Effect of Atomic Charges on Octanol–Water Partition Coefficient Using Alchemical Free Energy ...

15 Pages·2017·1.97 MB·English

molecules
Article
Effect of Atomic Charges on Octanol–Water Partition
Coefficient Using Alchemical Free Energy Calculation
KojiOgata* ID,MakotoHatakeyamaandShinichiroNakamura
RIKENInnovationCenter,NakamuraLaboratory,2-1Hirosawa,Wako,Saitama351-0198,Japan;
[email protected](M.H.);[email protected](S.N.)
* Correspondence:[email protected];Tel.:[phone]
Received:19January2018;Accepted:14February2018;Published:15February2018
Abstract: The octanol–water partition coefficient (logP ) is an important index for measuring
ow
solubility, membrane permeability, and bioavailability in the drug discovery field. In this paper,
the logP values of 58 compounds were predicted by alchemical free energy calculation using
ow
moleculardynamicssimulation. Infreeenergycalculations,theatomicchargesofthecompoundsare
alwaysfixed. However,theymustberecalculatedforeachsolvent. Therefore,threedifferentsets
ofatomicchargesweretestedusingquantumchemicalcalculations,takingintoaccountvacuum,
octanol,andwaterenvironments. Thecalculatedatomicchargesinthedifferentenvironmentsdo
notnecessarilyinfluencethecorrelationbetweencalculatedandexperimentallymeasured∆G
water
values. Thelargestcorrelationcoefficientvaluesofthesolvationfreeenergyinwaterandoctanol
were 0.93 and 0.90, respectively. On the other hand, the correlation coefficient of logP values
ow
calculatedfromfreeenergies,thelargestofwhichwas0.92,wassensitivetothecombinationofthe
solvationfreeenergiescalculatedfromthecalculatedatomiccharges. Theseresultsrevealthatthe
solventassumedintheatomicchargecalculationisanimportantfactordeterminingtheaccuracyof
predictedlogP values.
ow
Keywords: MDsimulation;thermodynamicintegration;solvationenvironment;atomiccharge
1. Introduction
The octanol–water partition coefficient (logP ) is an index used in drug discovery processes
ow
to estimate the solubility, membrane permeability, and bioavailability of compounds [1,2].
Severalexperimentalmethodsformeasuringithavebeendeveloped[2–6],buttheyaretimeconsuming
andcostly,becauseexperimentalmethodsusetheactualcompounds,andsometimes,thesynthesisof
acompoundtakesalongtime. Toacceleratethedrugdiscoveryprocessandtoreduceitscost,weneed
alogP measurementmethodthatiseasier,faster,andmoreaccuratethanthecurrentones.
ow
Computational methods for predicting the logP value have been developed using various
ow
techniques. The methods summing the contributions of a compound’s atoms and fragments
(e.g., XLOGP3 [7], KOWWIN [8], etc.) rapidly calculate logP values similar to those obtained
ow
experimentally,andhavethereforebeenusedinthescreeningofdrug-likecompounds[9],makingit
possible to calculate the logP values for the tens of millions of compounds in databases such as
ow
PubChem[10]andZINC[11].
The logP values of compounds can also be predicted accurately by alchemical free energy
ow
calculationtechniquesusingmoleculardynamics(MD)simulationandMonteCarlosimulation,suchas
thermodynamicintegration(TI)[12]andfreeenergyperturbation(FEP)[13]. Thesemethodshave
beenusedtocalculatehydrationfreeenergyofaminoacids[14],nucleobases[15],andligand/protein
bindingfreeenergy[16–28]. Theycantreatwatermoleculeseitherimplicitlyorexplicitly. Thus,inthe
caseofligand/proteinbindingfreeenergycalculation,theycanbeusedtopredictthethermodynamic
Molecules2018,23,425;doi:10.3390/molecules23020425 www.mdpi.com/journal/molecules
Molecules2018,23,425 2of15
behavior of a ligand in solvents. In compounds containing water molecules bridging between
the protein and ligand, the calculation with explicit water molecules is efficient for calculating
binding free energy. In the application of alchemical free energy calculation to logP calculation,
ow
DeBolt and Kollman successfully estimated the logP using FEP method with modified force
ow
field [29]. They were able to reproduce the structural and thermodynamic behaviors of liquid
octanol. Using an implicit solvation model, Huang et al. reported a logP prediction method
ow
in which the 3D-RISM-KH theory was used to calculate the solvation free energy in water and in
octanol[30]. Toreproducetheexperimentalconditions,Bhatnagaretal. reportedanadaptivebiasing
forcemethodusingexplicitwaterandoctanolsolvents[31]. Inanotherapplication,saturatedoctanol
solvation was used for the calculation, taking the hydrate state of octanol in the experiment into
account [32,33]. These methods were able to estimate logP values in agreement with the ones
ow
measuredexperimentally. Thealchemicalmethodsusingall-atomMDsimulationrequiretimeand
computerresources,comparedwithatom-andfragment-basedmethods. However,thesemethodsare
abletopredictthepartitioncoefficientofseveralsolvents,andobservethethermodynamicbehavior
ofcompoundsinthesolvents. Therefore,thefreeenergycalculationusingthealchemicalmethodis
expectedtoprovideusefulinformationonphysicalchemistrypropertiesofthecompounds.
Inthispaper,thelogP valuesforrelativelysmallcompoundswerepredictedfromthesolvent
ow
freeenergiescalculatedbyTI[34,35]. Thecalculationofthedifferencefreeenergy,∆G,wasestimated
by the Bennett’s acceptance ratio (BAR) method [36]. To analyze the contribution of the atomic
charges of the compounds, three sets of atomic charges were examined: one in vacuum, one in
octanol,andtheotherinwater. Solvationfreeenergiesinwaterandinoctanolareingoodagreement
withtheonesmeasuredexperimentally. Thecorrelationcoefficient(R)ofthesolvationfreeenergies
indicatedstrongcorrelationbetweencalculatedandexperimentallymeasuredvalues. Theydidnot
differ significantly among the three sets of atomic charges. The logP values, however, showed
ow
slightlydifferentbehaviors. Infact,theRvaluesoflogP dependedonthecombinationoftheatomic
ow
chargescalculatedinthedifferentsolvents. Theseresultsrevealthattheenvironmentassumedin
thecalculationoftheatomicchargesisaverycriticalfactorforthelogP calculations. Therefore,
ow
ourresultsprovideusefulinformationforimprovingthequalityofthecalculations. Finally,thelogP
ow
valuesof17drugscalculatedusingthebestcombinationoftheatomicchargesshowedgoodagreement
withthevaluesmeasuredexperimentally.
2. ResultsandDiscussion
2.1. SolvationFreeEnergyinWater
Tocalculatefreeenergyinwater,thethreechargesetswereusedindependently. Inthispaper,
the notation of the parameter sets calculated with the atomic charges in the different solvents are
simplifiedasP {x},wherexiseitherv(vacuum),o(octanol),orw(water). Itshouldbenotedthat,
water
inthiswork,wedidnotchangetheatomicchargesinwatermolecules,becausetheforcefieldofwater
moleculeswasestablishedbythemanystudiesconductedonwatermolecules[37].
Strong correlations between calculated and experimentally measured ∆G values were
water
observed(Figure1). Inparticular,thefreeenergycalculatedusingP {w},forwhichthecoefficient
water
of determination (R2) is 0.87, indicated good agreement with experimentally measured values.
ThefreeenergycalculatedusingP {v}alsoshowedastrongcorrelationwiththeexperimentaldata,
water
eventhoughR2(=0.84)wasthesmallestinthethreecases. Theseresultsconfirmthatthecalculated
atomic charges in the different environments do not necessarily influence the correlation between
calculatedandexperimentallymeasured∆G values.
water
Molecules2018,23,425 3of15
Molecules 2018, 23, x FOR PEER REVIEW 3 of 15
Molecules 2018, 23, x FOR PEER REVIEW 3 of 15
25

FFiigguurree 11.. SSccaatttteerr ddiiaaggrraamm ooff ccaallccuullaatteedd aanndd eexxppeerirmimenentatlallyly mmeaesausruerde d∆G∆ Gvavlualeuse isn iwnawteart esrolsvoelnvte.n Rt.2
Ra2nadn rdegreregsrseisosnio lninlein aerea rsehsohwonw. n.
Figure 1. Scatter diagram of calculated and experimentally measured ∆G values in water solvent. R2
OOnn tthhaened oo rttehhgererers hshiaoannn dldin,,e t thahreee svvhaoalwluunee.s s ooff aattoommiicc cchhaarrggee wweerree sseennssiittiivvee ttoo tthhee ssoollvveenntt iinn tthhee qquuaannttuumm
cchheemmiissttrryy ccaallccuullaattiioonn ((FFiigguurree 22)).. IInn tthhee tthhrreeee ssoollvveennttss,, ssoommeewwhhaatt llaarrggee ddiiffffeerreenncceess iinna attoommiicc cchhaarrggee
On the other hand, the values of atomic charge were sensitive to the solvent in the quantum
vvaalluueessc caannb beef foouunnddi nint htheec chhaarrggeeddg grroouuppc coonnttaaininininggh heetteerrooaattoommss,,e e.g.g.,.,o oxxyyggeenni inna acceettoonnee,,n niittrrooggeenn
chemistry calculation (Figure 2). In the three solvents, somewhat large differences in atomic charge
iinnp pyyrriiddiinnee,,a anndd ooxxyyggeenn iinn ooccttaannooll.. TThhee ccaallccuullaatteedd aattoommiicc cchhaarrggeess iinn ooccttaannooll aanndd wwaatteerr wweerree ssiimmiillaarr,,
values can be found in the charged group containing heteroatoms, e.g., oxygen in acetone, nitrogen
aannddw weereres lsilgihghtltylyd idffieffreernetnftr ofrmomth ethoen eosniens tihne tvhaec uvuacmuustmat es.taTthei. sTthenisd etenncdyecnacnyb ceaunn bdee rustnodoedrsfrtooomd
in pyridine, and oxygen in octanol. The calculated atomic charges in octanol and water were similar,
tfhreomgr atphhe sgdrarapwhsn dforarwthne faotro mthiec cahtoamrgiecs cvhsa.rdgieesl evcstr diciecloencstrtaicn tcovnaslutaenst( Fviagluurees S(1F)i.gTuhree Sa1to).m Tihcec haatorgmeisc
and were slightly different from the ones in the vacuum state. This tendency can be understood
dcrhaamrgafertsoic madl rtlahymei ngacrtaircpeaahlsslye d orianrwcdrnee caforsere a tosheer aadtteodcmrieeicla ecschet araricgt ecdso ivenslse tdcaitnerlitecsc tacroricon ucsotnandnstt1as0n ,at arvonauldunebdse (c1Fo0igm, uaernec dSo 1nb)s.e tTcaohnemt ateth ocemorenicas fttaenr.t
Tthheerseeacdhftiaefrfrge. erTse nhdcereasmes cadatiinfcfaeallrfyef enicnctcersteh acesaern eo gar rfdefesecsctri oetanhseel i narete gdirnieeslteshciteornisc c lcaionttnees rtiandn ittash gearr aosmcuanstdt(e F1r0i gd, uaianrgedr 1ab)me.csTo mh(Feei gsclouonrpsete a1no)t.f Tthhee
rselgorpeest shoioef rntehaliefnt erere.fg oTrreh∆sessGieow ndati eflrfienvreae lnfuoceerss ∆ wcGainwth ataerPf fvweacattle urt(hewse )wriesigtcrhleo sPsseiwoattneor (lwtihn)ae it siwn c ilttohhsee Ps wtcoaat tettreh(roa )td, iwwagihtreharm ePasw sa(tFetrh(igoau)t,r wwe i1ht)he. rPTewhaaest etrh(va)t
iws sitlhig sPhltwolapyteer( dvoi)ff ftihes rese rlniegtghrfertlsoysmi odnit fhlfieenreoe fntohtr e f∆rrsGo.mwaHte rt ohvwael ueovetshe rew,ristth.h e HPwRoawtevr(ewavl)u eirse, s ctldhoseoe Rnto ov ttahdlauitf ewfsei rtdhso iP gnwnaoteirtfi( odc)a,i fwnfethlrye rseaigamsn otihfniacgta nthtley
tahmreoenpwga irtthha meP twehatterer(erves). piFsa usrlraitgmhheetrltyme rdosi.rf efFe,urterhnteht referromwmeo rrtehee,s ttohrtoehnreegr sw.c oHerrorewe lseatvrtioeornn, gtsh caeom Rrro evnlaaglutiteohsnr dese oa. mnoot ndgif ftehrr esieg n ificantly
∆∆aGGmwwoaantteergr vthavelu athelusre,e efs o,pra rwafmohriectherw st.hh Feiuc Rrht hveartmlhueoerse ,oR tfh ePrvweaa twelru(ever)es– sPtwrooatfner(go c)P,o wrPrawteealrtae(rtv(ivo)–)n–PsP wawamatteeorr((nwog)) ,t, harnePedw aPtewra(tver)(–o)P–wPawtearte(rw(w),)
apnadirPs, wer(∆eoG )0–w.Pa9te9r 1v2a,l (u0we.9s),8 pf8oa5ri, r wasn,hwdic he0 r.t9eh9e09 .6R9, 9 vr1ea2slu,pe0es.c9 ot8ifv8 Pe5wl,yatae.r n(Ivnd)– t0Ph.w9east9ere9(o 6c),a, rsPeewssatp,e rt(evhc)et–i Povwreadtleyre(.wr I)in,n a twnhdhe siPcewhact etar(hsoe)e– scP,owtmahterep(woo)ur dnedrs
water water
pairs, were 0.9912, 0.9885, and 0.9996, respectively. In these cases, the order in which the compounds
ianrwe ahriarcrahen atghrereadnc agocemcdo parocdcuionnrgdd istnoga rttheoe at hr∆erGa ∆nwGagtweera,td eir,s ai smc cmooorrerde io norrg lleetsossst tthhheee ∆ssaaGmmweae ta earm,moisnogmn gtoh rtehe teho rtrehlere epsesa iptrhsa.e iTrssha.e mTsehe aeansmeal yaosnneagsl ythsees
tshhroeewp tahirast. tThhee saetoamnaicl ycsheasrsgheosw wtehraet athffeeactteodm ibcyc hthaerg seoslvweenrte tayfpfeecst eadssbuymtheed sionl vtehnet ctaylpceuslaatsisounm, beudt
show that the atomic charges were affected by the solvent types assumed in the calculation, but
itnhtehsee tcdhaeilfscfeeu rdleaifntfiecorenesn, dcbeiudst dntihodet n saeoftfd eaicffftfe etcrhte etnh cceoe crsordrerlieadltaintoioontn o aofff f tethhceet t∆∆hGGewwcaateotre rrv vraeallulauetseio.s n. ofthe∆Gwatervalues.

Figure 2. Calculated atomic charges of (a) Acetone, (b) Pyridine, and (c) Octanol in vacuum, octanol, and water.
Figure 2. Calculatedatomicchargesof(a)Acetone, (b)Pyridine, and(c)Octanolinvacuum, octanol,

andwater.
Figure 2. Calculated atomic charges of (a) Acetone, (b) Pyridine, and (c) Octanol in vacuum, octanol, and water.
Molecules2018,23,425 4of15
TheRMSEandMAEvaluesinthethreeparametersetsshowoppositerelationstotheRvalues;
i.e.,thecalculateddatahavingstrongcorrelationshowedlargeerrors(Table1). The∆G ofP {v}
water water
hadthesmallestRandR2values,buttheerrors,forwhichtheRMSEandMAEvaluesare4.49kJ/mol
(=1.07 kcal/mol) and 3.65 (=0.87 kcal/mol), respectively, were the smallest in the three parameter
sets. Ontheotherhand,thecalculationwithP {w}showsthelargestRvalue,buttheRMSEand
water
MAEvaluesarethelargest. Inthesecalculations,thedifferenceofRMSEandMAEvalues,however,
are1.2kJ/moland0.6kJ/molbetweenP {v}andP {w}. Thesemaynotbesignificantdifferences
water water
amongthethreeparameters. Therefore,foralltheselectionsofatomiccharges,theBARmethodcan
estimatethe∆G valuesaccuratelyenough.
water
Table1.Summaryoffreeenergyinwatercalculations.
Parameter R R2 RMSEa(kJ/mol) MAEb(kJ/mol)
Pwater{v} 0.92 0.84 4.47 3.63
Pwater{o} 0.93 0.87 5.05 3.74
Pwater{w} 0.93 0.87 5.69 4.28
aRootmeansquareerror;bMeanaverageerror.
2.2. SolvationFreeEnergyinOctanol
Incalculatingthefreeenergyinoctanol,ninesetsoftheatomicchargeswereused:allcombinations
ofthethreesetsofatomicchargesofthecompound(3sets)andoctanol(3sets).Theatomicchargesof
octanolmoleculeinoctanolsolvation,theoctanolenvironment,shouldbeconsidered.However,inthis
work,tounderstandtheeffectoftheatomicchargesinoctanolonthelogP calculation,wetookinto
ow
accounttheatomicchargesintheoctanolmoleculeforvacuum,octanol,andwaterstate.
Thecompoundandoctanolparametersetscalculatedwiththeatomicchargesinoctanolisdefined
as P {x, y}, in which x and y (for compound and octanol, respectively) are either v(vacuum),
octanol
o(octanol),orw(water).
Tendenciessimilartothoseseenintheresultsobtainedwiththe∆G calculationcouldbeseen
water
intheresultsobtainedwiththe ∆G calculation. ItcanbeseeninFigure3thatallthecalculated
octanol
∆G valuesshowedstrongcorrelationswiththeonesmeasuredexperimentally.ThelargestRvalue
octanol
was0.9(P {v,o}andP {v,w}),thoughthesevaluesareslightlysmallerthanthatin∆G (0.93).
octanol octanol water
Thecalculated∆G valuesdistributedtowardthesmallrangeofthehorizontalaxis,thus,allthe
octanol
calculationsmayunderestimatethe ∆G value. ThetendencyoftherelationshipbetweentheR2
octanol
valuesanderrorvalues(RMSEandMAE)issimilartothatseeninthe∆G results;i.e.,thelargertheR2
water
valuesare,thelargertheRMSEandMAEvaluesare.ThelargestMAEis13.26kJ/mol(=3.16kcal/mol)in
the∆G withP {w,w}.Thisvalueisalittlebitlargerthanthatin∆G .Thisresultrevealsthat
octanol octanol water
thecalculationof∆G valuesaccumulatesmoreerrorsthanthatof∆G .However,these∆G
octanol water octanol
valuesstillshowedstrongcorrelationwiththeexperimentaldata.
In Figure 3 and Table 2, the correlations between the calculated and experimentally measured
∆G valuesareshowntobeindependentoftheatomiccharges. ThevaluesofRandR2 areclose
octanol
inallthe∆G calculations. TheR,R2,RMSE,andMAEvaluesofthe∆G withP {o,o}are
octanol octanol octanol
comparablewiththeotherones. Thismeansthattheatomicchargesdidnotaffectthecorrelationof
∆G calculations.The∆G calculatedwitheitherP {v,o}orP {v,w}hadthelargestRand
octanol octanol octanol octanol
R2values. Thosevaluesindicatedastrongcorrelationwiththeexperimentaldata. Ontheotherhand,
the∆G calculatedwithP {w,v}hadthesmallestRandR2values. However,thesevaluesstill
octanol octanol
indicatedstrongcorrelation.ThedifferencesofRandR2valuesbetweenP {v,o}(orP {v,w})and
octanol octanol
P {w,v},are0.02and0.04,respectively.Thesearenotnecessarilysignificantdifferences.Therefore,
octanol
itispossibletoconcludethatthecalculatedatomicchargesinthedifferentenvironmentsdidnotaffect
theRandR2valuesin∆G calculations.
octanol
Molecules 2018, 23, x FOR PEER REVIEW 5 of 15
Molecules2018,23,425 5of15
Table 2. Summary of free energy in octanol calculations.
Table2.Summaryoffreeenergyinoctanolcalculations.
Parameter R R2 RMSEa(kJ/mol) MAEb(kJ/mol)
PaProactmanoel{tve,r v} 0.R89 0.8R02 RMS1E1.a18(k J/mol) MA1E0.b3(6k J/mol)
Poctanol{v, o} 0.90 0.81 11.23 10.49
P {v,v} 0.89 0.80 11.18 10.36
PoPctoacntaonlo{lv{v,o, }w} 00..9900 0.80.18 1 111.12.62 3 101.506.4 9
octanol
PocPtaonctoaln{ovl{,ow, }v} 00..8980 0.70.88 1 131.15.92 6 121.503.5 6
PoPctaocntoaln{ool{,ov, }o} 00..8898 0.70.87 8 131.37.05 9 121.727.5 3
PoPctoacntaonlo{lo{,o,o }w} 00..8899 0.70.97 8 131.36.57 0 121.722.7 7
P {o,w} 0.89 0.79 13.65 12.72
PoPctoacntaonl{owl{w,v, }v} 00..8888 0.70.77 7 141.41.81 8 131.035.0 5
octanol
PPoctan{owl{w,o,} o} 00..8899 0.70.97 9 141.41.51 5 131.138.1 8
octanol
PoPctoacntaonl{owl{w,w, w} } 00..8899 0.70.97 9 141.42.32 3 131.236.2 6
a RaoRoot omtmeaenan sqsquuaarree eerrrroorr;; bb MMeeaanna avvereargaegeer reorrr.or.

FFiigguurree 33.. SSccaatttteerr ddiaiaggrraamm oof fcacalcluculaltaetded anadn dexepxepreimrimenetnatlalyll mymeaesausruedre ∆dG∆ vGalvuaelsu eins oinctoacntoaln soollvsoenlvte. Rnt2.
aRn2da nredgrreegssreiosnsi olinneli nareea srheoswhonw. n.
22..33.. EEffffeecctt ooff WWaatteerr aanndd OOccttaannooll SSoollvveennttss oonn FFrreeee EEnneerrggyy
TToo iinnvveessttiiggaattee tthhee eeffffeeccttss ooff ssoollvveennttss oonn ffrreeee eenneerrggyy ccaallccuullaattiioonn,, tthhee ddiieelleeccttrriicc ccoonnssttaanntt ooff wwaatteerr
aanndd ooccttaannoolls osolvlvenentstsw wereereev eavluaaluteadteidn tihne tshime usilmatuiolnat.iTonhe. Tdhieele dctireilceccotrnics taconntwstaanstc awlcausl actaeldcualsa[t3e8d, 3a9s]
[38,39]
4π (cid:110)(cid:68) (cid:69) (cid:111)
ε =ε1+=13+kbT4(cid:104)πV(cid:105) { MM22 −−M(cid:104)M2}(cid:105) 2 (1()1 )
3k T V
b
where V, k and T are volume, Boltzmann constant, and temperature, respectively. M is the total
where V, kbb and T are volume, Boltzmann constant, and temperature, respectively. M is the total
dipole moment. To calculate the dielectric constant of water and octanol solvents, additional 5 ns
dipole moment. To calculate the dielectric constant of water and octanol solvents, additional 5 ns
MD simulations were performed to generate the products, after 10,000 steps optimization, 50 ps
MD simulations were performed to generate the products, after 10,000 steps optimization, 50 ps
Molecules2018,23,425 6of15
heat-up,and2nsequilibration. Thedielectricconstantswerecalculatedforthetrajectoriesof5ns
MDsimulations.
Overestimated dielectric constants of water solvents were obtained by simulation (Table 3).
This value is very similar to that reported by Vega et al. [40]. In Figure 1, the largest slope of the
regulationslineisfoundinthecalculationwithP (v),ofwhichabsoluteatomicchargevalueswas
water
smallestinthethreeparameters. Therefore,thepairofthewatersolventwithwhichthedielectric
constantwasunderestimated,andthecompoundwithP (v)providedtheclosestabsolutevaluesof
water
∆Ginourcalculation.
Ontheotherhand,thedielectricconstantsofoctanolsolventwerealsounderestimated. Allthe
valuesinthedifferentchargesweresmallerthantheexperimentallymeasuredones. Thesevalues
wereslightlysmallerthanthatinthepapersreportedbyDeBoltandKollman[29]. Theyobtained
dielectricconstantsnear5.1fortheliquidoctanolat40◦C.Thedielectricconstantinoctanolsolvent
graduallydecreasedbytheatomicchargesintheorderofvacuum,octanol,andwater,i.e.,thesevalues
decreased in proportion to the absolute values of atomic charges. In Table 3, <µ> of octanol with
atomicchargeinwaterwaslargerthanthatofvacuumbecauseofincreasingabsoluteatomiccharges.
Thismeansthat, owingtoincreasing<µ>, thevaluesofelectrostaticinteractionincreased. Onthe
otherhand,thevanderWaalsinteractiondropswithincreasingabsoluteatomiccharges. Sincethe
vanderWaalsparameterswerethesameamongthedifferentsimulations,theelectrostaticinteraction
isthoughttodominatethesimulation. However,inFigure3,theslopesoftheregulationlinewere
dependent on the atomic charges of compounds, rather than those of octanol solvents. Moreover,
thedielectricconstantwithatomicchargesinwatersolventfurtherdifferedfromtheexperimentally
measuredvaluesthanthatwithinvacuum. Inthesimulationofliquidoctanol,ofwhichthedielectric
constantoftheoctanolisrelativelysmallerthanthatofwatersolvent,astrongcontributionofthe
electrostaticinteractionleadstosmallerdielectricconstantvaluesthatappearassimulationerrors.
Therefore,inordertoimprovethecalculatedfreeenergyvalues,thebalancebetweenelectrostaticand
vanderWaalsinteractionsmayneedtobeinvestigatedinfurtherstudies.
Table3.Propertiesofsolventsinsimulation.
ε <µ> vdW Elec.
Solvents Charge (Debye) Fluc(Debye2) <V>(Å3) (kJ/mol) (kJ/mol)
Exp. Sim.
Water 78.49(25◦C)a 92.70 2.35 20,914.2 22,290.7 14,371.9 −33,641.5
Octanol Vacuum 9.34(32.1◦C)b 4.21 2.08 836.1 26,547.7 −3860.9 −2778.5
Octanol 3.63 2.24 678.0 26,320.5 −3768.3 −3687.8
Water 3.42 2.27 625.2 26,347.2 −3714.9 −3879.3
aUematsuandFrank[41];bSmythandStoops[42,43];cFlu=<M2>−<M>2.
2.4. LogP forTestedCompounds
ow
ThelogP valueswerecalculatedusingtheFormula(7)(SeeSection3). Here,thenotationforthe
ow
logP valuecalculatedfrom∆G usingP {x},and∆G usingP {y,z}wassimplifiedto
ow water water octanol octanol
P {x,{y,z}},wherex,y,andzareeitherv(vacuum),o(octanol),orw(water).
logP
ThelogP valuesweresensitivetotheatomicchargescalculatedinthesolvent. Thecorrelation
ow
ofthelogP withtheexperimentaldataisstronglydependentonthepairofsolvationfreeenergies
ow
∆G and ∆G (Figure 4 and Figure S2). For instance, in Figure 4, completely different
water octanol
correlations of logP values can be seen in the scatter diagrams with the largest and smallest R2,
ow
whichareP {w,{v,o}}andP {v,{w,o}},respectively. InthecaseofP {w,{v,o}},thelogP was
logP logP logP ow
calculatedfrom∆G withP {w},and∆G withP {v,o}. Thiscombinationisexpectedto
water water octanol octanol
resultinlogP valuescloselycorrelatedwiththeexperimentalones.
ow
Ontheotherhand,inthecaseofP {v,{w,o}},thelogP valuesshowedveryweakcorrelationwith
logP ow
theexperimentaldata.ThecalculatedlogP valueswerebasedon∆G withP {v}and∆G with
ow water water octanol
P {w,o}.Thefreeenergiesinwaterandoctanolbothshowedstrongcorrelationswiththeexperimental
octanol
Molecules2018,23,425 7of15
Mdoalteacu,laesn 2d01t8h, e23R, xM FOSER PaEnEdRM REAVEIEvWa l ueswerenotassignificantlydifferentfromtheothers,asment7io onf e1d5
above.Theslopeoftheregressionlinefor∆G withP {v},however,wasover1,whereasthatofthe
water water
orevgerre 1s,s iwonhelirneeasf othra∆tG oofc ttahnoel wreigthrePssocitoanno ll{iwn,eo }fowr a∆sGuonctadnoel rw1i.thT hPeocsteanodl{iwff,eor}e wncaess urnaidseerd 1t.h Tehlaersgee dRifMfeSreEnacneds
rMaiAseEdv tahleu elasrsglieg RhtMlyS(ET aabnled 4M).AAEs avarelusueslt ,stlihgehltolygP (oTwavbalelu 4e)s. Ashso aw reedsuvletr, ythwee laokgPcoowr rvealaltuioens .sThohweseedr evseurlyts
wreevaeka lctohrartetlhaetioconm. bTihneasteio nreosfutlhtse ∆reGvweaatelr athnadt ∆tGheoc tacnoolmisbvinearytioimn poofr ttahnet f∆orGtwhateer caonrrde ct∆lGoogctPanoowl .isT hvaetriys ,
itmheposertleacntti ofnoro tfhteh ceosrorelvcet nlotginPotwh. eThcaaltc iusl,a tthioen seolfecthtieona toofm tihcec shoalrvgeenst iisnv tehrey ciamlcpuolrattaionnt foofr tthhee altoogmPoicw
cchaalcrugleast iiosn v.eTrhyu ism,tphoeritnaanpt pforor pthriea tleogsePloewc ctiaolncuolfatthioens.o Tlvheunst,s tfhoer itnhaepcparlcouplraitaioten soefleactotimonic ocfh tahreg essolrveseunlttss
fionrt htheew ceaalkcucloartrieolnat ioofn abteotmwiece nchthaergloegs Proewsuanltds tihne tehxep ewriemaken ctaolrrdealtaat.ioTnh ibsetetwndeeennc ythcea nlobgePoowb saenrvde dthien
etxhpeelroigmPeowntwali tdhaPtalo.g TP{hwis,{ wte,nwd}e}n. cTyh eca∆nG bwea toerbwseitrhvePdw aitner {twhe}, laongdPo∆w Gwocittahn oPlwlogPit{hw,P{woct,a nwol}{}w. T,whe}, ∆shGowwatere dwitthhe
Pstwratoern{wg}e,s tancodr r∆eGlaotcitaononl winitohu rPotcetasnotl{dwa, taw.}T, hsheovwaelude st,hhe oswtreovnegre,ssth ocowrreedlamtioond eirna toeucro rtreeslta dtiaotna.( RTh=e0 .v7a7l)uneos,t
hsotrwonegveerr,t shhaonwtheadt mofotdheera∆tGe wcoatrerrewlaitthioPn lo(gRP {=w 0,.7{v7,) on}}o.t stronger than that of the ∆Gwater with PlogP{w, {v, o}}.

FFiigguurree 44.. SSccaatttteerr ddiiaaggrraamm ooff ccaallccuullaatteedd aanndd eexxppeerriimmeennttaallllyy mmeeaassuurreedd llooggPPooww vvaalluueess.. TThhee ddiiaaggrraammss
wwiitthh tthhee lalargrgeeststa nadndsm samllaelslteRst2 Rar2e asrheo wshno,wannd, tahnedd itahger admiagorfaPm o{fw P,{lowgP,{ww},} {awre, swh}o} wanref osrhroewfenre nfocre .
logP
rRe2fearnendcree.g Rr2e sasniodn relignreesasrieosnh loinwen a.re shown.
TThhee cchheemmiiccaall ggrroouupp’s’se feffefcetcot nonth ethleo glPogPvowa lvuaelsuoefs aocf oam cpoomupndouisndsh iosw snhoinwFni giunr eFi5g.uInret h5e. lIong tPhe
ow ow
lcoaglcPuowl actaiolcnuwlaittihonP wit{hw P,l{ovgP,{ow},} ,{vth, eo}e}r, rtohres eorfroerasc hofc eoamchp ocuonmdpwouenred~ w2.e0rein ~a2l.0l ginro aulpl gs,reoxucpesp, tetxhceepetth tehres
logP
e(ftohrerest h(fyolrp ehtehnyyl lpehtehneyr,l tehteheerrr, othrew earsro3r.1 w6)a.sT 3h.e16c)a.l cTuhlea tceadlc∆uGlated ∆vGalwuateer ovfaeluthey olfp hetehnyyll pehtheenrywl eatshaenr
water
wovaes raesnt iomvaetree.stTimheatcea. lcTuhlae tecdalcaunldattehde aenxdp etrhime eenxtpaelrlyimmeneataslulyre dme∆aGsuredv ∆alGuweaster wvearleue−s 1w0.e2r2e k−J1/0m.2o2l
water
kaJn/mdo−l 17a.n9d2 k−J/17m.9o2l , rkeJs/mpeoclt,i vreelsyp. eOctnivtehley.o tOhenr hthane d,otthheerc ahlcaunldat, edth∆e Gcalculwateads a∆nGuonctadnoel rewstaism aatne .
octanol
uTnhdeecraelsctuimlataetde. aTnhdee cxaplecurilmateendt aalnlydm exepaseurirmeden∆tGally mevaasluureesdw ∆eGreoct−ano3l 4v.9a1lukeJs/ wmeorlea −n3d4.−912 3k.6J/5mkoJl/ amnodl ,
octanol
−r2e3sp.6e5c tkivJ/emlyo.lT, rheesspeedctifivfeerleyn. cTehsecsaeu dseifdfelraerngeceesr rcoarussiendl loagrPge evrraolurse si.nS liomgPilaowr vearrluoress.c Sainmbielafro eurnrdorisn ctahne
ow
bloeg fPounvda ilnu ethsec alolcguPloawt evdalwueitsh cPalcul{awte,d{w w,iwth}} .PTloghP{ewp, r{owf,i lwe}o}.f Thhiset opgrroafmiles ofof rhiPstog{rwam,{sw f,owr }P}liosgPs{wim, {ilwa,r
ow logP logP
wto}}t ihsa stimofilhairs ttoog trhaamt osff ohrisPtogra{wm,s {fvo,ro P}}l.ogPT{whe, {evr, roo}r}. oTfheet heryrlopr hoefn eythlyelt hpehresntyaln edtsheoru sttfarnodms othuet fortohmer
logP
the other compounds. The error of each compound was around 2.0, but these errors are slightly
compounds.Theerrorofeachcompoundwasaround2.0,buttheseerrorsareslightlylargerthanthat
loafrgthere tvhaalnu ethsacta locfu tlhaete vdawluietsh cPalcu{lawt,e{dv ,woi}t}h. TPhlogePr{ewf,o {rve,, oth}}e. TRhveraelufoersef, otrheP R v{awlu,e{ws ,fowr} P}lwogPe{rwe, s{lwig, hwt}ly}
logP logP
wsmerael lselrigthhatlny tshmosaellfeorr tPhan t{hwo,s{ev ,foo}r} .PlogP{w, {v, o}}.
logP
OOnn tthhee ootthheerr hhaanndd,,m mosotsot fotfh ethleo glPogPovwa lvuaelsuecas lccuallcauteldatwedit hwPith P{lvog,P{{wv,, o{w}},w oe}}r ewlaerrgee lratrhgaenr tthhoasne
ow logP
those calculated with the other parameters. Those of the compounds in the phosphate group, which
calculatedwiththeotherparameters. Thoseofthecompoundsinthephosphategroup,whichhas
has a strong polarity at the phosphoric acid moiety, showed particularly large errors. The selected
a strong polarity at the phosphoric acid moiety, showed particularly large errors. The selected
environments in the charge calculation was inconsistent, i.e., the vacuum state was selected in ∆Gwater
environments in the charge calculation was inconsistent, i.e., the vacuum state was selected in
c∆aGlculaticoanl cualnadti onwaatnedr weantveirroennmvieronnt mwenast wsaeslesceteledc teidn in∆G∆oGctanol caclcaulcluatliaotniosn. s.TThhesees eiinnaaddeeqquuaattee
water octanol
ccoommbbiinnaattiioonnss iinndduuccee llaarrggee eerrrroorrss iinn tthhee llooggPPow ccaallccuullaattiioonn. .AA ssimimilialarr tteennddeennccyy ccaann bbee ffoouunndd iinn tthhee
ow
other groups with polar moieties, such as ether and ketone groups. The selection of the environment
othergroupswithpolarmoieties,suchasetherandketonegroups. Theselectionoftheenvironment
ooff tthhee ccaallccuullaatteedd cchhaarrggeess,, tthheerreeffoorree,, iiss iimmppoorrttaanntt iinn llooggPPow ccaallccuullaattiioonn..
ow
To analyze the contributions of the atomic charges in different environments, the R and R2
Toanalyzethecontributionsoftheatomicchargesindifferentenvironments,theRandR2values
voafluloegsP of liongTPaowb lien 4Twabelree 4c owmerpea rceodm.pInarethde. Icna lcthuela cteadlcu∆lGated ∆,GthweaterR, tahned RR a2nvda lRu2e svableuceosm beecsommaell
ow water
small in the order of Pwater{v}, Pwater{o}, and Pwater{w} (Figure S3a). In terms of the atomic charges of the
in the order of P {v}, P {o}, and P {w} (Figure S3a). In terms of the atomic charges of the
water water water
compounds in ∆Goctanol calculations, the R and R2 values of logPow become small in the order of water,
octanol, and vacuum environments (Figure S3b). However, the atomic charges of the octanol in
octanol solvent seem to affect the logPow values very slightly (Figure S3c). To briefly summarize
these results, the atomic charges of the compound in the ∆Gwater and ∆Goctanol calculations are better in
Molecules2018,23,425 8of15
compounds in ∆G calculations, the R and R2 values of logP become small in the order of
octanol ow
water,octanol,andvacuumenvironments(FigureS3b). However,theatomicchargesoftheoctanol
inoctanolsolventseemtoaffectthelogP valuesveryslightly(FigureS3c). Tobrieflysummarize
ow
theseMreolsecuulletss 2,0t1h8,e 23a, txo FmORic PEcEhRa RrgEVesIEoWf thecompoundinthe∆Gwaterand∆Goctanolcalculations8a roef 1b5 etter
inwaterandvacuumenvironments,respectively. Infreeenergy,theatomicchargesoftheoctanol
molecwualeteirn aoncdt avnaoculusomlv eennvtirsohnomuledntbs,e rreesapseocntiavbellye., nIno nfreeteh eelneesrsg,yt,h tehye daotonmoitc icnhflaurgeensc eoft htheel oogcPtanovl alue
ow
muchm.oItleschuoleu ilnd obcteannoolt seodlvtehnatt sthhoiusldte bned reenascoynwabillel, bneoninetdheepleesns,d theenyt doof tnhoet ifnuflnucetniocen tahlea lnodgPbowa vsiaslusee tsin
much. It should be noted that this tendency will be independent of the functional and basis sets in
thecalculationofatomiccharges,becausetheRMSEshowsthesamebehavior(FigureS4),andthe
the calculation of atomic charges, because the RMSE shows the same behavior (Figure S4), and the
correlationefficientvaluesofourprocedureareverylargewiththeotherproceduresusingthedifferent
correlation efficient values of our procedure are very large with the other procedures using the
functionalsandbasissetsinfivecompounds(TableS4).
different functionals and basis sets in five compounds (Table S4).

FigurFeig5u.reE r5r.o Errorofrl oogf PloowgPwow itwhit(ha )(aP) loPglPog{Pw{w,, {{vv,, oo}}}},, ((bb)) PPllooggP{Pv{,v {,w{,w o,}}o,} }a,nadn (dc)( cP)logPP{lwog,P {{ww,, w{w}}, fwor} }thfoer the
experimental values. Here, the left-to-right order of the compounds in each group is the same as the
experimentalvalues.Here,theleft-to-rightorderofthecompoundsineachgroupisthesameasthe
top-down order in Table S1.
top-downorderinTableS1.
Table 4. Summary of logPow calculations.
Table4.SummaryoflogPowcalculations.
Parameters R R2 RMSE1(kJ/mol) MAE2(kJ/mol)
ParaPmlogeP{tve,r s{v, v}} R0.77 0.R592 RM2S.E161 (kJ/mol) M2A.0E4 2(kJ/mol)
PlogP{v, {v, o}} 0.80 0.64 2.17 2.07
PlogPP{vlo,gP{{vv,, v{}v}, w}} 0.07.782 00.6.589 2.172 .16 2.07 2.04
PlogPP{vlo,gP{{vv,,o {}o}, v}} 0.08.055 00.3.614 2.612 .17 2.42 2.07
PlogP{Pvl,og{Pv{v,,w {}o}, o}} 0.08.260 00.3.668 2.632 .17 2.46 2.07
PlogPP{vlo,gP{{ov,,v {}o}, w}} 0.05.562 00.3.381 2.622 .61 2.45 2.42
PlogPP{vlog,P{{ov,, o{}w}, v}} 0.06.049 00.2.346 2.722 .63 2.51 2.46
PPllooggPPP{{vvlo,,gP{{w{ov,,,w v{w}}}}, o}} 00..064.2954 000.2..32984 2.7222 ..6722 2.53 22..4551
PlogPP{vlo,gP{{wv,, {ow}}, w}} 0.05.454 00.2.299 2.742 .72 2.55 2.53
PlogP{Pvl,og{Pw{o,,w {v}}, v}} 0.05.492 00.8.249 1.402 .74 1.31 2.55
PlogPP{olo,g{Pv{o,,v {}v}, o}} 0.09.292 00.8.854 1.421 .40 1.34 1.31
PlogPP{olo,gP{{vo,, o{}v}, w}} 0.09.292 00.8.855 1.431 .42 1.35 1.34
PlogP{Pol,og{Pv{,o,w {}o}, v}} 0.09.285 00.7.835 1.791 .43 1.69 1.35
PlogP{o, {o, o}} 0.87 0.76 1.82 1.73
PlogP{o, {o, w}} 0.88 0.77 1.81 1.72
PlogP{o, {w, v}} 0.82 0.67 1.90 1.78
PlogP{o, {w, o}} 0.84 0.71 1.90 1.81
Molecules2018,23,425 9of15
Table4.Cont.
Parameters R R2 RMSE1(kJ/mol) MAE2(kJ/mol)
PlogP{o,{o,v}} 0.85 0.73 1.79 1.69
PlogP{o,{o,o}} 0.87 0.76 1.82 1.73
PlogP{o,{o,w}} 0.88 0.77 1.81 1.72
PlogP{o,{w,v}} 0.82 0.67 1.90 1.78
PlogP{o,{w,o}} 0.84 0.71 1.90 1.81
Molecules 2018, 23P, xlo gFPO{Ro ,P{EwE,Rw R}E}VIEW 0 .84 0.71 1.92 1.82 9 of 15
PlogP{w,{v,v}} 0.92 0.85 1.26 1.17
PlogPP{wlog,P{{ov,, {ow}}, w}} 0.09.284 00.7.816 1.921 .29 1.82 1.20
PlogP{Pwlo,gP{{vw,,w {}v}, v}} 0.09.292 00.8.855 1.261 .31 1.17 1.21
PlogPP{wlog,P{{ow,,v {}v}, o}} 0.08.892 00.8.768 1.291 .63 1.20 1.55
PlogPP{wlog,P{{wo,, o{}v}, w}} 0.09.092 00.8.850 1.311 .66 1.21 1.59
PlogP{Pwlo,gP{{ow,,w {}o}, v}} 0.09.088 00.7.881 1.631 .66 1.55 1.58
PlogP{Pwlo,gP{{ww,, v{}o}, o}} 0.08.690 00.8.705 1.661 .73 1.59 1.64
PlogPP{wlog,P{{ww,, o{o}}, w}} 0.08.890 00.8.717 1.661 .75 1.58 1.66
PlogP{Pwlog,P{{ww,, w{w}}, v}} 0.08.886 00.7.757 1.731 .76 1.64 1.68
PlogP{w, {w,1 oR}}o ot0m.8ea8n sq0u.7a7r eerror;2M1.e7a5n averageerror. 1.66
PlogP{w, {w, w}} 0.88 0.77 1.76 1.68
2.5. LogP for17Compounds 1 Root mean square error; 2 Mean average error.
ow
T2.h5e. LboegsPtowc foomr 1b7i Cnaomtipoonunodfst heparametersoftheadditional17compounds(PlogP{w,{v,w}})was
different from those of the small compounds (P {w, {v, o}}) (Table S5). However, the R and R2
The best combination of the parameters of tlohgeP additional 17 compounds (PlogP{w, {v, w}}) was
valuesofP {w,{v,v}},P {w,{v,o}},andP {w,{v,w}}wereveryclosetoeachother. Therefore,
differenlotg Pfrom those ofl otghPe small compoundlosg P(PlogP{w, {v, o}}) (Table S5). However, the R and R2
weconcludethatchoosingoneofP {w,{v,*}}(*=v,o,andw)parametersetwillprovideRandR2
values of PlogP{w, {v, v}}, PlogP{w, {v,l oog}P}, and PlogP{w, {v, w}} were very close to each other. Therefore, we
valuecsocnlcolusedeto ththate cehxopoesrinimg eonntea olfo nPleogsP.{w, {v, *}} (* = v, o, and w) parameter set will provide R and R2
Tvhaleuecsa lcclouslea tteod thleo gexPpoewrivmaelnuteasl oonfetsh. eadditional17compoundswiththebestcombinationofthe
atomicchTarhgee csailncuwlaatetedr loagnPdowo vctaaluneosl o(Pf ltohgeP {awd,d{ivti,own}a}l) 1s7h coowmepdoaungdoso wdiathg rteheem beesntt cwomithbitnhaetioenx poef rtihme ental
data(aFtoigmuicr ec6h)a.rTgehse iRn awndateRr 2avnadlu eosctwaneorle (0P.l9og3P{wan, d{v0, .8w6},})r esshpoewcteidv ealy .gToohde seagvraeelumeesnwt ewrieths imthiel arto
thoseeoxbpteariimneedntbayl dthatea o(tFhigeurrme e6t)h. oTdhse bRa asendd oRn2 vthaeluceos mwperoeu 0n.d93s ’aantdo m0.s86a,n rdesfpreacgtmiveelnyt. sT[h4e4s]e, tvhaoluuegsh our
were similar to those obtained by the other methods based on the compounds’ atoms and fragments
methodneedsmorecomputationaltimethantheothermethods. TheRMSEandMAEwere2.58and
[44], though our method needs more computational time than the other methods. The RMSE and
2.26,respectively,whichwereslightlylargerthanthoseofthesmallcompounds. Theseerrorsaffect
MAE were 2.58 and 2.26, respectively, which were slightly larger than those of the small
the slope of the regression line, which is somewhat smaller than that of the line obtained for the
compounds. These errors affect the slope of the regression line, which is somewhat smaller than that
smallcompoundswhenusingP {w,{v,o}}(Figure4). Theseresultsindicatethattheorderofthe
of the line obtained for the smloagPll compounds when using PlogP{w, {v, o}} (Figure 4). These results
compionudincdatse stohratte tdheb oyrdtheer olof gthPeo wcovmapluoeusn,diss svoerrteyds bimy itlhaer ltoogPthowe voarldueesr, oisf vthereyc soimmiplaoru tno dthses oorrdteedr obfy the
logPotwhev acluomespmouenadsus resodretexdp ebryim tehnet allolyg.PTowh ivsamlueeas nmstehaasuttrhede aelcxhpeermimiceanltfarlelye. enTherisg ymceaalcnus latthiaotn tmhee thod
withPallcoghPe{mwi,c{avl ,fwre}e} wenilelrbgey ecfafelccutilvateiotno pmreetdhiocdt thweitlhip PolpoghP{iwli,c i{tvy, owf}c} owmipll obuen defsf,eactnivdew toil lpbreedaiucts ethfuel tool
fordrluipgopdheisliicginty. of compounds, and will be a useful tool for drug design.

FigurFeig6u.rSec a6tt. erScdaitategrr admiaogfracmal cuofl atceadlcuanladteedx paenrdim eexnptearlilmyemnteaalslyu remdealosugrPeodw vloagluPoews fvoarlu1e7s cofomr p1o7u nds.
compounds.
The logPow values of the other additional 32 compounds were calculated for comparing our
results with the previous results reported by Bannan et al. [45]. The logPow values show strong
correlation with the experimentally measured values, of which the R and R2 values were 0.85 and
0.72, respectively (Figure 7). These values are very close to those calculated using GAFF-DC that
Molecules2018,23,425 10of15
The logP values of the other additional 32 compounds were calculated for comparing our
ow
rMesolueclutslesw 20i1th8, 2t3h, ex FpOrRev PiEoEuRs RrEeVsIuElWts reported by Bannan et al. [45]. The logP values show s1t0r oonf 1g5
ow
correlationwiththeexperimentallymeasuredvalues,ofwhichtheRandR2 valueswere0.85and
were reported by Bannan et al., of which R and R2 values are 0.85 and 0.74, respectively. These
0.72,respectively(Figure7). ThesevaluesareveryclosetothosecalculatedusingGAFF-DCthatwere
rreepsourlttesd rebvyeBaal ntnhaant ethtea l.c,oonfswidheircahtiRona nodf Rth2ev aaltuoemsiacr ec0h.a8r5gaen ids 0i.m74p,orertsapnetc tfiovre lyim. Tphreosveinregs uthltes rleovgePaolw
values.
thattheconsiderationoftheatomicchargeisimportantforimprovingthelogP values.
ow

FFiigguurree 77.. ScSactattetre rdidaigargarmams sofo cfaclcaulcluatlaetde dusuinsgin g(a)( aG)AGFAFF, F(,b)( bG)AGFAFF-DF-CD, Ca,ndan (dc) (Pc)logPP{lwog,P {{wv,, o{}v},, aon}}d,
aenxdpeerximpeernimtaellnyt amllyeamsueraesdu relodglPoogw Pvowaluvaelsu feosrf o3r2 3c2ocmopmopuonudnsd. sT.hTeh evavlauluese sccaalclcuulalatteedd bbyy GGAAFFFF aanndd
GGAAFFFF--DDCC,, aanndd tthhee eexxppeerriimmeennttaallllyy mmeeaassuurreedd vvaalluueess wweerree ttaakkeenn ffrroomm tthhee rreeffeerreennccee bbyy BBaannnnaann eett aall.. [[4455]]..
33.. MMaatteerriiaallss aanndd MMeetthhooddss
33..11.. SSeettttiinngg PPaarraammeetteerrss ooff CCoommppoouunnddss
TThhee ggeenneerraall aammbbeerr foforcrcee fifieledld (G(AGFAFF)F [)46[]4 6w]aws uasseuds feodr bfoorndbionngd pinagrapmaertaemrse (tbeorsnd(b loenngdthle, nbgotnhd,
baonngdlea, ntogrles,iotonr sainognlea,n ganled, ainmdpirmopperor pteorrstioornsi oanngalneg) lea)nadn fdofro nronnobnobnodnidnign gvvaann ddeerr WWaaaallss ppaarraammeetteerrss
((rraaddiiuuss aanndd wweellll--ddeepptthhss)) ooff tthhee ccoommppoouunnddss aanndd 11--ooccttaannooll.. AAttoommiicc cchhaarrggeess wweerree ccaallccuullaatteedd bbyy uussiinngg
GGaauussssiiaann0099 ssooffttwwaarree[ [4477]]a attt thheeB B33LLYYPP//66--3311GG((dd)) lleevveell.. TThhee ppoollaarriizzaabbllee ccoonnttiinnuuuumm mmooddeell ((PPCCMM)) [[4488]]
wwaassu usseeddt otoc ocnosnisdiedretrh tehseo slvoelvnetnetf feefcfteoctn othne thcael ccuallacutiloantioofna otof matiocmchica rcgheasr.gAens.t eAchnatemchbaermsboeftrw saorfetwwaarse
uwsaesd fuosredre sftorra inreesdtrealiencetdro setlaetcitcropsotatetinct ipalo(tRenEtSiaPl) (cRhEarSgPe)- ficthtainrgge[-4f9it–ti5n1g] f[r4o9m–5t1h]e frreosmul ttshoef qreusaunlttsu mof
cqhueamnitcuaml ccahlecmuliactailo cna.lcIunlatthioenp. Irne ptharea ptiroenpsarfaotriotnhse fosirm thuel astiimonusl,atbioionms, oblieocmuloel’escuatleo’ms aictocmhaicr gchesaragrees
caarlec uclaaltceudlaotnecde oinncoen eins oolvneen ts,oil.ve.e,nint, wi.ea.t,e rins owlvaetnetr, isnolpvreontte,i nin,o prrinotveianc,u uorm inst avtea.cuWuhme nsctaatlec.u lWathinegn
acaclocmulpaotiunngd a’s cforemepeonuenrgdy’si nfroecet aennoelr,ghyo iwn eovcetra,nboelt,t ehrorweseuvletsr,c baenttbeer orbetsauilntse dcauns ibneg othbetaaitnoemdi cuscihnagr gtehse
caatlocmuliact ecdhaforgretsh ecaclocmulpaoteudn dfoirn thoect aconmolp. Touhenrde fionr eo,citnanthoils. Tsthuedrye,ftohree,a itno mthiics cshtuardgye,s tohfet ahteocmoimc pchouarngdess
aonfd th1e-o ccotamnoplowunedres caanlcdu l1a-toecdtafonrotl hwreeeres tacatelsc:uilnatveadc ufourm th,irnee1 -sotcattaenso: li,na nvdaciunuwma,t einr. I1n-otchteancaollc, ualnatdio inn
owfathteerf. rIene tehnee crgaylcuinlawtiaotne ro,ft htheet hfrreeee cehnaerrggey sient swwaeterre, uthseed thinredee pchenadrgeen tsleyt.sT woecarelc uuslaetde itnhdeefpreeenedneenrtglyy.
iTnoo ccatalcnuolal,ten itnhee fsreetes eonfetrhgeya itno omcitcancohla, rngiense wseetrse ouf sthede :ataollmciocm chbainrgaetiso wnseroef uthseedt:h arlel ecosmetbsionfataitoonms iocf
cthhaer tgherseeo fstehtse ocfo matopmouicn dch(a3rgseetss )ofa nthde occotmanpoolu(3nds e(t3s )s.eTtsh) eancodm opctoaunnodl (a3n sdetosc).t aTnhoel cpoamrapmoeutnedr saentsd
coacltcaunlaotle dpawraitmhethteer astoetms iccaclhcuarlgateesdi nwoicttha ntohlei sadtoemfinice dchaasrPgoecsta nionl{ xo,cyt}a,ninolw ish idchefxinaendd ays( fPoorctcanoolm{xp, oyu},n idn
awnhdicohc taxn oaln,dre syp e(cfotirv ecloym)aproeuenitdh earnvd(v aoccutaunmol),, or(eoscpteacntoivl)e,loyr) wa(rwe aetietrh)e.rT hve(vlaocguPumv),a lou(eosctbaansoeld), oonr
ow
twhe(wseaftreere). eTnheerg lioegsPwowe rveaclaulecsu lbaatseedd. Tohne tdheepsee nfdreeen ceyneorfgtihees cwalecruel actaeldcualtaotmedi.c Tchhaer dgeespeinndtheencdyif foefr etnhte
ecnavlciurolantmede nattsoomnict hcehafrregeees niner gthyea dnidffleorgenPto wenvvailruoensmweenretse oxna mthine efdre.e energy and logPow values were
examined.
3.2. InitialModelsofCompoundsinSolventBox
3.2. Initial Models of Compounds in Solvent Box
We constructed the model systems as follows. All the compounds were hydrated using
aTIP3WPe[ 3co7n]swtrautcetrebdo txhec omnosdisetil nsgysotefm72s3 aws faotlelorwmso. lAecllu tlhees ,caonmdpaolulnthdes cwoemrep ohuydnrdastewde uresinpgla ac eTdIPin3Pto [3a7n]
owctaatnero lbbooxx coconnsissitsitningg oof f72130 0w1a-toecrt amnoollemcuolleesc,u alneds. all the compounds were placed into an octanol box
consAistllintgh eofs 1y0s0te 1m-osctwaneroel mmoinleicmuilzeesd. by 10,000 steps of the steepest-descent method, first with
constAraliln tthoen styhsetepmossi tiwoenrseo mftihneimheizaevdy abtyo m10s,,0a0n0d stthepens wofi tthhoeu tstceoenpsetsrta-idnet.scAefntte rmtheethmodin, imfiriszta twioitnh,
constraint on the positions of the heavy atoms, and then without constraint. After the minimization,
7 ns MD simulation for the compound was performed with Gromacs 4.5.3 software suite in a
periodic boundary condition, by using particle-mesh Ewald (PME) calculations [52,53] for
coulombic interactions. The temperature was set at 298.15 K by using a stochastic dynamics
algorithm, and pressure was maintained at 1 bar by scaling the box size in accordance with the