1
A Multiscale Simulation Approach to Modelling Drug-Protein Bind-ing Kinetics. SusantaHaldar§⊥,FedericoComitani†⊥,GiorgioSaladino†,ChristopherWoods§,MarcW.vanderKamp#§,AdrianJ.Mulholland§*andFrancescoLuigiGervasio†‡*.
†DepartmentofChemistry,and‡InstituteofStructuralandMolecularBiology,UniversityCollegeLondon,LondonWC1E6BT,UnitedKingdom.§CentreforComputationalChemistry,SchoolofChemistry,UniversityofBristol,Bristol,BS81TS,UK.#SchoolofBiochemistry,UniversityofBristol,Bristol,BS81TD,UK.KEYWORDS:Bindingkinetics,moleculardynamics,computer-aideddrugdesign,enhancedsamplingalgorithms,multi-scalesimu-lations,metadynamics,MonteCarlo,QM/MM.
ABSTRACT:Drug-targetbindingkineticshasrecentlyemergedasasometimescriticaldeterminantofinvivoefficacyandtoxicity.Itsrationaloptimizationtoimprovepotencyorreducesideeffectsofdrugsis,however,extremelydifficult.Molecularsimulationscanplayacrucialroleinidentifyingfeaturesandpropertiesofsmallligandsandtheirproteintargetsaffectingthebindingkinetics,butsignificantchallenges include the longtimescales involved in(un)bindingeventsandthelimitedaccuracyofempiricalatomisticforce-fields(lackinge.g.changesinelectronicpolarization).Inanefforttoovercomethesehurdles,weproposeamethodthatcombinesstate-of-the-artenhancedsamplingsimulationsandquantummechanics/mo-lecularmechanics(QM/MM)calculationsattheBLYP/VDZleveltocomputeassociationfreeenergyprofilesandcharacterizethebindingkineticsintermsofstructureanddynamicsofthetransitionstateensemble.WetestourcombinedapproachonthebindingoftheanticancerdrugImatinibtoSrckinase,awell-characterizedtargetforcancertherapywithacomplexbind-ingmechanisminvolvingsignificantconformationalchanges.Theresultsindicatesignificantchangesinpolarizationalongthebindingpathways,whichaffectthepredictedbindingkinetics.Thisislikelytobeofwidespreadimportanceinligand-targetbinding.
Introduction
Understandingprotein-ligandbindingmechanismsandtheirassociatedthermodynamicsandkineticsisofparamountimportancefortherationaloptimi-zationof lead compounds indrugdiscovery.1–3 Incomputer-aided drug discovery (CADD) themainemphasishassofarbeenplacedonpredictingthemost likely bindingpose (usually by docking andother fast but approximatemethods)4 and deter-miningrelativebindingaffinity5,6.Incontrast,onlyrecently, it hasbeenpossible topredict thepath-waysforbinding/unbindingeventsandtheirasso-ciated free energy profiles through more refinedcomputationalmethods1,7–11.However,itisincreas-inglyrecognizedthatprotein-ligandbindingkinet-ics are crucial for understanding the efficacy andtoxicityof leadcompounds.Molecularsimulationshavenowbeenshowntobeanimportanttoolforthe investigation of molecular properties at the
baseofkineticbehaviorsinanumberofcases.12–14
Ligandefficacy in vivo is influencedby a complexnetworkofshort-andlong-livedinteractionswithaplethora of biomolecules in the crowded cellularandtissutalmilieu,wheretheconcentrationoftheligand itself is variable and dependent on its dy-namics and kinetic properties (absorption, distri-bution,metabolism,excretion).12Thus, inadditionto thebindingaffinity todesired (andunwanted)targets (Kd),whichhasreceivedmostattentioninrational drug discovery, the association/dissocia-tion rate constants (konand koff) or the residencetime(τdefinedas1/koff,theperiodofoccupancyofthetargetbindingsitebytheligand)arerelevantindeterminingthetherapeuticefficacyandtoxicityofdrugs.13,14Examplescanbefoundamongmanyap-proveddrugs, someofwhichhavevery longresi-dencetimes,asinthecaseoffinasteride,aninhibi-tor of 5α-reductase used to treat benignprostate
2
hyperplasia,orevenbindirreversibly,asforaspi-rin.15Moreevidenceofadirectcorrelationbetweenresidence time (oron- or off-rates) and the func-tionalefficacyofdrugs,(asintheexemplarycaseofadenosineA2agonists,16)isemerging.Also,shorterinteraction times with unwanted targets may re-ducesideeffectsandtoxicity.17
Theincreasingrealizationoftheimportanceofres-idencetimeandbindingkineticshasledtonumer-ous efforts to develop and use computational ap-proachesabletopredictandmodelthem.Manyarebasedonatomisticmoleculardynamics(MD)simu-lations,oftencomplementedbyMarkovStateMod-els, e.g. combined by Brownian dynamics simula-tionsand/orapplyingmilestoningapproaches11,18–24.Thepotentialofsuchmethodsinmodelingkinet-ics,isclear,especiallyofligandsbindingtosurfacepockets. However, a significant limiting factor isthatthetimescalesaccessibleinatomisticMDsim-ulations are much shorter than most unbindingevents.19,23Addingtothisisthelimitedaccuracyofmolecular mechanics (MM) force-fields, typicallyused in the forbiochemicalstudies.Thesolvationenvironmentofligandschangessignificantlyduringthebindingandunbindingevents, suggesting thatchanges in electronicpolarization, usuallynot ac-countedforinsuchforce-fields,mayplayaroleindeterminingthekinetics.1,25–27
Enhancedsamplingfreeenergymethodshavebeensuccessfullyusedtoaddressthetimescaleprobleminligandbindinginanumberofcases1,28–30.Byac-celerating rare events and facilitating the estima-tionofbindingfreeenergiesalongphysicallymean-ingfulassociationpathways,suchmethodsallowtoidentifythetransitionstateensembleandcomputeits associated energy.1,31–33 Among these,metady-namics-basedmethodswithoptimalpath-likevari-ables,suchasPathCollectiveVariable(PCV),34com-bined with Parallel Tempering (PTmetaD), haveprovedparticularlyusefulinpredictingthemecha-nismsandfreeenergyprofilesassociatedwithmo-lecularrecognition.8,21,28,30,35–37
Tiwari et al. have recently developed a protocolmakinguseofmetadynamicstoreconstructtheki-neticsofbindingeventsforwhichasinglefreeen-ergy barrier clearly separates the bound and un-bound states.38 In theseparticularly simple cases,thebindingkineticscanbeeffectivelypredictedun-derthestrictconditionthatthetransitionoverthebarrierismuchfasterthanthemetadynamicsbiasdepositiontime.39,40However,when(un)bindingis
characterizedbyacomplex,diffusivebarrier,withintermediatemetastablestates,thisconditionisnotfulfilled,makingitdifficulttoemploythismethod.This scenario ariseswhenmultiple weak bindingsitesarefoundenroutetothefinalbindingmode,orwhenconformationalchangesinthetargetupon,orprior to, the interactionwith the ligandarere-quiredforafullbinding.37,41–45Extracarehastobetakenwhendealingwithsuchsystems,asboththebinding and the conformational transition termscontributetothekinetics.TransitionPathSampling(TPS)46-basedapproaches,suchasTransitionState-Partial Path Transition Interface Sampling (TS-PPTIS)47arebettersuitedforsuchsystems.
TS-PPTIS combinesPCV34withPartial Path Inter-faceSampling.33Itprovidesanaccuratedescriptionofbindingeventsbelongingtoeithertheconforma-tionalselectionortheinduced-fitcategorieswhileallowing for an efficient calculation of rate con-stants. Metadynamics is first used in conjunctionwith the optimal PCV collective variables to dis-placetheligandfromthedeepfreeenergyminimaassociated with long residence times, which areotherwise very difficult to overcome by standardMDorTPSapproaches,whilePPTISisusedtoaccu-ratelysamplethediffusivebarriers,includingthosehaving additional shallow localminima. TS-PPTISbuildsonPPTISbyreformulatingthereactivefluxequation, to allow for the sampling of smallwin-dowsalongthebindingpathwayinsteadoftheen-tire trajectory fromreagentstoproducts, improv-ingtheconvergencetimes.
Thisisanaccuratebutcomputationallyexpensiveapproach.Bothaconvergedmetadynamicsrunanda number of short unbiased MD simulations runfrom the interfaces around the transition state,mustbeperformed.47ItishoweverexpectedtobemorerobustandaccuratethanotherMD-basedap-proaches, especially when the non-trivial confor-mationalrearrangementsoftargetplayaroleinthebinding.21Wehavepreviouslyusedthismethodtomodel the binding mechanism of the anti-cancerdrug imatinib to theprotein tyrosinekinasec-Srcandtocompute itskinetics.TS-PPTISwasable torecovertheexperimentalassociationkineticsasob-tainedbysurfaceplasmonresonanceand,bymod-elingthetargetconformationaldynamics,torecon-cile the contrasting conformational selection andinduced-fitmechanismshypothesizedforthiscom-plex.21
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MM force-fieldshavebeendevelopedand refinedovermanyyears,andcannowprovideanexcellentoveralldescriptionofproteinstructureanddynam-ics,whileroutinedevelopmentofappropriatepa-rameters for ligands requires some effort. 26,48–51The typical invariant atom-centered point chargeMMmodelcannotprovideafulldescriptionofmo-lecular electrostatic properties. Potentially im-portantfeaturessuchaspicloudinteractions52andsigmaholes53cannotberepresentedbymodelsthatincludechargesonlyanatomiccenters.Also,envi-ronmentalchangesdonotaffectthechargesandsochangesinelectronicpolarizationeffectsarenotin-cluded;polarization is included in anaverage, in-variantway(e.g.chargesgivinganenhanceddipolemoment)generallyappropriateforasolvatedmol-ecule.Sucheffects,however,mayplayasignificantrole in drug binding and unbinding: for example,theremaybesignificantchangesinpolarizationbe-causeofthechangeinsolvationastheligandbinds.Electronicpolarizationcanbecapturedbymoreso-phisticatedandphysicallyrealistictreatments,ide-allybasedonaquantummechanical(QM)levelofdescription.54
PioneeringworkbyGaoetal.demonstratedthepo-tential of QM/MM simulations to investigate andquantify electronic polarization effects in solva-tion.55Gaoalsowentontoapplythisapproachtoprotein− ligand binding affinities, e.g., a QM/MMstudy on the HIV-1 protease inhibitors that indi-catedthatpolarizationcontributestobinding.56
Onthebasisofsuchresults,wehavethusdevelopedamethodthatappliestheWarshelcyclewithaMe-tropolis-Hastingsalgorithmtoallowforarigorousandefficientquantificationofthechangeininterac-tionenergiesofaligandwhenchangingfromanMMto a QM description.57 The result of transitioningfromafullyMMforcefieldtoaQM/MMrepresen-tationisquantifiedbymeansoffreeenergysimula-tions driven by a reaction coordinate convertingfromone level of description toanother. Efficientsampling is achieved through replica exchangeacross valuesof the reaction coordinate,with thefreeenergyforchangingfromanMMHamiltoniantoaQMHamiltoniancalculatedbythermodynamicintegration.57,58 We have previously applied thismethodtochecktheeffectsofaQMdescriptionoftheligandonthebindingaffinity57,59.Forexample,polarizationeffectsontheabsolutebindingfreeen-ergyofthecavitywatermoleculesinInfluenzaNeu-raminidasewereinvestigatedinourworkofRef.60
,wherewehaveshownthatthepolarizationcanin-deedcauseanotableincreaseintheabsolutebind-ingfreeenergy,upto~1.0kcal/mol.
To address both the timescale problems and theforce-field inaccuracies, we combine here TS-TPPTIS,tocalculatebindingpathways,samplethetransitionstateandprovide themostaccurateki-neticsinformationattheempirical(MM)level,withtheimprovedaccuracyobtainedfromquantumme-chanicalcalculationswithinaQM/MMframework.Althoughtestedextensivelyonbindingaffinitypre-dictions,ourmethodhasneverbeenusedtocorrectthedrugbindingkineticsbefore.
Theresultingprotocolisefficientwhileallowingforelectronicpolarizationeffectsoftheligandtobein-cluded.57 Furthermore, other factors, such as thedefinitionofπsystems,andsigmaholesarelikelytobetakenintoaccountbythiscorrection,buttheireffectalongthebindingpathislikelytobenegligi-ble.
As a test case, we revisited the binding of theanticancer drug imatinib to Src non-receptortyrosine kinase. Src was the first viral oncogenicproteintobediscovered,61,62andprovidesanidealsystem for mechanistic explorations of complexdrugbindingeventsduetoitshighconformationalflexibility,63 biomedical importance and theavailability of extensive experimental andcomputational data,21,43,64–67 including highresolutioncrystalstructuresinboththeactive(PDBid:1Y57,1YI6)68andinactiveconformations(PDBid: 2SRC).69 Src is often mutated in a variety oftumors, including those of the colon, liver, lung,breast,andpancreas.Srcplaysanimportantroleinmetastasis and has been thus the subject ofnumerous drug design studies over many years.Inhibitors such as dasatinib, saracatinib, andbosutinibaresomeofthecompoundsdevelopedtotargetthisproteinwhichenteredclinicaltests.70
Aprototypicalinhibitorisimatinib,adrugusedtotreatanumberofdifferenttumors:forexample,itdeactivates the tyrosine kinase c-Abl, theautoinhibitionmechanismofwhichmalfunctionsinchronic myelogenous leukemia.71 Imatinib alsobindstoaninactiveconformationofSrc,72inwhichtheaspartate(D404)oftheconservedAsp-Phe-Glymotif(DFG),locatedattheendoftheactivationloop(A-loop),pointsoutwards(DFG-flip)fromtheATPbindingsite(seeFigure1).
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Figure1.a)Structureofthecatalyticdomainofc-Src,whererelevant secondary structures are highlighted with differentcolors.Imatinibisshowninblue.b)Lewisstructureofimatinib.c)The c-Src binding site: residues involved in the conforma-tional rearrangementuponbindingof imatinibare showninmauve.
ImatinibhasbeenproposedtoexertitseffectontheDFG-flip conformational change by either aconformational selection or induced-fitmechanisms.19,21,64,66,73,74 We have shown, bycombining state-of-the-art binding simulationswith NMR and surface plasmon resonanceexperiments, that at room temperature, theconformational selection path is dominant,althoughbothmechanismsarepossible(seeFigure2).21
Methods
TheSrcstructureswereretrievedfromtheProteinData Bank (PDB entries2SRCand2OIQ).Missingresidues in 2OIQ were added using the softwareModeller75, according to the respective UniProtsequenceandusing2SRCasatemplate.Fortheapostructure,weusedtheAmber99SB*-ILDN51,76forcefield, includingbackbonecorrectionswithexplicitsolvationofTIP3Pwatermolecules.TheligandwasparameterizedwithGAFF77withchargescalculatedattheHartreeFocklevelusinga6-31G(d)basissetwithGaussian0978andthedihedralsca-ca-n-candca-ca-c3-n3byDFTtorsionalscanswithastepof10degrees.21 All simulations and free energycalculationswere performed using Gromacs 4.679combinedwiththePLUMEDplug-in80.Thesystemwas minimized with 10000 steps of conjugatedgradient and equilibrated in the isothermal-
isobaric (NPT) ensemble for 10 ns, using aBerendsenbarostattokeepthepressureat1atm.The temperature was kept at 305 K with the V-rescale algorithm.81 A 1 μs production run wascarried out for all the systems in the canonical(NVT)ensemble.TheparticlemeshEwald(PME)-Switch algorithm was used for electrostaticinteractionswithacut-offof1nm.Asinglecut-offof1.2nmwasusedforvanderWaalsinteractions.The binding free energy was computed usingparallel-tempering metadynamics (PT-MetaD)82with 5 replicas using the Well-TemperedEnsemble83with3CollectiveVariables(CVs):the2Path Collective Variables (PCVs) s and z, keepingtrackoftheprogressionandthedistancefromtheunbinding path respectively,34 and a CV countingthe number of water molecules interacting withboththeligandandthecavity.Thebiasfactorwassetto15.0andtheGaussiansheightto1.25kJ/mol,with a deposition rate of 1/2000 steps. TheGaussianwidthwassetto0.1,0.005and0.1forthethree CVs, respectively. As customary for ligandbinding7, we performed a preliminarymetadynamicsrunusingasimplegeometricalCVtoobtainaninitialpathwayforthesetupofthePCVs.Weselected27framesfromthelowestenergypathobtainedinthepreliminaryrunandoptimizedthisinitial guess using themethodology described byBranduardietal.34ThepreliminarymetadynamicsshowedlargerearrangementsoftheA-loop,soweincludedCαatomsoftheloopandoftheaC-helixinthedefinitionofthePCVs.TwoextraCVsdefinedasthe distance between D404 and K295 and thedistance between P405 and L317 were used todescribetheDFG-flip.64Thesamplingconvergencewascheckedbycomparing thereconstructedfreeenergy surfaces at different time intervals duringthelast50nsofthesimulations.
FollowingtheenhancedsamplingMDsimulations,weappliedareactioncoordinate,λtotunetheQMvs MM descriptions, by scaling the HamiltonianfromaQM(λ=0)statetoanMM(λ=1)state.TheλcoordinateisusedinReplicaExchangeThermody-namic Integration (RETI)84 simulations, with theMetropolis-HastingMonteCarlomethod, toaccel-erate the sampling of the systemwith a QM/MMHamiltonian57 (for amore detailed description ofthe QM/MM FEP methodology, see SI). All theQM/MM simulations were performed at theBLYP85,86/VDZ level of theory, using the ‘quan-tomm’ application for QM<->MM transformationsavailable in Sire(www.siremol.org)87, using Sire’sMonte Carlo engine to drive the simulations and
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Molpro88 for QM energy calculations. Previoustests89havedemonstratedthattheBLYPfunctionalshows good consistencywithdifferentMMwatermodels.Shawetal.showedthatthefreeenergycostofperturbingaQMwatermoleculeintoanMMde-scriptioninbulkMMsolventislessthan1kcal/molwithBLYP (0.5kcal/mol forQM→TIP3Pand−0.1kcal/molforQM→TIP4Ptransformation).89
AllMonteCarlosimulationswererunintheNPTen-sembleatroomtemperature(300K).ThesameMMLennard-Jones parameters used for the MD andPTmetaD simulations were maintained in theQM/MM simulations; this has previously beenshowntoprovideareasonabledescriptionofbio-molecular interactions.90,91 The ligand confor-mationswereindeedfoundtobeconsistentlysimi-lar in both the QM/MM and theMM simulations.(seeSI,figureS2).
TheRETIschemewasperformedusing8differentλwidowsand thevalues:0.0,0.142,0.285,0.429,0.571,0.714,0.857and1.0andweranatotalof50blocks of multiscale Monte Carlomoves for eachwindowi.e. foreachlambdavalue.Onlytheinter-molecular component of the QM/MM energywasincludedfortheligand.Thismeansthatthefreeen-ergy correction between the QM/MM and MMmodel captured differences in the intermolecularinteractionsinvolvingtheligandonly.Thisparticu-larchoicewasmadetosimplifythedescriptionandavoid calculations on intramolecular interac-tions.92,93
We performed 2.5 million MC moves in the MMHamiltonianperlambdawindowandatotalof50QMenergyevaluationsperlambdawindow.Into-tal, over 8 lambda windows, 20 million MM MCmoves and 400 QM energies were evaluated.In all the QM/MM perturbation calculations, theproteinbackbonewaskeptfixed,whileaminoacidsidechainsandwatermoleculeswerefreetomove.
Results
Freeenergyandkinetics calculations.The freeenergy profile associated with the binding andunbinding of the ligand (imatinib) from c-Src isshowninupperpanelinFig.2.Inthelowerpanelsarerepresentativesnapshotsoftheunbindingtra-jectory.Thesystempresentstwoseparatebindingposes(AandB),distinctonlybythepositionoftheA-loopcoveringthebindingcavity,whichthroughapartialhingemotionopensanddetachesfromthe
β3-αClinker.Thismovementanticipatesandiscru-cialtotheunbindingofimatinibandwasthusex-plicitlytakenintoaccountduringtheMetaDsimu-lations.Withtheexceptionoflocalrearrangementsintheresidualchainsinthesesecondarystructures,nonoticeabledifferenceisobservedbetweenAandB in the binding conformation, in the level ofsolvationandintheinteractionwiththecavityres-idues. The difference in free energy between thetwominimaislessthan1kcal/molwithAbeingthemost stable of the two conformations. Looking attheensembleofAandBconformations,wecanob-serve that they are close to the reference X-raystructurebindingpose.Themainbodyislockedinposition by the presence of a tight-knitted saltbridges network betweenD404, R409, E310, andK295(showninmauveinFig.2bottom),whiletheterminalpiperazine, theonlysolvatedmoietyout-side of the cavity, hasmore freedom to fluctuate.The ligand interacts transiently with a few back-boneatoms,mainly through itsaromaticringsni-trogens. In particular T338, M341 and D404, theonly residue of the salt bridges network consist-entlyinteractingwiththeligandviaitsbackboneni-trogen. A few aromatic residues, Y340 and F405mayalsohelptopindowntheligandbymeansofπ-stacking.
The transition towardtheunboundstate(TS), re-quiresthebreakingofthesaltbridgesnetworkbymeans of steric hindrance, justifying the high en-ergybarrierseparatingthetwostates.InFig.2top,TS is locatedatSpath~12, and is indeed16±1.5kcal/molhigherthanthemainbindingposeA.TheA-loopopens,asmentionedpreviously,toallowforthe passage of the ligand, causing local defor-mationsintheresiduesbelongingtotheA-loopit-self,theD-loop,β3,αCandtheirlinker.Theconfor-mationsassumedbyimatinibforciblycutD404outofthesaltbridgesnetworkandpreventsitfromin-teractingwithR409andK295.ApartialunfoldingoftheαG-helixisalsoobservedinthisensemble,inagreement with observed folding free energychanges obtained from H/Dexchangeexperiments21.Beforereachingafullysolvatedstate,apre-bindingconformation(Corencountercomplex)isobservedatSpatharound15–16whereimatinibiswedgedun-derαC inwhatisknownas“deeppocket”21.Heretheterminalaminoringsoftheligandstillaffectthesalt bridges network, by transiently breaking thebond between K295 and E310 only. This can beseenasapreliminarysteptothefullbinding,useful
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inhelpingtheligandfinditswaytothebindingsiteand in lowering the energy penalty of the saltbridgesdisruption.Thefreeenergyofthisbasinisapproximatively4kcal/molhigher than themainbasinA.
Figure 2. Top: Binding free energy profile obtained withmetadynamicssimulationusingtheMM-onlyforcefield,alongthe path variable, which defines an optimal association anddissociation coordinate. The most relevant minima and thetransitionstatearelabeledanddiscussedinthetext.Theareaofthetransitionstateisrepresentedasadashedline.Thetwoprofilesintheregionfroms(PCV1)=16tos=27(i.e.fromthesecondary pocket to the unbound state) correspond to theconformationalselectionmechanism(cyanline,‘flip-bind’)andtoaninducedfitmechanism(orangeline,‘bind-flip’).Bottom:exemplesnapshotsofanunfoldingevent.Asbefore,theproteinis shown as a white cartoon, the ligand in blue licorice, theresiduestakingpartofthesaltbridgesnetworkareinmauveandtheremainingresiduesinteractingwiththeligandareincyan.
NMRexperimentshaveconfirmedthepresenceofthis minimum, which is suggestive of a two-stepbinding process, in which a fast binding event isfollowed by a slower conformationalrearrangement.21TS-PPTISwasdevelopedtodeal
withparticularlydifficultcasessuchasthis,wherethe complexity of the unbinding mechanismslowers the transmission coefficient well below1.21,47 In order to evaluate the kinetics, thetransitionpathwaywasfirstdividedintoanumberof non-overlapping interfaces, from which morethan 10000 short unbiasedMD trajectories wereinitiated.Asexpected, thecomputed transmissioncoefficient proved to be much smaller than 1,leadingtoadissociationrateof0.0114s−1,orfrom0.001to0.139s−1,whenthesamplingerroronthefree energy, estimated at 0.593 kcal/mol, isaccounted for. The predicted rate is in fairagreementwiththatmeasuredbysurfaceplasmonresonance(SPR)atpH7.4,0.11±0.08s−1.21
QM/MM corrections.We computed the QM/MMbindingfreeenergycorrectionsonfourrepresenta-tivestructuresextractedfromthePTmetaDsimula-tions: in three of them, imatinib was complexedwith c-Src (A, TS, C, corresponding to the fullybound complex, transition state and encountercomplex,respectively),whileinthefourththelig-andisunboundandfullysolvated(seeFig.3).ThebindingposeinstateBshowninFig.2wasfoundtobesimilarto theboundstateAintermsof ligandorientation and its interactions with watermole-culesandtheproteinandwasthusneglectedinthiscalculation.
TheresultsareshowninTable1.ItisapparentthattheMMtoQM/MMfreeenergycorrectionchangessignificantly in the different environments: it islargestinsolution(4.7±0.4kcal/mol),andsmallestwhenimatinibisfullybound(1.9±0.3kcal/mol).Asexpected,thisseemstosuggestthatMMpredictionsonligandbindingkineticsmayhavesignificantlim-itations as the MM model may not capture im-portanteffectsandchangesalongthebindingpath-way,notablechangesinligandpolarization.
Thecalculateddifferenceinthefreeenergycorrec-tionsbetweenthebound(A)andtheunboundstateis2.8kcal/molandcouldbeexplainedbythediffer-entlevelof ligandburial inthehydrophobicenvi-ronmentofthepocket.Intheboundstate,thelig-andisdeepinthecavityandonlyitspiperazineringisexposedtothesolvent(seeFig.3),allowingonlyafewwatermoleculesaround.Ontheotherhand,thecorrectionvalue(4.7kcal/mol)inthesolvatedstate, much larger than in the bound state (1.9kcal/mol), is consistent with the polar environ-
7
ment,surroundingthemolecule.Furthermore,dif-ferent conformation sampledby the ligand in thesolvatedstatemayalsoaffectthecorrection(seeSI,figureS2).
ThefreeenergycorrectionattheTSis2.4kcal/mol,still larger than that of the bound state by 0.5kcal/mol. In this state, imatinib is detached fromthehingeregionofc-SrcandhasmovedtowardtheDFGmotif,allowingalayerofwatermoleculesbe-tweentheligandandtheprotein.Alargeportionoftheligandisthusaccessibletothesolvent,forminga solvation shell. In the TS, the polar groups ofimatinibformnumeroushydrogenbondswithwa-ter,whileonlythepositivelychargedR154residuefromtheproteinformsasaltbridgewiththeligand(seeFig.2and3).Similarly, towhatobserved fortheunboundstate,theligandmovestoalesshydro-phobicregionwhengoingforAtotheTSjustifyingthe increase in free energy correction.Followingthistrend,theQM/MMtoMMcorrectiontothefreeenergyfortheencountercomplex(C)isrelatively large, intermediatebetween theTS andthe fullysolvatedstate.Here thecorrection is3.9kcal/mol,with2kcal/molofdifferencefromstateA. Here, the nitrogen atom of the pyridine headgroupoftheligandfacesoutwardandismoresol-vent accessible than in previous conformationsalongtheunbindingpath,whiletherestofthelig-andbodyisfoundbetweenthepositivelychargedArg154andMet59;an interaction with themethio-ninesulphuratomcouldalsoaffectthepolarizationofthisintermediatestateandhelpincreasethecor-rectionfactor52.
Basin ∆∆GQM/MM→
MM
[kcal/mol]
∆GMM[kcal/mol]
∆G+∆∆G[kcal/mol]
ATS
-1.9±0.3-2.4±0.3
-7.0±1.09.0±1.5
-4.2±0.911.3±1.2
C -3.9±0.3 -3.4±1.0 -2.6±0.9Unbound -4.7±0.4 0.0±0.0 0.0±0.0
Table1:QM/MMtoMMcorrectiontothefreeenergycal-culated for selectedconformationsalong theminimumfree energy pathway.TheQM/MM freeenergy correc-tioniscalculatedwithBLYP/VDZleveloftheory.Theen-ergiesareinkcal/mol.Thestatisticalerrorisestimatedfromthestandarddeviationofthefreeenergyaverage.Inthefinalcolumn,thefinalvaluesof∆Gcorrectedareshownrelativetotheunboundstate(setatzero).
Figure3:Schematic representationof theboundstate(A),thetransitionstate(TS)andtheencountercomplex(C) of the imatinib/c-Src system used to calculateQM/MM to MM free energy corrections. Imatinib isshown in blue licorice. Residues R154 and M59 areshown in magenta licorice. The water molecules areshown as red spheres excluding hydrogen atoms. Thebackboneofc-Srcisshownasawhitecartoon. Inallcases,bothintheboundstates(A,TSandC)aswellasinthesolvated(unbound)state,theMM-QMfreeenergychangeispositive,highlightinghowtheligandismoresolvatedormorestronglyboundat the QM level rather than in the MM one. TheQM/MMfreeenergycorrectionissignificantinallthecomplexes,rangingfrom1.9kcal/mol(bound)to4.7kcal/mol(unbound),increasingasthedegreeofsolvationoftheligandincreases.
ThechangeinQM/MMfreeenergyalongthepathisthemostimportantfactorfromthepointofviewofpredicting the effect of polarization changes onbindingkinetics.Thelargestdifferenceinthecor-rection free energy is 2.8 kcal/mol between thebound(A)andunboundstate,i.e.theunboundstateismorestablerelativelyto theboundstateattheQM/MMlevel.TheTSandtheencountercomplex(C)havesmallerdifferencesinthecorrectionfreeenergiesrelativetotheboundstate(A):0.5and2.0kcal/mol,fortheTSandstateC,respectively.FromthefullyboundstatetotheTS,thedifferenceincor-rectionfreeenergyisquitesmall,0.5kcal/mol.Thisindicates that the structure of the TS ensemblewouldnotbesignificantlydifferentattheQM/MMlevel,meaningthattheMMTSensembleremainsagoodrepresentationoftheTSitself.
The difference in QM/MM correction energy be-tween the TS and the intermediate (C) is larger,~1.5kcal/mol,becauseofthelargerchangeinsolv-ationbetweenthesestates,asoutlinedabove.ThismeansthatthefreeenergyofthestateCisloweredrelativetotheTS,whichinturnwouldhavetheef-fect of slowing the transition from the encountercomplex to the fullybound state.The rateof for-mation of the encounter complex (C) howevershouldbereducedslightlywithrespecttotheMM
8
prediction,giventhe0.8kcal/molFEcorrectiondif-ferencebetweenthisbasinandtheunboundstate.
Fromtheseresults,wecanconcludethatthenetef-fect of the QM/MM corrections is to stabilize themore solvated formsof the ligand, relative to themoreboundforms.Asaconsequence,theeffectivefree energy barrier to the binding (both startingfromsolution,andfromtheencountercomplex)isincreasedandthebarriertounbindingisreduced.Whiledynamicaleffectsaresignificantindetermin-ing rates for binding, as our calculations haveshown,toafirstapproximationwecanassumethattheywouldbesimilarattheMMandQM/MMlev-els;withthisassumption,thechangeinratecanbeestimated by simple transition state theory. TheQM/MMresultssuggestthatkonwouldbereduced,whilewouldbekoffincreasedwhencomparedtothepredictionsobtainedfromtheMMforce-field.Fol-lowing this approach, the corrected dissociationrateforimatinibisimprovedto0.0260s-1,closertotheexperimentalvalueof(0.11±0.08s–1,obtainedSPR.21
Conclusions
Theuseofan invariantpointchargemodel(as instandardMMforce-fields)mayhavesignificantlim-itationsinpredictingprotein-ligandbindingkinet-ics(on-andoff-rates).Theresultspresentedinthispaper show that there are significant changes inQM/MMcorrectionenergies,thuschangesinelec-tronicpolarizationoftheimatinibligandduringtheprocessof(un)bindingtoSrcthatshouldnotbene-glected.TheQM/MMcorrectionfreeenergyissig-nificantlydependentonthelevelofsolvationoftheligand, with its minimum being observed inhydrophobic environments (bound state) and itsmaximuminhydrophilicareas(solvatedstate).Themultiscaleapproachpresentedhere,combiningTS-PPTISandourMonteCarlobasedQM/MMcorrec-tionmethodprovidesapracticalroutetoassessingthe contributionof ligandpolarization changes todrug-targetbindingkinetics.
ASSOCIATED CONTENT SupportingInformation.DetailsoftheQM/MMtoMMFreeenergyperturbationsimula-tion, the diagram of the “Multiscale Monte Carlo” approach,Replica Exchange Thermodynamic Integration scheme, theconformationalsamplingoftheligandattheQM/MMandMMlevelintheboundstateandintheunboundstateattheQM/MMlevel.TheSupportingInformationisavailablefreeofchargeontheACSPublicationswebsite.
AUTHOR INFORMATION
Corresponding Authors *[email protected]*[email protected]
Author Contributions ⊥S.HandF.Ccontributedequallytothiswork.F.CandG.Sranand analyzed themetadynamics simulations. S.H ran all theQM/MMtoMMfreeenergyperturbationsimulations(assistedbyM.W.vdK.andC.W.).Themanuscriptwaswrittenthroughcontributionsofallauthors.Allauthorshavegivenapprovaltothefinalversionofthemanuscript.
Funding This work is funded by EPSRC [grants no EP/M013898/1,EP/P022138/1, EP/M015378/1 and EP/P011306/1] for fi-nancialsupport.HECBiosim[EPSRCgrantnoEP/L000253/1],CCPBioSim [grant no EP/M022609/1], PRACE and the Ad-vancedComputingResearchCentreattheUniversityofBristolareacknowledgedforcomputertime.CJWisanEPSRCRSEFel-low(EP/N018591/1).MWvdKisaBBSRCDavidPhillipsFel-low(BB/M026280/1).Notes Theauthorsdeclarenocompetingfinancialinterest
ACKNOWLEDGMENT The Authors would like to thank Dr. Reynier Suardiaz and Dr. Kara Ranaghan for useful discussions.
ABBREVIATIONS CV,collectivevariable;PCV,PathCollectiveVariables;PT,par-allel tempering; TPS, Transition Path Sampling; TS-PPTIS,TransitionState-PartialPathTransitionInterfaceSampling.
REFERENCES (1) Cavalli, A.; Spitaleri, A.; Saladino, G.; Gervasio, F. L.
Investigating Drug-Target Association and DissociationMechanisms Using Metadynamics-Based Algorithms. Acc.Chem.Res.2014,48(2),277–285.
(2) Núñez,S.;Venhorst,J.;Kruse,C.G.Target-DrugInteractions:First Principles and Their Application to Drug Discovery.DrugDiscoveryToday.2012,pp10–22.
(3) Jorgensen, W. L. Efficient Drug Lead Discovery andOptimization.Acc.Chem.Res.2009.
(4) Leach, A. R.; Shoichet, B. K.; Peishoff, C. E. Prediction ofProtein-LigandInteractions.DockingandScoring:SuccessesandGaps.J.Med.Chem.2006,49(20),5851–5855.
(5) Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.;Lupyan,D.;Robinson,S.;Dahlgren,M.K.;Greenwood,J.;etal.AccurateandReliablePredictionofRelativeLigandBindingPotencyinProspectiveDrugDiscoverybyWayofaModernFree-Energy Calculation Protocol and Force Field. J. Am.Chem.Soc.2015,137(7).
(6) Homeyer, N.; Stoll, F.; Hillisch, A.; Gohlke, H. Binding FreeEnergy Calculations for Lead Optimization: Assessment ofTheirAccuracyinanIndustrialDrugDesignContext.J.Chem.TheoryComput.2014,10(8),3331–3344.
(7) Masetti,M.;Cavalli,A.;Recanatini,M.;Gervasio,F.L.ExploringComplex Protein-Ligand Recognition Mechanisms withCoarseMetadynamics.J.Phys.Chem.B2009,113(14),4807–4816.
(8) Saleh,N.;Ibrahim,P.;Saladino,G.;Gervasio,F.L.;Clark,T.AnEfficientMetadynamics-BasedProtocolToModeltheBindingAffinity and the Transition State Ensemble of G-Protein-CoupledReceptorLigands.J.Chem.Inf.Model.2017,57(5),1210–1217.
(9) Fidelak, J.; Juraszek, J.; Branduardi, D.; Bianciotto, M.;
9
Gervasio,F.Free-Energy-BasedMethodsforBindingProfileDetermination in aCongeneric SeriesofCDK2 Inhibitors. J.Phys.Chem.B2010,114(29),9516–9524.
(10) Comitani, F.; Limongelli, V.; Molteni, C. The Free EnergyLandscapeofGABABindingtoaPentamericLigand-GatedIonChannel and Its Disruption by Mutations. J. Chem. TheoryComput.2016,12(7),3398–3406.
(11) Votapka, L.W.; Jagger, B. R.; Heyneman, A. L.; Amaro, R. E.SEEKR: Simulation Enabled Estimation of Kinetic Rates, AComputational Tool to Estimate Molecular Kinetics and ItsApplicationtoTrypsin–BenzamidineBinding.J.Phys.Chem.B2017,121(15),3597–3606.
(12) Zhang, R.; Monsma, F. The Importance of Drug-TargetResidenceTime.Curr.Opin.DrugDiscov.Devel.2009,12(4),488–496.
(13) Copeland, R. A.; Pompliano, D. L.; Meek, T. D. Drug–targetResidenceTimeand Its Implications forLeadOptimization.Nat.Rev.DrugDiscov.2006,5(9),730–739.
(14) Swinney,D.C.TheRoleofBindingKineticsinTherapeuticallyUsefulDrugAction.Curr.Opin.DrugDiscov.Devel.2009,12(1),31–39.
(15) Lewandowicz, A.; Tyler, P. C.; Evans, G. B.; Furneaux, R.H.;Schramm,V.L.AchievingtheUltimatePhysiologicalGoalinTransition State Analogue Inhibitors for PurineNucleosidePhosphorylase.J.Biol.Chem.2003,278(34),31465–31468.
(16) Guo, D.; Mulder-Krieger, T.; IJzerman, A. P.; Heitman, L. H.Functional Efficacy of AdenosineA2AReceptor Agonists IsPositivelyCorrelatedtoTheirReceptorResidenceTime.Br.J.Pharmacol.2012,166(6),1846–1859.
(17) Lu, H.; Tonge, P. J. Drug–target Residence Time: CriticalInformation for Lead Optimization. Curr. Opin. Chem. Biol.2010,14(4),467–474.
(18) Buch,I.;Giorgino,T.;DeFabritiis,G.CompleteReconstructionof an Enzyme-Inhibitor Binding Process by MolecularDynamicsSimulations.Proc.Natl.Acad.Sci.U.S.A.2011,108(25),10184–10189.
(19) Shan,Y.;Kim,E.T.;Eastwood,M.P.;Dror,R.O.;Seeliger,M.A.;Shaw,D.E.HowDoesaDrugMoleculeFindItsTargetBindingSite?J.Am.Chem.Soc.2011,133(24),9181–9183.
(20) Schmidtke, P.; Luque, F. J.;Murray, J. B.; Barril, X. ShieldedHydrogen Bonds as Structural Determinants of BindingKinetics:ApplicationinDrugDesign.J.Am.Chem.Soc.2011,133(46),18903–18910.
(21) Morando,M.A.;Saladino,G.;D’Amelio,N.;Pucheta-Martinez,E.; Lovera, S.; Lelli, M.; López-Méndez, B.; Marenchino, M.;Campos-Olivas, R.; Gervasio, F. L. Conformational SelectionandInducedFitMechanismsintheBindingofanAnticancerDrugtotheC-SrcKinase.Sci.Rep.2016,6(1),24439.
(22) Schames,J.R.;Henchman,R.H.;Siegel,J.S.;Sotriffer,C.A.;Ni,H.;McCammon,J.A.DiscoveryofaNovelBindingTrenchinHIVIntegrase.J.Med.Chem.2004,47(8),1879–1881.
(23) Pan,A.C.;Borhani,D.W.;Dror,R.O.;Shaw,D.E.MolecularDeterminants of Drug-Receptor Binding Kinetics. DrugDiscov.Today2013,18(13–14),667–673.
(24) Bisignano,P.;Doerr,S.;Harvey,M.J.;Favia,A.D.;Cavalli,A.;DeFabritiis,G.KineticCharacterizationofFragmentBindingin AmpC β-Lactamase by High-Throughput MolecularSimulations.J.Chem.Inf.Model.2014,140130073847005.
(25) Faver, J. C.; Benson, M. L.; He, X.; Roberts, B. P.; Wang, B.;Marshall, M. S.; Kennedy, M. R.; Sherrill, C. D.; Merz, K. M.Formal Estimation of Errors in Computed AbsoluteInteraction Energies of Protein−Ligand Complexes. J. Chem.TheoryComput.2011,7(3),790–797.
(26) Harder,E.;Damm,W.;Maple,J.;Wu,C.;Reboul,M.;Xiang,J.Y.;Wang,L.;Lupyan,D.;Dahlgren,M.K.;Knight,J.L.;etal.OPLS3:A Force Field ProvidingBroad Coverage ofDrug-like SmallMoleculesandProteins.J.Chem.TheoryComput.2016,12(1),281–296.
(27) Piana,S.;Klepeis,J.L.;Shaw,D.E.AssessingtheAccuracyofPhysical Models Used in Protein-Folding Simulations:Quantitative Evidence from Long Molecular DynamicsSimulations.Curr.Opin.Struct.Biol.2014,24C,98–105.
(28) Fidelak, J.; Juraszek, J.; Branduardi, D.; Bianciotto, M.;Gervasio,F.L.Free-Energy-BasedMethodsforBindingProfile
Determination in aCongeneric SeriesofCDK2 Inhibitors. J.Phys.Chem.B2010,114(29),9516–9524.
(29) Colizzi,F.;Perozzo,R.;Scapozza,L.;Recanatini,M.;Cavalli,A.Single-MoleculePullingSimulationsCanDiscernActivefromInactiveEnzymeInhibitors.J.Am.Chem.Soc.2010,132(21),7361–7371.
(30) Limongelli,V.;Bonomi,M.;Marinelli,L.;Gervasio,F.L.;Cavalli,A.; Novellino, E.; Parrinello, M. Molecular Basis ofCyclooxygenase Enzymes (COXs) Selective Inhibition. Proc.Natl.Acad.Sci.U.S.A.2010,107(12),5411–5416.
(31) Pohorille,A. (Andrew);Chipot,C. (Christophe).FreeEnergyCalculations : Theory and Applications in Chemistry andBiology;Springer,2007.
(32) Laio,A.;Gervasio,F.L.Metadynamics:AMethodtoSimulateRareEventsandReconstructtheFreeEnergyinBiophysics,ChemistryandMaterialScience.ReportsProg.Phys.2008,71(12),126601.
(33) Dellago,C.;Bolhuis,P.G.ActivationEnergiesfromTransitionPath Sampling Simulations.Mol. Simul. 2004, 30 (11–12),795–799.
(34) Branduardi,D.;Gervasio,F.L.;Parrinello,M.FromAtoBinFreeEnergySpace.J.Chem.Phys.2007,126(5).
(35) Gervasio, F. L.; Laio, A.; Parrinello, M. Flexible Docking inSolutionUsingMetadynamics.J.Am.Chem.Soc.2005,127(8),2600–2607.
(36) Saladino, G.; Gauthier, L.; Bianciotto, M.; Gervasio, F. L.Assessing the Performance of Metadynamics and PathVariables in Predicting the Binding Free Energies of P38Inhibitors.J.Chem.TheoryComput.2012,8(4),1165–1170.
(37) Herbert,C.;Schieborr,U.;Saxena,K.;Juraszek,J.;DeSmet,F.;Alcouffe,C.;Bianciotto,M.;Saladino,G.;Sibrac,D.;Kudlinzki,D.; et al. Molecular Mechanism of SSR128129E, anExtracellularlyActing,Small-Molecule,AllostericInhibitorofFGFReceptorSignaling.CancerCell2013,23(4),489–501.
(38) Tiwary,P.;Parrinello,M.FromMetadynamics toDynamics.Phys.Rev.Lett.2013.
(39) Tiwary, P.; Limongelli, V.; Salvalaglio, M.; Parrinello, M.Kinetics of Protein-Ligand Unbinding: Predicting Pathways,Rates,andRate-LimitingSteps.Proc.Natl.Acad.Sci.2015,112(5),E386-91.
(40) Casasnovas, R.; Limongelli, V.; Tiwary, P.; Carloni, P.;Parrinello,M.UnbindingKineticsofaP38MAPKinaseTypeIIInhibitorfromMetadynamicsSimulations.J.Am.Chem.Soc.2017,139(13),4780–4788.
(41) Barducci,A.;Chelli,R.;Procacci,P.;Schettino,V.;Gervasio,F.L.; Parrinello, M. Metadynamics Simulation of PrionProtein: β-Structure Stability and the Early Stages ofMisfolding.J.Am.Chem.Soc.2006,128(8),2705–2710.
(42) Berteotti, A.; Cavalli, A.; Branduardi, D.; Gervasio, F. L.;Recanatini, M.; Parrinello, M. Protein ConformationalTransitions:TheClosureMechanismofaKinaseExploredbyAtomisticSimulations.J.Am.Chem.Soc.2009,131(1),244–250.
(43) Shan, Y.; Seeliger,M. A.; Eastwood,M. P.; Frank, F.; Xu,H.;Jensen,M.Ø.;Dror,R.O.;Kuriyan,J.;Shaw,D.E.AConservedProtonation-DependentSwitchControlsDrugBindingintheAblKinase.Proc.Natl.Acad.Sci.U.S.A.2009,106(1),139–144.
(44) Oleinikovas, V.; Saladino, G.; Cossins, B. P.; Gervasio, F. L.UnderstandingCrypticPocketFormationinProteinTargetsbyEnhancedSampling Simulations. J.Am.Chem.Soc.2016,138(43),14257–14263.
(45) Durrant, J. D.; McCammon, J. A. Molecular DynamicsSimulationsandDrugDiscovery.BMCBiol.2011,9(1),71.
(46) Dellago,C.;Bolhuis,P.G.TransitionPathSamplingandOtherAdvanced Simulation Techniques for Rare Events. Adv.Comput.Simul.ApproachesSoftMatterSci.Iii2009,221,167–233.
(47) Juraszek,J.;Saladino,G.;VanErp,T.S.;Gervasio,F.L.EfficientNumerical Reconstruction of Protein Folding Kinetics withPartialPathSamplingandPathlikeVariables.Phys.Rev.Lett.2013,110(10),1–5.
(48) Robertson,M.J.;Tirado-Rives,J.; Jorgensen,W.L.ImprovedPeptide and Protein Torsional Energeticswith theOPLSAA
10
ForceField.J.Chem.TheoryComput.2015,11(7),3499–3509.(49) Maier, J. A.; Martinez, C.; Kasavajhala, K.; Wickstrom, L.;
Hauser,K.E.;Simmerling,C.Ff14SB:ImprovingtheAccuracyofProteinSideChainandBackboneParametersfromFf99SB.J.Chem.TheoryComput.2015,11(8),3696–3713.
(50) Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; deGroot,B.L.;Grubmüller,H.;MacKerell,A.D.CHARMM36m:AnImprovedForceFieldforFoldedandIntrinsicallyDisorderedProteins.Nat.Chem.Biol.2017,14(1),71–73.
(51) Lindorff-Larsen,K.;Piana,S.;Palmo,K.;Maragakis,P.;Klepeis,J. L.; Dror, R. O.; Shaw, D. E. Improved Side-Chain TorsionPotentialsfortheAmberFf99SBProteinForceField.ProteinsStruct.Funct.Bioinforma.2010,78(8),1950–1958.
(52) Ranaghan, K. E.; Hung, J. E.; Bartlett, G. J.; Mooibroek, T. J.;Harvey,J.N.;Woolfson,D.N.;vanderDonk,W.A.;Mulholland,A. J. A Catalytic Role for Methionine Revealed by aCombinationofComputationandExperimentsonPhosphiteDehydrogenase.Chem.Sci.2014,5(6),2191–2199.
(53) Politzer, P.; Murray, J.; Clark, T.; Resnati, G. The σ-HoleRevisited.Phys.Chem.Chem.Phys.2017,19,32166–32178.
(54) Amaro, R. E.; Mulholland, A. J. Bridging Biological andChemical Complexity in the Search for Cures: MultiscaleMethodsinDrugDesign.NatRevChem2018,2(4),0148.
(55) Monte,T.;Simulations,C.Q.0REPORTSAPrioriEvaluationofAqueous Polarization Effects. Science (80-. ). 1992, 258(October).
(56) Gao,J.EnergyComponentsofAqueousSolution :InsightfromHybridQMrMMSimulationsUsingaPolarizable.J.Comput.Chem.1997,18(8),1061–1071.
(57) Woods,C.J.;Manby,F.R.;Mulholland,A.J.AnEfficientMethodfor the Calculation of Quantum Mechanics/MolecularMechanics Free Energies. J. Chem. Phys. 2008, 128 (1),014109.
(58) Cave-Ayland,C.;Skylaris,C.K.;Essex,J.W.DirectValidationof the Single Step Classical to Quantum Free EnergyPerturbation.J.Phys.Chem.B2015,119(3),1017–1025.
(59) Genheden,S.;CabedoMartinez,A.I.;Criddle,M.P.;Essex,J.W.Extensive All-Atom Monte Carlo Sampling and QM/MMCorrectionsintheSAMPL4HydrationFreeEnergyChallenge.J.Comput.Aided.Mol.Des.2014,28(3),187–200.
(60) Woods,C.J.;Shaw,K.E.;Mulholland,A.J.CombinedQuantumMechanics/Molecular Mechanics (QM/MM) Simulations forProtein-LigandComplexes:FreeEnergiesofBindingofWaterMoleculesinInfluenzaNeuraminidase.J.Phys.Chem.B2015,119(3),997–1001.
(61) Pawson,T.;Scott,J.D.ProteinPhosphorylationinSignaling--50 Years and Counting. Trends Biochem. Sci.2005, 30 (6),286–290.
(62) Stehelin,D.;Fujita,D.J.;Padgett,T.;Varmus,H.E.;Bishop,J.M.DetectionandEnumerationofTransformation-DefectiveStrainsofAvianSarcomaViruswithMolecularHybridization.Virology1977,76(2),675–684.
(63) Huse,M.;Kuriyan,J.TheConformationalPlasticityofProteinKinases.Cell2002,109(3),275–282.
(64) Lovera, S.; Sutto, L.; Boubeva, R.; Scapozza, L.; Dölker, N.;Gervasio, F. L. The Different Flexibility of C-Src and c-AblKinases Regulates theAccessibility of aDruggable InactiveConformation.J.Am.Chem.Soc.2012,134(5),2496–2499.
(65) Deng, Y.; Roux, B. Computations of Standard Binding FreeEnergieswithMolecularDynamicsSimulations.J.Phys.Chem.B2009,113(8),2234–2246.
(66) Roux,B.;Banavali,N.K.ConformationalEnergyLandscapeofSrc KinaseActivation Processes.Abstr. Pap. Am. Chem. Soc.2006,231.
(67) Lin,Y.-L.;Meng,Y.;Jiang,W.;Roux,B.ExplainingWhyGleevecIs a Specific and Potent Inhibitor of Abl Kinase. Proc. Natl.Acad.Sci.2013,110(5),1664–1669.
(68) Cowan-Jacob,S.W.;Fendrich,G.;Manley,P.W.; Jahnke,W.;Fabbro,D.;Liebetanz,J.;Meyer,T.TheCrystalStructureofaC-SrcComplex inanActiveConformationSuggestsPossibleStepsinc-SrcActivation.Structure2005,13(6),861–871.
(69) Xu,W.; Doshi, A.; Lei, M.; Eck, M. J.; Harrison, S. C. CrystalStructures of C-Src Reveal Features of Its AutoinhibitoryMechanism.Mol.Cell1999,3(5),629–638.
(70) Zhang,S.;Yu,D.TargetingSrcFamilyKinasesinAnti-CancerTherapies:TurningPromiseintoTriumph.TrendsPharmacol.Sci.2012,33(3),122–128.
(71) Nagar,B.C-AblTyrosineKinaseandInhibitionbytheCancerDrugImatinib(Gleevec/STI-571).J.Nutr.2007,137(6Suppl1),1518S–1523S;discussion1548S.
(72) Seeliger,M.A.;Nagar,B.;Frank,F.;Cao,X.;Henderson,M.N.;Kuriyan,J.C-SrcBinds totheCancerDrugImatinibwithanInactive Abl/c-Kit Conformation and a DistributedThermodynamicPenalty.Structure2007,15(3),299–311.
(73) Seeliger,M.A.;Ranjitkar,P.;Kasap,C.; Shan,Y.; Shaw,D.E.;Shah,N.P.;Kuriyan,J.;Maly,D.J.EquallyPotentInhibitionofC-SrcandAblbyCompoundsThatRecognizeInactiveKinaseConformations.CANCERRes.2009,69(6),2384–2392.
(74) Wilson,C.;Agafonov,R.V;Hoemberger,M.;Kutter,S.;Zorba,A.;Halpin,J.;Buosi,V.;Otten,R.;Waterman,D.;Theobald,D.L.;etal.KinaseDynamics.UsingAncientProteinKinasestoUnravelaModernCancerDrug’sMechanism.Sci.(NewYork,NY)2015,347(6224),882–886.
(75) Sali, A.; Blundell, T. L. Comparative Protein Modelling bySatisfactionofSpatialRestraints.J.Mol.Biol.1993,234(3),779–815.
(76) Best,R.B.;Hummer,G.OptimizedMolecularDynamicsForceFieldsAppliedtotheHelix-CoilTransitionofPolypeptides.J.Phys.Chem.B2009,113(26),9004–9015.
(77) Wang,J.M.;Wolf,R.M.;Caldwell,J.W.;KOLLMAN,P.A.;Case,D. A. Development and Testing of a General Amber ForceField.J.Comput.Chem.2004,25(9),1157–1174.
(78) Frisch,M.J.;Trucks,G.W.;Schlegel,H.B.;Scuseria,G.E.;Robb,M.A.;Cheeseman,J.R.;Scalmani,G.;Barone,V.;Mennucci,B.;Petersson,G.A.; etal. Gaussian 09,RevisionD.01.GaussianInc.Gaussian,Inc.2009,pWallingfordCT.
(79) Hess,B.;Kutzner,C.;vanderSpoel,D.;Lindahl,E.GROMACS4: Algorithms for Highly Efficient, Load-Balanced, andScalableMolecularSimulation.J.Chem.TheoryComput.2008,4(3),435–447.
(80) Bonomi,M.;Branduardi,D.;Bussi,G.;Camilloni,C.;Provasi,D.;Raiterie,P.;Donadio,D.;Marinelli,F.;Pietrucci,F.;Broglia,R. A.; et al. PLUMED: A Portable Plugin for Free-EnergyCalculations with Molecular Dynamics. Comput. Phys.Commun.2009,180(10),1961–1972.
(81) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Samplingthrough Velocity Rescaling. J. Chem. Phys. 2007, 126 (1),14101.
(82) Bussi,G.;Gervasio,F.L.;Laio,A.;Parrinello,M.Free-EnergyLandscapeforBetaHairpinFoldingfromCombinedParallelTempering andMetadynamics. J. Am. Chem. Soc.2006,128(41),13435–13441.
(83) Bonomi, M.; Parrinello,M. Enhanced Sampling in theWell-TemperedEnsemble.Phys.Rev.Lett.2010,104(19),190601.
(84) Woods,C.J.;Essex,J.W.;King,M.A.EnhancedConfigurationalSamplinginBindingFree-EnergyCalculations.JPhysChemB2003,107,13711–13718.
(85) Becke, A. D. Density-Functional Exchange-EnergyApproximationwithCorrectAsymptoticBehavior.Phys.Rev.A1988,38(6),3098–3100.
(86) Lee,C.;Yang,W.;Parr,R.G.DevelopmentoftheColle-SalvettiCorrelation-EnergyFormulaintoaFunctionaloftheElectronDensity.Phys.Rev.B1988,37(2),785–789.
(87) Woods,C.J.siremol.orghttps://siremol.org/(accessedDec6,2017).
(88) Werner,H.J.;Knowles,P.J.;Knizia,G.;Manby,F.R.;Schütz,M.Molpro: A General-Purpose Quantum Chemistry ProgramPackage.WileyInterdiscip.Rev.Comput.Mol.Sci.2012,2(2),242–253.
(89) Shaw, K. E.;Woods, C. J.;Mulholland, A. J. Compatibility ofQuantum Chemical Methods and Empirical (MM) WaterModelsinQuantumMechanics/MolecularMechanicsLiquidWaterSimulations.J.Phys.Chem.Lett.2010,1(1),219–223.
(90) Pentika, U.; Shaw, K. E.; Woods, C. J.; Mulholland, A. J.;Senthilkumar, K. Lennard # Jones Parameters for B3LYP /CHARMM27QM/MMModelingofNucleicAcidBasesQM/MMModelingofNucleicAcidBases.2009,No.Mm,396–410.
(91) Senthilkumar,K.;Mujika, J.I.;Ranaghan,K.E.;Manby,F.R.;
11
Mulholland, A. J.; Harvey, J. N. Analysis of Polarization inQM/MMModellingofBiologicallyRelevantHydrogenBonds.J.R.Soc.Interface2008,5(Suppl_3),207–216.
(92) Huang, J.;Mei,Y.;König,G.; Simmonett,A.C.;Pickard,F.C.;Wu,Q.;Wang,L.P.;MacKerell,A.D.;Brooks,B.R.;Shao,Y.AnEstimation of Hybrid Quantum Mechanical MolecularMechanicalPolarizationEnergiesforSmallMoleculesUsingPolarizableForce-FieldApproaches.J.Chem.TheoryComput.2017,13(2),679–695.
(93) Beierlein, F. R.; Michel, J.; Essex, J. W. A Simple QM/MMApproachforCapturingPolarizationEffectsinProtein-LigandBindingFreeEnergyCalculations.J.Phys.Chem.B2011,115(17),4911–4926.
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