Molecular Mechanics Force Fields
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1 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).
2 Molecularmechanicsforcefields ThemolecularinteracAons,alsoknownasthepotenAals,togetherformaforcefield, Aforcefieldisamathema8caldescrip8onoftheclassicalforcesorenergies betweenpar8cles(atoms).energy=func%onofatomicposi%ons(x,y,z) Theforcefieldequa%onconsistsofseveralfunc%onsthatdescribemolecular proper%esbothwithinandbetweenmolecules Theforcefieldalsocontainsparameters(numbers)inthepotenAalfuncAonsthatare tunedtoeachtypeofmolecule(protein,nucleicacid,carbohydrates) TherearemanydifferentforcefieldequaAonsandparametersets Aforcefieldmustbesimpleenoughthatitcanbeevaluatedquickly,butsufficiently detailedthatitreproducesthekeyfeaturesofthephysicalsystembeingmodelled.
3 Forcefieldclassifica8on Ingeneral,forcefieldscanbeclassifiedaseither: Specific(manyparameters,limitedapplicability,highaccuracy) O>endevelopedinacademiclabsforstudyofspecificmolecularclasses or Generic(fewerparameters,moregeneraliza-ons,wideapplicability,pooraccuracy) Easiesttouseinpoint andclickso>ware ForceFieldParameterscancomefrom: Experimentalsources(mainlyfromx raydiffrac-on) or Theore-calcalcula-ons(mainlyfromQM) ManyforcefieldsemploysimilarmathemaAcalequaAonsbutdifferinthe parametersusedintheequaaons.itisthereforeextremelydangerousmixto parametersbetweenforcefields.
4 DifferentForceFields: AMBER(AssistedModelBuildingwithEnergyRefinement). CHARMM(ChemistryatHARvardusingMolecularMechanics). GROMOS(GROenigenMolecularSimulaAon) OPLS(OpAmizedParametersforLarge scalesimulaaons) MMFF(theMerckMolecularForceField) DREIDINGGenericforcefieldduetoMayoetal.(1990) UNIVERSAL(UFF)GenericforcefieldduetoRappeetal.(1992) CVFF/PCFFForcefieldsforfluorinatedhydrocarbons MM2,MM3,MM4DevelopedbyAllingeretal.forcalculaAonsonsmallmolecules COMPASSCommercialforcefieldmarketedbyAccelrysInc.
5 DifferentForceFields: AMBER(AssistedModelBuildingwithEnergyRefinement). CHARMM(ChemistryatHARvardusingMolecularMechanics). GROMOS(GROenigenMolecularSimulaAon) OPLS(OpAmizedParametersforLarge scalesimulaaons) MMFF(theMerckMolecularForceField) DREIDINGGenericforcefieldduetoMayoetal.(1990) UNIVERSAL(UFF)GenericforcefieldduetoRappeetal.(1992) CVFF/PCFFForcefieldsforfluorinatedhydrocarbons MM2,MM3,MM4DevelopedbyAllingeretal.forcalculaAonsonsmallmolecules COMPASSCommercialforcefieldmarketedbyAccelrysInc.
6 ForceFieldPoten8alFunc8ons ThepotenAalfuncAonsmaybedividedintobondedterms,whichgivetheenergy containedintheinternaldegreesoffreedom,andnon bondedterms,which describeinterac8onsbetweenmolecules. E pot = V r Vθ Vτ VvanderWaals + bonds angles torsions atoms atoms V electrostatics Poten8alsbetweenbondedatoms Poten8alsbetweennon bondedatoms Totalpoten8alEnergy,E pot orv tot
7 ForceFieldPoten8alEnergyFunc8ons i R ij j V V vanderwaals Electrostatic σ ij = 4ε Rij qiq j = 4πεR ij 12 σ ij Rij 6 (JohnLennard Jones 1931) (CharlesAugus-ndeCoulomb 1785) i r ij j V bonds = 1 2 k ij r 0 ( r r ) 2 ij ij (RobertHooke 1660) k j k j θ ijk i V angles = 1 2 k ijk θ 0 ( θ θ ) 2 ij ij V torsions τ ijkl l i 1 = 2 n k ijkl n ( 1 cos( nτ )) (JeanBap-steJosephFourier 1822)
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10 AlternaAvely,apower seriesexpansionofthemorsepotenaalcanbeused GraphicalcomparisonofMorseandpowerlawpotenAals ProblemwithharmonicapproximaAon: Bondscannotbreak(essenceofMolecularMechanics;nobondsarebrokenorformed, cannotbeusedforchemicalreacaons).
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14 TorsionAngleorDihedralAngleEnergy Thetorsionalenergyisdefinedbetweeneveryfourbondedatoms(1 4interacAons), anddependsonthetorsion(akadihedral)angleϕmadebythetwoplanes incorporaangthefirstandlastthreeatomsinvolvedinthetorsion TorsiontermsaccountforanyinteracAonsbetween1 4atompairsthatarenotalready accountedforbynon bondedinteracaonsbetweentheseatoms Forexample:theycouldbeusedtodescribebarrierstobondrotaAonfromelectron delocalizaaon(doublebondsorparaaldoublebonds),orstereo electroniceffects
15 TorsionExample TheSingleBond Usingthestandardcos3φpotenAal,therearethreeequilibriumposiAons:ϕ=180 (transstate)and±60 (gauchestates). InpracAce,theenergiesofthegauchestatesareslightlydifferentthanthatofthe transstate,dependingontheatomsinvolvedinthetorsion.
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18 TointroduceadifferencebetweenthestabiliAesofthe gaucheandtransconformaaons,thetorsionfuncaoncanbe expandedwithaddiaonalterms,eachwithit sunique contribuaontotherotaaonalenergy:
19 Electrosta8cs DifferenceinelectronegaAvitybetweenatomsgeneratesunequalcharge distribuaoninamolecule OmenelectronegaAvitydifferencesarerepresentedasfracAonalpointcharges(q) withinthemolecule(normallycenteredatthenuclei(paraalatomiccharges) ElectrostaAcinteracAonenergyiscalculatedasasumofinteracAonsbetween paraalatomiccharges,usingcoulombslaw Naturally,thisequaAonisalsousedformodelinginteracAonsbetweenintegral charges,suchasbetweenions V Electrostatic = q q i j 4πεR TheproblemwiththisapproachisthatthereisnosuchthingasafracAonalelectron, thereforethereisnoperfectmethodtoderivetheparaalatomiccharges ij
20 VanderWaalsInterac8ons Non bondedinteracaonthatarenotelectrostaac(e.g.betweenatomsinnoble gas)arelabeledvanderwaalsinteracaons Containsdispersionandshort rangecomponents DispersioninteracAonsalwaysaoracAve.Arisefrominstantaneousdipolesthat occurduringfluctuaaonswithinthemolecularelectroncloud Short rangeinteracaonsarealwaysunfavorable.alsolabeledexchange,or overlap,forces.theyoccurbetweenelectronswiththesamespinsotheydonot occupysameregioninspace(pauliexclusionprinciple)
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23 SUMMARY ForceFieldTerms ElectrostaAcenergyisrepresentedusingasetofparAalatomiccharges vanderwaalsenergyhasbothweaklyaoracaveandstronglyrepulsivecomponentsand arisesfromrepresentselectroncorrelaaon ThedispersiontermisalwaysnegaAvewhereasshort rangeenergyisalwaysrepulsive. TorsiontermsdescribebondrotaAonalproperAesthatarisefromnon classicaleffects, suchaselectrondelocalizaaon Theremainingbondandangletermsdescribecovalentbonding Oncewehaveourforcefield,whatcanwedowithit? EnergyminimisaAon MolecularDynamics ConformaAonalanalysis Theaccuracyoftheoutputfromallthesetechniqueswillobviouslybesensi8vetoa greaterorlesserextentontheparameteriza8onoftheforcefield
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