Molecular Mechanics Force Fields -...
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Molecular Mechanics Force Fields Basic Premise If we want to study a protein, piece of DNA, biological membranes, polysaccharide, crystal la;ce, nanomaterials, diffusion in liquids,… the number of electrons (i.e. the number of energy calculaAons) make quantum mechanical calcula-ons impossible even with present‐day computers. Instead, we replace the nuclei and electrons, and their interacAons, by new potenAal funcAons: ”Classical” atoms. Based on simple physical concepts Enables the systems under study to be VERY large (100,000 atoms).
Transcript of Molecular Mechanics Force Fields -...
MolecularMechanicsForceFields
BasicPremiseIfwewanttostudyaprotein,pieceofDNA,biologicalmembranes,polysaccharide,crystalla;ce,nanomaterials,diffusioninliquids,…thenumberofelectrons(i.e.thenumberofenergycalculaAons)makequantummechanicalcalcula-onsimpossibleevenwithpresent‐daycomputers.Instead,wereplacethenucleiandelectrons,andtheirinteracAons,bynewpotenAalfuncAons:”Classical”atoms.BasedonsimplephysicalconceptsEnablesthesystemsunderstudytobeVERYlarge(100,000atoms).
ThemolecularinteracAons,alsoknownasthepotenAals,togetherformaforcefield,Aforcefieldisamathema8caldescrip8onoftheclassicalforcesorenergiesbetweenpar8cles(atoms).Energy=func%onofatomicposi%ons(x,y,z)Theforcefieldequa%onconsistsofseveralfunc%onsthatdescribemolecularproper%esbothwithinandbetweenmoleculesTheforcefieldalsocontainsparameters(numbers)inthepotenAalfuncAonsthataretunedtoeachtypeofmolecule(protein,nucleicacid,carbohydrates)TherearemanydifferentforcefieldequaAonsandparametersetsAforcefieldmustbesimpleenoughthatitcanbeevaluatedquickly,butsufficientlydetailedthatitreproducesthekeyfeaturesofthephysicalsystembeingmodelled.
Molecularmechanicsforcefields
Ingeneral,forcefieldscanbeclassifiedaseither:Specific(manyparameters,limitedapplicability,highaccuracy)O>endevelopedinacademiclabsforstudyofspecificmolecularclassesorGeneric(fewerparameters,moregeneraliza-ons,wideapplicability,pooraccuracy)Easiesttouseinpoint‐andclickso>wareForceFieldParameterscancomefrom:Experimentalsources(mainlyfromx‐raydiffrac-on)orTheore-calcalcula-ons(mainlyfromQM)ManyforcefieldsemploysimilarmathemaAcalequaAonsbutdifferintheparametersusedintheequaAons.Itisthereforeextremelydangerousmixtoparametersbetweenforcefields.
Forcefieldclassifica8on
AMBER(AssistedModelBuildingwithEnergyRefinement).CHARMM(ChemistryatHARvardusingMolecularMechanics).GROMOS(GROenigenMolecularSimulaAon)OPLS(OpAmizedParametersforLarge‐scaleSimulaAons)
DifferentForceFields:
MMFF(theMerckMolecularForceField)DREIDINGGenericforcefieldduetoMayoetal.(1990)UNIVERSAL(UFF)GenericforcefieldduetoRappeetal.(1992)CVFF/PCFFForcefieldsforfluorinatedhydrocarbonsMM2,MM3,MM4DevelopedbyAllingeretal.forcalculaAonsonsmallmoleculesCOMPASSCommercialforcefieldmarketedbyAccelrysInc.
AMBER(AssistedModelBuildingwithEnergyRefinement).CHARMM(ChemistryatHARvardusingMolecularMechanics).GROMOS(GROenigenMolecularSimulaAon)OPLS(OpAmizedParametersforLarge‐scaleSimulaAons)
DifferentForceFields:
MMFF(theMerckMolecularForceField)DREIDINGGenericforcefieldduetoMayoetal.(1990)UNIVERSAL(UFF)GenericforcefieldduetoRappeetal.(1992)CVFF/PCFFForcefieldsforfluorinatedhydrocarbonsMM2,MM3,MM4DevelopedbyAllingeretal.forcalculaAonsonsmallmoleculesCOMPASSCommercialforcefieldmarketedbyAccelrysInc.
ThepotenAalfuncAonsmaybedividedintobondedterms,whichgivetheenergycontainedintheinternaldegreesoffreedom,andnon‐bondedterms,whichdescribeinterac8onsbetweenmolecules.
ForceFieldPoten8alFunc8ons
∑∑∑∑∑ ++++=atoms
ticselectrostaatoms
svanderWaaltorsionsanglesbonds
rpot VVVVVE τθ
Poten8alsbetweenbondedatoms Poten8alsbetweennon‐bondedatoms
Totalpoten8alEnergy,EpotorVtot
jiRij
jirij
ij
kθijk
jk
l i
τijkl
−
=
612
4ij
ij
ij
ijsvanderWaal RR
Vσσ
ε
( )20
21
ijijijk
angles kV θθθ −=
ij
jiticElectrosta R
qqV
πε4=
( )20
21
ijijijrbonds rrkV −=
( ))cos(121
τnkVn
ijklntorsions −= ∑
(JohnLennard‐Jones–1931)
(CharlesAugus-ndeCoulomb‐1785)
(RobertHooke‐1660)
(JeanBap-steJosephFourier–1822)
ForceFieldPoten8alEnergyFunc8ons
AlternaAvely,apower‐seriesexpansionoftheMorsepotenAalcanbeused
GraphicalcomparisonofMorseandpowerlawpotenAals
ProblemwithharmonicapproximaAon:
Bondscannotbreak(essenceofMolecularMechanics;nobondsarebrokenorformed,cannotbeusedforchemicalreacAons).
Thetorsionalenergyisdefinedbetweeneveryfourbondedatoms(1‐4interacAons),anddependsonthetorsion(akadihedral)angleϕmadebythetwoplanesincorporaAngthefirstandlastthreeatomsinvolvedinthetorsion
TorsionAngleorDihedralAngleEnergy
TorsiontermsaccountforanyinteracAonsbetween1‐4atompairsthatarenotalreadyaccountedforbynon‐bondedinteracAonsbetweentheseatomsForexample:theycouldbeusedtodescribebarrierstobondrotaAonfromelectrondelocalizaAon(doublebondsorparAaldoublebonds),orstereo‐electroniceffects
Usingthestandardcos3φpotenAal,therearethreeequilibriumposiAons:ϕ=180°(transstate)and±60°(gauchestates).InpracAce,theenergiesofthegauchestatesareslightlydifferentthanthatofthetransstate,dependingontheatomsinvolvedinthetorsion.
TorsionExample–TheSingleBond
TointroduceadifferencebetweenthestabiliAesofthegaucheandtransconformaAons,thetorsionfuncAoncanbeexpandedwithaddiAonalterms,eachwithit’suniquecontribuAontotherotaAonalenergy:
DifferenceinelectronegaAvitybetweenatomsgeneratesunequalchargedistribuAoninamoleculeOmenelectronegaAvitydifferencesarerepresentedasfracAonalpointcharges(q)withinthemolecule(normallycenteredatthenuclei(parAalatomiccharges)ElectrostaAcinteracAonenergyiscalculatedasasumofinteracAonsbetweenparAalatomiccharges,usingCoulombslawNaturally,thisequaAonisalsousedformodelinginteracAonsbetweenintegralcharges,suchasbetweenions
Electrosta8cs
ij
jiticElectrosta R
qqV
πε4=
TheproblemwiththisapproachisthatthereisnosuchthingasafracAonalelectron,thereforethereisnoperfectmethodtoderivetheparAalatomiccharges
Non‐bondedinteracAonthatarenotelectrostaAc(e.g.betweenatomsinnoblegas)arelabeledvanderWaalsinteracAonsContainsdispersionandshort‐rangecomponentsDispersioninteracAonsalwaysaoracAve.ArisefrominstantaneousdipolesthatoccurduringfluctuaAonswithinthemolecularelectroncloudShort‐rangeinteracAonsarealwaysunfavorable.Alsolabeledexchange,oroverlap,forces.Theyoccurbetweenelectronswiththesamespinsotheydonotoccupysameregioninspace(Pauliexclusionprinciple)
VanderWaalsInterac8ons
ElectrostaAcenergyisrepresentedusingasetofparAalatomicchargesvanderWaalsenergyhasbothweaklyaoracAveandstronglyrepulsivecomponentsandarisesfromrepresentselectroncorrelaAonThedispersiontermisalwaysnegaAvewhereasshort‐rangeenergyisalwaysrepulsive.TorsiontermsdescribebondrotaAonalproperAesthatarisefromnon‐classicaleffects,suchaselectrondelocalizaAonTheremainingbondandangletermsdescribecovalentbonding
SUMMARY–ForceFieldTerms
Oncewehaveourforcefield,whatcanwedowithit?–EnergyminimisaAon–MolecularDynamics–ConformaAonalanalysisTheaccuracyoftheoutputfromallthesetechniqueswillobviouslybesensi8vetoagreaterorlesserextentontheparameteriza8onoftheforcefield
