPathogenandSpeciesBarcoding 199
11 Metabolic Networks and Metabolic Engineering 205
11.1 BooleanNetworks 205
Contents ix
11.2 ExtendingBooleanNetworks,withILP 211
11.3 FantasyNetworkAnalysis 216
11.4 Time:TheFinalFrontier 219
12 ILP Idioms 221
12.1 GeneralIf-ThenIdiomsforLinearFunctionswithBinary
Variables 221
12.2 GeneralOnly-If IdiomsforLinearFunctionsandBinary
Variables 224
12.3 ExploitingtheIdioms 225
12.4 TheKeytotheIdioms 229
Part II
13 Communities,Cuts,and High-Density Subgraphs 235
13.1 CommunityDetectioninaNetwork 235
13.2 Cuts:Max,Min,andMulti 247
13.3 High-DensitySubgraphs:ARefinementforLarge,
SparseGraphs 256
14 Character Compatibility with Corrupted Data and Generalized
Phylogenetic Models 260
14.1 HandlingMissingandCorruptedDatainCharacter
CompatibilityProblems 260
14.2 HandlingBothMissingandCorruptedData 264
14.3 BacktotheArtifactProbleminPancreaticCancer 266
14.4 AnExtensionofPerfectPhylogenytoLess
RestrictedModels 268
15 More Tanglegrams,More Trees,More ILPs 273
15.1 MinimizingSubtreeExchangesWithinAnOptimalSolution 273
15.2 ADistance-BasedObjectiveFunctionforTanglegrams 274
15.3 AnILPFormulation 275
15.4 RootedSubtree-Prune-and-Regraft(rSPR)Distance 281
16 Return to Steiner Trees and Maximum Parsimony 287
16.1 TheSteiner-TreeProblemandExtensions 287
16.2 iPoint:DeducingProteinPathways 288
16.3 MaximumParsimonyandDuctalCarcinomaProgression 290
17 Exploiting and Leveraging Protein Networks 295
17.1 Example 1:Exploiting PPI Networks to Find Disease-
RelatedProteins 295
17.2 Example2:LeveragingPPIKnowledgeAcrossSpecies 298
17.3 Example3:IdentifyingDriverGenesinCancer 309
18 More String and Sequence Problems Solved by ILP 313
18.1 TheLCSProblemforMultipleStrings 313
18.2 TransformingGeneOrderbyReversals 316
