TABLE 1.
Parameter estimates of the mechanism-based population pharmacodynamic model for two wild-type P. aeruginosa strains (PAO1-RH and PAO1-AO) and a PAO1-mexZ mutant (isogenic to PAO1-AO)
| Parameter | Symbol | Unit | Population mean (SE%), PAO1-RH | Performance of simplified models, Δ(−2× log likelihood)g | Population mean (SE%) |
|
|---|---|---|---|---|---|---|
| PAO1-AO | PAO1-ΔmexZ mutant | |||||
| Bacterial growth | ||||||
| Log10 for: | ||||||
| Low initial inoculum | Log10 CFUo | 6.10 (1.2)d | 4.85 (2.5) | 4.85 (2.5) | ||
| Medium initial inoculum | Log10 CFUo | 7.71 (0.8) | 6.97 (2.0) | 6.97 (2.0) | ||
| High initial inoculum | Log10 CFUo | 8.84 (0.7) | 7.50 (1.6) | 7.50 (1.6) | ||
| Log10 (fraction of intermediate population at time zero) | Log10 FrI | −4.16 (1.7) | −3.47 (4.5) | −3.47 (4.5) | ||
| Log10 (fraction of resistant population at time zero) | Log10 FrR | −6.43 (1.9) | 108 (P < 0.0001)h | −6.16 (2.9) | −5.83 (2.8) | |
| Fastest mean generation time at low bacterial density | ||||||
| Susceptible population | MGT12,low,Sa | min | 49.2 (5.5) | 38.8 (18.9) | 38.8 (18.9) | |
| Intermediate population | MGT12,low,Ia | min | 49.2 (5.5) | 58.4 (44.1) | 58.4 (44.1) | |
| Resistant population | MGT12,low,Ra | min | 49.2 (5.5) | 99.9 (64.9) | 99.9 (64.9) | |
| Slowest mean generation time at high bacterial density | MGT12,higha | min | 720 (fixed) | 161 (P < 0.0001)i | 720 (fixed) | 720 (fixed) |
| Log10 (maximum population size) | Log10 CFUmax | 9.78 (0.8) | 9.23 (1.5) | 9.23 (1.5) | ||
| Mean turnover time of hypothetical signal molecules | MTTSigb | h | 11.4 (10.3) | 154 (P < 0.0001)j | 3.48 (29.6) | 3.48 (29.6) |
| Log10 of signal molecule concn causing 50% of change from low to high bacterial density | Log10 C50,Sig | 7.91 (1.1) | 232 (P < 0.0001)k | 7.55 (2.9) | 7.55 (2.9) | |
| Bacterial killing | ||||||
| Mean equilibration half-life between tobramycin in broth and in the intracellular space (t1/2eq was ln(2) · Vbroth/CLd) | t1/2eq | min | 27.4 (11.3) | 16.3 (23) | 16.3 (23) | |
| Maximum killing rate constant for immediate killing of the: | ||||||
| Susceptible population | kmaximm,S | 1/h | 134 (9.7) | 110 (P < 0.0001)l | 262 (9.4) | 262 (9.4) |
| Intermediate population | kmaximm,I | 1/h | 10.6 (8.9) | 33.4 (16.9) | 33.4 (16.9) | |
| Resistant population | kmaximm,R | 1/h | 0.255 (7.3) | 0.410 (24.8) | 0.410 (24.8) | |
| Intracellular tobramycin concn causing 50% of kimm | SC50,imm | mg/liter | 37.6 (7.9) | 76.8 (24.8) | 76.8 (24.8) | |
| Hill coefficient for immediate killing | Hillimm | 1.31 (4.6) | 52.5 (P < 0.0001) | 1.09 (6.1) | 1.09 (6.1) | |
| Maximum killing rate constant at low bacterial density for delayed killing of the: | ||||||
| Susceptible population | kmaxdelay,S,low | 1/h | 14.8 (8.7)e | 5.54 (34.7) | 5.54 (34.7) | |
| Intermediate population | kmaxdelay,I,low | 1/h | 3.80 (8.2)e | 1.19 (29.0) | 1.19 (29.0) | |
| Resistant population | kmaxdelay,R,low | 1/h | 2.12 (12.8)e | 0.634 (13.7) | 0.634 (13.7) | |
| Maximum killing rate constant at high bacterial density for delayed killing of the: | ||||||
| Susceptible population | kmaxdelay,S,high | 1/h | 0.179 (18.4)e | 0.162 (22.4) | 0.162 (22.4) | |
| Intermediate population | kmaxdelay,I,high | 1/h | 0.0461 (8.2)e | 0.0350 (29.0) | 0.0350 (29.0) | |
| Resistant population | kmaxdelay,R,high | 1/h | 0.0257 (12.8)e | 0.0186 (13.7) | 0.0186 (13.7) | |
| Intracellular tobramycin concn causing 50% of kdelay | SC50,delay | mg/liter | 3.91 (11.7) | 0.958 (20.1) | 0.958 (20.1) | |
| Hill coefficient for delayed killing | Hilldelay | 1.86 (8.7) | 14.5 (P = 0.0001) | 5.61 (38.6) | 5.61 (38.6) | |
| Mean turnover time of lethal protein(s) at: | ||||||
| Low bacterial density | MTTProt,lowc | h | 2.05 (9.0) | 33.3 (P = 0.0001)m | 4.29 (33.0) | 4.29 (33.0) |
| High bacterial density | MTTProt,highc | h | 24 (fixed) | 8.73 (P = 0.003)n | 24 (fixed) | 24 (fixed) |
| Adaptive resistance | ||||||
| Baseline of adaptive resistance | Adapt1Base | 0 (fixed) | 0 (fixed) | 0.981 (27.8) | ||
| Maximum extent of stimulation of adaptive resistance | SmaxAdapt | 32.4 (6.5) | 53.3 (P = 0.0001)o | 58.3 (6.8) | 44.1 (17.0) | |
| Intracellular tobramycin concn causing 50% of SmaxAdapt | SC50,Adapt | mg/liter | 36.5 (7.2) | 1.38 (35.5) | 1.38 (35.5) | |
| Turnover rate constant for adaptive resistance | k10,adt | 1/h | 0.314 (9.7) | 0.174 (18.3) | 0.174 (18.3) | |
| Intercompartmental transfer rate constant between the central and peripheral compartment for adaptive resistance | k12,adt | 1/h | 0.921 (21.1) | 50.1 (P < 0.0001)p | 1.99 (14.6) | 1.99 (14.6) |
| Intercompartmental transfer rate constant between the peripheral and central compartment for adaptive resistance | k21,adt | 1/h | 0.167 (fixed)f | 0.167 (fixed) | 0.167 (fixed) | |
| Residual variability | ||||||
| SD of additive residual error on log10 scale | σ | 0.241 (4.0) | 0.354 (5.3) | 0.354 (5.3) | ||
The growth rate constant of the susceptible population (k12,low,S) at low bacterial density was calculated as 1/MGT12,low,S. The same equation was applied for the intermediate and resistant populations. The growth rate constant at high bacterial density (k12,high) was calculated as 1/MGT12,high. The k21 was fixed to 50 1/h.
The turnover rate constant (kturn) of hypothetical signal molecules was calculated as 1/MTTsig.
The first-order rate constant kProt,low was calculated as 5/MTTProt,low and kProt,high as 5/MTTProt,high, reflecting the five transit compartments for the protein synthesis.
Owing to the small between-curve variability for in vitro static time-kill experiments, the between-curve variability was fixed to a small value (15% coefficient of variation for log-normally distributed parameters and a standard deviation of 0.1 for parameters estimated on a log10 scale).
The ratios of kdelay,S divided by kdelay,I and of kdelay,I divided by kdelay,R were estimated.
This estimate was fixed to a mean transfer time (1/k21,adt) of 6 h based on the data from Hocquet et al. (23).
Difference in the −2× log likelihood for a model which lacked the respective model parameter or model feature compared to the final model for strain PAO1-RH.
For a model which lacked the resistant population. A model lacking both the intermediate and resistant population could not adequately describe the data.
For this model, MGT12,high was set to the value of MGT12,low,S.
For this model, MTTSig was fixed to a very small value (0.01 h), which results in an immediate (i.e., nondelayed) inoculum effect.
This model lacked the inoculum effect.
This model lacked the immediate killing effect.
For this model, the delayed killing effect was delayed only by a very short time (i.e., MTTProt,low and MTTProt,high were fixed to 0.05 h).
For this model, MTTProt,low was not inoculum dependent and MTTProt,high was not included in the model.
This model lacked adaptive resistance (i.e., SmaxAdapt was fixed to zero).
For this model, adaptive resistance was described by one instead of two compartments.