topological data analysis of water networks from simulations · topological data analysis of water...
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TopologicalDataAnalysisofWaterNetworksfromSimulations
LeeSteinberg&JeremyFreyUniversityofSouthampton,TMCS
ls2m15@soton.ac.ukUnderstandingthestructureofwaternetworkshasmajorimplicationsinthefieldofdrugdiscovery.Forexample,understandinghowthepresenceofasoluteaffectsthenativewaterstructurecouldenableustobuildbettermodelsforthepredictionoffreeenergychangesofsolvation.Investigationofwaternetworkshaspreviouslytakenagraph-theoreticalapproach,definingagraphstructurebasedonameasureofcorrelationbetweenwatermolecules,suchasin[1].Suchmethodshavealsobeenusedinstudyingradiationdamage[2].
However,thesetechniquesrequireauser-input,forexampledefiningavalueofdistancewheretwowatermoleculescanbeconsideredtobecorrelated.Weproposeanalternativeapproachbasedontheuseofpersistenthomology[3],atechniqueinthefieldoftopologicaldataanalysis(TDA),whichdefinesasetofstructuresforthefullrangeofparametervalues,andconsidershowthisseriesevolvestodeterminewhichfeaturesarethemostuseful.Wepresentaninvestigationintothestructureofwaternetworksinvariousmodelsusedinmoleculardynamicssimulations–TIP3P,TIP4P,andSPC.Wediscusstheadaptationofpersistenthomologymethodstotime-seriesdata,suchasthepersistencelandscape[4].Werelatepersistentloopstotheradialdistributionfunctionofthemoleculardynamicsmodel.Wealsodiscussthepresenceofthree-dimensionalvoidsinwaternetworks,andrelateittootherproperties.
Figure1-ThesurfaceofasimulatedTIP3Pwaternetworkat300K.Holesareclearlyvisibleinthesystem.
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[1]B.Mooney,L.Corrales,A.Clark,MoleculaRnetworks:Anintegratedgraphtheoreticanddataminingtooltoexploresolventorganizationinmolecularsimulation,JournalofComputationalChemistry,2012[2]A.Archer,H.Foxhall,N.Allenetal,Orderparameterandconnectivitytopologyanalysisofcrystallineceramicsfornuclearwasteimmobilization,JournalofPhysics:CondensedMatter,2014[3]H.Edelsbrunner,J.Harer,PersistentHomology–ASurvey,ContemporaryMathematics,2007[4]P.Bubenik,StatisticalTopologicalDataAnalysisusingPersistenceLandscapes,JournalofMachineLearningResearch,2015