Biochemical Kinetics Made Easier

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1 1 The task of mechanistic enzyme kinetics SELECT MG MULTIPLE CDIDTE MECHISMS Petr Kuzmič, Ph.D. BioKin, Ltd. competitive? 1. Theory: differential equations - DYFIT software 2. Example I: Initial rate experiment uncompetitive? mixed type? MECHISMS - p56 lck kinase / TP analog inhibitor Select most plausible model 3. Example II: Time course experiment - p38α kinase / desatinib / competitive ligand displacement Bio/Chemical Kinetics Made Easy 2 From mechanistic to mathematical models DERIVE MTHEMTICL MDEL FRM BICHEMICL IDES Problem: Simple mechanisms MERELY FIVE RECTIS k +1 k +2 k -1 k +3 k -3 MECHISM v = k+ 2[ E] k ( k k+ 1k[ S] + k ) + k k [ S] + k ( k k )[ I] E + E E. E..B + 2 reactants (, B) 1 product (P) 5 reversible reactions 1 rate constant "RDM BI-UI" MECHISM MTHEMTICL MDEL Bio/Chemical Kinetics Made Easy 3 Bio/Chemical Kinetics Made Easy 4 lead to complex algebraic models MERELY FIVE RECTIS Segel, I. (1975) Enzyme Kinetics. John Wiley, ew York, p ew approach: umerical Enzyme Kinetics E + E. E + E..B MRE LGEBR: LET THE CMPUTER DEL WITH IT! "RDM BI-UI" MECHISM Bio/Chemical Kinetics Made Easy 5 Bio/Chemical Kinetics Made Easy 6

2 2 Theoretical foundations: Mass ction Law RTE IS PRPRTIL T CCETRTI(S) Theoretical foundations: Mass Conservation Law PRDUCTS RE FRMED WITH THE SME RTE S RECTTS DISPPER MMLECULR RECTIS products rate is proportional to [] -d[] / d t = k [] EXMPLE P + Q - d[ ]/dt = + d[ P ]/dt = + d[ Q]/dt BIMLECULR RECTIS CMPSITI RULE DDITIVITY F TERMS FRM SEPRTE RECTIS products rate is proportional to [] [B] -d [] / d t = - d [B] / d t = k [] [B] mechanism: k 1 B d [B] / d t = + k 1 [] - k 2 [B] B k 2 C Bio/Chemical Kinetics Made Easy 7 Bio/Chemical Kinetics Made Easy 8 Program DYFIT Initial rate kinetics REFERECES FREE T CDEMIC USERS 1. Kuzmic P. (1996) nal. Biochem. 237, Program DYFIT for the analysis of enzyme kinetic data 2. Kuzmic P. (29) Methods in Enzymology, in press DYFIT software package for enzymology Ref. [1] total citations: TW BSIC PPRXIMTIS 1. Rapid-Equilibrium pproximation assumed very much slower than k k 1, k 2 1 k 3 k 2 2. Steady-State pproximation ew in Mathematical details in BB Proteins & Proteomics, submitted DynaFit 2 1 no assumptions made about relative magnitude of k 1, k 2, k Bio/Chemical Kinetics Made Easy 9 Bio/Chemical Kinetics Made Easy 1 Initial rate kinetics - Traditional approach DERIVE MTHEMTICL MDEL FRM BICHEMICL IDES Initial rate kinetics in DynaFit GD EWS: MDEL DERIVTI C BE FULLY UTMTED! k +1 k +2 k -1 k +3 k -3 MECHISM v = k+ 2[ E] k ( k k+ 1k[ S] + k ) + k k [ S] + k ( k derive equations k )[ I] DynaFit input file task = fit data = rates approximation = steady-state E + <==> E. : k1 k2 E. <==> E..B : k3 k4 E <==> : k5 k6 + <==> E..B : k7 k8 E..B <==> : k9 k1 push button MTHEMTICL MDEL = [E] + [E.] + [] + [E..B] [E] tot = [] + [E.] + [E..B] [] tot = [B] + [] + [E..B] [B] tot = + k 1 [E][] k 2 [E.] k 3 [E.][B] + k 4 [E..B] = + k 5 [E][B] k 6 [] k 7 [][] + k 8 [E..B] = + k 3 [E.][B] + k 7 [][] + k 1 [E][P] (k 4 +k 8 +k 9 )[E..B] MTHEMTICL MDEL [constants] MECHISM Bio/Chemical Kinetics Made Easy 11 Bio/Chemical Kinetics Made Easy 12

3 3 Initial rate kinetics in DynaFit vs. traditional method WHICH D YU LIKE BETTER? task = fit data = rates approximation = steady-state [reaction] --> P DynaFit applications to protein kinases E + E E. E..B + E + <==> E. : k1 k2 E. <==> E..B : k3 k4 E <==> : k5 k6 + <==> E..B : k7 k8 E..B <==> : k9 k1 Case study #1: IITIL RTES F EZYME RECTIS inhibition constants and kinetic mechanism [constants] [s] Bio/Chemical Kinetics Made Easy 13 WI-61651: Presumably an TP analog? TRDITIL STUDY: KISE IHIBITR WI IS CMPETITIVE WITH TP Lineweaver-Burk plots for WI LIEWEVER-BURK PLTS T VRIED [PEPTIDE] D FIXED [TP] RE LIER Faltynek et al. (1995) J. Enz. Inhib. 9, Faltynek et al. (1995) J. Enz. Inhib. 9, H 2 15 H 2 [I] = WI /v 1 5 WI Bio/Chemical Kinetics Made Easy 15 [I] = 8 μm 1 2 1/[RRSRC] Bio/Chemical Kinetics Made Easy 16 Direct plot for WI-61651: Initial rate vs. [peptide] MIXED-TYPE IHIBITI MECHISM: WHICH IS SMLLER, K is or K ii? dding a substrate inhibition term improves fit GLBL UMERICL FIT IS BTH MRE PRECISE D MRE CCURTE Faltynek et al. (1995) J. Enz. Inhib. 9, FIGURE 1B 1 E + S <===> ES ES ---> <===> EI ES + I <===> ESI 1 [I] = E + S <===> ES ES ---> ES + S <===> ES2 <===> EI ES + I <===> ESI rate 5 rate 5 E.S.S K s2 E E.S E E.S K is K ii Kis K ii E.S.I E.S.I [RRSRC], μm Bio/Chemical Kinetics Made Easy 17 [RRSRC], μm Bio/Chemical Kinetics Made Easy 18

4 4 How do we know which mechanism is "best"? CMPRE Y UMBER F MDELS I SIGLE RU model = mixed-type? WI summary: Comparison of methods WI IS MIXED-TYPE IHIBITR, T CMPETITIVE WITH TP [reaction] [enzyme] [modifiers] S ---> P E I parameter (mm) Faltynek DynaFit et al. (1995) model = competitive? model = uncompetitive? kaike Information Criterion Review: Burnham & nderson (24) Bio/Chemical Kinetics Made Easy 19 competitive: uncompetitive: K s 91 ± ± 14 K s2 11 ± 45 K is 28 ± 2 18 ± 4 K ii 14 ± 5 67 ± 18 residual squares Bio/Chemical Kinetics Made Easy 2 Kinase ntibody Tracer Inhibitor assay FUR-CMPET MIXTURE DynaFit applications to protein kinases Case study #2: RECTI PRGRESS rate constants for kinase-inhibitor interactions competitive ligand displacement FRET assay Preliminary experimental data: Bryan Marks, Invitrogen (life Technologies) Bio/Chemical Kinetics Made Easy 22 Kinase ntibody Tracer Inhibitor: mechanism PURPSE: BTI RTE CSTTS FR IHIBITR SSCITI & DISSCITI Rate constants and receptor-ligand residence time IS IT WRTH CHSIG FTER RTE CSTTS? Mbalaviele et al. (29) J. Pharm. Exp. Ther. 329, PH-48 is an TP competitive inhibitor, which binds IKK-2 tightly with a relatively slow off rate. E T I enzyme antibody (FRET donor) tracer (FRET acceptor) inhibitor Puttini et al. (28) haematologica 93, The present results suggest a slower off-rate (dissociation rate) of [a novel bl kinase inhibitor] compared to imatinib as an explanation for the increased cellular activity of the former. four components five complexes (3 binary, 2 ternary) six unique rate constants Tummino & Copeland (28) Biochemistry 47, the extent and duration of responses to receptor-ligand interactions depend greatly on the time period over which the ligand is in residence on its receptor. Bio/Chemical Kinetics Made Easy 23 Bio/Chemical Kinetics Made Easy 24

5 Kinase - ntibody - Tracer - Inhibitor: data KISE: p38α TIBDY: anti-gst TRCER: Invitrogen Tracer-199 IHIBITR: desatinib Data: Bryan Marks, Invitrogen Kinase - ntibody - Tracer - Inhibitor: fitting model UTMTICLLY DERIVED BY DYFIT EXPERIMET: 1. incubate [E] = 4 nm [b] = 4 nm [In] = varied 3 minutes 2. dilute 1:2 with Tracer final s [E] =.2 nm [b] = 2 nm [Tr] = 1 nm [In] = varied signal Bio/Chemical Kinetics Made Easy nm [In] system of simultaneous ordinary differential equations DynaFit Input d[e]/dt = - k ai [E][In] + k di [n] - k at [E][Tr] + k dt [E.Tr] - k a [E][b] + k d [E.b] d[in]/dt E + = In - k ai [E][In] <===> + k di [n] - k ai [E.b][In] + k di :[n.b] kai kdi d[n]/dt E + Tr = + k ai <===> [E][In] - k di E.Tr [n] - k a [n][b] + : k d [n.b] kat kdt d[tr]/dt = - k at [E][Tr] + k dt [E.Tr] - k at [E.b][Tr] + k dt [E.Tr.b] E + b <===> E.b : ka kd d[e.tr]/dt = + k at [E][Tr] - k dt [E.Tr] - k a [E.Tr][b] + k d [E.Tr.b] d[b]/dt n = -+ k a [E][b] <===> + k d [E.b] n.b - k a [n][b]: + k d [n.b] ka - kkd a [E.Tr][b] + k d [E.Tr.b] d[e.b]/dt = k a [E][b] - k d [E.b] - k ai [E.b][In] + k di [n.b] - k at [E.b][Tr] + k dt [E.Tr.b] d[n.b]/dt E.b + = In + k a [n][b] <===> -n.b k d [n.b] + k : ai [E.b][In] kai - k di [n.b] kdi d[e.tr.b]/dt + = b + k a <===> [E.Tr][b] - k d [E.Tr.b] + k at :[E.b][Tr] ka - k dt [E.Tr.b] kd E.b + Tr <===> E.Tr.b : kat kdt Bio/Chemical Kinetics Made Easy 26 Kinase - ntibody - Tracer - Inhibitor: rate constants SSUMPTI: IDEPDET BIDIG SITES LY TW DDITIL RTE CSTTS Kinase - ntibody - Tracer - Inhibitor: state variables EVLUTI F SPECIES CCETRTIS DURIG THE KIETIC EXPERIMET EXPERIMET: E b Tr E b + MDEL signal 1. incubate [E] = 4 nm [b] = 4 nm [In] = 37 nm 3 minutes.15 In E b LEST-SQURES FIT k ai = M -1.s -1 PRMETERS k di = 19 s dilute 1:2 with Tracer final s [E] =.2 nm [b] = 2 nm [Tr] = 1 nm [In] = 18.5 nm, nm.1.5 Tr E τ =.5 sec RESIDECE TIME Bio/Chemical Kinetics Made Easy 27 optimize design! Bio/Chemical Kinetics Made Easy 28 cknowledgments Questions? CDEMIC CLLBRTI: Bryan Marks: all kinase experiments Invitrogen, a.k.a. Life Technologies, Madison, Wisconsin Steve Riddle: project management Invitrogen, a.k.a. Life Technologies, Madison, Wisconsin IVITTI T PRESET: IPK29 organizers, Jan ntosiewicz (IBB) Bio/Chemical Kinetics Made Easy 29 Bio/Chemical Kinetics Made Easy 3