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
Outline
 Background
 Resistance hypotheses
 Semi-mechanism-based PK/PD models
 Model interpolation and validations
 Concluding remarks
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
Neuhauser MM, JAMA 2003;289:885

Binding Target (reduce quinolone affinity via mutation of DNA gyrase of topoisomerase IV)

Metabolic Pathway

Efflux Pump
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
Reversible with HipB
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)
Hypothesis 1:
Toxin-Antitoxin Relationship
(RelE and Antibiotic Tolerance Example)
(A): Retarted Growth
RelE Induced
Control
(white bar) RelE Induced
(black bar) Control
1. Strains carrying RelE inducible promoters
(pBAD)
2. RelE expression induced by arabinose
(Growth stopped within 30 min)
(B): Reduced Drug Effects:
Inhibition of growth when
RelE expression is induced
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)
Dormant PK/PD Model
Model Highlights:
D = Dormant
S = Susceptible
• Conversion from (S) to (D) population is both
stochastic and environment dependent
ke = Stochastic
Switching
• Antimicrobial only kills dividing cells, render (D) a safe
haven
D
ks = synthesis rate
constant
kd = degradation rate
constant
• Drug stimulates killing of (S) population and favors (D)
conversion
ke
+ ke
• Assumptions:
• Antimicrobials have no effect on (D) population
H(C(t))
• Initial (D) and population loss is negligible
S
+ kd
• CFU only measures (S) population
ks
Hypothesis 2:
Compensatory Mutation
Number of Induced Mutations
Marcusson et al., PLoS Pathogens, 5:e1000541 (2009)
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)
Compensatory PK/PD Model
S = susceptible
R = Resistant with low
fitness
Rfit = Resistant with
high fitness
kc = mutation rate
constant
ks = synthesis rate
constant
Model Highlights:
ks
S
• Mutant maturity in stages required to restore
bacterial fitness while retain resistant
characteristics
• CIP stimulate killings of (S) and (Rfit)
population independently
kd
+ H(C(t))
Assumptions:
• Replications and killings of (R) are negligible
due to low fitness
kc
kd = degradation rate
constant
kc
R
kd
Rfit
ks
• CFU based on total populations
+ H’(C(t))
Hypothesis 3:
Combinations of Dormant and Compensatory Mutation
D = Dormant
Model Highlights:
S = Susceptible
• Dual effects of dormant conversion
and compensatory mutation
Rfit = Resistant
ke = stochastic conversion
rate constant
• Assumptions:
• Drug has no effect on Rfit
kc = mutation rate
constant
+ ke
ks = synthesis rate
constant
kd = degradation rate
constant
D
• CFU = S + Rfit
ke
kc
H(C(t))
S
+ kd
Rfit
ks
kd
ks
Literature Resistant Model
S = susceptible
Rfit = Resistant with
fitness
ks or kss = synthesis
rate constant
kd or kdd =
degradation rate
constant
Model Highlights:
ks
S
kc
kc = mutation rate
constant
Rfit
kss
• (S) population is mutated to (Rfit) as an
independent population
kd
+ H(C(t))
kdd
+ H’(C(t))
• Drug induces killing of (S) and (Rfit)
population independently
Assumptions:
• (Rfit) population represents resistant
mutants
• CFU = S+Rfit
CFU/mL
Extensive In vitro Profiles for Modeling
Time (hr)


Clinical isolates (MIC in µg/mL)
• Two flasks
–
Staphylococcus aureus 452 (0.6)
•Flask 1: Ca2+ and Mg2+ Mueller-Hington broth
–
Escherichia coli 11775 (0.013)
•Flask 2: broth + bacteria or bacteria/antibiotics (Central CMT)
–
Escherichia coli 204 (0.08)
–
Pseudomonas aeruginosa 48 (0.15)
Inoculum size = 106 CFU/mL
• 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
Firsov et al.,ACC, 42:2848 1998
Model 1
14
12
Log CSF
10
8
6
ks
4
2
S
0
0
10
20
30
40
kc
Time (hr)
Model 1 (Literature)
Model
Parameter
Estimates
ks (/hr)
5.92
kd (/hr)
5.79
kc (/hr)
0.119
SMAX, S
0.100
SC50, S (µg/mL)
kss (/hr)
kdd (/hr)
SMAX, R
SC50, R (µg/mL)
Proportional Error
50
%CV
14.4
15.0
14.8
20.0
0.249
3.06
2.93
0.0342
20.7
0.873
1.15
15.8
0.192
0.198
44.7
6.71
Rfit
kss
kd
+ H(C(t))
kdd
+ H’(C(t))
The values of boostrap statistics
are used to evaluate the
statistical accuracy of the
original sample statistics.
1,000X
0.5
1.0
1.5
2.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.14
0.22
200
50
100
Frequency
100
Frequency
50
150
100
8
0
0
theta4
6
0.0
0.4
0.8
theta5
1.2
1
2
3
theta6
0.015
0.025
0.035
s igma11
150
200
150
250
0.18
theta3
50
4
60
Frequency
40
20
0
0.10
theta2
0
2
80
100 120 140
120
100
80
60
20
0
0.0
theta1
Frequency
Sigma Param
40
Frequency
200
150
Frequency
0
0
50
100
150
100
50
Frequency
200
250
250
Bootstrap Parameter Distribution
4
5
0.045
14
Model 1
12
Log CSF
10
8
ks
6
4
S
2
0
0
10
20
30
40
50
Time (hr)
Parameter
ks (/hr)
kd (/hr)
kc (/hr)
SMAX, S
Model 1 (Literature)
Model
Bootstrap
Estimates
%CV
Mean
5.92
14.4
5.80
5.79
15.0
5.64
0.119
14.8
0.126
0.100
20.0
0.120
Bootstrap
90% CI
3.18-8.77
3.13-8.65
0.0916-0.176
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
1.72-4.02
SMAX, R
0.0342
15.8
0.0559
0.0392-0.0969
SC50, R (µg/mL)
0.192
0.198
44.7
6.71
0.114
0.188
0.029-0.256
0.157-0.215
Proportional Error
No. of Parameters = 9
kc
Rfit
kd
+ H(C(t))
kdd
+ H’(C(t))
kss
• Bootstrap Success Rate: 78.5%
• VPC: Observed outside the 90%CI = 9.4%
Model 2
(Dormant)
14
12
Log CSF
10
8
D
6
4
2
ke
+ ke
0
0
10
20
30
40
50
Time (hr)
Parameter
ks (/hr)
kd (/hr)
ke (/hr)
SMAX, S
H(C(t))
Model 2 (Dormant)
Model
Bootstrap
Estimates
%CV
Mean
0.921
66.1
1.05
0.709
88.5
0.805
0.108
15.5
0.124
0.188
42.4
0.225
Bootstrap
90% CI
0.811-1.52
0.603-1.17
0.0835-0.183
0.116-0.365
SC50, S (µg/mL)
0.0588
56.4
0.0751
0.0140-0.164
SMAX, 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
No. of Parameters = 7
S
+ kd
ks
• Bootstrap Success Rate: 71.3%
• VPC: Observed outside the 90%CI = 11.4%
Model 3
(Compensatory)
14
12
Log CSF
10
8
ks
6
4
S
2
0
0
10
20
30
40
50
kd
+ H(C(t))
kc
Time (hr)
kc
R
Model 3 (Compensatory)
Parameter
ks (/hr)
kd (/hr)
kc (/hr)
SMAX, S
Model
Estimates
0.813
0.660
0.172
1.020
%CV
14.5
18.3
10.7
18.9
Bootstrap
Mean
0.819
0.664
0.325
1.364
Bootstrap
90% CI
0.654-0.941
0.538-0.771
0.166-0.565
0.890-2.087
SC50, S (µg/mL)
0.358
14.6
0.346
0.215-0.542
SMAX, 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
No. of Parameters = 7
kd
Rfit
+ H’(C(t))
ks
• Bootstrap Success Rate: 83.9%
• VPC: Observed outside the 90%CI = 8.3%
Model 4
(Dual Effects)
14
12
Log CSF
10
8
6
D
4
+ ke
2
0
0
10
20
30
40
50
kc
H(C(t))
S
Time (hr)
Model 4 (Combo)
+ kd
Parameter
ks (/hr)
kd (/hr)
ke (/hr)
kc (/hr)
Model
Estimates
0.142
0.0235
0.088
0.00326
Bootstrap
Mean
0.139
0.0447
0.0845
0.0234
90% CI
0.0556-0.417
0.0101-0.227
0.0179-0.182
0.0001-0.0471
SMAX, S
28.60
12.4
1.01-44.3
SC50, S (µg/mL)
0.374
0.291
0.0109-0.515
SMAX, D
4.230
3.74
0.139-8.933
SC50, D (µg/mL)
0.2680
0.231
2.51
0.189
0.0991-16.4
0.157-0.218
Proportional Error
No. of Parameters = 8
ke
Rfit
ks
kd
ks
• Bootstrap Success Rate: 61.3%
• VPC: Observed outside the 90%CI = 7.3%
Interpolation of Sub-compartmental PK/PD
Profiles
Cipro Concentration
Susceptible
Dormant
100
14
12
80
10
60
8
6
40
4
20
2
0
0
0
10
20
30
40
Time (hr)
• Larger % of Dormant population
needed
• Dormant population account for
regrowth?
120
16
Cipro Concentration
Susceptible
Initial Mutation
Compensatory Mutation
100
14
12
80
10
8
60
6
40
4
2
20
0
0
0
10
20
30
40
Time (hr)
• Dual characteristics of drug
resistant and fitness restoration
account for regrowth?
Log CFU
16
Simulated Plasma Cipro Concentration (µg/mL)
120
Compensatory Hypothesis
Log CFU
Simulated Plasma Cipro Concentration (µg/mL)
Dormant Hypothesis
Dormant PK/PD Model
(Equivalent to clinical 200 mg BID for 5 days)
CIP Conc (µg/mL)
PK profile
Log CFU/mL
Time (hr)
Dormant
Susceptible or
Observable
Population
Time (hr)
Compensatory Mutation PK/PD Model
(Equivalent to clinical 200 mg BID for 5 days)
Total
Observable
Population
Log CFU/mL
CIP Conc (µg/mL)
PK profile
Time (hr)
R without fitness
Log CFU/mL
Susceptible
Time (hr)
R with fitness
Subpopulation Analysis of P. aeruginosa Following
200 mg CIP Exposure in an in vitro Model
 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
Dudley et al., Ameri J Med 82:363 (1987)
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
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)