Which method to estimate Kd and Ki in fluorescence polarization?

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1 Outline Whih metho to estimte n i in fluoresene polriztion? Methoology n Exmples Armel Slngros Freelne ontrtor) Dorothée mrelle eyrus Biophrm) Véronique Ono Snofi) Sturtion experiment Fluoresene Polriztion Avntges Priniple Estimtion of in fluoresene polriztion Comprison of moels Exmples & Simultions Estimtion of i in fluoresene polriztion Comprison of moels Exmples & Simultions Conlusion Context: ign Bining Assy A ining ssy is use to mesures the mount of ining or ffinity etween two moleules here re numerous types of lign ining ssys Wiely pplie in life siene Exmples rgeting protein-protein intertions Protein protein intertion PPI) n ontriute to mny iseses, inluing ner, n plys key role in mintining the mlignnt phenotype in tumor ells Seletive, smll-moleule moultion of PPIs is therefore n re of interest to phrmeutil siene wo si steps: sturtion n ompetition experiments wo si types of lign ining experiment Sturtion experiment In sturtion ining ssys, lelle lign,, ins to reeptor, k + + k k k Conservtion of mss requires : 0 09 = + n = with, totl onentrtion of lelle lign 06, totl onentrtion of reeptor At equilirium: k = k = k = 0 00 eeptor onentrtion nm) k he equilirium issoition onstnt ) provies mesure of ffinity etween the reeptor n the lelle lign Speifi ining 4

2 wo si types of lign ining experiment Competition experiment In ompetitive ining ssys, n unlelle lign ompetitor),, ins to reeptor in ompetition with lelle lign, Conservtion of mss requires : 06 = + = + = with &,, totl onentrtion of lelle lign n reeptor, totl onentrtion of unlelle lign 00 At equilirium: i = Unlelle lign nm) When the of the lelle lign is known, the equilirium inhiition onstnt i) provies n iniret mesure of ffinity etween reeptor n unlelle lign Speifi Bining 0 Outline Sturtion experiment Fluoresene Polriztion Avntges Priniple Estimtion of in fluoresene polriztion Comprison of moels Exmples & Simultions Estimtion of i in fluoresene polriztion Comprison of moels Exmples & Simultions Conlusion 5 6 Why use Fluoresene Polriztion? Previously, tritionl riolign ining experiments were wiely use for sturtion n ompetition experiments Fluoresene Polriztion FP) is one lterntive to the tritionl ining riolign experiments, in prtiulr for smll moleules Applition res of FP: Protein/Protein intertions Enzyme/Sustrte Antigen/Antioies Fluoresene Polriztion FP) offers numerous vntges over the more onventionl methos: Cn e use in HS Fster n highly reprouile results low vriilities intr/inter experiment) No seprtion of oun n free lign require No riotive mterils FP priniple n signl expression Fluoresene Polriztion FP) ssys re se on mesuring the polriztion P) of light use y hnges in moleulr size he rottionl spee of moleule is erese one it is oun to reeptor Polrize emission n e mesure y polriztion n nisotropy, r 7 8

3 eltionship etween nisotropy r) n F oun In FP, there is no neessity for seprtion of oun n free lign he frtion of oun to free, F oun, is iretly eue from the nisotropy, r, using the eqution: F oun ining _ site _ oupie r rfree totl _ lign r r Q r r ) r free is the nisotropy of the free lelle lign, r oun is the nisotropy of the lign-protein omplex t sturtion n Q is the rtio of fluoresene intensities of oun versus free lign he ining of lign to reeptor is expresse y the frtion of oun reeptors F oun oun free Outline Sturtion experiment Fluoresene Polriztion Avntges Priniple Estimtion of in fluoresene polriztion Comprison of moels Exmples & Simultions Estimtion of i in fluoresene polriztion Comprison of moels Exmples & Simultions Conlusion 9 0 Estimtion of in sturtion experiment in FP F oun = ining sites oupie) / totl lign) = / F oun llows to estimte the ffinity lign hs to reeptor ): + = / Cse : Speifi se Cse : Generl se >> Assumption of no reeptor epletion Foun not >> = - Foun ² 4 Exmples of estimtions of in FP In FP experimentl ssy, when n we ssume the ssumption of no reeptor epletion? Exmple : =5 nm is etween 000 nm to 57 nm Exmple : =0 nm is etween 5 to 80 nm 95%CI nm) 95%CI nm) Exmples Cse : Cse : = No reeptor epletion Exmple 47 0 ; ; 0798 Exmple , ,458 with ) In those exmples, there is ftor roun etween oth methos to estimte the equilirium issoition onstnt

4 Simultions for estimtion Outline Design he FP were generte using reeptor epletion hypothesis moel se ) with the following ftors: onentrtions: 0-4 to 0 4 nm onentrtions: nm heoritil from 0nM to 00nM =00nM =0nM Sturtion experiment Fluoresene Polriztion Avntges Priniple Conlusion: proviing < 0% of, we n ssume tht =nm =0nM Experimentl exmple Experimentl exmple 0 Estimtion of in fluoresene polriztion Comprison of moels Exmples & Simultions Estimtion of i in fluoresene polriztion Comprison of moels Exmples & Simultions Conlusion 4 Estimtion of i in ompetition experiment he ffinity of the ompetitor, unlelle lign, for the reeptor n e iniretly etermine y mesuring its ility to ompete with, n thus inhiit, the ining of lelle lign to its reeptor he ffinity of the unlelle lign for the reeptor n e otine from ifferent methos: Estimtion of onstnt of inhiition i) he Cheng-Prusoff eqution he Nikolovsk-Colesk & ll eqution Diret estimtion of the ffinity of the ompetitor ) he Wng ext mthemtil expression Methos se on eqution Shre ssumptions A single lss of reeptor ining sites Assy is t equilirium Cheng-Prusoff eqution Nikolovsk-Colesk & l eqution = - = - i 0 ) IC i ) onentrtion of issoition ons lelle tn t lelle lign 0 Initil onentrtion of reeptor Conentrtion of unlelle lign 05 0 ) ) 4 ) ) / / IC / ) of lign 5 6 4

5 Wng moel: An ext nlytil tretment of ompetitive ining Wng hs esrie n ext expression of ompetitive ining: Conservtion of mss requires: ) ) ) After sustitution n rerrngement, this les to the following eqution: Foun os os n re the experimentl onstnts must hve een previously otine from iret ining experiment Comprison of i Exmple : = 5 nm n = 6 nm is etween 05 nm to 0000 nm = 08 nm n IC = 75 ; 86 nm Exmple : = 00 nm n = 00 nm is etween 067 to 8 nm = nm n IC = ; 5 nm i Correte i Experiment Cheng Prusoff Nikolovsk-Colesk & l Wng moel Exmple ; 888 Exmple ; Simultions of ompetition experiment ) Simultions of ompetition experiment ) Simultion & Exemple Simultion & Exemple Design FP were generte using the Wng moel uner experimentl onitions with the following ftors: is etween 0 nm to 0000 nm heoretil of ompetitor from 0nM to 0nM st simultion Exmple ): = 5 nm = 6 nm n =08 nm n simultion Exmple ): = 0 nm = 0 nm n = nm Cheng-Prusoff ki Corr i ExpCheng Prusoff i Exp Corr i t=5 nm t=6 nm =08 nm Cheng-Prusoff ki Corr i ExpCheng Prusoff i Exp Corr i t=0 nm t=0 nm = nm EC, Cheng-Prusoff i n Coor i Nikolovsk-Colesk & l) were estimte In these experimentl onitions: the Cheng-Prusoff i ws over estimte he Corr i ws: lwys lower thn the Cheng-Prusoff i very lose to the ffinity of the ompetitor simulte with the Wng moel ) 9 0 5

6 Conlusion In FP, lssil ining moels nee to e pte to the Foun Whih metho to estimte in FP? he lssil moel,, is not well pte: over estimtion of he generl moel, tken into ount the reeptor epletion =, must e use in FP experiments Whih metho to estimte i in FP? i lulte with Cheng-Prusoff iise the ffinity of ompetitor for reeptor he Nikolovsk-Colesk eqution orr i) n the ext nlytil tretment of ompetitive ining Wng moel) re equivlent methos: Avntge of Wng moel : 95% onfiene intervl is estimte Avntge of Corr i : eqution for unompetitive inhiition is ville Both methos: iffiult to generlize in prtiulr ses s imeri moels eferenes Mihel H A OEH, Juli Y WANG, Gerhr WAGNE A generl frmework for evelopment n t nlysis of ompetitive high-throughput sreens for smll-moleule inhiitors of protein-protein intertions y fluoresene polriztion, Biohemistry, 004, 4 5), Zhi-Xin WANG An ext mthemtil expression for esriing ompetitive-ining of ifferent ligns to protein moleule, FEBS etters, 995, 60, -4 Znet NIOOVSA-COESA n l Development n optimiztion of ining ssy for the XIAP BI omin using fluoresene polriztion, Anl Biohem, 004,, 6-7 Xinyi HUANG Fluoresene polriztion ompetition ssy: the rnge of resolvle inhiitor poteny is limite y the ffinity of the fluoresent lign, J Biomol Sreen, 00, 8, 4-8 Bk-up slies Estimtion of in sturtion experiment in FP F oun = ining sites oupie) / totl lign) = / F oun llows to estimte the ffinity lign hs to reeptor ): + = / Cse : Speifi se Cse : Generl se >> Assumption of no reeptor epletion not >> = - Foun Foun ² 4 with ) 4 6

7 7 5 Estimtion of in sturtion experiment in FP Cse : Speifi se Assumption of no reeptor epletion oun F ) ) ) 6 Estimtion of in sturtion experiment in FP ) ) ) ) 0 ) ) 0 ) ) ² 4 )² ) 4 )² ) 4 )² ) oun F Cse : Generl se Assumption of reeptor epletion 7 Wng moel: An ext nlytil tretment of ompetitive ining ) Wng hs esrie n ext expression of ompetitive ining: Conservtion of mss requires: Expressing n s funtion of totl lign ) n totl ompetitor onentrtions ) yiel 4 n 5 Sustitution of 4 n 5 in, yiels 6, whih fter rerrngement orrespons to the ui 7 5) 4) 0 7) ) ) ) 6) 8 Wng moel: An ext nlytil tretment of ompetitive ining ) he only meningful solution of 7 n e written s in 8 n the expression of is given in 9 n re the experimentl onstnts must hve een previously otine from iret ining experiment 8) 7 9 ros os where 9) os os