utilizing mechanism-based pharmacokinetic/pharmacodynamic models to understand and prevent...

Utilizing Mechanism-Based Utilizing Mechanism-Based Pharmacokinetic/Pharmacodynamic Models to Pharmacokinetic/Pharmacodynamic Models to Understand and Prevent Antimicrobial ResistanceUnderstand and Prevent Antimicrobial Resistance

Utilizing Mechanism-Based Utilizing Mechanism-Based Pharmacokinetic/Pharmacodynamic Models to Pharmacokinetic/Pharmacodynamic Models to Understand and Prevent Antimicrobial ResistanceUnderstand and Prevent Antimicrobial Resistance

Benjamin WuDepartment of PharmaceuticsUniversity of FloridaISAP 2009

Advisor: Hartmut Derendorf, PhD University of Florida

OutlineOutline

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

Diversity of Resistant MechanismsDiversity 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

Why Model?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)

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


(RelE and Antibiotic Tolerance Example)


(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

Dormant PK/PD ModelDormant 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

D

ks

S

ke

kd

H(C(t))

ke

+

+

Hypothesis 2:Compensatory Mutation


Marcusson et al., PLoS Pathogens, 5:e1000541 (2009)

Number of Induced Mutations



Low-Cost or Compensatory Mutations may result in restored microbial fitness while retaining resistance

Marcusson et al., PLoS Pathogens, 5:e1000541 (2009)

Compensatory PK/PD ModelCompensatory PK/PD Model

Model Highlights:

• Mutant maturity in stages required to restore bacterial fitness while retain resistant characteristics

• CIP stimulate killings of (S) and (Rfit) 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



Skd

R

kc

kc

Rfitkd

ks

H(C(t))

ks

H’(C(t))

+

+

Hypothesis 3:Combinations of Dormant and Compensatory Mutation

Hypothesis 3:Combinations of Dormant and Compensatory Mutation

Model Highlights:

• Dual effects of dormant conversion and compensatory mutation

• Assumptions:• Drug has no effect on Rfit

• CFU = S + Rfit

D = Dormant

S = Susceptible

Rfit = Resistant

ke = stochastic conversion rate constant




D

ks

S

ke

kc

Rfitkd

kdks

ke

H(C(t))

+

+

Literature Resistant ModelLiterature Resistant Model

Model Highlights:

• (S) population is mutated to (Rfit) as an independent population

• Drug induces killing of (S) and (Rfit) population independently

Assumptions:

• (Rfit) population represents resistant mutants

• CFU = S+Rfit

S = susceptible

Rfit = Resistant with fitness

ks or kss = synthesis rate constant

kd or kdd = degradation rate constant


ks

Skd

kc

Rfitkdd

kss

H’(C(t))

H(C(t))+

+

Extensive In vitro Profiles for ModelingExtensive 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 = 106 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 t1/2 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 20th hr to Flask 2

• Kill curve ends when growth reaches ~1011 CFU/mL

Model 1

ks

Skd

kc

Rfitkdd

kss

H’(C(t))

H(C(t))+

+

Time (hr)

0 10 20 30 40 50

Log

CS

F

0

2

4

6

8

10

12

14

ParameterModel

Estimates %CVks (/hr) 5.92 14.4kd (/hr) 5.79 15.0kc (/hr) 0.119 14.8SMAX, S 0.100 20.0

SC50, S (µg/mL) 0.249 20.7kss (/hr) 3.06 0.873kdd (/hr) 2.93 1.15

SMAX, R 0.0342 15.8SC50, R (µg/mL) 0.192 44.7

Proportional Error 0.198 6.71

Model 1 (Literature)

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

1,000X

Bootstrap Parameter DistributionBootstrap Parameter Distribution

0.5 1.0 1.5 2.0

05

01

00

15

02

00

25

0

theta1

Fre

qu

en

cy

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

05

01

00

15

02

00

25

0

theta2

Fre

qu

en

cy

0.10 0.14 0.18 0.22

02

04

06

08

01

00

12

0

theta3

Fre

qu

en

cy

2 4 6 8

05

01

00

15

02

00

25

0

theta4

Fre

qu

en

cy

0.0 0.4 0.8 1.2

05

01

00

15

0

theta5

Fre

qu

en

cy

1 2 3 4 5

05

01

00

15

02

00

theta6

Fre

qu

en

cy

0.015 0.025 0.035 0.045

02

04

06

08

01

00

12

01

40

sigma11

Fre

qu

en

cy

Sigma Parameters Bootstrap Analysis Run 3

Model 1

ks

Skd

kc

Rfitkdd

kss

H’(C(t))

H(C(t))+

+

Time (hr)

0 10 20 30 40 50

Log

CS

F

0

2

4

6

8

10

12

14

• Bootstrap Success Rate: 78.5%

• VPC: Observed outside the 90%CI = 9.4%

ParameterModel

Estimates %CVBootstrap

MeanBootstrap

90% CIks (/hr) 5.92 14.4 5.80 3.18-8.77kd (/hr) 5.79 15.0 5.64 3.13-8.65kc (/hr) 0.119 14.8 0.126 0.0916-0.176SMAX, S 0.100 20.0 0.120 0.0765-0.190

SC50, S (µg/mL) 0.249 20.7 0.32 0.107-0.753

kss (/hr) 3.06 0.873 2.97 1.88-4.29

kdd (/hr) 2.93 1.15 2.79 1.72-4.02SMAX, R 0.0342 15.8 0.0559 0.0392-0.0969

SC50, R (µg/mL) 0.192 44.7 0.114 0.029-0.256Proportional Error 0.198 6.71 0.188 0.157-0.215

Model 1 (Literature)

No. of Parameters = 9

Model 2(Dormant)Model 2

(Dormant)

D

ks

S

ke

kd

H(C(t))

ke

+

+

Time (hr)

0 10 20 30 40 50

Log

CS

F

0

2

4

6

8

10

12

14



ParameterModel


MeanBootstrap

90% CIks (/hr) 0.921 66.1 1.05 0.811-1.52kd (/hr) 0.709 88.5 0.805 0.603-1.17ke (/hr) 0.108 15.5 0.124 0.0835-0.183SMAX, S 0.188 42.4 0.225 0.116-0.365

SC50, S (µg/mL) 0.0588 56.4 0.0751 0.0140-0.164SMAX, D 3.610 21.1 3.23 1.33-4.91

SC50, D (µg/mL) 0.263 31.4 0.346 0.0979-0.894

Proportional Error 0.212 6.78 0.198 0.159-0.233

Model 2 (Dormant)


Model 3(Compensatory)

Skd

R

kc

kc

Rfitkd

ks

H(C(t))

ks

H’(C(t))

+

+

Time (hr)

0 10 20 30 40 50

Log

CS

F

0

2

4

6

8

10

12

14



ParameterModel


MeanBootstrap

90% CIks (/hr) 0.813 14.5 0.819 0.654-0.941kd (/hr) 0.660 18.3 0.664 0.538-0.771kc (/hr) 0.172 10.7 0.325 0.166-0.565SMAX, S 1.020 18.9 1.364 0.890-2.087

SC50, S (µg/mL) 0.358 14.6 0.346 0.215-0.542SMAX, R 0.193 21.3 0.215 0.163-0.269

SC50, R (µg/mL) 0.113 31.6 0.139 0.0636-0.365

Proportional Error 0.220 0.210 1.04 0.812-1.237

Model 3 (Compensatory)


Model 4(Dual Effects)

Model 4(Dual Effects)

D

ks

S

ke

kc

Rfitkd

kdks

ke

H(C(t))

+

+

Time (hr)

0 10 20 30 40 50

Log

CS

F

0

2

4

6

8

10

12

14

ParameterModel

EstimatesBootstrap

Mean 90% CIks (/hr) 0.142 0.139 0.0556-0.417kd (/hr) 0.0235 0.0447 0.0101-0.227ke (/hr) 0.088 0.0845 0.0179-0.182kc (/hr) 0.00326 0.0234 0.0001-0.0471SMAX, S 28.60 12.4 1.01-44.3

SC50, S (µg/mL) 0.374 0.291 0.0109-0.515SMAX, D 4.230 3.74 0.139-8.933

SC50, D (µg/mL) 0.2680 2.51 0.0991-16.4Proportional Error 0.231 0.189 0.157-0.218

Model 4 (Combo)




Interpolation of Sub-compartmental PK/PD ProfilesInterpolation of Sub-compartmental PK/PD Profiles

Time (hr)

0 10 20 30 40

Sim

ula

ted

Pla

sma

Cip

ro C

on

cen

trat

ion

(µ

g/m

L)

0

20

40

60

80

100

120

Lo

g C

FU

0

2

4

6

8

10

12

14

16

Cipro ConcentrationSusceptibleDormant

Time (hr)

0 10 20 30 40S

imu

late

d P

lasm

a C

ipro

Co

nce

ntr

atio

n (

µg

/mL

)0

20

40

60

80

100

120

Lo

g C

FU

0

2

4

6

8

10

12

14

16

Cipro ConcentrationSusceptibleInitial MutationCompensatory Mutation

Compensatory HypothesisDormant Hypothesis

• Larger % of Dormant population needed

• Dormant population account for regrowth?

• Dual characteristics of drug resistant and fitness restoration account for regrowth?

Dormant PK/PD Model(Equivalent to clinical 200 mg BID for 5 days)Dormant PK/PD Model(Equivalent to clinical 200 mg BID for 5 days)

Susceptible or Observable Population

CIP

Con

c (µ

g/m

L)

Time (hr)

Dormant

Time (hr)

Log

CFU

/mL

PK profile

Compensatory Mutation PK/PD Model(Equivalent to clinical 200 mg BID for 5 days)Compensatory Mutation PK/PD Model(Equivalent to clinical 200 mg BID for 5 days)

Total Observable Population

R with fitnessR without fitnessSusceptible

C

IP C

onc

(µg/

mL)

PK profile

Time (hr)

Log

CFU

/mL

Time (hr)

Log

CFU

/mL

Subpopulation Analysis of P. aeruginosa Following 200 mg CIP Exposure in an in vitro ModelSubpopulation 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

ConclusionsConclusions

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

AcknowledgementAcknowledgement

Advisor: Dr. Hartmut DerendorfUniversity 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)

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