Article Figures & Data
Figures
- Fig 1
Subpopulation synergy concept. Bacterial cells inside the solid line are susceptible to drug A; bacterial cells inside the long dashed lines are susceptible to drug B. Bacteria within the dotted lines are resistant to either drug A or drug B. The combination of drug A and drug B will eradiate these bacterial populations due to the lack of a population resistant to both drugs.
- Fig 2
Mechanistic synergy with drug B enhancing the rate of killing by drug A for the population susceptible to drug A, the population resistant to drug A, or both populations.
- Fig 3
Life cycle growth model for the population susceptible to both nisin and amikacin. This two-state life cycle growth model was applied to each of the six populations in Fig. 4. k12, first-order growth rate constant; k21, first-order replication rate constant (representing doubling); InhRep, inhibition of the probability of successful replication; Inhk12, inhibition of the first-order growth rate; other symbols are explained in Table 1 and Materials and Methods.
- Fig 4
Subpopulation synergy model for nisin and amikacin comprising six populations with different susceptibility to each antibiotic. Niss, nisin susceptible; Nisi, nisin intermediate; Nisr, nisin resistant; Amis, amikacin susceptible; Amir, amikacin resistant. Thick arrows represent fast growth or fast killing. Solid downward arrows represent killing by nisin, and dashed arrows represent killing by amikacin. See Table 1 for parameter explanations.
- Fig 5
Observed and individual fitted viable count profiles from S-ADAPT for nisin (A) and amikacin (B) in monotherapy and sequential (C) and simultaneous (D and E) combinations. Time is the time after start of the experiment. For the sequential combinations, the time axis shows the time after switching treatment to amikacin at 1.75 h after the start of the experiment. Plates with zero colonies are plotted as 0 log10 CFU/ml.
- Fig 6
Observed and individual fitted viable count profiles from S-ADAPT for nisin (A) and linezolid (B) in monotherapy and sequential (C) and simultaneous (D and E) combinations.
Tables
- Table 1
Parameter estimates for nisin combinations with amikacin or linezolid
Parameter Symbol (unit) Estimate (relative SE [%]) Nisin + amikacin Nisin + linezolid S-ADAPT NONMEM S-ADAPT NONMEM Growth parameters Log10 (initial inoculum) 7.89 (2.0)c 7.84 (2.2) 7.88 (1.4)c 7.83 Mean generation time Niss/Amis and Nisi/Amis k12−1 (min) 57.3 (7.0)b 67.5 (9.5) Niss/Lins and Nisi/Lins k12−1 (min) 83.9 (7.5)b 56.6 Growth rate factors Nisr/Amis and Niss/Amir fk12_RS_SR Very lowa Very lowa Nisi/Amir fk12_IR 0.532d 0.519 (14) Nisr/Amir fk12_RR 0.413d 0.386 (12) Nisr/Lini fk12_R 0.144 (15) 0.102 Replication rate constant k21 (h−1) 50 (fixed) 50 (fixed) 50 (fixed) 50 (fixed) Log10 (maximum population size) CFUmax 9.23 (2.5)c 9.23 (2.0) 9.38 (1.7)c 9.25 Log10 (mutation frequencies) Nisi/Amis −4.25 (15)c −3.63 (8.2) Nisr/Amis −3.25 (7.1) −3.89 (8.0) Niss/Amir −2.57 (23) −2.58 (18) Nisi/Amir −4.37 (9.3) −4.48 (8.2) Nisr/Amir −7.42 (7.7) −7.47 (4.5) Nisi/Lins −2.88 (6.2)c −3.02 Nisr/Lini −4.15 (7.3) −3.59 Second-order killing rate constants for nisin Susceptible population k2S [liters/(mg · h)] 5.67 (14)b 3.58 (17) 4.49 (12)b 3.08 Intermediate population k2I [liters/(mg · h)] 0.0664 (6.9) 0.0605 (19) 0.0209 (12) 0.0605 Resistant population k2R [liters/(mg · h)] 0.00691 (13) 0.00484 (21) 0.00318 (13) 0.00383 Killing by amikacin Maximum killing rate constants Susceptible population KmaxS (h−1) 10.1 (19) 9.10 (21) Resistant population KmaxR (h−1) 0.771 (18) 0.635 (10) Amikacin concn causing 50% of Kmax KC50 (mg/liter) 14.7 (7.7) 16.5 (7.2) Hill coefficient Hill 2.45 (12)b 2.83 (14) Inhibition of replication and growth rate by linezolid Inhibition of successful replication by linezolid (InhRep) for Niss/Lins and Nisi/Lins Maximum inhibition of replication ImaxRep 1.0 (fixed) 1.0 (fixed) Linezolid concn causing half-maximum inhibition of protein synthesis IC50,Prot (mg/liter) 3.92 (19) 7.35 Inhibition of rate of growth (all populations, Inhk12) Maximum inhibition of rate of growth Imax,k12 0.858 (12) 0.918 Linezolid concn causing 50% of effect IC50,k12 (mg/liter) 4.25 (31) 19.4 Hill coefficient Hillk12 10 (fixed) 10 (fixed) Turnover rate constant for protein pool kProt (h−1) 0.72 (7.1) 0.458 Standard deviation of additive residual error on log10 scale SDCFU 0.395 (9.5) 0.775 (15) 0.307 (7.6) 0.549 ↵a Replication for these two populations was estimated to be very slow in the present static time-kill experiment. Eventually, fk12_RS_SR was fixed to 0.
↵b For the population PD modeling analysis in S-ADAPT, the biological variability between the viable count profiles (between-curve variability) was set to a coefficient of variation of 15% for all parameters except those estimated on a log10 scale. The between-curve variability was set to 10% for the Hill coefficient.
↵c The between-curve variability for parameters estimated on a log10 scale in S-ADAPT was set to a variance of 0.25. For the maximum population size and the experimentally standardized initial inocula, the variances were estimated to be small and therefore eventually fixed to 0.01.
↵d As these fractions were estimated via a logistic transformation in S-ADAPT, their mean estimate was close to zero on a transformed scale (equivalent to 50% on a linear scale). This resulted in relative standard errors of 222% for fk12_IR and of 65.4% for fk12_RR, since the mean on transformed scale was almost zero. These artificially inflated relative standard errors did not impact the performance of the model or the curve fits, as also suggested by the small standard error in the NONMEM analysis which did not use this transformation.
Supplemental material
Files in this Data Supplement:
- Supplemental file 1 -
Supplemental material: differential equations for the intermediate and resistant bacterial populations.
PDF, 19K
- Supplemental file 1 -
