第四章 分子力學(xué)簡(jiǎn)介 Introduction to Molecular Mechanics課件

第四章分子力學(xué)簡(jiǎn)介

IntroductiontoMolecularMechanics

1第四章分子力學(xué)簡(jiǎn)介

IntroductiontoM分子力學(xué)，MolecularMechanics,MM計(jì)算速度快，幾何構(gòu)型，能量，振動(dòng)光譜，應(yīng)用于生物大分子和藥物分子。經(jīng)驗(yàn)方法依賴于大量的實(shí)驗(yàn)參數(shù)不適用于過渡態(tài)力場(chǎng)方法（ForceField)：將能量寫為核坐標(biāo)的參數(shù)函數(shù)。用“球”和“彈簧”描述分子體系。2分子力學(xué)，MolecularMechanics,MM計(jì)算分子力學(xué)主要應(yīng)用分子力場(chǎng)方法計(jì)算分子的勢(shì)能，分子力學(xué)使用解析經(jīng)驗(yàn)勢(shì)能函數(shù)來描述分子的勢(shì)能面。每個(gè)分子都有固定的力場(chǎng)。在分子力學(xué)實(shí)際計(jì)算時(shí)，將力場(chǎng)分解成不同的組分，使用理論計(jì)算和實(shí)驗(yàn)擬合的方法建立力場(chǎng)參數(shù)。力場(chǎng)參數(shù)要有可移植性，它要適應(yīng)于同類分子的計(jì)算，即同一類分子也要有很高的計(jì)算精度。由于分子力學(xué)是經(jīng)驗(yàn)的計(jì)算方法，不同的分子力學(xué)方法采用不同的勢(shì)能函數(shù)表達(dá)式，而且力場(chǎng)參數(shù)值也不相同。通常將分子的勢(shì)函數(shù)分解成鍵伸縮能Estretch、角彎曲能Ebend、二面角扭曲能Etorsion、范德華作用能EVdW和靜電作用能Eelectrostatic等項(xiàng)，總能量可以表示為：

StericEnergy=Estretch+Ebend+Etorsion+EVdW+Eelectrostatic分子力學(xué)的基本原理3分子力學(xué)主要應(yīng)用分子力場(chǎng)方法計(jì)算分子的勢(shì)能，分子力學(xué)使用解析其中與化學(xué)鍵有關(guān)的有：鍵伸縮能Estretch、角彎曲能Ebend、二面角扭曲能Etorsion，與化學(xué)鍵無關(guān)的有范德華作用能EVdW和氫鍵以及靜電作用能Eelectrostatic。對(duì)于更精確的力場(chǎng)，可以在勢(shì)函數(shù)表達(dá)式中增加一些交叉項(xiàng)，如鍵伸縮-鍵彎曲振動(dòng)交叉項(xiàng)、二面角扭曲-鍵伸縮交叉項(xiàng)等，也可以加入氫鍵函數(shù)項(xiàng)等其他修正項(xiàng)。4其中與化學(xué)鍵有關(guān)的有：鍵伸縮能Estretch、角彎曲能E分子力學(xué)是模擬分子行為的一種計(jì)算方法。分子力學(xué)認(rèn)為分子體系的勢(shì)能函數(shù)時(shí)分子體系中原子位置的函數(shù)。分子力學(xué)將分子體系作為在勢(shì)能面上運(yùn)動(dòng)的力學(xué)體系來處理，求解的是經(jīng)典力學(xué)方程，而不是量子力學(xué)的薛定諤方程。所以分子力學(xué)方法可以求得分子的平衡結(jié)構(gòu)和熱力學(xué)性質(zhì)等，但不能得到分子體系與電子結(jié)構(gòu)有關(guān)的其它性質(zhì)。分子力學(xué)的勢(shì)能函數(shù)表達(dá)方程很簡(jiǎn)單，其計(jì)算速度很快（約是半經(jīng)驗(yàn)量子化學(xué)計(jì)算方法速度的1000倍），能夠用于生物大分子體系的計(jì)算。對(duì)于力場(chǎng)參數(shù)成熟的分子力學(xué)方法，已經(jīng)可以達(dá)到很高的計(jì)算精度。5分子力學(xué)是模擬分子行為的一種計(jì)算方法。分子力學(xué)認(rèn)為分子體系的ASimpleMolecularMechanicsForceFieldTorsions

H-C-C-Hx12 H-C-C-Cx6Non-bonded

H-Hx21 H-Cx6Bonds

C-Cx2 C-Hx8Angles

C-C-Cx1 C-C-Hx10 H-C-Hx76ASimpleMolecularMechanics基本概念

HarmonicPotentialFunctionxenergyEnergy(能量)

EnergyasafunctionofacoordinateX. EnergypenaltyfordistortingXfromitsequilibriumposition. StericEnergy=a+k(X-X0)2(Hook'slaw).Parameterization(參數(shù)化)

Matchingafunctiontoasetofdatapointsbyvaryingitsparameters(aandk).Minimization(最小化)

Findingtheminimumofapotentialfunction.

7基本概念HarmonicPotentialFunctiStericEnergyThedifferencebetweentheactualenergyofthesystemandtheenergyofahypotheticalsystemwhereallstructuralparametersareattheirequilibrium(minimumenergy)values.StericEnergy=Estretch+

Ebend+Etorsion+

EVdW+

Eelectrostatic+

Estretch-bend+Etorsion-stretch+…Estretch

Stretchenergy(overallbonds)Ebend

Bendingenergy(overallangles)Etorsion

Torsional(dihedral)energy(overalldihedralangles)EVdW

VanDerWaalsenergy(overallatompairs>1,3)Eelectrostatic

Electrostaticenergy(overallchargedatompairs>1,3)Estretch-bend

StretchbendenergyEtorsion-stretch

Torsionstretchenergy(EVdW+Eelectrostaticareoftenreferredtoasnon-bondedenergies)8StericEnergyThedifferencebe鍵伸縮能根據(jù)經(jīng)典力學(xué)的胡克定律，兩個(gè)成鍵原子可以視為有一根彈簧連接的兩個(gè)小球，其勢(shì)函數(shù)是簡(jiǎn)諧振動(dòng)勢(shì)函數(shù)，其計(jì)算非常方便，非常實(shí)用于生物大分子的計(jì)算。kb鍵伸縮常數(shù)，r0平衡鍵長(zhǎng)StretchingEnergy9鍵伸縮能根據(jù)經(jīng)典力學(xué)的胡克定律，兩個(gè)成鍵原子可以視為有一根彈

StretchingEnergy10StretchingEnergy10BondStretchingHarmonicpotential(AMBER)rE20)(2)(llklv-=11BondStretchingHarmonicpotentBondStretchingCubic(MM2)andquadratic(MM3)potentialsharmoniccubicquadratic3020)(22)(21)(llkllklv---=403020)(23)(22)(21)(llkllkllklv-+---=12BondStretchingCubic(MM2)andBondStretchingParameters(MM2)13BondStretchingParameters(MM角彎曲能BendingEnergy

兩個(gè)相連的化學(xué)鍵（三個(gè)成鍵原子）具有一定的鍵角，鍵角彎曲勢(shì)能函數(shù)與鍵伸縮勢(shì)函數(shù)類似，可用虎克定律描述。鍵彎曲能常數(shù)，實(shí)際鍵角和平均鍵角。14角彎曲能BendingEnergy

兩個(gè)相連的化學(xué)鍵（三1515energyangleAngleBendingMM3MM2AMBERAMBER:MM2:MM3:16energyangleAngleBendingMM3MM2AngleBendingParameters(MM2)17AngleBendingParameters(MM2)TorsionEnergy（二面角扭曲轉(zhuǎn)動(dòng)能）

三個(gè)相連的化學(xué)鍵（四個(gè)成鍵原子）具有一定的二面角（扭角）。頭尾兩個(gè)成鍵原子繞中間化學(xué)鍵旋轉(zhuǎn)時(shí)，需要一定的能量，存在明顯的旋轉(zhuǎn)勢(shì)壘，在分子力學(xué)中，二面角扭曲轉(zhuǎn)動(dòng)勢(shì)函數(shù)常用傅立葉級(jí)數(shù)模擬。18TorsionEnergy（二面角扭曲轉(zhuǎn)動(dòng)能）三個(gè)相連的1919FunctionalFormw:

Torsionalangle.n(multiplicity):

Numberofminimaina360ocycle.Vn:

Correlateswiththebarrierheight.g(phasefactor):

Determineswherethetorsionpassesthroughitsminimumvalue.Vn=4,n=2,g=180Vn=2,n=3,g=020FunctionalFormw:TorsionalanFunctionalForm:AMBER21FunctionalForm:AMBER21FunctionalForm:MM2,MM3V3:

Stericinteractionsbetween1,4atoms(minimumat60o,180oand300owhereatomsarestaggeredandmaximumat0o,120oand240owhereatomsaresyn).V1:

Bonddipoleinteractions(minimumat180owheredipolesaretransandmaximumat0owheredipolesarecis).V2:

1-2and3-4bondsorbitalinteractions(minimumat0oand180owhereorbitalsoverlapandmaximumat90o

wheretheyareorthogonal).22FunctionalForm:MM2,MM3V3:SExample:ButaneType V1V2V3C-C-C–C0.2000.2700.093C-C-C–H0.0000.0000.267H-C-C–H0.0000.0000.237ThebarriertorotationaroundtheC-Cbondinbutaneis~20kJ/mol.All9torsionalinteractionsaroundthecentralC-Cbondshouldbeconsideredforanappropriatereproductiononthetorsionalbarrier.23Example:ButaneType V1Non-BondedEnergy

非鍵相互作用能非鍵相互作用能主要包括范德華相互作用能和靜電相互作用能。24Non-BondedEnergy

非鍵相互作用能非鍵相互作VanDerWaals(VdW)Interactions范德華相互作用能范德華相互作用能是分子力學(xué)中重要的作用，它可分為進(jìn)程作用的排斥力和遠(yuǎn)程的吸引力，一般以Lennard-Jones公式來模擬范德華非鍵相互作用分子力場(chǎng)。其中r表示原子之間的距離，A和B是非鍵原子對(duì)的范德華常數(shù)。R的六次方為原子對(duì)的吸引作用，R的12次方位排斥作用。25VanDerWaals(VdW)InteractioHydrogenBondingH-bondgeometryindependent:risthedistancebetweentheH-bonddonorandH-bondacceptor.H-bondgeometrydependent:NHOCDonAccqw26HydrogenBondingH-bondgeometrPointChargeElectrostaticModelsqi,qjarepointcharges.Charge-chargeinteractionsarelongranged(decayasr-1).Whenenoughpointchargesareusedalltheelectricmomentscanbereproduced.Whenqi,qjarecenteronthenucleitheyarereferredtoas

partialatomiccharges.Partialatomiccharges

Fittothermodynamicproperties.

AbinitioCalculations(6-31G*,MNDO). Mullikencharge.

Reflectmolecularconstitutionratherthanmolecular

interactions. Electrostaticpotential.27PointChargeElectrostaticMod分子力學(xué)總能量并沒有嚴(yán)格的物理意義，為了獲得精確的計(jì)算結(jié)果，分子力場(chǎng)的能量函數(shù)表達(dá)式的復(fù)雜程度沒有限制。根據(jù)適用范圍不同，目前已發(fā)展了很多的分子力場(chǎng)，分子力學(xué)方法根據(jù)適用范圍可分為小分子和大分子兩類。適用于小分子的分子力學(xué)的函數(shù)形式較復(fù)雜和精確。例如MM2/MM3/MM4TINKERUFFMOMECCOSMOS等。適用于大分子的分子力學(xué)函數(shù)形式較簡(jiǎn)單，例如：AMBERCHARMMGROMOSOPLSCVFFCFFMMFF等。28分子力學(xué)總能量并沒有嚴(yán)格的物理意義，為了獲得精確的計(jì)算結(jié)果，分子力場(chǎng)的參數(shù)化分子力學(xué)計(jì)算結(jié)果的精確性除了與力場(chǎng)勢(shì)函數(shù)表達(dá)式有關(guān)外，還與力場(chǎng)參數(shù)的數(shù)值密切相關(guān)。有效的力場(chǎng)勢(shì)函數(shù)和正確的力場(chǎng)函數(shù)可使分子力學(xué)計(jì)算達(dá)到很高的精度，有些分子力學(xué)方法對(duì)分子的性質(zhì)計(jì)算結(jié)果非常好，可以達(dá)到實(shí)驗(yàn)值的精度。由于不同的分子力學(xué)方法所用的勢(shì)函數(shù)表達(dá)方式不同，其力場(chǎng)參數(shù)不能相互代替。由于化合物的原子類型很多，目前分子力場(chǎng)不可能適用于各種的原子類型，滿足各種化合物計(jì)算的要求。在缺乏力場(chǎng)參數(shù)時(shí)，就需要進(jìn)行分子力場(chǎng)參數(shù)的優(yōu)化。29分子力場(chǎng)的參數(shù)化分子力學(xué)計(jì)算結(jié)果的精確性除了與力場(chǎng)勢(shì)函數(shù)表達(dá)分子力學(xué)勢(shì)函數(shù)是由一系列的可調(diào)參數(shù)組成的。對(duì)可調(diào)參數(shù)進(jìn)行優(yōu)化，是分子力學(xué)的計(jì)算值最符合分子的某些性質(zhì)的實(shí)驗(yàn)數(shù)值，得到一套力場(chǎng)的優(yōu)化參數(shù)，再使用這套參數(shù)去預(yù)測(cè)相同原子類型的其它分子的結(jié)構(gòu)和性質(zhì)。傳統(tǒng)的分子力場(chǎng)參數(shù)化方法是通過擬合實(shí)驗(yàn)數(shù)據(jù)（幾何構(gòu)型、構(gòu)象能、生成熱、光譜數(shù)據(jù)等）來優(yōu)化參數(shù)。分子的幾何結(jié)構(gòu)和力場(chǎng)參數(shù)可由實(shí)驗(yàn)或量子化學(xué)計(jì)算獲得。鍵伸縮振動(dòng)常數(shù)可直接由價(jià)鍵力場(chǎng)計(jì)算或振動(dòng)光譜獲得。平衡鍵長(zhǎng)、平衡鍵角和角彎曲常數(shù)可由X射線衍射、中子衍射、電子衍射等方法測(cè)定，也可由量子化學(xué)計(jì)算得到。扭轉(zhuǎn)位能參數(shù)來自于NMR譜帶和弛豫時(shí)間。構(gòu)象能可從光譜和熱化學(xué)數(shù)據(jù)得到。非鍵參數(shù)可從晶格參數(shù)和液體的物理性質(zhì)數(shù)據(jù)得到。分子力場(chǎng)的參數(shù)化30分子力學(xué)勢(shì)函數(shù)是由一系列的可調(diào)參數(shù)組成的。對(duì)可調(diào)參數(shù)進(jìn)行優(yōu)化優(yōu)化力場(chǎng)參數(shù)時(shí)，首先要選擇某些代表性化合物，根據(jù)其原子和成鍵化學(xué)環(huán)境不斷修正力場(chǎng)參數(shù)，使得力場(chǎng)參數(shù)的計(jì)算結(jié)果與真實(shí)分子的結(jié)構(gòu)、能量和分子的振動(dòng)光譜一致，接著進(jìn)行同類型化合物分子的計(jì)算，驗(yàn)證這套參數(shù)的可靠性。力場(chǎng)參數(shù)的優(yōu)化可使用最小二乘擬合法和嘗試法。分子力場(chǎng)的參數(shù)化31優(yōu)化力場(chǎng)參數(shù)時(shí)，首先要選擇某些代表性化合物，根據(jù)其原子和成鍵ParameterizationChoosingvaluesfortheparametersinthepotentialfunctionequationstobestreproduceexperimentaldata.Parameterizationtechniques

Trialanderror Leastsquaremethods(CFF)Typesofparameters

Stretch:naturalbondlength(l0)andforceconstants. Bend:naturalbondangles(q0)andforceconstants. Torsions:Vi’s. VdW:(e,VdWradii). Electrostatic:Partialatomiccharges. Cross-terms:Crosstermparameters.32ParameterizationChoosingvalueParameters-QuantityForNatomtypesrequire:

Nnon-bondedparameters N*Nstretchparameters N*N*Nbendparameters N*N*N*NtorsionparametersExample

MacroModelMM2*:39atomtypesRequiredActualStretchBendTorsion152158,3192,313,44116435750833Parameters-QuantityForNatoParameters-SourceExperiment:geometriesandnon-bondedparameters

X-Raycrystallography Electrondiffraction Microwavespectroscopy

LatticeenergiesAdvantages

RealDisadvantages

Hardtoobtain Non-uniform LimitedavailabilityAforcefieldparameterizedaccordingtodatafromonesource(e.g.,experimentalgasphase,experimentalsolidphase,abinitio)willfitonlyqualitativelydatafromothersources.34Parameters-SourceExperiment:Parameters-Source

Highlevelmolecularorbitalcalculations

Conformationalpreferencesandpartialcharges(HF/6-31G*).

Correctionsforelectroncorrelationeffectsareoften important:MP2,MP3etc.

Chargesobtainedbyfittingelectrostaticpotentials.Advantages

Relativelyeasytoobtain. Uniform. Unlimitedavailability. Completepotentialenergysurfacesareavailable.Disadvantages

“Unreal”. Modeldependent. Computationallyexpensive.35Parameters-SourceHighlevelConstructgraphicalrepresentationofmoleculetobemodeled(“frontend”)Selectforcefieldmethodandterminationcondition(gradient,#cycles,ortime)PerformgeometryoptimizationExamineoutputgeometry...isitreasonable?Searchforglobalminimum.StepsinPerformingMolecularMechanicsCalculations36ConstructgraphicalrepresentaInputisusuallydonegraphically(bysketchingorbuildingstructuresatom-by-atomorbyassemblingcomponentparts).Thisgraphicalmodelisconvertedtoamathematicalmodelbythesoftware.Eachsoftwarepackagehasitsownfiletype,butmosthavesomecommonfeatures.InputFileStructure37Inputisusuallydonegraphica

C1-1.1291.281-0.000 C2-2.5581.772-0.000 C3-3.5190.606-0.000

H4-0.5961.6370.890

H5-0.5961.637-0.890

H6-2.7332.3920.890

H7-2.7332.392-0.890

H8-4.5580.9520.000

H9-3.359-0.017-0.890

H10-3.359-0.0170.890

H11-1.1100.183-0.000(thisMAYbethesameasthe.PDBfile,asshownhere,ortheorientationofthemoleculemaybedifferent,makingthenumbersdifferent)Cartesiancoordinate(XYZ)file38 C1-1.1291.2

distance

angle

dihedralconnectivityN0.000000.000000.00000000H1.020010.000000.00000100H1.02001104.536810.00000120H1.02001104.53681109.579611230(endoffile) (1meansoptimize,0meanskeepconstant,-1meansvaryaccordingtoadesignatedpattern)(sometimescalledZ-matrix)InternalCoordinates(forNH3)39 distance angle LocalminimumvsglobalminimumManylocalminima;onlyONEglobalminimumMethods:Newton-Raphson(blockdiagonal),steepestdescent,conjugategradient,others.globalminimumlocalminimaEnergyMinimization40Localminimumvsglobalminimu“Stericenergy”hasNOphysicalmeaning,anditisdefineddifferentlyindifferentprogramsThereforeitCANNOTbeusedtocomparestructurescalculatedbydifferentprogramsItsuseislimitedtocomparingISOMERICstructureshavingtheSAMEnumberandkindsofbonds(conformers,stereoisomers).Usesof“StericEnergy”41“Stericenergy”hasNOphysicaCalculationsareveryfastGeometryoptimizationsofsmalltomedium-sizemoleculescanbeaccomplishedonapcConformationsofmacromolecules(includingbiomacromoleculessuchaspeptidesandpolysaccharides)canbecalculatedusingworkstationsorparallelprocessingcomputers.SuccessesofMolecularMechanicsCalculations42CalculationsareveryfastSuccReasonablegeometriesareusuallyobtained:Bondlengthswithin0.1AngstromofexperimentalvaluesBondangleswithin2°ofexperimentalvalues.Calculatedenergiesareusuallyquitegood:Enthalpiesofformationwithin2kcal/mol(8kJ/mol)ofexperimentalvaluesProvidesinputstructureformoreinvolvedcalculations(molecularorbitalmethods).SuccessesofMolecularMechanicsCalculations43ReasonablegeometriesareusuaThecalculationsdonotaccountforelectrons!Orbitalinteractionsareignored!Theselectionof“atomtype”iscrucialtothecomputationalresult:e.g.,AMBERhas5typesofOxygen:carbonyl,alcohol,acid,ester/ether,water(seenextslide)NoconsiderationisgiventotheimportanceofdelocalizedpelectronsystemsOnlygroundstatesconsidered...notT.S.or*LimitationsofMolecularMechanics44ThecalculationsdonotaccounObtainingareasonablygoodgeometry(instructureswherepielectronsarenotinvolved.Asastartingpointforfurthercalculations,suchassemi-empirical,abinitio,ordensityfunctional.Searchingtheenergysurfaceforminimumenergyconformations(itisusuallytooexpensivetodothisusingMOmethods).UsesofMolecularMechanics45ObtainingareasonablygoodgeOptimizedgeometry(minimumenergyconformation)Equilibriumbondlengths,bondangles,anddihedral(torsional)anglesDipolemoment(vectorsumofbonddipoles)EnthalpyofFormation(insomeprograms).PropertiesCalculated46Optimizedgeometry(minimumenEqualto“stericenergy”plussumofgroupenthalpyvalues(CH2,CH3,C=O,etc.),withafewcorrectiontermsNotcalculatedbyallmolecularmechanicsprograms(e.g.,HyperChemandTitan)Calculatedvaluesaregenerallyquiteclosetoexperimentalvaluesforcommonclassesoforganiccompounds.EnthalpyofFormation47Equalto“stericenergy”plusEnthalpyofFormation...48EnthalpyofFormation...48EnthalpyofFormation...49EnthalpyofFormation...49

Sybyl

MM+ MM3

ExptCH3CH3 C-C 1.554 1.532 1.5311.526 C-H 1.095 1.115 1.1131.109CH3COCH3 C-C 1.518 1.517 1.516 1.522 C-H 1.107 1.114 1.1111.110 C=O 1.223 1.210 1.2111.222BondLengths50 Sybyl MM+ MM3Exp

Sybyl MM+ MM3CH3CH3 H-C-C 109.5 111.0 111.4 H-C-H 109.4 107.9 107.5CH3COCH3 C-C-C 116.9 116.6 116.1 H-C-H 109.1 108.3 107.9 C-C-O 121.5 121.7 122.0BondAngles51 Sybyl MM+ MM3BondAnglesMM2/MM3

(Allinger)best;generalpurposeMMX(Gilbert)addedTS’s,otherelements;goodMM+

(Ostlund)inHyperChem;general;goodOPLS

(Jorgenson)proteinsandnucleicacidsAMBER(Kollman)proteinsandnucleicacids+BIO+

(Karplus)CHARMm;nucleicacidsMMFF(MerckPharm.)general;newer;goodCommonForceFields52MM2/MM3(Allinger)best;HyperChem

(MM+,OPLS,AMBER,BIO+)Spartan

(MM3,MMFF,Sybyl;onSGIorviax-windowsfrompc)Alchemy2000

(Sybyl)MolecularModelingPrograms53HyperChem(MM+,OPLS,AMBER,B1 C sp3carbon2 C sp2carbon(C=C)3 C sp2carbon(C=O)4 C spcarbon5 H hydrogen(seeothers)6 O oxygen(singlebonded)7 O oxygen(doublebonded)8 N sp3nitrogen9 N sp2nitrogen10 N sp

nitrogen11 F fluorine12 Cl chlorine13 Br bromine14 I iodine15 S sulfide(-S-)16 S+ sulfonium17 S sulfoxide(useS=O)18 S sulfone(usetwoS=O)19Si silane20 LP lonepairofelectrons21 H hydroxylhydrogen22 C cyclopropanecarbon23 H aminehydrogen24 H carboxylicacidhydrogenMM2AtomTypes(morethan60!)541 C sp3carbon13 Br bromineMM2第四章分子力學(xué)簡(jiǎn)介

IntroductiontoMolecularMechanics

55第四章分子力學(xué)簡(jiǎn)介

IntroductiontoM分子力學(xué)，MolecularMechanics,MM計(jì)算速度快，幾何構(gòu)型，能量，振動(dòng)光譜，應(yīng)用于生物大分子和藥物分子。經(jīng)驗(yàn)方法依賴于大量的實(shí)驗(yàn)參數(shù)不適用于過渡態(tài)力場(chǎng)方法（ForceField)：將能量寫為核坐標(biāo)的參數(shù)函數(shù)。用“球”和“彈簧”描述分子體系。56分子力學(xué)，MolecularMechanics,MM計(jì)算分子力學(xué)主要應(yīng)用分子力場(chǎng)方法計(jì)算分子的勢(shì)能，分子力學(xué)使用解析經(jīng)驗(yàn)勢(shì)能函數(shù)來描述分子的勢(shì)能面。每個(gè)分子都有固定的力場(chǎng)。在分子力學(xué)實(shí)際計(jì)算時(shí)，將力場(chǎng)分解成不同的組分，使用理論計(jì)算和實(shí)驗(yàn)擬合的方法建立力場(chǎng)參數(shù)。力場(chǎng)參數(shù)要有可移植性，它要適應(yīng)于同類分子的計(jì)算，即同一類分子也要有很高的計(jì)算精度。由于分子力學(xué)是經(jīng)驗(yàn)的計(jì)算方法，不同的分子力學(xué)方法采用不同的勢(shì)能函數(shù)表達(dá)式，而且力場(chǎng)參數(shù)值也不相同。通常將分子的勢(shì)函數(shù)分解成鍵伸縮能Estretch、角彎曲能Ebend、二面角扭曲能Etorsion、范德華作用能EVdW和靜電作用能Eelectrostatic等項(xiàng)，總能量可以表示為：

StericEnergy=Estretch+Ebend+Etorsion+EVdW+Eelectrostatic分子力學(xué)的基本原理57分子力學(xué)主要應(yīng)用分子力場(chǎng)方法計(jì)算分子的勢(shì)能，分子力學(xué)使用解析其中與化學(xué)鍵有關(guān)的有：鍵伸縮能Estretch、角彎曲能Ebend、二面角扭曲能Etorsion，與化學(xué)鍵無關(guān)的有范德華作用能EVdW和氫鍵以及靜電作用能Eelectrostatic。對(duì)于更精確的力場(chǎng)，可以在勢(shì)函數(shù)表達(dá)式中增加一些交叉項(xiàng)，如鍵伸縮-鍵彎曲振動(dòng)交叉項(xiàng)、二面角扭曲-鍵伸縮交叉項(xiàng)等，也可以加入氫鍵函數(shù)項(xiàng)等其他修正項(xiàng)。58其中與化學(xué)鍵有關(guān)的有：鍵伸縮能Estretch、角彎曲能E分子力學(xué)是模擬分子行為的一種計(jì)算方法。分子力學(xué)認(rèn)為分子體系的勢(shì)能函數(shù)時(shí)分子體系中原子位置的函數(shù)。分子力學(xué)將分子體系作為在勢(shì)能面上運(yùn)動(dòng)的力學(xué)體系來處理，求解的是經(jīng)典力學(xué)方程，而不是量子力學(xué)的薛定諤方程。所以分子力學(xué)方法可以求得分子的平衡結(jié)構(gòu)和熱力學(xué)性質(zhì)等，但不能得到分子體系與電子結(jié)構(gòu)有關(guān)的其它性質(zhì)。分子力學(xué)的勢(shì)能函數(shù)表達(dá)方程很簡(jiǎn)單，其計(jì)算速度很快（約是半經(jīng)驗(yàn)量子化學(xué)計(jì)算方法速度的1000倍），能夠用于生物大分子體系的計(jì)算。對(duì)于力場(chǎng)參數(shù)成熟的分子力學(xué)方法，已經(jīng)可以達(dá)到很高的計(jì)算精度。59分子力學(xué)是模擬分子行為的一種計(jì)算方法。分子力學(xué)認(rèn)為分子體系的ASimpleMolecularMechanicsForceFieldTorsions

H-C-C-Hx12 H-C-C-Cx6Non-bonded

H-Hx21 H-Cx6Bonds

C-Cx2 C-Hx8Angles

C-C-Cx1 C-C-Hx10 H-C-Hx760ASimpleMolecularMechanics基本概念

HarmonicPotentialFunctionxenergyEnergy(能量)

EnergyasafunctionofacoordinateX. EnergypenaltyfordistortingXfromitsequilibriumposition. StericEnergy=a+k(X-X0)2(Hook'slaw).Parameterization(參數(shù)化)

Matchingafunctiontoasetofdatapointsbyvaryingitsparameters(aandk).Minimization(最小化)

Findingtheminimumofapotentialfunction.

61基本概念HarmonicPotentialFunctiStericEnergyThedifferencebetweentheactualenergyofthesystemandtheenergyofahypotheticalsystemwhereallstructuralparametersareattheirequilibrium(minimumenergy)values.StericEnergy=Estretch+

Ebend+Etorsion+

EVdW+

Eelectrostatic+

Estretch-bend+Etorsion-stretch+…Estretch

Stretchenergy(overallbonds)Ebend

Bendingenergy(overallangles)Etorsion

Torsional(dihedral)energy(overalldihedralangles)EVdW

VanDerWaalsenergy(overallatompairs>1,3)Eelectrostatic

Electrostaticenergy(overallchargedatompairs>1,3)Estretch-bend

StretchbendenergyEtorsion-stretch

Torsionstretchenergy(EVdW+Eelectrostaticareoftenreferredtoasnon-bondedenergies)62StericEnergyThedifferencebe鍵伸縮能根據(jù)經(jīng)典力學(xué)的胡克定律，兩個(gè)成鍵原子可以視為有一根彈簧連接的兩個(gè)小球，其勢(shì)函數(shù)是簡(jiǎn)諧振動(dòng)勢(shì)函數(shù)，其計(jì)算非常方便，非常實(shí)用于生物大分子的計(jì)算。kb鍵伸縮常數(shù)，r0平衡鍵長(zhǎng)StretchingEnergy63鍵伸縮能根據(jù)經(jīng)典力學(xué)的胡克定律，兩個(gè)成鍵原子可以視為有一根彈

StretchingEnergy64StretchingEnergy10BondStretchingHarmonicpotential(AMBER)rE20)(2)(llklv-=65BondStretchingHarmonicpotentBondStretchingCubic(MM2)andquadratic(MM3)potentialsharmoniccubicquadratic3020)(22)(21)(llkllklv---=403020)(23)(22)(21)(llkllkllklv-+---=66BondStretchingCubic(MM2)andBondStretchingParameters(MM2)67BondStretchingParameters(MM角彎曲能BendingEnergy

兩個(gè)相連的化學(xué)鍵（三個(gè)成鍵原子）具有一定的鍵角，鍵角彎曲勢(shì)能函數(shù)與鍵伸縮勢(shì)函數(shù)類似，可用虎克定律描述。鍵彎曲能常數(shù)，實(shí)際鍵角和平均鍵角。68角彎曲能BendingEnergy

兩個(gè)相連的化學(xué)鍵（三6915energyangleAngleBendingMM3MM2AMBERAMBER:MM2:MM3:70energyangleAngleBendingMM3MM2AngleBendingParameters(MM2)71AngleBendingParameters(MM2)TorsionEnergy（二面角扭曲轉(zhuǎn)動(dòng)能）

三個(gè)相連的化學(xué)鍵（四個(gè)成鍵原子）具有一定的二面角（扭角）。頭尾兩個(gè)成鍵原子繞中間化學(xué)鍵旋轉(zhuǎn)時(shí)，需要一定的能量，存在明顯的旋轉(zhuǎn)勢(shì)壘，在分子力學(xué)中，二面角扭曲轉(zhuǎn)動(dòng)勢(shì)函數(shù)常用傅立葉級(jí)數(shù)模擬。72TorsionEnergy（二面角扭曲轉(zhuǎn)動(dòng)能）三個(gè)相連的7319FunctionalFormw:

Torsionalangle.n(multiplicity):

Numberofminimaina360ocycle.Vn:

Correlateswiththebarrierheight.g(phasefactor):

Determineswherethetorsionpassesthroughitsminimumvalue.Vn=4,n=2,g=180Vn=2,n=3,g=074FunctionalFormw:TorsionalanFunctionalForm:AMBER75FunctionalForm:AMBER21FunctionalForm:MM2,MM3V3:

Stericinteractionsbetween1,4atoms(minimumat60o,180oand300owhereatomsarestaggeredandmaximumat0o,120oand240owhereatomsaresyn).V1:

Bonddipoleinteractions(minimumat180owheredipolesaretransandmaximumat0owheredipolesarecis).V2:

1-2and3-4bondsorbitalinteractions(minimumat0oand180owhereorbitalsoverlapandmaximumat90o

wheretheyareorthogonal).76FunctionalForm:MM2,MM3V3:SExample:ButaneType V1V2V3C-C-C–C0.2000.2700.093C-C-C–H0.0000.0000.267H-C-C–H0.0000.0000.237ThebarriertorotationaroundtheC-Cbondinbutaneis~20kJ/mol.All9torsionalinteractionsaroundthecentralC-Cbondshouldbeconsideredforanappropriatereproductiononthetorsionalbarrier.77Example:ButaneType V1Non-BondedEnergy

非鍵相互作用能非鍵相互作用能主要包括范德華相互作用能和靜電相互作用能。78Non-BondedEnergy

非鍵相互作用能非鍵相互作VanDerWaals(VdW)Interactions范德華相互作用能范德華相互作用能是分子力學(xué)中重要的作用，它可分為進(jìn)程作用的排斥力和遠(yuǎn)程的吸引力，一般以Lennard-Jones公式來模擬范德華非鍵相互作用分子力場(chǎng)。其中r表示原子之間的距離，A和B是非鍵原子對(duì)的范德華常數(shù)。R的六次方為原子對(duì)的吸引作用，R的12次方位排斥作用。79VanDerWaals(VdW)InteractioHydrogenBondingH-bondgeometryindependent:risthedistancebetweentheH-bonddonorandH-bondacceptor.H-bondgeometrydependent:NHOCDonAccqw80HydrogenBondingH-bondgeometrPointChargeElectrostaticModelsqi,qjarepointcharges.Charge-chargeinteractionsarelongranged(decayasr-1).Whenenoughpointchargesareusedalltheelectricmomentscanbereproduced.Whenqi,qjarecenteronthenucleitheyarereferredtoas

partialatomiccharges.Partialatomiccharges

Fittothermodynamicproperties.

AbinitioCalculations(6-31G*,MNDO). Mullikencharge.

Reflectmolecularconstitutionratherthanmolecular

interactions. Electrostaticpotential.81PointChargeElectrostaticMod分子力學(xué)總能量并沒有嚴(yán)格的物理意義，為了獲得精確的計(jì)算結(jié)果，分子力場(chǎng)的能量函數(shù)表達(dá)式的復(fù)雜程度沒有限制。根據(jù)適用范圍不同，目前已發(fā)展了很多的分子力場(chǎng)，分子力學(xué)方法根據(jù)適用范圍可分為小分子和大分子兩類。適用于小分子的分子力學(xué)的函數(shù)形式較復(fù)雜和精確。例如MM2/MM3/MM4TINKERUFFMOMECCOSMOS等。適用于大分子的分子力學(xué)函數(shù)形式較簡(jiǎn)單，例如：AMBERCHARMMGROMOSOPLSCVFFCFFMMFF等。82分子力學(xué)總能量并沒有嚴(yán)格的物理意義，為了獲得精確的計(jì)算結(jié)果，分子力場(chǎng)的參數(shù)化分子力學(xué)計(jì)算結(jié)果的精確性除了與力場(chǎng)勢(shì)函數(shù)表達(dá)式有關(guān)外，還與力場(chǎng)參數(shù)的數(shù)值密切相關(guān)。有效的力場(chǎng)勢(shì)函數(shù)和正確的力場(chǎng)函數(shù)可使分子力學(xué)計(jì)算達(dá)到很高的精度，有些分子力學(xué)方法對(duì)分子的性質(zhì)計(jì)算結(jié)果非常好，可以達(dá)到實(shí)驗(yàn)值的精度。由于不同的分子力學(xué)方法所用的勢(shì)函數(shù)表達(dá)方式不同，其力場(chǎng)參數(shù)不能相互代替。由于化合物的原子類型很多，目前分子力場(chǎng)不可能適用于各種的原子類型，滿足各種化合物計(jì)算的要求。在缺乏力場(chǎng)參數(shù)時(shí)，就需要進(jìn)行分子力場(chǎng)參數(shù)的優(yōu)化。83分子力場(chǎng)的參數(shù)化分子力學(xué)計(jì)算結(jié)果的精確性除了與力場(chǎng)勢(shì)函數(shù)表達(dá)分子力學(xué)勢(shì)函數(shù)是由一系列的可調(diào)參數(shù)組成的。對(duì)可調(diào)參數(shù)進(jìn)行優(yōu)化，是分子力學(xué)的計(jì)算值最符合分子的某些性質(zhì)的實(shí)驗(yàn)數(shù)值，得到一套力場(chǎng)的優(yōu)化參數(shù)，再使用這套參數(shù)去預(yù)測(cè)相同原子類型的其它分子的結(jié)構(gòu)和性質(zhì)。傳統(tǒng)的分子力場(chǎng)參數(shù)化方法是通過擬合實(shí)驗(yàn)數(shù)據(jù)（幾何構(gòu)型、構(gòu)象能、生成熱、光譜數(shù)據(jù)等）來優(yōu)化參數(shù)。分子的幾何結(jié)構(gòu)和力場(chǎng)參數(shù)可由實(shí)驗(yàn)或量子化學(xué)計(jì)算獲得。鍵伸縮振動(dòng)常數(shù)可直接由價(jià)鍵力場(chǎng)計(jì)算或振動(dòng)光譜獲得。平衡鍵長(zhǎng)、平衡鍵角和角彎曲常數(shù)可由X射線衍射、中子衍射、電子衍射等方法測(cè)定，也可由量子化學(xué)計(jì)算得到。扭轉(zhuǎn)位能參數(shù)來自于NMR譜帶和弛豫時(shí)間。構(gòu)象能可從光譜和熱化學(xué)數(shù)據(jù)得到。非鍵參數(shù)可從晶格參數(shù)和液體的物理性質(zhì)數(shù)據(jù)得到。分子力場(chǎng)的參數(shù)化84分子力學(xué)勢(shì)函數(shù)是由一系列的可調(diào)參數(shù)組成的。對(duì)可調(diào)參數(shù)進(jìn)行優(yōu)化優(yōu)化力場(chǎng)參數(shù)時(shí)，首先要選擇某些代表性化合物，根據(jù)其原子和成鍵化學(xué)環(huán)境不斷修正力場(chǎng)參數(shù)，使得力場(chǎng)參數(shù)的計(jì)算結(jié)果與真實(shí)分子的結(jié)構(gòu)、能量和分子的振動(dòng)光譜一致，接著進(jìn)行同類型化合物分子的計(jì)算，驗(yàn)證這套參數(shù)的可靠性。力場(chǎng)參數(shù)的優(yōu)化可使用最小二乘擬合法和嘗試法。分子力場(chǎng)的參數(shù)化85優(yōu)化力場(chǎng)參數(shù)時(shí)，首先要選擇某些代表性化合物，根據(jù)其原子和成鍵ParameterizationChoosingvaluesfortheparametersinthepotentialfunctionequationstobestreproduceexperimentaldata.Parameterizationtechniques

Trialanderror Leastsquaremethods(CFF)Typesofparameters

Stretch:naturalbondlength(l0)andforceconstants. Bend:naturalbondangles(q0)andforceconstants. Torsions:Vi’s. VdW:(e,VdWradii). Electrostatic:Partialatomiccharges. Cross-terms:Crosstermparameters.86ParameterizationChoosingvalueParameters-QuantityForNatomtypesrequire:

Nnon-bondedparameters N*Nstretchparameters N*N*Nbendparameters N*N*N*NtorsionparametersExample

MacroModelMM2*:39atomtypesRequiredActualStretchBendTorsion152158,3192,313,44116435750887Parameters-QuantityForNatoParameters-SourceExperiment:geometriesandnon-bondedparameters

X-Raycrystallography Electrondiffraction Microwavespectroscopy

LatticeenergiesAdvantages

RealDisadvantages

Hardtoobtain Non-uniform LimitedavailabilityAforcefieldparameterizedaccordingtodatafromonesource(e.g.,experimentalgasphase,experimentalsolidphase,abinitio)willfitonlyqualitativelydatafromothersources.88Parameters-SourceExperiment:Parameters-Source

Highlevelmolecularorbitalcalculations

Conformationalpreferencesandpartialcharges(HF/6-31G*).

Correctionsforelectroncorrelationeffectsareoften important:MP2,MP3etc.

Chargesobtainedbyfittingelectrostaticpotentials.Advantages

Relativelyeasytoobtain. Uniform. Unlimitedavailability. Completepotentialenergysurfacesareavailable.Disadvantages

“Unreal”. Modeldependent. Computationallyexpensive.89Parameters-SourceHighlevelConstructgraphicalrepresentationofmoleculetobemodeled(“frontend”)Selectforcefieldmethodandterminationcondition(gradient,#cycles,ortime)PerformgeometryoptimizationExamineoutputgeometry...isitreasonable?Searchforglobalminimum.StepsinPerformingMolecularMechanicsCalculations90ConstructgraphicalrepresentaInputisusuallydonegraphically(bysketchingorbuildingstructuresatom-by-atomorbyassemblingcomponentparts).Thisgraphicalmodelisconvertedtoamathematicalmodelbythesoftware.Eachsoftwarepackagehasitsownfiletype,butmosthavesomecommonfeatures.InputFileStructure91Inputisusuallydonegraphica

C1-1.1291.281-0.000 C2-2.5581.772-0.000 C3-3.5190.606-0.000

H4-0.5961.6370.890

H5-0.5961.637-0.890

H6-2.7332.3920.890

H7-2.7332.392-0.890

H8-4.5580.9520.000

H9-3.359-0.017-0.890

H10-3.359-0.0170.890

H11-1.1100.183-0.000(thisMAYbethesameasthe.PDBfile,asshownhere,ortheorientationofthemoleculemaybedifferent,makingthenumbersdifferent)Cartesiancoordinate(XYZ)file92 C1-1.1291.2

distance

angle

dihedralconnectivityN0.000000.000000.00000000H1.020010.000000.00000100H1.02001104.536810.00000120H1.02001104.53681109.579611230(endoffile) (1meansoptimize,0meanskeepconstant,-1meansvaryaccordingtoadesignatedpattern)(sometimescalledZ-matrix)InternalCoordinates(forNH3)93 distance angle LocalminimumvsglobalminimumManylocalminima;onlyONEglobalminimumMethods:Newton-Raphson(blockdiagonal),steepestdescent,conjugategradient,others.globalminimumlocalminimaEnergyMinimization94Localminimumvsglobalminimu“Stericenergy”hasNOphysicalmeaning,anditisdefineddifferentlyindifferentprogramsThereforeitCANNOTbeusedtocomparestructurescalculatedbydifferentprogramsItsuseislimitedtocomparingISOMERICstructureshavingtheSAMEnumberandkindsofbonds(conformers,stereoisomers).Usesof“StericEnergy”95“Stericenergy”hasNOphysicaCalculationsareveryfastGeometryoptimizationsofsmalltomedium-sizemoleculescanbeaccomplishedonapcConformationsofmacromolecules(includingbiomacromoleculessuchaspeptidesandpolysaccharides)canbecalculatedusingworkstationsorparallelprocessingcomputers.SuccessesofMolecularMechanicsCalculations96CalculationsareveryfastSuccReasonablegeometriesareusuallyobtained:Bondlengthswithin0.1An