ContentslistsavailableatScienceDirect
Current
Plant
Biology
j ourn a l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / c p b
Computational
approaches
to
identify
regulators
of
plant
stress
response
using
high-throughput
gene
expression
data
Alexandr
Koryachko
a,
Anna
Matthiadis
b,
Joel
J.
Ducoste
c,
James
Tuck
a,
Terri
A.
Long
b,∗,
Cranos
Williams
a,∗∗aElectricalandComputerEngineering,NorthCarolinaStateUniversity,Raleigh,NC,USA bPlantandMicrobialBiology,NorthCarolinaStateUniversity,Raleigh,NC,USA
cCivil,Construction,andEnvironmentalEngineering,NorthCarolinaStateUniversity,Raleigh,NC,USA
a
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received4April2015 Accepted28April2015 Keywords: Stressresponse Transcriptionfactors Generegulatorynetworks AlgorithmsArabidopsisthaliana
a
b
s
t
r
a
c
t
Insightintobiologicalstressregulatorypathwayscanbederivedfromhigh-throughputtranscriptomic datausingcomputationalalgorithms.Thesealgorithmscanbeintegratedintoacomputationalapproach toprovidespecifictestablepredictionsthatanswerbiologicalquestionsofinterest.Thisreview conceptu-allyorganizesawidevarietyofdevelopedalgorithmsintoaclassificationsystembasedondesiredtypeof outputpredictions.Thisclassificationisthenusedasastructuretodescribecompletedapproachesinthe literature,withafocusonprojectgoals,overallpathofimplementedalgorithms,andbiologicalinsight gained.Thesealgorithmsandapproachesareintroducedmainlyinthecontextofresearchonthemodel plantspeciesArabidopsisthalianaunderstressconditions,thoughthenatureofcomputationaltechniques makestheseapproacheseasilyapplicabletoawiderangeofspecies,datatypes,andconditions.
©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Plantsaresessileorganismssubjecttoconstantlychanging envi-ronments.Theabilitytorespondtotheseenvironmentalchanges, therefore,iskeytoplantadaptationandsurvival.Anoverallgoal of plantabiotic stressresearch is todevelop anunderstanding ofthemolecularcomponentsofasingleorcombinatorialstress response and show how these components interact, enabling directedgeneticmanipulationsthatcanenhancestresstolerance
[1].Transcriptionfactorsareoneofthefirstcategoriesofgenes activatedinresponsetoastress[2].Transcriptionfactoractivity canleadtoalterationsinactivityandaccumulationofdownstream transcriptionfactorsandproteinsthatmodulateplantmorphology andmolecularcomposition.Inthisway,manipulationofthe activ-ityofjustonetranscriptionfactororasmallfamilyoftranscription factorscanlead toalterationsin a transcriptionalcascadewith dramaticoutcomes.Thisstrategyisthebasisforboth evolution-aryadaptationaswellasgeneticmanipulationofstressresponses
[3,2,4].Despiteawidespreadfocusonstress-inducedtranscription
factorsandarecentbreadthofhighthroughputdata,successful
∗Correspondingauthor.Tel.:+19195150478. ∗∗Co-correspondingauthor.
E-mailaddresses:[email protected](T.A.Long),[email protected] (C.Williams).
geneticmanipulationsoftranscriptionfactorsincropplantsthat improvestresstolerancearelimited.Identificationof transcriptio-nalregulatorsinthemodelspeciesArabidopsisthalianaisafirst steptothesearchforcandidatesforgeneticmodificationincrop species,yetanumberoflimitationsexistinthisidentification.First, with5–10%ofplantgenomesreportedtocodefortranscription factors,thenumberofcandidategenestostudyisextensive[5–7]. Second,itisdifficulttopredicttheeffectsofonetranscription fac-torin isolationandevenmoredifficulttopredictcombinatorial effectsoftranscriptionfactorsactingonthesametargetsor act-ingincomplexes.Finally,thewaysinwhichtranscriptionfactor activityismodulatedinresponsetoonestressoracombination ofstressesarecomplex.Inotherwords,ahugenumberofpossible experimentsexisttotesttheeffectofcombinationsoftranscription factorsundercombinationsofstresses.Computationalapproaches playacriticalroleintheresearchprocessbyproducinga setof testablepredictions,thuslimitingthespaceofexperimentsneeded toyieldabetterunderstandingofthecascadingresponses result-ingfromstress.These predictionsrange frominvolvementof a transcriptionfactorin astressresponsetodetaileddescriptions oftranscriptionfactorand targetgeneinteractiondynamics.An increasingabundanceofcomputationalapproachesnecessitatesa carefulevaluationoftheutilityandapplicationofthesetools.
Inthisreview,wesummarizeandorganizealgorithmsinvolved incurrentandpromisingcomputationalapproachesinto5 cate-gories(“Types”)basedonthetypeofinferenceanalgorithmaims http://dx.doi.org/10.1016/j.cpb.2015.04.001
2214-6628/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4. 0/).
toobtainfromabiologicaldataset.Wefocusonalgorithmsthat canoperateongeneexpressiondata,asthisiscurrentlythemost availableformofhighthroughputdata.Wethendemonstratehow algorithmsfromdifferentcategorieshavebeencombinedinthe scopeofcomputationalapproachestoachievespecificobjectives associatedwithplantstressresponse.Additionalexamplesof algo-rithmsthatfallintotheproposedclassificationsystemcanbefound eitherinplantrelated[8–10]orgeneralcomputationalapproach
[11–15]reviewarticles.Webuildonthesereviewsbyorganizing
algorithmsbasedontheirutilityandhighlightinghowinferences achievedbyalgorithmsinmultiplecategoriescanbesystematically combinedtoachieveabetterunderstandingofthetranscriptional cascadeinvolvedinstressresponse.We thendiscusshowthese algorithmshavebeenutilizedinrecentstudiestoachievea cer-tainobjective.Inthisway,researchersaimingtoacquirespecific predictionsfromanexpressiondatasetcanmoreefficientlychoose appropriatealgorithms.
2. Background
Environmental conditions in agricultural settings are highly variable, leading to suboptimal crop yields and survival rates
[16].Thefrequencyandintensityofenvironmentalextremes, par-ticular drought, heat, and pests are expected to increase with climatechange[1,17,16].Alargenumberofstressresponse stud-iesarefocusedonelucidatingtranscriptionalcascadesregulating responsestoindividualandcombinedstresses.Transcription fac-tors thatplay important rolesin modulating suchcascadesare candidatesforgeneticengineeringapproachesandareworthyof intensivestudy.
Geneexpressionanalysisisawidelyproposedmeansofbringing a greater understandingto allabiotic stress responsesfor sev-eralreasons.Alargenumberofgeneshavealteredexpressionin responsetostressandthesealterationsplayanimportantrolein adaptation[18,19].Expressiondataisalsorelativelycheap.Because ofthis,high-throughputgeneexpressiondatasetshavebeen gen-eratedandarepubliclyavailableforamultitudeofstresses,both bioticandabiotic,withexamplesinA.thalianaincludingbutnot limitedtopathogeninfection[20–22],cold[23],pH[24],salt[25], light [26],and nutrient [25,27–30]stress.Though thesestudies arecomparableintheory,afewlargestudieshaveattemptedto mitigatethe effects ofvariations in experimentalsetupby col-lecting expression data under different stresses imposed with otherwiseidenticalgrowthconditions[18]orundercombinations ofstresses[31–34].Analysesoftheseconcurrentand combinato-rialexperimentsinparticularhave revealeddistinctpatternsof differentstressresponsesalongwithsomecommonfeatures, infer-ringthatbothgeneralandspecificstressresponsepathwaysexist. For example, analysisof theAtGenExpress databaseof concur-rentstressapplicationindicatesthatsomeabioticstressesresult insustainedgeneexpressionalterationsand othersintransient alterations[18].Asetofearly-andcommonlyinducedgenes, rep-resentingthesocalledPlantCoreEnvironmentalStressResponse (PCESR),includestranscriptionfactors,indicating thata general stressresponsemaybetranscription factormediatedand likely occurs earlyin stress response cascades [18,35]. Combinatorial studiesindicatethatgenesrespondingtocombinedstressesare oftendistinctfromthoserespondingtoindividualstresses, high-lighting a need for both more studies of this type as well as computational methods to attempt to predict these emergent behaviors[31–34].Despitetheseextensiveanalyses,limiteddirect predictionsconcerningstresspathwayshavebeenmadeand val-idated.Themajorityofdetailedcharacterizationsoftranscription factors,includingdirect promoterbindingandinfluenceon tar-getgene expression,are theresultof traditional studies.These
studiesaretimeandcostintensive.Furthermore,sincemanykey regulatorshavebeenfoundthroughphenotypicmutantscreens, subtleyetimportantphenotypesandgenescaneasilybemissed. Redundancyisexpectedincriticalregulatorymechanisms[36],and predictionsconcerningwhichregulators ormutantstocombine in a geneticengineering strategywould beextremely valuable. Arecent increaseinalgorithm developmentand utilizationwill helptoincreasethepredictivepowerinavailabledatasetssothat regulatorsandcombinatorialregulatorymechanismsbeyondthe “lowhanging fruit” canbeidentified.In thefollowing sections, wedescribeandorganizesetsofalgorithmsandimplementations thereofinexperimentalapproaches,aimingtobringattentionto thebenefitoftheseapproachesandfacilitatefutureincreasesin frequencyandstrengthofcomputationalbiologystudies.
3. Classificationofinferencealgorithms
Manycomputationalalgorithmshavebeendevelopedfor ana-lyzinggeneexpressiondata.Wefocushereonalgorithmscapable of identifyingstress related genes,groupinggenes byfunction, inferringconnectionsbetweengenes,estimatinggeneinteraction direction and type, and predicting gene expression states and values ininterconnectedregulatorynetworks.Thesealgorithms differincomplexityandimpliedassumptions,butcanbeclassified basedonfunctionality.Wecategorizethesealgorithmsin5distinct groupsbasedonthetypeofinsighttheyprovidetoabiological pro-cessofinterest.Dependingonresearchobjectives,thesealgorithms caneitherbeusedseparatelyorasapartofasystematic compu-tationalapproachwhereinferencesfromalgorithmsofonetype canbeusedasinputforalgorithmsofanothertype.Forexample,a computationalapproachdesignedtopredictgeneinteractionsand theirtypebasedontimecoursemicroarraydatacanbecomprised of3algorithmsofdifferenttypesthatsequentiallyprocessinput datatoobtainadesiredoutput(Fig.1).
Thealgorithmsdescribedcanbeappliedtotranscriptomicdata obtainedatMtimepointsortreatments(tj,j=1,...,M)foraset ofNgenes(gi,i=1,...,N).Examplesofsuchdatasetsincludethe globalabioticstressexpressiondatabaseAtGenExpress[18].This databaseincludesdatasetsformultipleabioticstresstreatments thatareobtainedforN≈24,000genesatM=7timepointsusing AffymetrixATH1GeneChipmicroarrayanalysis.Hence,theactivity ofeachgenecanberepresentedbyasetofnumbersgi(t1),gi(t2),
...,gi(tM),formingapatternthatisusedbyalgorithmstomake inferences.
Type1algorithmsattempttocapturegenesthatarerelevantto a particular condition. Techniques for determining differentially expressedgenes are an example of algorithmsfalling into this category[37].Differentialexpressiontechniquesworkby assum-ing that significant changein transcript levelsof a given gene understressconditionrelativetoitsactivityundernormal condi-tionsindicatesthatthegeneplaysaroleinthestressresponse. Thisassumption disregardsposttranscriptional modificationsas alternatemeansofgeneproductregulation.Sincetranscript mea-surementprecisioncanvaryfromoneexperimentalapproachto another,statisticaltestsareoftenappliedtodeterminethe sig-nificanceofthechangeintranscriptlevels.Student’st-testfor2 treatmentsorANOVAforasetoftreatmentsarecommonlyapplied to deduce statistical significance. Other differential expression inferencealgorithmsweredevelopedforlargescaleexperimental techniquessuchasmicroarrays,forwhichthecorrelationbetween within-arrayreplicatescan betakeninto consideration [38],or RNA-Seq, forwhichcountbasedstatistics aremoreappropriate
[39,40].
Type 2algorithmsaimto identifyrelationshipsbetween genes. These algorithms work by assuming that genes with “similar”
Fig.1.Conceptualviewoftheinformationflowinacomputationalapproach.Biologicaldataisusedtoidentifygenesofinterest(Type1algorithm),inferconnections betweenthesegenes(Type2algorithm),andpredicttypesoftheseconnections(Type3algorithm).
expressionpatternsareco-regulatedorarepartofthesame regula-torypathway[13].Techniqueslikeco-expressionanalysis[41–45]
fallintothiscategory.
Common metrics that have been used to assess similarities betweengenesbasedontheirexpressionpatternsincludePearson correlation coefficient [42,46–48], Spearman correlation coeffi-cient [49–51], partial correlation coefficient [52–54], Euclidean distance[55,56],andmutualinformation[57–59].Thesemetrics typicallyrepresenta quantifiedmeasurethatestablishesa pair-wisecomparisonbetweentheexpressionlevelsoftwogenes,g1 and g2, acrosstime points or experimentaltreatments. Kumari etal.[60]presentedastudythatevaluatedtheutilityofSpearman rankcorrelation,WeightedRankCorrelation,Kendall,HoeffdingsD measure,Theil-Sen,RankTheil-Sen,DistanceCovariance,and Pear-soncorrelationcoefficientontranscriptionaldatafordetermining geneassociation.TheauthorsfoundthatSpearman,Hoeffding,and Kendallcorrelationcoefficients weremore effectivein identify-ingrelatedpathwaygenesthanothers.Incontrast,Maetal.[61]
claimthatbasedonmanualinspectionoftheexpressionpatterns ofseveralpairsofTF-targetgenes,theGinicorrelationcoefficient cancompensatefortheshortcomingsofthePearson,Spearman, Kendall,andTukeysbiweightcorrelationsindetectingtransient regulatoryrelationshipsbetweentranscription factorsandtheir targets.Metricssuchasareabetweenexpressioncurves[62],Z -score[63],andothersappearintheliteraturebuthavenotbeen extensivelyevaluated.
Relationshipsbetweenindividualgenesoracrossestablished groupsofgenescanbegeneratedbasedonthesesimilaritymetrics. Atypicalprocedureforestimatingrelationshipsbetween individ-ualgenesistosetathresholdvalueandassignconnectionsbetween geneswhosepairwisesimilarity valueishigherthan aselected threshold[62,58].Thestatisticalsignificanceofthesimilaritycan alsobetakenintoconsiderationwhenestablishingaconnection
[57].Groupsofsimilarlybehavinggenesareinmostcasesidentified usingclusteringalgorithms.Clusteringalgorithmsapplysimilarity metricstoisolategroupsofco-expressedgenes.k-means cluster-ing[64],theMarkovClusteralgorithm[65,66],biclustering[67], self-organizingmaps[68],hierarchicalclustering[69],and affin-itypropagation[70]areexamplesofclusteringalgorithmsapplied totranscriptomicdata.Martinetal.[64]appliedk-means cluster-ing,hierarchicalclustering,andself-organizingmapstotimeseries transcriptomicdatafrommice.Theresultssuggestedthatk-means wasabletoconveycomparablegroupingtohierarchicalclustering, andself-organizingmaps(morethan80%agreement)while main-taininglessofacomputationalloadthanotherapproaches.Freyand Dueck[70]showedthattheaffinitypropagationalgorithmyields morecompactclusterscomparedtok-meansintermsofthesum ofinterclusterdistanceswhichmightimplytighterrelationships betweengenesinthesamecluster.
Clustering has also been used to reduce the complexity of buildingtranscriptionalnetworksbyreducing highdimensional networkswithmanygenestolowerdimensionalnetworksof clus-tersof genesor “metagenes”,which represent groups ofgenes withsimilarexpressionactivity.Theexpressionpatternofa meta-gene may be defined as thecluster average or the expression pattern of the gene with the highest sum of similarities with itsclustermembers.Somealgorithmshaveextracted metagene expressionpatternsfirstbyapplyingprincipalcomponentanalysis (PCA)orsingularvaluedecomposition(SVD)totheoverall expres-siondataset.Theclustersarethenassembledbasedonsimilarities betweengeneandmetageneexpressionpatterns[71,72].
Type3algorithmsaimtoinfercausalrelationshipsbetweengenes. Causalinferenceproceduresareoftenbasedontheassumptionthat achangeinonegene(g1)willresultina subsequentchangein anothergene(g2)atsomelatertimeifg1activatesorinhibitsg2
[73–77].Thus,theapproachissimilartoco-expressionanalysisin
thatitaimstofindgeneswithsimilartemporalexpression pat-terns.Thekeydifferencedistinguishingthisapproachfromthose inType2istheassumptionthatthesesimilaritieswilloccurata delay,allowingforinferenceonthedirectionofregulation(which genecomesfirstinaregulatorycascade)inadditiontoa relation-shipconnection.TheequationforPearsoncorrelationcoefficient, forexample,canbemodifiedtoassessthistemporalcharacteristic byincorporatingatimedelay.Eq.(1)reflectssimilarityatthedelay ofonetimeunit.Thealgorithmscapturetheregulationdelayfor apairofgenesbyselectingthetimeunitdurationthatmaximizes thecorrelationcoefficient[75].
g1→g2 =
M−1 j=1 (g1(tj)−g¯1)(g2(tj+1)−g¯2) M−1 j=1 (g1(tj)−g¯1)2 M−1 j=1 (g2(tj+1)−g¯2)2 , where g¯1= 1 M−1 M−1 j=1 g1(tj), g¯2= 1 M−1 M−1 j=1 g2(tj+1) (1)Twosets ofsimilarity values,each correspondingtoa range of delaysforacertaindirectionofshift,arecalculatedtoassessthe strength anddirectionality ofconnectionin each pairofgenes. Smallsimilarityvalues,correspondingtoalowprobabilityof reg-ulation,canberemoved,leavingtheremaininghighconfidence connectionstocharacterizegenesthathavepotentialcausal rela-tionships.Approachesthatusemodificationsofthemetricin(1)
havebeeneffectiveforsingledatasetswith50and27timepoints andsamplingintervalsof20min[75]andfor acollectionof18 datasetswith7timepointsineachandsamplingintervalsranging from0.5to12h[78].Othersampletimesmayberelevant depend-ingonthefeaturesthatexistinthedata.
Anotherclassofalgorithmsthatinferregulatoryinteractions betweengenesisBayesiannetworks[79,80].Bayesiannetworks arecapableofinferringregulatoryconnectionsfromtimecourse andnon-timecoursedata.Thesealgorithmsattempttofindcausal connectionsbasedonBayes’rulebyexplicitlychoosinganetwork structure that best describesexperimental data. The algorithm considersanetworkofgeneregulationsasasetofdependencies wheretheprobabilityofexpressionofatargetisconditionedon theexpressionofitsregulator.Theseregulationsaredescribedas conditionalprobabilities.Algorithmsthentrytofinda network structurethatbestdescribesthedatabasedonascoringfunction. Identificationofthenetworkstructureisacomputationally inten-siveproblem.Complexitygrowsexponentiallywithanincreasing numberofnodes[11].Forexample,around1018different topolo-giesariseforanetworkofonly10genes[12].Thus,mostofthe approachesusingBayesiannetworksconcentrateonasmallsubset ofgenes(typicallywhensomeportionofageneregulatorynetwork isalreadyknown)oremploysub-optimalbutlesscomputationally intensesolutionstohandlelargernetworks[11].
DynamicBayesianNetworks(DBN)[81,82]incorporate order-inginformationintimecoursedatatoallowforfeedbackloops(not allowedinstandardBayesiannetworks).Thesefeedbackloopsare allowedbytreatingexpressionofthesamegeneatdifferenttime pointsasdifferentnodes.Nodescorrespondingtothesamegene arecombinedafterthestructureinferenceprocedure.This algo-rithmleadstoanincreaseincomplexitysincethenumberofnodes involvedinstructureinferenceroutineisaproductofthenumber ofgenesandthenumberoftimepoints.
Type4algorithmsaimtoinfercombinationsofregulator expres-sionstatesthatarenecessarytoresultinaparticularstateoftarget. Thesealgorithms canbeconceptualizedasa search fora func-tionalrelationshipbetweenatargetanditsregulator(s)(gi=f(g1,
g2,...,gN)).Inthiscase,aqualitativemeasureofgenebehavior canbeused,withgeneexpressionvalues representedaseither highorlow, activeor inactive,or“ON”or“OFF”tosimplifythe problem.An“ON”stateofonlyacoupleregulatorsmaysufficeto upregulatetheexpressionofthetarget.Thisqualitativeassumption allowstheuseofBooleannetworks[83]inType4inference prob-lems.ExpressionvaluesinBooleannetworkinferenceapproaches arediscretizedmostlyintwostates,representinganactivitylevel ateachtimepoint[84–86].Regulatoryconnectioninference algo-rithmstrytofindabinaryfunctionthatcomputesthenextstateof agenebasedonacombinationofothergenes’statesusingsimple Booleanoperations,e.g.AND(&)ifmorethanoneregulatorshould haveacertainstatetoinfluenceacommontarget,OR(|)ifanyof theregulatorstatessufficeforthesamepurpose,andNOT(¬)inthe caseofrepression(Fig.2).Thegoalofthisapproachistofindthe simplestfunctionforeachgene,whichisthefunctionthatdepends onthefewestregulatorgenespossible.
Adirectapproach tofindthesimplestBooleanfunctionthat satisfiesagivendatasetistocompareallpossiblefunctions capa-bleofgeneratingtheobservedexpressionpattern.Thenumberof Booleanfunctionsthatcanrepresenttheexpressionactivityofa generegulatedbyasmanyasntranscriptionfactorsis22n
[87],
makingtheproblemcomputationallyinfeasibleforalarge(more than10)numberofgenes.Somealgorithmsusepriorknowledge toconfinethenumber of genestoanalyze.Othersrelyon net-workstructuresinferredbyothertypesofalgorithmstoconfine thenumber,type and directionalityofpossibleregulatory rela-tionshipsbetweenindividualgenesorgroupsofgenes.Another factorconstrainingtheuseofBooleannetworksinwholegenome datasetanalysisisthesmallnumberofsamples(timepoints) asso-ciatedwithmostdatasets.Thesesmallsamplesizestypicallydo notprovidethediversityneededtouniquelydefinerelationships acrossalargenumberofindividualgenes.Forexample,for5time points,which isthemedian numberin typicalgeneexpression
Fig.2.Booleannetworkrepresentationingraphicalandfunctionalforms. Combi-nationsoftranscriptionfactorsg1,g2,andg3influenceexpressionofeachotherand targetgenes.Thestateofg6,forexample,isinfluencedbyacombinationofg2and g3orbyg1alone.
Fig.3. Type5algorithmsoutputintermsofthesystemofODEsandpredictedgene expressiondynamics(gi(t))basedonexperimentalvalues(gi(tj)).Inthisexample,
theexpressionpatternofeachgeneisinfluencedbytheexpressionofatleastone othergene,withsomegenes(g4)influencedbytheirownexpression(feedback loop).
datasets[88],thenumberofgeneswithdistinctBoolean expres-sionpatternsislimitedtoonly25=32.Anyattemptedanalysisof morethan32geneswithsuchadatasetwouldresultinatleast 2geneswithidenticalbehaviorwhichwouldlimitresolutionto groupsofgenes(e.g.metagenes)asopposedtoindividualgenes.
Type5algorithmsaimtodescribedynamicbehaviorina trans-criptionalnetwork.Theresultingnetworkrepresentationallowsfor thereconstructionofcontinuouschangesintranscriptsovertime (Fig.3).Ordinarydifferentialequationsarecommonlyusedto cap-turethedynamicsassociatedwithgeneexpressionchanges[89]. Theseequationsallowfortheestimationofgeneexpression val-uesatanygiventimepointeitherbetweensamples(interpolation) orbeyondthelastcollectedsample(extrapolation)[29].Whena generegulatorynetworkisrepresentedintermsoflinear differ-entialequations,theinstantaneouschangeinexpressionofagene isrelatedtothesumofweightedexpressionvaluesofinfluencing genes: dgi dt = N
k=1 aikgk, (2)whereaikrepresentinfluencecoefficients.Coefficientsforlinear differentialequationsareofteninferredusingtheLeastAbsolute ShrinkageandSelectionOperator(LASSO)algorithm[90],a modi-ficationofthelinearregressionapproach.WhenLASSOisusedfor ODEinferencepurposes,thechangesinexpression,i.e.differences betweenexpressionvaluesatconsecutivetimepoints,are approx-imatedbyalinearcombinationofothergenes’expressionvalues. Expressionpatternsfortargetgenesarereplacedwithpatternsof changesinexpression[91–93]toinferinfluencecoefficients.Given thatbiologicalprocessesareassumedtobeinherentlynonlinear, linearOrdinaryDifferentialEquation(ODE)inferencealgorithms fortranscriptionalnetworksrelyontheassumptionthatthe sys-temoperatesclosetoastabilitypoint[93].Thesystemmaynotstay closetoastabilitypointinthecaseofstressinducedresponses, where a plant may transition from one stable steady state to another.NonlinearODEs,thoughpotentiallymorebiologically rel-evantbecausetheydonotrely onthesteadystateassumption, typically requirethe estimation of more coefficients associated withnonlinearterms[94].Coefficientestimationroutinesfor infer-encealgorithms searchtheparameterspacetofindcoefficients that yield solutions closest to measured expression values
[95,96].
Allof the described algorithms requireimplementation and validation in biological systems in order to assess theirutility. Anumberofvalidationtechniquesexist,dependingonthetype ofalgorithm[97–113].Thesevalidationtechniquesarevisualized withkeyreferencesinFig.4.ValidationforalgorithmsofTypes1
and2,whichpredictassociationsbetweenageneandaprocess oragene anda groupof genes,are limitedtoanalysisof Gene Ontology(GO)enrichmentorphenotypesinmutantsof transcrip-tionalregulators.Thesephenotypesrangewidelydependingonthe stressresponseinquestion,andcouldinvolveextensive experi-mentationtosearchforaphenotypeofinterest.Awiderrangeof techniquesexistforalgorithmsofTypes3–5,algorithmsthat pre-dictrelationshipsbetweentranscriptionfactorsandtargetgenes. Theserelationshipscanbetested indirectly throughexpression profiling,computationallythroughpromoteranalysis,ordirectly throughbindinginteractions.Giventhatno“goldstandard” vali-dationtechniqueexists[114],convincingsupportofteninvolves thecombinationofmultiplevalidationtechniques,suchas expres-sionanalysis and binding activityfor a regulator and target of interest.Similarly,complexpredictionssuchasthosederivedfrom
Type4andType5algorithmsrequireacombinationofstaticand dynamicvalidationtechniques–includingexpressionprofilingat multipletimepoints,preferablyalongwithdeterminationof bind-ingactivity.
4. Computationalapproaches
Computationalapproachesareusedwidelytogaininsightinto processesunderlyingplantresponse tostressconditions. These approacheshaveasimilarstructureintermsofthetypesof algo-rithms theyuseand differin thecombination of and order in whichthesealgorithmsareapplied.Inthefollowingexamples,we describehowalgorithmsofdifferenttypeshavebeencombinedin particularcomputationalapproachestoanswerresearchspecific questions.
4.1. Relevantgeneidentification
A large number of current computational approaches are focusedonidentifyinggenesthatplayakeyroleinaprocessof interest.The importanceofthese genesisthen typically tested throughmutantphenotypicanalysis.Maetal.[56]analyzedaset ofA.thalianaabioticstressresponsetranscriptomedatasetswith
6timepointstoidentifystressrelatedgenes.Thecomputational approachstartedbypartitioning eachstressdatasetinto “infor-mative” and “noninformative” genesusing differential network analysis(Type1algorithm).Theauthorsstatedthatdifferential net-workanalysisthatinvolvesmachinelearningandtrainingbasedon
aprioriinformationismoresensitivethandifferentialexpression analysis,whichisstatisticsoriented.TheGinicorrelationcoefficient wasthencalculatedforpairsof“informative”genestoestablish sig-nificantconnections(Type2algorithm).Stressrelatedgeneswere identifiedfromtheresultingnetworkbasedonthecombinationof 33topologyscoresobtainedfromthenetworkofsignificant con-nections(Type1algorithm).Theauthorsvalidatedtheiralgorithm byperformingaphenotypicscreenfor89candidatesidentifiedas saltstressrelated.Mutantsof2previouslyunreportedsalt stress-relatedgenesshowedphenotypes.
Dinnenyetal.[25]conductedDNAmicroarrayexperimentson
A.thalianarootresponsetoirondeficientmediawith7timepoints spanning72htoidentifycommonstressresponsebehavior pat-terns.Theauthorsapplieddifferentialexpressionanalysis[115]to identifygeneshavingatleasta1.5-foldchangeinexpressionwith afalsediscoveryratevaluelessthan10−4atasamplingtimepoint comparedtonotreatment(Type1algorithm).Theanalysisshowed thatthestrongesttranscriptionalresponseoccurredafter24hof treatment.Dinnenyetal.[25]thenappliedtheaffinity propaga-tionclusteringalgorithm[70]toformgroupsofsimilarlyexpressed genesandthusidentifygeneralpatternsofgeneexpression(Type 2algorithm).Longetal.[28]usedtheresultsofthisanalysisand screenedthroughmutantsof38identifiedgenescodingfor coex-pressedtranscriptionfactors.Thescreensledtoidentificationof importantironhomeostasisregulatorsPOPEYE(PYE)andBRUTUS (BTS).
Linetal.[30] investigatedtheeffectofphosphatestarvation onA.thalianarootgene signalingusingaDNAmicroarray time coursewith 3 time pointsto infer functional modules in early transcriptionalresponses.Theauthorsuseddifferentialexpression analysiswiththerequirementofa2-foldchangeinexpressionwith ap-valuecutoffof0.05toidentifystressrelatedgenes(Type1 algo-rithm).Additionalinformationfrom2671experimentaldatasets, 300ofwhicharerootspecific,wasusedtoselect187rootspecific genes(Type1algorithm).TheauthorsusedtheMulti-Array Corre-lationComputationUtility(MACCU)toolboxbasedonthresholding pairwise Pearson correlation coefficients toobtain 3 functional modulesofstressspecificgenes(Type2algorithm).Tovalidatethe results,Linetal.[30]conductedmutantscreenson31members ofaclusterwheremostofthegenesareknowntoparticipatein rootdevelopment.Only5testedlinesdidnotshowastatistically significantroothairlengthphenotype.
4.2. Genefunctionelucidation
Anothergroupofcomputationalapproachesaimtoassociate geneswithaspecificfunctionduringaprocessofinterest.The guilt-by-associationheuristic[43]isoftenusedtoassignafunctiontoan unknowngenebasedonknownfunctionsofco-regulatedgenes (GeneOntologyenrichment).Polanskietal.[48]analyzedsixA. thalianastressresponse transcriptomedatasetstoidentifygene modulesshowingevidenceforco-regulation.Thecomputational approachrevealed78modulesofco-regulatedgenes,71ofwhich wereoverrepresentedinGeneOntologycategoriesand51ofwhich wereenrichedin transcription factorbindingmotifs(compared to24and6of78randomlyassignedmodules,respectively).The approachusedinformationaboutwhichgenesweredifferentially expressedineachstressresponseasaninput(previously deter-minedinotherpublications usingType 1algorithms).For each genedifferentiallyexpressedunderatleast2conditions,the algo-rithmassembledasetofcorrelatedgenesforeachcondition(Type
Fig.4. Validationtechniquesforalgorithmtypeswithkeyreferences.Examplesshownarethosetypicallyseenincurrentcomputationalresearchapproaches,specifically forresearchprojectsinA.thaliana.
2algorithm).Aco-regulationrelationshipinapairofgeneswas establishedifthesegeneshadsharedasignificantnumberof corre-latedgenesacrossstressconditions(Type2algorithm).Theauthors usedGeneOntologyenrichment,promoteranalysis,andyeast one-hybridprotein–DNAinteractionstovalidatetheresultingmodules ofco-regulatedgenes.
MaandBohnert[116]integratedtimecourseandcellspecific transcriptomics data with gene promoter structures to iden-tifystressrelatedcis-elementsinA. thaliana.Thecomputational approach used in this work detectedknown stress related cis -elementsandidentifiedsecondarymotifs.Theauthorscombined abioticandbioticstress,hormoneand chemicaltreatmenttime coursesanddifferentlightconditionsamplestocreateone com-bined expression pattern of 145values pergene. Differentially expressedgeneswereidentified bycombiningtheresultsfrom fuzzyk-meansclustering[117]appliedtoallgeneprobesandthe ‘limma’statisticalprogram[118]whichidentifiedgenes differen-tiallyexpressedinatleastonecondition(Type1algorithm).Fuzzy
k-meansclusteringwasagainappliedtotheresultingsetto iden-tifystressrelatedclustersofgenes(Type2algorithm).Theauthors assignedfunctionstoclustersbasedonGOenrichment.Binding motif analysis using Plant Cis-acting Regulatory DNA Elements (PLACE)database[105]revealedmotifssignificantlyoverexpressed inthefunctionrelatedclusters.Furtheranalysisof22majorclusters resultedintheidentificationofnewDNAregulatorymotifs[119].
4.3. Generelationshipinference
Computationalapproachesthataimtounravelinfluential rela-tionshipsbetweenregulatorsandtheirtargetsarelesscommonbut areincreasinginfrequency.Windrametal.[22]applieda computa-tionalapproachtoidentifytranscriptionfactorfamiliesoperating atdifferentstagesofA.thalianapathogendefenseresponse.The authorsanalyzedtranscriptionalprofilesat24time pointswith 4 replicates per time point. The computational approach pre-dictedgeneregulatoryinteractions,confirmedexperimentallyor by bindingmotif enrichment.The analysisstarted with assess-ment of differentiallyexpressed genesbased ona combination ofMAANOVA(MicroArrayANalysisOf VAriance)[120], approx-imateFtests,GP2S(Gaussianprocess2sample)test[121],and Hotellingstatistic(T2)[122](Type1algorithm).Next,a
SplineClus-ter[123]algorithmseparateddifferentiallyexpressedgenesinto
clustersassociatedwithdifferentstagesofstressresponse(Type 2algorithm).TheclusterswerevalidatedbyGOenrichment anal-ysis.NonparametricmodificationofBayesiannetwork inference algorithm [124] wasapplied to clusterrepresentatives toinfer regulatoryconnectionsbetweenclusters(Type3algorithm).The authors validated the regulatory effect of one of the clusters throughexperimentswithaknockoutmutantlineforthe tran-scription factor TGA3. Experimental data showed altered gene expressioninpredictedTGA3targetclustersinthetga3-2mutant,
Fig.5. Transitionsbetweenalgorithmsofdifferenttypes.Typicalexperimentaltransitionsbetweenalgorithmsareindicatedwithbluearrowsandperspectivefuture transitions,lesscommonbutpossiblewithmorereliablesupportingalgorithms,areindicatedwithwhitearrows.
whereastargetsregulatedbynonTGA3clusterswerelessaffected. Theeffectofanothertranscriptionfactor,ANAC055,wasvalidated bybindingmotifenrichmentintargetclusters.
Redestigetal.[78]analyzedasetof18DNAmicroarraytime seriescorrespondingtoninedifferentabioticstresseswithseven timepointsobtainedfromrootandshootofA.thalianaseedlings withtheaimofassociatingstressresponsivetranscriptionfactors with theirtargets. The authors concluded that their computa-tional approach delivered a usable number of high-confidence targetgenes(12–59%ofidentifiedtruetargets)forstressrelated transcriptionfactors.Thecomputationalapproachidentifiedstress relatedtranscriptionfactorsbyselectingoneswithmaximum over-allresponseandmaximumchangeinresponsesatisfyingaspecific thresholdcriteria(Type1algorithm).Covariancevaluesbetween atranscriptionfactorandothergenesoverasetofdelayswere calculatedforasetofconditions(Type3algorithm).Highscores correspondedtoahighprobabilityofregulation.
Krouketal.[29]conductedDNAMicroarrayexperimentsonA. thaliananitrateresponsewithsixtimepointsspanning20minutes tocaptureageneregulatorynetworkunderlyingplantadaptation tonitrateprovision.Theinferredtemporalmodelofthereaction processbuiltfor20 clusterrepresentativesresultedin 70% cor-rect predictions of expression value direction changeafter the lasttimepoint inthetimecourse.Thecomputationalapproach startedwithANOVAtoidentifynitrogenregulatedgenes(Type 1algorithm).Next,MeVsoftware[125]wasusedtoseparatethe nitrogenregulatedgenesinto20clusters,eightofwhichappeared tohaveover-representedbiologicalfunctions(Type2algorithm). TheapplicationofLASSObasedalgorithmtocluster representa-tivesprovidedcoefficientsforasystemoflinearODEsdescribing thedynamicsofeachcluster(Type5algorithm).Predictionsonthe directionofchangeobtainedfromODEsweretestedbycomparing themwithexpressionvaluesfromatimepointthatwasnotused forinferencepurposes.
4.4. Summary
Ascanbesurmisedfromtheexamplesgiven,algorithmsfrom
Type1,Type2,andType3aremorecommonincurrent experimen-talapproachesappliedtoplants.Theproblemofdimensionality preventstheextensiveuseofType4andType5algorithmsfor individualgenes based onwhole genomedatasets due todata requirementsforsuchtype of inference[13].Thus, the dimen-sionoftheproblemistypicallyreducedbylimitingasetofgenes toonesknowntointeractorparticipate inthesame biological process.Recentnon-stressrelatedapproachesinA.thalianahave
employedsuchtechniques.Espinosaetal.[126]used experimen-tally obtainedknowledge aboutrelationshipsof 15 genes in A. thalianaflowerdevelopmentprocesstopredictdevelopment sce-nariosusingBooleannetworksapproach(Type4algorithm).Sankar
et al. [127] built a model to predict states of thecomponents
fromauxinandbrassinosteroidsignalingnetworksinA.thaliana
byapplyingBooleanlogicapproach(Type4algorithm)andthen transformed theresulting discrete network representation to a setofordinarydifferentialequations(Type5algorithm)toobtain quantitativepredictions.Cruz-Ramirezetal.[128]investigatedthe dynamicsofasymmetriccelldivisionwithintheA.thalianarootby analyzingasystemofnonlineardifferentialequationsfor7 inter-actingcomplexes(Type5output).Theanalysispredictedabistable behavioroftheprocess.Finally,Pokhilkoetal.[129]refinedthe interactionmodeldescribingcircadianrhythmsinA.thalianaby modelingtheprocesswithasystemofnonlinear ODEs(Type5
output).
Similaritiesinregulatoryprocesses onagenomiclevel allow fortheapplicationofcomputationalapproachesthatwere devel-opedfornon-plantspecies.Somecomputationalapproachesare availableinsoftware packages.Anextensiveuseofthese pack-ages showsthat even ifa technique wasdeveloped and tested for one species, it can be applied to a similar dataset from anotherspecies.Examplesoftheseapproachesarebrieflydescribed here. Vermeirssen et al. [130] combined the Learning Module Networksalgorithm[131]developedforyeast,ContextLikelihood ofRelatednessalgorithm[132]testedonEscherichiacoli,and Dou-bleTwo-wayt-testsalgorithmtestedonE.colitoidentifyoxidative stressregulatorytranscriptionfactorsinA.thaliana(Type3output). TheAlgorithmfortheReconstructionofGeneRegulatoryNetworks (ARACNE)[58]wasdevelopedtoinfertranscriptionalregulations inhumanBcells,butthenusedforotherapplicationsincluding theinferenceoftranscriptionalinteractionsunderlyingroot devel-opmentandphysiological processesinA.thaliana[133](Type3
output).Othersoftwarepackagesthatshowedtheabilitytorecover generegulatorynetworksfromtranscriptomicdatainclude CLR
[132],MRNET[134],C3NET[57],andARTIVA[135].TheDialogue
onReverseEngineeringAssessmentandMethods(DREAM)project attemptedto comparesuch GRNinferencemethods appliedto
E.coli,Staphylococcusaureus,Saccharomycescerevisiaeandinsilico
microarraydata[136].Theauthorsdiscoveredthatthesemethods havecomplementaryadvantagesandlimitationsunderdifferent contexts.Inthecaseofmulticellularorganisms,theperformance oftechniqueshassofarbeenmeasuredbasedongoalsachieved foraspecificapplication.Suchperformanceisdifficulttocompare betweenmethodssincegoalsandapplicationsareoftendiverse.
5. Conclusions
We presented a classification of computational algorithms basedonthetype of information theyaimtoinfer.This struc-turewasusedtodescribeapproachesintheliteraturethathave been used to gain insight into biological processes of interest basedontranscriptomicsdata.Examplesofexistingcomputational approachesappliedtoplantstresstranscriptionaldatasets demon-stratedapatternoftransitionbetweenalgorithmsofdifferenttypes (displayedgraphicallyinFig.5).Thisprogressiondemonstratesthat thequalityofpredictionsmadebyanalgorithminthescopeofa computationalapproachoftendependsonthequalityof predic-tionsmadebyaprecedingalgorithmaswellasonthequalityofthe originalbiologicaldata.Basedonavailablealgorithmsandexample implementations,wecanstatethateventhoughbothstressrelated geneidentificationandgroupingalgorithms(Type1andType2) arestill evolving,confidenceinType 2algorithm predictionsis sufficienttoallowforatransitiontocausalityinference(Type3).
Type3algorithmshavethepotentialtosupplyType4andType 5algorithmswithinformationaboutthestructureofgene regula-torynetworks.Thisinformationwillreducethenumberofpossible functionalrelationshipstoconsiderforthesetypesofalgorithms dramaticallyandthusallowfortheincreaseinscopeand predic-tivepower.Therefore,theperspectivetransitionsshowninFig.5
willlikelyappearmoreofteninfuturecomputationalapproaches asreliabilityofType3algorithmspredictionsincrease.
Acknowledgements
Thismaterialisbasedupon worksupportedbytheNational ScienceFoundationunderGrantNo.1247427andbytheNational ScienceFoundationGraduateResearchFellowshipunderGrantNo. 1252376.WethankRosangelaSozzaniandRobertFranksforcritical readingofthismanuscript.
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