Multiscale Modeling of Biopolymers Numerical Atomi

MultiscaleModelingofBiopolymers:NumericalAtomisticSimulationsMichelePavoneaSilvanaDeLillo,bVincenzoBaronec(a)[e-mail]-UniversitàdiNapoliFedericoII(b)[e-mail]-INFNedUniversitàdiPerugia(c)[e-mail]-CNRIstitutoperiProcessiChimico-FisicicomputationalapproachestomolecularsciencefocusonsystemsfromthequantumworldtothemesoscaleHierarchyoftheoreticalmodels:alookatspace×calesStructuralfeaturesofBiomolecules:therelevanceofHelices•BiologicalmacromoleculesaswellassyntheticpolymersadopthelicalstructuresHelicalconformationsof(1)DNA(nucleicacid)(2)Collagen(protein)(3)Isotacticvinylpolymers(1)(2)(3)•NucleicacidstructureanddynamicsStructuralfeaturesofBiomolecules:therelevanceofHelicesA-DNAB-DNAZ-DNA•Mechanicalpropertiesofproteins:theCollagenStructuralfeaturesofBiomolecules:therelevanceofHelices•Mechanicalpropertiesofproteins:theCollagenStructuralfeaturesofBiomolecules:therelevanceofHelicesTheAnalyticalModel:theElasticStripseenextpresentationbyM.SommacalKirchhoffequationsforthinelasticrodsM.Argeri,V.Barone,S.DeLillo,G.Lupo,M.Sommacal“Elasticrodsinlife-andmaterial-sciences.Ageneralintegrablemodel”submittedtoPhysicaDMicroscopicparametersaremappedinto3mechanicalproperties(stiffnesses)WheredoesanHelixcomefrom?•Isitanintrinsicpropertyofitsbuildingblocks(aminoacids,nucleicacids,etc.)?–Thephysico-chemicalpropertiesofmonomers•Ordoesitdependonexternalfeatures?–Long-rangeeffectsoringenerealthechemicalenvironmentatoughissueforexperimentalinvestigationsheretheorycomesintoplay•Empiricalmodelscouldnotprovidedefinitiveanswers:–EarlycalculationsbasedonMMpredictanintriscpreferenceforhelicalstructuresevenforisolateddipeptideanalogues•QMeffectivelydescribestheforcesactingonnuclei:–Isolateddipepetideanaloguesshowednopreferredminimaintheregionofa-helixconformations–Silumationsofinfinitelongchainspredictedthehelicalstructurestobestablethankstoshort-rangeH-bondingandtolong-rangedipole-dipoleinteractions–Thephysico-chemicalpropertiesofthesolventarecrucialintunigthebalanceoftheseinteractionsabcdnumericalatomisticsimulations•b-strand(C5)•27-ribbon(C7)•310-helix•a-helixdescribingthestrucutraldetailsfromamicroscopicperspective•Themaintool:PotentialEnergySurface(PES)Theatomisticperspective:numericalsimulationsonthebasisoftheadiabaticseparationofnuclearandelectronicdegreesoffreedom(Born-Oppenheimerapproximation)mostoftheidentityandbehaviorofaphysicalsystemcouldbeinvestigatedbydetermininganenergysurfaceinthespaceofnuclearcoordinatesandmomentaSTATICAPPROACHSearchforstationarypoints:MINIMA(molecularstructure)SADDLEPOINTS(reactivity:transitionstates,energybarriers)NORMALMODES(internalmotions:vibrations,freeenergies)PROPERTIES(linearresponsetoexternalfieldperturbations:spectroscopicproperties)DYNAMICAPPROACHSamplingofthepotentialenergysurface:MOLECULARDYMANICS(collectionoftrajectories–configurations–integratingtheNewtonequationsofmotionsontheforcefielddeterminedbythePES)PROPERTIES(fromanindividualmoleculetothebehaviorofmacroscopicsamples–statisticalanalysis)jiijjijiijijijijijimpropersdihedralsNnnanglesbondsbDrqqrrKnKkbbkV,,61220120204cos1MolecularMechanics(MM)approximatesthepotentialenergyofamolecularsystemasasumofindependenttermsbasedonclassicalmechanicsidealforverylargenumberofvariables:thousandsofatomsNumericalatomisticsimulation:theclassicalapproachQuantumMechanics(QM)couldbeusedtocomputetheenergyasafunctionofnuclearpositions(withintheBorn-Oppenheimerapproximation)time-independentSchrödingerequationaaaiiNjiijiNiNiirZrvrrvHEH)(1)()21(ˆˆ112EnergyfunctionalNuclearKE“Fictitious”KEofeE(R,P)MVVTr21TL21/41/4WμμTr21PPΛTr2LagrangianConstraintvariationalsolutionpropagationSelf-ConsistentField(SCF)equationFC=SCEExtendedLagrangianapproach(Car-Parrinello)Numericalatomisticsimulation:theabinitioapproach•ThePolarizableContinuumModelNumericalatomisticsimulation:thechemicalenvironment0垐?1ˆ,2RFRFsurfaceHHVVDddrrrrrrAsharpboundary(cavity)isdefinedbetweenthesoluteandthesolvent(r)istheelectrostaticpotentialD(r′,r)isafunctiondependingoncavitygeometryandsolventdielectricconstantM.Cossi,G.Scalmani,N.Rega,V.Barone,J.Chem.Phys.2002,117,43.Generalexpressionfortheenergy:layerslayersNijijNiiHHHA.Warshel,M.Levitt,J.Mol.Biol.103,227,1976“Layer”describedathighlevel:Mainsiteofthephysicalevent“Layer”describedatalowerlevel:indirectinfluence“Bulk”Numericalatomisticsimulation:hybridmethods–thegeneralconceptsQMMMPCMTheGLOBmodelisacontinuumbasedmodelwell-suitedforclassicalorabinitiomoleculardynamicssimulationsofcomplexsystemsinsolution.()(;)(;)AEWRRPRP(;)()(;)()caveldisrepRPRRPRWorktoexcludebulksolventfromacavity(fixed)Electrostaticworktopolarizesolvent(C-PCM)Worktochargedispersionandrepulsioninteractions(empirical)N.Rega,G.BrancatoandV.Barone,Chem.Phys.Lett.,2006,422,367.G.Brancato,V.BaroneandN.Rega,Theor.Chem.Acc.,2007,117,1001.G.Brancato,N.RegaandV.Barone,J.Chem.Phys.,2008,inpress.Numericalatomisticsimulat