1
Modélisa)onMul)-échelle:
Modélisa)ondesMacromoléculesbiologiques
Séance7(1H30)
CoursdeMasterM22016-2017
LaboratoireModélisa;onetSimula;onMul;-Echelle(MSME)
2
Résumédescours1à6
• Modélisa;on:Mo;va;on
• Visualisa;ondesprotéines(VMDTP1)
• Champsdeforces
• Protona;ondesprotéines(H++etVMDTP2)
• Algorithmesdeminimisa;on
• Algor;hmesdedynamiquemoléculaire(MD)
• Miseenplaced’uneMD(TP3)
• Analyse(TP4,5et6)
• MC
QM/MM• WhatisQM/MMandwhyusingit?• Substrac;veandaddi;vesschemes• Embeddingtechniques• Treatmentsoftheborders• So]wareapproaches.
WhatisQM/MMandwhyusingit?QM/MM:Quantumchemistry/molecularmechanics
TheNobelPrizeinChemistry2013wasawardedjointlytoMar;nKarplus,MichaelLeviaandAriehWarshel"forthedevelopmentofmul$scalemodelsforcomplexchemicalsystems".
WhatisQM/MMandwhyusingit?
2013Nobelprizeillustra;on:Mul;-copper-oxidaseembeddedinwater
WhatisQM/MMandwhyusingit?
Thekeypartsofalyzozymeenzymearecircled-onlytheseatomsrequirequantummechanicaldescrip)on(fromwww.nobelprize.org)
WhatisQM/MMandwhyusingit?
Warshelgroupsite:hap://laetro.usc.edu/MechanismofPhosphateMonoesterHydrolysisinAqueousSolu)on
WhatisQM/MMandwhyusingit?
Illustra;onofQM/MMinperiodicmaterial
WhatisQM/MMandwhyusingit?Wewanttostudyaphenomenaatthequantumlevel:
-op;miza;on(DFT)-transi;ons(TD-DFT)-dynamic-reac;vity-electronicormagne;cproprie;es(RMN,….)
Butweneedtotakeintoaccountthesurrounding:
-solvent-protein-zeolites-surface….
Andwanttoanalyzetheinfluenceofthesurroundingonthestudiedsystem.
WhatisQM/MM?
Reac;vesite:• Smallsize• Highaccuracy• Reac;vity:bondbreaking,electronictransi;ons,…
• UsingofQM:DFTorpost-HF
WhatisQM/MM?
Surrounding:• largesize• fairaccuracy• Expliciterepresenta;on• UsingofMMforcefield
WhatisQM/MM?
Interac;onsbetweenthe2parts:• Mechanicalconstraint• Electrosta;c• Dispersion
QM/MM: subtractive vs additive
Addi;vescheme:MMQMMMQMtot HHHH /
ˆˆˆˆ ++=
Subtrac;vescheme:exONIOM
Htot = HQMsmallSyst + HMM
TotalSyst − HMMsmallSyst"
#$
%
&'
Total energy = MM - +
QM MM
Total energy =
MM ++QM
interaction
20 )( ωωω −= kEimpr
∑ −=bonds
lbonds llkE 20 )(
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ijijLJijLJ r
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∑<
=ji ij
jielijelec rqqfE
ε
∑ ++=φ
φ γφdiedrals
ndiedrals n
VE )²]cos(1[
2,
∑ −=θθ θθ
anglesangles kE 2
0 )(
MM (ex AMBER ff) LJelecdiedimpranglesbondsMM EEEEEEE +++++=
parameters
Nonbondingterms
MM
QM/MMinterac;onsEnergetic contributions
ü Nuclei kinetic energy (B.O.) ü Electrons kinetic energy ü attraction electrons-nuclei ü Repulsion electrons-electrons ü Repulsion nuclei-nuclei ü Bonded terms (stretch, bending, torsion) ü Non-bonded terms (vdW, elect.)
Ø vdW MM atom-MM atom Ø electrostatic charges-charges Ø electrostatic interaction electrons-charges Ø electrostatic interaction nuclei-charges Ø vdW interactions QM atom-MM atom
QM/MMinterac;onsEnergetic contributions : QM
ü Nuclei kinetic energy (B.O.) ü Electrons kinetic energy ü attraction electrons-nuclei ü Repulsion electrons-electrons ü Repulsion nuclei-nuclei ü Bonded terms (stretch, bending, torsion) ü Non-bonded terms (vdW, elect.)
Ø vdW MM atom-MM atom Ø electrostatic charges-charges Ø electrostatic interaction electrons-charges Ø electrostatic interaction nuclei-charges Ø vdW interactions QM atom-MM atom
QM/MMinterac;onsEnergetic contributions : QM MM
ü Nuclei kinetic energy (B.O.) ü Electrons kinetic energy ü attraction electrons-nuclei ü Repulsion electrons-electrons ü Repulsion nuclei-nuclei ü Bonded terms (stretch, bending, torsion) ü Non-bonded terms (vdW, elect.)
Ø vdW MM atom-MM atom Ø electrostatic charges-charges Ø electrostatic interaction electrons-charges Ø electrostatic interaction nuclei-charges Ø vdW interactions QM atom-MM atom
QM/MMinterac;onsEnergetic contributions : QM MM QM/MM
ü Nuclei kinetic energy (B.O.) ü Electrons kinetic energy ü attraction electrons-nuclei ü Repulsion electrons-electrons ü Repulsion nuclei-nuclei ü Bonded terms (stretch, bending, torsion) ü Non-bonded terms (vdW, elect.)
Ø vdW MM atom-MM atom Ø electrostatic charges-charges Ø electrostatic interaction electrons-charges Ø electrostatic interaction nuclei-charges Ø vdW interactions QM atom-MM atom
QM/MMEmbedding
• ME:MechanicalEmbedding(VdW,bonds,angles,…)«stericinterac;ons»,geometricalconstrains.
• EE:Electrosta;cEmbedding(MMpointchargesinteractwithQMpar;cles)polariza;onoftheelectronicwavefunc;on,modified«Fock»operator
• PE:PolarizableEmbedding(mutualpolariza;onoftheQMandMMparts)
Mechanicalembedding
• CrudestlevelofQM/MM• IncludeonlyvanderWaalsinEQM/MM
• UsefultoimposeonlystericconstraintThisistakeintoaccountattheMMlevel:Sumonallthenuclei(QMsystandMmsyst)
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Op;miza;onwithQM/MM
• Aseriesofmicroitera;onscanbeemployedtofullyop;mizetheMMregionforeachop;miza;onstepintheQMregion.
• CartesiancoordinatesareusedfortheMMregionandarechosensothattheinternalcoordinatesoftheQMregionremainconstantduringthemicroitera;ons.
ThomVreven1,2,KeijiMorokuma1,ÖdönFarkas3,4,H.BernhardSchlegel4,*andMichaelJ.Frisch2JournalofComputa;onalChemistryVolume24,Issue6,pages760–769,30April2003
ME: subtractive vs additive
Addi;vescheme:MMQMMMQMtot HHHH /
ˆˆˆˆ ++=
Subtrac;vescheme:exONIOM
Htot = HQMsmallSyst + HMM
TotalSyst − HMMsmallSyst"
#$
%
&'
Total energy = MM - +
QM MM
Total energy =
MM ++QM
interaction ClassicalvdWterm
Electrosta;cembedding• Electrosta;cembeddingincorporatesthepar;alchargesoftheMM
regionintothequantummechanicalHamiltonian.• Thistechniqueprovidesabeaerdescrip;onoftheelectrosta;c
interac;onbetweentheQMandMMregions(asitistreatedattheQMlevel)andallowstheQMwavefunc;ontobepolarized.
• Inthecalcula;onoftheQMenergy,wenowadd: Ee−q = Ψ
qiriΨ
i
MMSyst
∑
QM
Electrosta;cembedding
Rm/Ex: ESPF: (Electrosta;cPoten;alFiaed)
Total energy =
MM +
QM N.FerréChemPhysLea2002,p331
MM MM
Eelec = fijel qi qj
ε riji< j∑ +
nuclei: j∈QMSyst∑ fij
el qi qjε riji∈MMSyst
∑
Inthecalcula;onforaddi;veschemeoftheMMenergy,wenowadd:
WhichCHARGEfortheQMpart?Mulliken,Hirshfeld,Bader(AIM),…
ME+EE: subtractive vs additive
Addi;vescheme:MMQMMMQMtot HHHH /
ˆˆˆˆ ++=
Subtrac;vescheme:exONIOM
Htot = HQMsmallSyst + HMM
TotalSyst − HMMsmallSyst"
#$
%
&'
Total energy = MM - +
QM MM
Total energy =
MM ++QM interaction
ClassicalvdWterm
PolarizableEmbedding• PE:PolarizableEmbedding(mutualpolariza;onoftheQMandMMparts)• Mostofthe;me,MMforcefieldsaredefinedtoreproducecondensed
phaseproper;es.TheMMchargesarealready(implicitely)polarized.That’sgoodenoughforgroundstateproper;es,exceptwhentheQMpartvariesdras;cally.
• Howcanwepolarizethesurroundings?
-polarizableforcefields(AMOEBA,SIBFA,…)- NewtermsintheHamiltonianduestotheinduceddipolesµ- Speciallyimportantwhendealingwithelectronictransi;on:responseof
thesurrounding.- ERS(ElectronicResponsesurrounding)(groupofXavierAssfeld,Nancy)
QM/MMborder:QM/MM,QM:MMorQM-MM?
Nomenclature:• QM:MMmeansnochemicalbondbetweenQMsystandMMsyst
• QM-MMmeansthereisachemicalbondtobecutbetweenQMsystandMMsyst
• QM/MMmeansanyofbothsitua;on
– SOHOWTODEALWITHQM-MM?
QM-MMjunc;ons
Whatshallwedowiththe2electronsoftheX-Ybond?
C2C1
Y
X
Q1Q2QM
MM
C2C1
Y
X
Q1Q2
. .
C2C1
Y
X
Q1Q2−
++
−C2C1
Y
X
Q1Q2
QM-MMjunc;ons
3maintypes:
-LinkAtom
-ConnexionAtom(Pseudo-bond,Connec;onAtom,CappingPoten;al,…)
-Frozendensity(LSCF,GHO,EFP)
• SaturatedanglingbondwithHatom:simple!
C2----C1----Y-----X-----Q1----Q2
C2----C1----Y-H----X-----Q1----Q2
LinkAtom
QMMM
-DoesHfeelsMMpointcharges?Yes!Otherwisethewavefunc;oncanbeinstable!
Ferré,OlivucciTHEOCHEM632(2003)71Problem:overpolariza;on(non-physical),duetonearbycharges
⇒progressivelycancelpointchargesinMMclosetotheQMpartBecareful:• thetotalelectricchargeshouldremainthesame.• theMMelectricchargeshouldbeinteger• Avoidcuwngbetween2heteroatoms
LinkAtom
-Howtocalculatethebond,angleanddihedralsintheMMpart:
LinkAtom
M.J.Field,P.A.Bash&M.KarplusJCompChem111990700
non-bonded
1-4
C2—C1—Y–H–X—Q1Q2—Q3
C2—C1—Y–H–X—Q1—Q2Q3
Problemwithbreakingbonds
Pseudo-bondZhangJChemPhys112(1999)3483AdjustedConnectionAtomsAntes,ThielJPhysChemA103(1999)9290QuantumCappingChris;ansenJChemPhys116(2002)9578Mar;nezJChemPhys124(2006)084107
Effec;fGroupPoten;al(EGP)
Poteauetal.JPhysChemA105(2001)293
Y(1or7electrons)
ParametrizedPseudopoten;el
Y
ConnexionatomNoextraatom!
Advantages:
-noextrageometricalparameters
-nooverpolariza;on
Problems:
Neednewparametersforeach:newatomtype,newbasisset,newQMmethod,newbondtype…
1994:Rivail"LocalSCF"(JCC1994)(semi-empiricallevel:-frozenhybridatomicorbitalonX)
QM MM
χX = a X s + (1- aX2 ) p
aX =cX,s2
cX,l2l=s,px,py,pz∑
C2C1
Y
X
Q1Q2
FrozenDensity:LSCFLocalself-consistentfield
- RequestthattheremainingatomicorbitalsonXbeorthogonaltothehybridorbital.- localtransforma;on(LSCF)- rota;ontobringpzalongtheX-Ybond- Hybridiza;on:mixingofsandpz- orthogonaliza;onoftheAOs(sandpz)ofX- Needforaspecificbondpoten;al(r0changed)- onlyparameters:aX,PXandr0.butgenerally,aX=0.5(sp3)andPX=1(covalent)
( )2021 rrk XYXY −
Frozendensity:GeneralizedHybridOrbital
Electronicpopula;onoftheaux.AOisafunc;onoftheMMpointchargeofYGao"GeneralizedHybridorbitalJPhysChem(1998)
-iden;caltoLSCFwith3HOonY
Frozendensity:LSCF:Localself-consistentfieldHypothesis:
-bondproper;esaretransferable
-eachcutbondisrepresentedbyafrozenSLBO(strictlylocalizedBondingOrbitals)
-SLBOobtainedon(small)modelmolecules
-Varia;onalMOshavetobeorthogonaltotheSLBO
QMMM MM
SLBO:LoosandAssfeld,JCTC,2007,1047
ME: subtractive vs additive
Addi;vescheme:MMQMMMQMtot HHHH /
ˆˆˆˆ ++=
Subtrac;vescheme:exONIOM
Htot = HQMsmallSyst + HMM
TotalSyst − HMMsmallSyst"
#$
%
&'
Total energy = MM - +
QM MM
Total energy =
MM ++QM interaction
ClassicalvdWterm
Difficul;es• ChoiceoftheQMmethod(DFT,Post-HF…)andMMmethod(forcefield)
• ChoiceoftheQMsystemssize:cuts?• ChoiceofthemovingpartoftheMMpart• Numberingorderinthefilescoordinatessystems:
– IntheQMprogram:QMatomnumerota;on– IntheMMprogram:MMatomnumerota;onTrytoputalwaysthesameorderofthexyzcoordfilesoftheQMatoms
• MMParametersfortheQMpart• Newparameters(charges)fortheMMpartiflinkatom
So]wareapproachesDifferentimplementa;ons:- Internal:so]warewithbothQMandtheMMintheso]ware.(ex:AMBERso]ware-QMMM)
- Oneso]warecalltheother:QMso]waremodifiedtocallMMso]wareorMMso]waremodifiedtocallQMso]ware
- Interfaceso]ware:Oneso]warethatcallbothMMso]wareandQMso]ware.
Biblio• Combined QM/MM calculations in Chemistry and Biochemistry Theochem, Special
Issue, 632 (2003) • Theoretical treatment of large molecular systems Theochem, Special Issue, 898
(2009)
• Gao J., Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials, Lipkowitz K.B; Boyd D.B., Eds.; Reviews in Computational Chemistry Vol. 7; VCH, 1996; 119-185
• P. Amara and M. Field Combined Quantum Mechanics and Molecular Mechanics Potentials, Encyclopedia of Computational Chemistry, Vol. 1, Ed. P.v.R. Schleyer, Wiley & sons, 1998, Pg 431-437
• M. F. Ruiz-López and J.L. Rivail, Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity., Encyclopedia of Computational Chemistry, Vol. 1, Ed. P.v.R. Schleyer, Wiley & sons, 1998, Pg 437-448
• G. Monard and K.M. Merz Jr. , Combined Quantum Mechanics and Molecular Mechanics Methodologies Applied toBiomolecular Systems, Acc. Chem. Res. 1999, 32, 904-911
TP
TutorielAMBERsurQMMM:hap://ambermd.org/tutorials/advanced/tutorial2/