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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
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
Hypothesis 1:Toxin-Antitoxin Relationship
(RelE and Antibiotic Tolerance Example)
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
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
Hypothesis 2:Compensatory Mutation
Marcusson et al., PLoS Pathogens, 5:e1000541 (2009)
Number of Induced Mutations
Hypothesis 2:Compensatory Mutation
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 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
ks = synthesis rate constant
kd = degradation 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
kc = mutation rate constant
ks = synthesis rate constant
kd = degradation 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
kc = mutation 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
• Bootstrap Success Rate: 71.3%
• VPC: Observed outside the 90%CI = 11.4%
ParameterModel
Estimates %CVBootstrap
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)
No. of Parameters = 7
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
• Bootstrap Success Rate: 83.9%
• VPC: Observed outside the 90%CI = 8.3%
ParameterModel
Estimates %CVBootstrap
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)
No. of Parameters = 7
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)
• Bootstrap Success Rate: 61.3%
• VPC: Observed outside the 90%CI = 7.3%
No. of Parameters = 8
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)