Alchemical-free-energy-calculation-with-Gromacs

Alchemicalfreeenergycalculationswithgromacsgromacsworkshop-Stanford,CA-Apr7-8,2008JohnD.Chodera1,DavidL.Mobley2,MichaelR.Shirts31DepartmentofChemistry,StanfordUniversity2DepartmentofPharmaceuticalChemistry,UniversityofCalifornia,SanFrancisco3DepartmentofChemistry,ColumbiaUniversityBuildingupontheworkofmany,manyothers...1ManyquestionsinbiologyandpharmaceuticalchemistryinvolvefreeenergydifferencesHowdoescompoundXpartitionbetweendifferentenvironments?HowtightlydoescompoundXbindproteinY?ProteinZ?HowdoIaffectthebindingaffinityifImodifycompoundX?OrifImutateormodifytheprotein?Howdooneormoremutationsataprotein-proteininterfaceaffectbinding?e.g.howwelldoeslipitorpartitionbetweenoctanolandwater?e.g.howwelldoesclomifenebind/discriminateERα/ERβe.g.whatisthedifferenceinbindingbetweenpseudoephedrineandphenylephrinetoadrenergicreceptor?e.g.whichresiduesattheinterfacecontributemosttobinding,andhowcanmutationscausedisease?2FreeenergydifferencesareofteneasiertocomputethroughalchemicalroutesAbsolutefreeenergiesofbindingRelativefreeenergiesofbindingΔGbindPLP+LPøP+øΔG1ΔG2ΔGbΔGaΔΔG=ΔGa−ΔGbPL1P+L1PL2P+L23Zn=!dxe−βU(x)AlchemicalintermediatescanfacilitateconvergenceZ=!e−βH(x)dx(1)ΔF=−β−1lnZ(2)P(x)=e−βH(x)Z=eβ(F−H(x))(3)PA(x)PB(x)=expβ(FA−HA(x))expβ(FB−HB(x))=eβ(ΔF−ΔH(x))(4)PA(x)PB(x)=exp(β(ΔF−ΔE(x))(5)PA(ΔEPB(−ΔE)=exp(β(ΔF−ΔE))(6)PA(x)=PB(x)eβΔF−βΔE(x)(7)1=(eβ(ΔF−ΔE(x))#B(8)ΔF=−β−1lne−βΔE(x)#B(9)ΔF1→N=−β−1lnZNZ1=−β−1lnZ2Z1·Z3Z2···ZNZN−1=N−1$n=1ΔFn→n+1(10)1D.WuandD.A.Kofke.Phase-spaceoverlapmeasures.I.Fail-safebiasdetection...,J.Chem.Phys.123:054103(2005).numberofsamplesbias(kT)ErrorincreasesexponentiallywithdiminishingphasespaceoverlapInstead,introduceintermediatestatestoensureacontiguouschainofgoodoverlape.g.twoharmonicoscillatorsseparatedbyvariousdistances4ΔF=!λ2λ1dλ!∂H∂λ#λ!≈Δλ2$∂H∂λ#λ1+∂H∂λ#λ2%ΔF=−β−1ln!e−β(U2−U1)λ1=+β−1ln!e−β(U1−U2)λ2ΔF=−β−1lnf(U2−U1)#λ1f(U1−U2)exp[−β(U2−U1)]#λ2Multiplewaystoextractfreeenergydifferencesfromsimulationsofintermediatestates-10-5051015200.000.050.100.150.200.250.30-5051015200.000.050.100.150.200.250.30TI(thermodynamicintegration)EXP(exponentialreweighting)BAR(Bennettacceptanceratio)quadratureerrorhardtoquantifysuffersfromlargebiasandvariance5(MBAR)estimatorextractsoptimalestimatefrommultiplestatesMichaelR.Shirts(DepartmentofChemistry,ColumbiaUniversity),JohnD.Chodera(DepartmentofChemistry,StanfordUniversity):Freeenergiesofsolvation•Example:Solvationof3-methylindole•5nsexplicitwaterMDat9statesMethodValueEXP(fwd)3.80±0.10EXP(rev)2.94±0.14EXP(avg)3.37±0.17BAR3.29±0.06MBAR3.23±0.077T.Steinbrecher,D.L.Mobley,andD.A.Case.Non-linearscalingschemesforLennard-Jonesinteractionsinfreeenergycalculations,J.Chem.Phys.127:214108(2007).(DOI)OptimalalchemicalintermediatesdependonproblemGoalsinchoiceofintermediates:fewintermediatesgoodoverlapbetweenintermediatesminimizecorrelationtimesminimizevarianceandsizeofspacetobesampledForexample:128intermediatesforextractingtoluenefromwaterprobablyoverkill8HydrationfreeenergiesNHNgaswaterSgasΔGSaqSgas,neutralØSaq,neutralØM.R.Shirts,J.W.Pitera,W.C.Swope,andV.S.Pande.J.Chem.Phys.119:5740(2003)D.L.Mobley,E.Dumont,J.D.ChoderaandK.A.Dill.J.Phys.Chem.B.111:2242-2254(2007)(DOI)9ChoiceofintermediatesforhydrationfreeenergyelectrostaticsLennard-Jonesannihilationdecoupling(nointeractionswithinannihilatedmoleculeretained)(interactionswithinannihilatedmoleculeretained)smaller∆Glongercorrelationtimesduetonakedchargesnovacuumrechargingcalculationrequired3PMEevaluationspertimestep,trickytousepotentiallylarge∆GshortcorrelationtimesrequiresvacuumrechargingcalculationrequiresLJannihilationvacuumsimulationnovacuumsimulationrequiredeliminatespotentiallyunphysicalconformationsAlsopossibletoturnoffbothelectrostaticsandLJsimultaneously(e.g.pullingin4thdimension),butmuchmoretricky.10Hydrationfreeenergies:ExampleworkflowM.R.Shirts,J.W.Pitera,W.C.Swope,andV.S.Pande.J.Chem.Phys.119:5740(2003)D.L.Mobley,E.Dumont,J.D.ChoderaandK.A.Dill.J.Phys.Chem.B.111:2242-2254(2007)(DOI)IUPACnamemoleculeconformations(mol2)AMBERmoleculeparametersgromacsmoleculetopologyLexichem(OpenEyetoolkit)Omega(OpenEyetoolkit)(AmberTools)://flowM.R.Shirts,J.W.Pitera,W.C.Swope,andV.S.Pande.J.Chem.Phys.119:5740(2003)D.L.Mobley,E.Dumont,J.D.ChoderaandK.A.Dill.J.Phys.Chem.B.111:2242-2254(2007)(DOI)gromacsmoleculetopologygromacssolvatedtopologyandcoordinatesmanypainfulstepsdischarginginwaterdecouplingLJinwaterrecharginginvacuumcustomtopologymodi