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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

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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-

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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

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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 *f.l.gervasio@ucl.ac.uk*Adrian.Mulholland@bristol.ac.uk

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.

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