1. Utilizing Mechanism-Based Pharmacokinetic/Pharmacodynamic Models to Understand and Prevent Antimicrobial Resistance Benjamin Wu Department of Pharmaceutics University of Florida ISAP 2009 Advisor: Hartmut Derendorf, PhD University of Florida

2. Outline  Background  Resistance hypotheses  Semi-mechanism-based PK/PD models  Model interpolation and validations  Concluding remarks

3. Diversity of Resistant Mechanisms Intrinsic Protection Upregulations  Drug Deactivation ( Beta-lactamases against Penicillin G )  Efflux Pump ( Decrease intracellular quinolone ) Dormant/Persister Conversion  Toxin-antitoxin regulations Mutation Induced Mechanisms  Binding Target (reduce quinolone affinity via mutation of DNA gyrase of topoisomerase IV)  Metabolic Pathway  Efflux Pump Neuhauser MM, JAMA 2003;289:885

4. Why Model?  “In the absence of reliable data, mathematics can be used to help formulate hypotheses, inform data-collection strategies….which can permit discrimination of competing hypotheses” (Grassly and Fraser 2008)  “….in some cases the model might need to be revised in the light of new observations, which would lead to an iterative process of model development” (Grassly and Fraser 2008)  “A well-conceived modeling task yields insights, regardless of whether at its conclusion a model is discarded, retained for revision, or immediately accepted…” (McKenzie 2000)

5. Hypothesis 1: Toxin-Antitoxin Relationship  RMF inhibits translation by forming ribosome dimers  UmuDC inhibits replication  SulA inhibits septation  RelE inhibits translation  HipA inhibits translation Falla and Chopra AAC 42:3282 (1998); Hayes Science 301:1496 (2003); Opperman et al Proc. Natl. Acad. Sci. 96:9218 (1999); Lewis, Nature Rev Microbial 5:48 (2007); Pedersen et al. Cell 112:131 (2003); Wada, Genes Cells 3:203 (1998); Karen et al., J of Bac 186:8172 (2004) Reversible with HipB

6. Hypothesis 1: Toxin-Antitoxin Relationship (RelE and Antibiotic Tolerance Example) (A): Retarted Growth 1.Strains carrying RelE inducible promoters (pBAD) 2.RelE expression induced by arabinose (Growth stopped within 30 min) (B): Reduced Drug Effects: 1.Three hrs post induction, samples were exposed to lethal dose of several antibiotics (10X MIC) –Ofloxacin – DNA gyrase –Cefotaxime – cell wall –Tobramycin – protein 2.RelE protects lysing compare to control from all antibiotics except mitomycin C Karen et al., J of Bac 186:8172 (2004) Inhibition of growth when RelE expression is induced RelE Induced Control (white bar) RelE Induced (black bar) Control

7. Dormant PK/PD Model Model Highlights: Conversion from (S) to (D) population is both stochastic and environment dependent Antimicrobial only kills dividing cells, render (D) a safe haven Drug stimulates killing of (S) population and favors (D) conversion Assumptions: Antimicrobials have no effect on (D) population Initial (D) and population loss is negligible CFU only measures (S) population D = Dormant S = Susceptible ke = Stochastic Switching ks = synthesis rate constant kd = degradation rate constant

8. Hypothesis 2: Compensatory Mutation Marcusson et al., PLoS Pathogens, 5:e1000541 (2009) Number of Induced Mutations

9. Hypothesis 2: Compensatory Mutation Low-Cost or Compensatory Mutations may result in restored microbial fitness while retaining resistance Marcusson et al., PLoS Pathogens, 5:e1000541 (2009)

10. Compensatory PK/PD Model Model Highlights: Mutant maturity in stages required to restore bacterial fitness while retain resistant characteristics CIP stimulate killings of (S) and (R fit ) population independently Assumptions: Replications and killings of (R) are negligible due to low fitness CFU based on total populations S = susceptible R = Resistant with low fitness Rfit = Resistant with high fitness kc = mutation rate constant ks = synthesis rate constant kd = degradation rate constant

11. Hypothesis 3: Combinations of Dormant and Compensatory Mutation Model Highlights: Dual effects of dormant conversion and compensatory mutation Assumptions: Drug has no effect on R fit CFU = S + R fit D = Dormant S = Susceptible Rfit = Resistant ke = stochastic conversion rate constant kc = mutation rate constant ks = synthesis rate constant kd = degradation rate constant

12. Literature Resistant Model Model Highlights: (S) population is mutated to (R fit ) as an independent population Drug induces killing of (S) and (R fit ) population independently Assumptions: (R fit ) population represents resistant mutants CFU = S+R fit S = susceptible Rfit = Resistant with fitness ks or kss = synthesis rate constant kd or kdd = degradation rate constant kc = mutation rate constant

13. Extensive In vitro Profiles for Modeling  Clinical isolates (MIC in µg/mL) – Staphylococcus aureus 452 (0.6) – Escherichia coli 11775 (0.013) – Escherichia coli 204 (0.08) – Pseudomonas aeruginosa 48 (0.15)  Inoculum size = 10 6 CFU/mL Firsov et al.,ACC, 42:2848 1998 Time (hr) CFU/mL Two flasks Flask 1: Ca2+ and Mg2+ Mueller-Hington broth Flask 2: broth + bacteria or bacteria/antibiotics (Central CMT) Replace 7 mL/hr with fresh broth in a 40 mL system to simulate clinical t 1/2 of 4 hrs CIP concentration ranges 950-fold for E. Coli II Flask 2 is inoculated with 18 hr-cultured bacteria + 2 hrs incubation Ciprofloxacin injected at 20 th hr to Flask 2 Kill curve ends when growth reaches ~10 11 CFU/mL

14. Model 1

15. The values of boostrap statistics are used to evaluate the statistical accuracy of the original sample statistics.

17. 1,000X

18. Bootstrap Parameter Distribution

19. Model 1 Bootstrap Success Rate: 78.5% VPC: Observed outside the 90%CI = 9.4% No. of Parameters = 9

20. Model 2 (Dormant) Bootstrap Success Rate: 71.3% VPC: Observed outside the 90%CI = 11.4% No. of Parameters = 7

21. Model 3 (Compensatory) Bootstrap Success Rate: 83.9% VPC: Observed outside the 90%CI = 8.3% No. of Parameters = 7

22. Model 4 (Dual Effects) Bootstrap Success Rate: 61.3% VPC: Observed outside the 90%CI = 7.3% No. of Parameters = 8

23. Interpolation of Sub-compartmental PK/PD Profiles Compensatory HypothesisDormant Hypothesis Larger % of Dormant population needed Dormant population account for regrowth? Dual characteristics of drug resistant and fitness restoration account for regrowth?

24. Dormant PK/PD Model (Equivalent to clinical 200 mg BID for 5 days) Susceptible or Observable Population CIP Conc (µg/mL) Time (hr) Dormant Time (hr) Log CFU/mL PK profile

25. Compensatory Mutation PK/PD Model (Equivalent to clinical 200 mg BID for 5 days) Total Observable Population R with fitnessR without fitness Susceptible CIP Conc (µg/mL) PK profile Time (hr) Log CFU/mL Time (hr) Log CFU/mL

26. Subpopulation Analysis of P. aeruginosa Following 200 mg CIP Exposure in an in vitro Model Dudley et al., Ameri J Med 82:363 (1987)  Total population at 12 hours similar to pretreatment with increased MIC  Same dose at 12 hours showed reduced effects  Compensatory mutation model appears to describe multiple dose effects better than dormant model

27. Conclusions  Semi-mechanistic PK/PD models were developed for various antimicrobial resistance hypotheses including experimental data from recent literature  PK/PD Models provide a “learn and confirm” approach to hypothesis testing  Models were validated using bootstrap statistics. Additional bacterial strains and external data sets are needed to further test these models  The dormant model suggests that a large percentage of dormant population is needed to explain the in vitro kill curve data  The compensatory mutation model appears to describe current data set better than the dormant model

28. Acknowledgement  Advisor: Dr. Hartmut Derendorf University of Florida  Drs. Karen et. al., J of Bac 186:8172 (2004)  Drs. Marcusson et al., PLoS Pathogens, 5:1000541 (2009)  Drs. Firsov et al., ACC, 42:2848 (1998)  Drs. Dudley et al., Ameri J Med 82:363 (1987)  Drs. Grassly and Fraser, Nature Rev Micro 6:477 (2008)  Dr. McKenzie, Parasitol Today 16:511 (2000)