RelationshipsbetweenInhibitionConstants,TypesofInhibitionandIC50CalculationandComparisononIC50ofTwoModelTyrosinaseInhibitorsHairongMao1,JiangangXie1,QimengZhang2,XinyuL3,ShubaiLi2,*1DepartmentofChemistry,ZhengzhouTeachersCollege,Zhengzhou,China2DepartmentofChemicalEngineeringTechnology,ChangzhouInstituteofEngineeringTechnology,Changzhou,China3InstituteofFineChemicals,JiangsuPolytechnicUniversity,Changzhou,China*Correspondingauthor.E-mail:AbstractCalculatingmethodsforinhibitorconcentration(IC50)leadingto50%activitylost(fordiphenolaseactivity)ofanovelparaboliccompetitiveinhibitor(thetrifluoromethyl-containing1,2,3-triazole,TF-TA)andanovelmixedinhibitor(E-4-(1-imidazoylmethyl)cinnamicacid(ozagrel)werederivedonthebasisofkineticsoftyrosinaseinhibition.ThesemethodswereappliedtocalculateIC50valuesofthetwotyrosinaseinhibitingcompounds.TheexperimentalIC50valuesofTF-TAandozagrelwere41.9Mand3.45mM,respectiviely.Moreover,thecalculatedIC50valueofTF-TAandozagrelwere82.8Mand3.15mM,respectively.Thecalculationresultofozagrelisclosertoexperimentaldata.Keywords-tyrosinase；IC50；trifluoromethyl-containing1,2,3-triazole(TF-TA)；E-4-(1-imidazoylmethyl)cinnamicacid(ozagrel)I.INTRODUCTIONTheregulationofenzymeactivityisofgreatinterestforbiochemicalresearchpurposesandforanumberofapplicationsinmedicine,physiology,andpharmacology.Inhibitionofenzymesfromanybiologicalsourcecanbeachievedbyseveralagents,suchasself-inactivatingsubstratesandreversibleorirreversibleinhibitors.Tyrosinase(EC)isacoppercontainingenzymewithresponsibilitiesforskin,hair,melanizationandenzymaticbrowninginfruitsandvegetables1-3.Itcatalyzesthehydroxylationofmonophenols(monophenolaseactivity)andtheoxidationofo-diphenolstoo-quinones(diphenolaseactivity),bothdependingonmolecularoxygen4,5.Thebrowningisresponsibleforlossinnutritionalquality,andthereforebecomesamajorprobleminthefoodindustry.Therefore,thecontrolofthetyrosinaseactivityisofimportanceinpreventingthesynthesisofmelanininthebrowningofmushroomsandothervegetablesandfruits.Manyeffortshavebeenputinthesearchforfeasibleandeffectivetyrosinaseinhibitors6-9.Inoursearchfortyrosinasenovelinhibitors,trifluoromethyl-containing1,2,3-triazoles10,andozagrelanalogues11,werefoundtohaveobviousinhibitoryeffectsonthemonophenolaseactivityandthediphenolaseactivityofmushroomtyrosinase.TheIC50(inhibitorconcentrationleadingto50%activitylost)isameasureoftheeffectivenessofacompoundininhibitingbiologicalorbiochemicalfunction.Often,thecompoundinquestionisadrugcandidate.Thisquantitativemeasureindicateshowmuchofaparticulardrugorotherinhibitorsneededtoinhibitagivenbiologicalprocessbyhalf.Itiscommonlyusedasameasureofantagonistdrugpotencyinpharmacologicalresearch.However,itappearsnottohavebeennoticedpreviouslythatthereisaverysimplerelationshipbetweenIC50withinhibitionconstantsandtypesofinhibitiontype.Therefore,theaimofthepresentworkwastodevelopamethodtocalculateIC50oftwonoveltyrosinaseinhibitors.II.CALCULATIONANDCOMPARISONONIC50A.CalculationofIC50fortheParabolic-competitiveInhibitorThetrifluoromethyl-containing1,2,3-triazolesexhibitantimicrobial,antiviralandantitumoractivitiesandhavearangeofimportantapplicationsinpharmaceuticalandagrochemicalindustries12.NNNF3COHFig.1.Structureofthetrifluoromethyl-containing1,2,3-triazole(TF-TA).Wefoundanoveltrifluoromethyl-containing1,2,3-triazole(TF-TA,seestructureinFig.1)caninhibitmushroomtyrosinaseactivity(IC50=41.9M)withitsincreasingconcentrations.Theinhibitionkinetics,analyzedbyLineweaver-Burkplots,indicatedTF-TAtobeaparabolic-competitiveinhibitorofdiphenolasewhenL-DOPAwasusedassubstrate.ItissuggestedthattwoTF-TAmoleculescancombinewithfreetyrosinasetoformadead-endcomplexatenzymeactivesite.Theinhibitionconstants(Ki1forinhibitor-enzymecomplexandKi2forinhibitor-enzyme-inhibitor978-1-4244-4713-8/10/$25.002010IEEEcomplex)wereestimatedtobe92.9mMand1.36mM,respectively.Themechanismrepresentingparabolic-competitiveinhibitionforthetyrosinase-catalyzedreactionisasfollows:E+SESE+Pk1k2k-1k-3k3k-4+I-IEIk4EI2-I+IE,S,I,Pdenoteenzyme(mushroomtyrosinase),substrate(L-DOPA),inhibitor(TF-TA),andproduct(dopachrome),respectively；ES,EI,andEI2aretherespectivecompounds.AsitisusuallythecasethatSETandIET.Inthesteadystate,therateofformationanddisappearanceofthecomplexesareidentical:ES)(ES211kkk+=(1.1)33IEEIkk=(1.2)EIIEI244=kk(1.3)Theexpressionsforthetotalenzymeconcentrationandthereactionrate:EIEIESEE2T+=(1.4)ES2kV=(1.5)InsertionoftheexpressionsforE,EI,andEI2intermofES,intotheexpressionforthetotalenzymeconcentrationgivesES)I1(IS1SE4433121121T+=kkkkkkkkkk(1.6)I1(ISSE4433121121T2+=kkkkkkkkkkkV(1.7)Because(k-1+k2)/k1istheMichaelisconstant(Km)forthereactionintheabsenceofinhibitor,k-3/k3istheequilibriumconstant(Ki1)forthedissociationofthecomplexEIintoEandI,andk-4/k4istheequilibriumconstant(Ki2)forthedissociationofthecomplexEI2intoEIandI,therateequationmaybewrittenintheform)II1(SSi2i12i1mmaxKKKKVV+=(1.8)whichinreciprocalforbecomesmaxi2i12i1maxm1)II1(S1VKKKVKV+=(1.9)ItisevidentfromEq.1.9thattheslopeofLineweaver-BurklinesisinfluencedbythechangingIandI2.AccordingtoEq.1.8,intheabsenceofTF-TZ,thekineticfunctionisSSmmax0+=KVV(1.10)Theinhibitionratio:0%(1)100ViV=SS)II1(SS1mmaxi2i12i1mmax+=KVKKKKV(1.11)Wheni%reaches50%,I=IC50,so,)II1(SS21i2i12i1mmKKKKK+=(1.12)TheIC50value(thenegativevalueshouldberemoved)is()mm2mmi1i1i1i250mi1i24S-()IC2KKKKKKKKKKK+=(1.13)AccordingtotheexperimentconditionsandEq.1.13(Km=0.117mM,Ki1=92.9mM,Ki2=1.36mM,andS=1.0mM),sothecalculatedIC50valueofistobe82.8M.Then,accordingtoFig.5,theexperimentalIC50valueis41.9M.Inthisinvestigation,thecalculatedIC50valueisabouttwotimesthatoftheexperimentalone.B.CalculationofIC50fortheMixedInhibitorOzagrel(E-4-(1-imidazoylmethyl)cinnamicacid,seestructureinFig.2),asaselectiveinhibitorofthromboxanesynthase(TXAS)inhumanplateletsespecially,isusedinthetreatmentandpreventionofvariousthromboticdiseases13.Wefoundthatozagrelinhibitedmushroomtyrosinaseactivity.TheIC50valuewas3.45mM.Ozagrelwasestimatedtobeareversiblemixed-typeinhibitorofdiphenolaseactivitywhenL-DOPAwasusedassubstratewiththeconstants(KS1,KS2,Ki1,andKi2)determinedtobe2.21,3.89,0.454,0.799mM,repectively.Theinhibitionkinetics,analyzedbyLineweaver-Burkplots,indicatedozagreltobeamixedinhibitorofdiphenolasewhenL-DOPAwasusedassubstrate.Itdemonstratedthatozagrelboundtheenzymeatasitedistinctedfromthesubstrateactivesite,butitboundtoeitherEorES.Fig.2.Structureof(E-4-(1-imidazoylmethyl)cinnamicacid(ozagrel).Inthistypeofreversibleinhibition,ozagrelcaninteractwithboththefreeenzyme(tyrosinase)andtheenzyme-substratecomplexatasiteotherthantheactivesitewithaclassicalMichaelis-Mentenreactionmechanism:E+SESE+PkcatEI+S+I+IESIKi1KS1KS2Ki2Here,E,S,I,Pdenoteenzyme(mushroomtyrosinase),substrate(L-DOPA),inhibitor(ozagrel),andproduct(dopachrome),respectively；ES,EI,andESIaretherespectivecompounds.AsitisusuallythecasethatSE0andIE0.ItisassumedthattheeffectisnotonlyonaffinitybutalsoontherateofthebreakdownoftheEScomplex；thusozagrelwouldinfluencetheenzymeactivityintwoways,affectingVmaswellasKm.ItisformallyconvenienttoregardKS1,KS2,Ki1andKi2asthedissociationconstantsoftherespectivecomplexes:ESintoEandS,ESIintoEIandS,EIintoEandI,andESIintoESandI,respectively.IntheMichaelis-Mentenstate,thesubstrate-bindingstepandformationoftheEScomplexarefastrelativetothebreakdownrate.Asistheusuallythecase,theequilibriumequationsoftheenzyme,substrate,inhibitor,product,andtheirrespectivecompounds(ES,EI,ESI)aregiven:S1ESESK=(2.1)i1EI=EIK(2.2)S2EISESIK=(2.3)i2ESI=ESIK(2.4)AccordingtoEq.2.1toEq.2.4,therelationshipwithKS1,KS2,Ki1andKi2isgiven:S1i1S2i2KKKK=(2.5)Theexpressionsforthetotalenzymeconcentrationandthereactionrate:TEEESEIESI=+(2.6)Theoverallvelocitywillbegivenasfollows:catESVk=(2.7)InsertionoftheexpressionsforE,EI,andESIintermofES,intotheexpressionforthetotalenzymeconcentrationgivesS1S1Ti1i2IIE(1)ESSSKKKK=+(2.8)catTS1i1i2ESII(1)S(1)kVKKK=+(2.9)TherateequationmaybewrittenintheformmaxS1i1i2SII(1)S(1)VVKKK=+(2.10)whichinreciprocalformbecomesS1i1i2maxmaxII(1)(1)11SKKKVVV+=+(2.11)ItisevidentfromEquation11thatthemixed-typeinhibitionaffectsbothKmandVmax(itsspecialcaseisnoncompetitiveinhibitionwhichwouldaffecttheVmaxbutnottheKm).So,theslopeandinterceptofEquation11aregivenasthefollowingform:S1i1maxI(1)SlopeKKV+=(2.12)i2maxI(1)InterceptKV+=(2.13)Forthesteady-statemodel,substratebindingoccursfasterthanthebreakdownoftheEScomplex,sothekineticfunctionintheabsenceofinhibitorismax0S1SSVVK=+(2.14)Theinhibitionratio:0%(1)100ViV=maxS1i1i2maxS1SII(1)S(1)1SSVKKKVK+=+(2.15)Wheni%reaches50%,I=IC50,so,S15050S1i1i2S11ICIC2(1)S(1)KKKK+=+(2.16)TheIC50valueisS150S1i2i1SICSKKKK+=+(2.17)AccordingtoEq.2.17andKS1,KS2,Ki1,andKi2,thecalculatedIC50is3.15mM,itisveryclosetotheexperimentaldataofIC50(3.45mM).III.CONCLUSIONTheIC50valuesoftwonoveltyrosinaseinhibitorswerecalculatedandcompared.ThecalculatedIC50valueofozagreliscloserthanitsexperimentaldata.Theresultssofarobtainedindicatedthatthefurtherassayisneeded,fromnotonlyoneaspect,butfromawholeperspective.REFERENCES1L.Yu,“Inhibitoryeffectsof(S)-and(R)-6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylicacidontyrosinaseactivity,”J.Agr.FoodChem.vol51,pp.2344-2347,2003.2Y.J.Kim,J.E.Chung,M.Kurisawa,H.Uyama,andS.Kobayashi,“Newtyrosinaseinhibitors,(+)-catechin-aldehydepolycondensates,”Biomacromolecules.vol.5,pp.474-479,2004.3M.Jimnez,S.Chazarra,J.Escribano,J.Cabanes,andF.Garca-Carmona,“Competitiveinhibitionoftyrosinaseby4-substitutedbenzaldehydes,”J.Agr.FoodChem.vol.49,pp.4060-4063,2001.4F.G.Molina,J.L.Muoz,R.Varn,J.N.RodrguezLpez,F.GarcaCnovas,andJ.Tudela,“Anapproximateanalyticalsolutiontothelagperiodofmonophenolaseactivityoftyrosinase,”Int.J.Biochem.CellBiol.vol.39,pp.238-252,2007.5L.G.Fenoll,M.J.Pealver,J.N.Rodrguez-Lpez,R.Varn,F.Garca-Cnovas,J.Tudela,“Tyrosinasekinetics:discriminationbetweentwomodelstoexplaintheoxidationmechanismofmonophenolanddiphenolsubstrates,”Int.J.Biochem.CellBiol.vol.36,pp.235-246,2004.6J.C.EspnandH.J.Wichers,“Kineticsofactivationoflatentmushroom(Agaricusbisporus)tyrosinasebybenzylalcohol,”J.Agr.FoodChem.vol.47,pp.3503-3508,1999.7I.Kubo,I.Kinst-Hori,Y.Kubo,Y.Yamagiwa,T.Kamikawa,andH.Haraguchi,“Moleculardesi