1

Modélisa)onMul)-échelle:

Modélisa)ondesMacromoléculesbiologiques

Séance7(1H30)

CoursdeMasterM22016-2017

IsabelleNavizetIsabelle.navizet@u-pem.fr

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"

#$

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&'

Total energy = MM - +

QM MM

Total energy =

MM ++QM

interaction

20 )( ωωω −= kEimpr

∑ −=bonds

lbonds llkE 20 )(

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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"

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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"

#$

%

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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/