CYP Time Dependent Inhibition Atypical Kinetics. Ken Korzekwa Temple University School of Pharmacy and Kinetics & Simulation, LLC

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1 CYP Time Dependent Inhibition Atypical Kinetics Ken Korzekwa Temple University School of Pharmacy and Kinetics & Simulation, LLC

2 Acknowledgements TUSP Swati Nagar Jaydeep Yadav Pharma - Donald Tweedie - Andrea Whitcher-Johnstone - Leslie Bell - Shari Bickford - Upendra Argikar WSU Jeff Jones Jim Brozik Carlo Barnaba NIH Grants 5R01GM R01GM

3 Are Numerical Solutions from Differential Equations Today like Nonlinear Least-Squares in 1979? 3

4 Michaelis-Menten Kinetics Numerical Solution P k3 E S k1 S k2 ES For a hyperbolic saturation curve, we can solve for two parameters. Assume a value for k1 ( M -1 sec -1 ) Solve for k 2 (affinity) and k 3 (k cat ) K m = (k 2 +k 3 )/k 1 4

5 Numerical MM Fitting 5

6 Numerical Method for Enzyme Kinetics Advantages No assumptions steady state initial rates etc. Completely flexible Any number of parameters can be introduced. Provided that you have sufficient data Any change at any time can be incorporated into the model. Statistics are available. 6

7 Numerical Method for Enzyme Kinetics Disadvantages Nice equations are not available Must be derived if needed Equations often provide insight to internal relationships Results need to be evaluated carefully Parameter errors Correlation must be considered (e.g. V max /K m ) 7

8 CYP Two Binding Site Model Figure 2. Models for two substrates binding simultaneously to the CYP active site, (A) Substrates are randomly oriented within the active site. (B) substrates bind to specific sites within the active site. Reference: K. Korzekwa, Cytochrome P450 Kinetics, in Enzyme Kinetics in Drug Metabolism: Fundamentals and Applications. Nagar, Argikar, Tweedie, Eds, Springer

9 velocity velocity velocity velocity Complex Enzyme Kinetics- ESS A Hyperbolic K 1 m1 =10, K m2 =10, V m1 =10, V m2 =10 0 H Biphasic K m1 =10, K m2 =1000, V m1 =10, V m2 = [substrate] [substrate] D Sigmoidal K m1 =10, K m2 =10, V m1 =10, V m2 = [substrate] B Substrate Inhibition K m1 =10, K m2 =10, V m1 =10, V m2 = [substrate] 9

10 ESI Model 10

11 Metabolism - Non-Michaelis-Menten Kinetics S ΜM I ΜM

12 Kinetic Rate Equations vs Numerical Solutions of Differential Equations Nonlinear least squares solutions to appropriate kinetic rate equations gives results identical to numerical solutions from differential equations. The numerical method can be used when standard equations are not available or when fewer assumptions are required. Time dependent inhibition is an example where rate equations are available only for MM kinetics. 12

13 Time-Dependent Inhibition When a drug binds irreversibily to a drug metabolizing enzyme Enzyme activity is lost over time Can be identified by preincubating the drug with the enzyme and measuring activity Time dependent inhibition is a major cause of drug-drug interactions Cytochrome P450 enzymes Aldehyde oxidase 13

14 TDI with MM Kinetics Standard kinetic scheme for TDI Typically analyzed by the replot method Measure rate of inactivation (k obs ) at different Inhibitor concentrations Plot k obs vs inhibitor concentration Calculate k inact and K I from the hyperbola k4 k6 EI E* I k5 k1 E ES k2 S k3 P 14

15 Standard Method to Determine TDI 15

16 Standard Method to Determine TDI k inact K I 16

17 Direct Simulation of TDI k6 EI E* I k4 k5 k1 E ES k2 S k3 P The MM TDI model was simulated 500 times each with random errors of 2.5%, 5%, and 10%. The MM TDI model was fit to each datasets to obtain K I and k inact. 17

18 Probability Density Probability Density Probability Distribution of K I and k inact Estimates Distribution is shown for 500 runs at each condition Probability Density Probability Density Probability Density Probability Density 10% error 5% error 2.5% error Blue: replot method Red: numeric method Ki ΜM Ki ΜM Ki ΜM K I Kinact min Kinact min Kinact min 1 Nagar, S., Jones, J. P. & Korzekwa, K., Drug Metab Dispos 42, (2014). k inact 18

19 A) MM EI k6 E* k4 I k5 E k1 ES k2 S k3 P D) Partial inactivation EI k6 E* k4 I k5 k2 k1 E E*S k7 k1 ES k2 S k3 P TDI Kinetic Schemes k4 E P B) EII EII I k7 k9 k8 k6 EI E* I k5 k1 ES k2 S k3 P C) Quasi-irreversible k6 EI E* I k4 k5 k7 k1 E ES k2 S k3 P E) Enzyme loss k7 k6 EI E* I k7 k4 k5 k1 E k2 S k3 P k7 ES 19

20 TDI with EII kinetics K m1 =10 mm K m2 =1000 mm V m1 =0.025 min -1 V m2 =0.25 min -1 K m1 =10 mm K m2 =100 mm V m1 =0.025 min -1 V m2 = min -1 K m1 =20 mm K m2 =20 mm V m1 = min -1 V m2 =0.05 min -1 20

21 Simulations with MM and EII Kinetics Simulations were performed for MM, biphasic, inhibitor inhibition, and sigmoidal kinetics. 100 simulations were performed for each kinetic scheme with errors of 2.5%, 5%, and 10%. The correct model was identified (lowest AIC) by the numerical method 100% of the time for 5% error, and % of the time for 10% error The correct model could not be identified even at 2.5% error with the modified replot method. EII I k7 k9 k8 k6 EI E* k4 E I k5 EII Kinetics k1 ES k2 S k3 P 21

22 MDZ-TAO data Model: Quasi-irreversible Korzekwa, K., Tweedie, D., Argikar, U. A., Whitcher- Johnstone, A., et al., Drug Metab Dispos 42, (2014). 22

23 MDZ-TAO data Model: Partial inactivation 23

24 Parameter estimates Quasi Partial Standard replot K I 0.93 (0.11) 2.1 (0.35) 0.3 (0.03) k inact 0.25 (0.02) 0.38 (0.04) 0.06 (0.002) AICc NA 24

25 Inhibition of CYP2C8 by Gemfibrozil Glucuronide Quasi-irreversible k 6 EI E* k 4 k 5 I k 7 E k 1 ES k 2 k 3 S AICc = -302 P Partial inactivation k 6 EI E* k 4 k 5 I k 2 E*S k 1 k 7 P E k 2 k 1 S ES AICc = -302 k 3 P 25

26 Inhibition of CYP2B6 by PPP EII-Partial inactivation EII k7 k 8 I k 9 EI k 6 E* k I 4 k 5 E k 1 k 2 S k 2 k 1 E*S ES P k 10 k 3 P 26

27 Spectral Analysis TDI with Podophyllotoxin 27

28 Dynamic Components by SVD Analysis Baculosomes 28

29 Dynamic Components by SVD Analysis Human Liver Microsomes 29

30 Mechanism-based Inhibition of CYPs by Methylenedioxyphenyl Compounds. 30

31 TDI with Podophyllotoxin Human Liver Microsomes 31

32 ESI-Quasi-irreversible Intermediate Model 32

33 Kinetic Parameters PPT HLM TDI 33

34 PRA Plot for TDI with Podophyllotoxin Rat Liver Microsomes 34

35 Midazolam C (ng/ml) In Vivo TDI for PPT Rat Midazolam+PPT 1000 Midazolam AUCi/AUC = 1.2 ± Time (min) 35

36 Summary For MM kinetics, much better estimates of KI can be obtained with the numerical method compared with the standard replot method. Even IC50 shift data can provide meaningful estimates of TDI kinetic parameters. The replot method can be modified to fit non-mm data, but normal experimental error precludes this approach. The numerical method consistently predicts the correct non-mm model at errors of 10% or less, whereas the replot method cannot identify the correct kinetic model at experimental errors of 2.5% or greater. EII formation, quasi-irreversible inhibition and partial inactivation can only be modeled with the numerical method. The initial phase for MIC formation should not be used to predict TDI. Numerical methods provides tools for exploration and incorporation of complex schemes into any kinetic analyses. 36

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