Modelling rate and extent of resistance development against colistin in Klebsiella pneumoniae and Pseudomonas aeruginosa
A.D. Pham (1), Fleur A.M. Janmaat (1), J. G. C. van Hasselt (1)
Leiden University, Leiden, The Netherlands
Objectives: Klebsiella pneumonia (KP) and Pseudomonas aeruginosa (PA) are commonly associated with serious life-threatening infections and antibiotic resistance1. Colistin is one of the last resorts treatments for resistant pathogens2, hence, making it crucial to limit the risk of colistin resistance emergence3,4.
Mathematical modelling of in vitro time kill (TK) experiments are commonly used to study antibiotic pharmacodynamics (PD). Combining PD models with established clinical pharmacokinetic (PK) models can derive optimized dosing regimens5. However, resistance development is often only indirectly inferred from observed bacterial dynamics. The explicit rate and extent of resistance development during antibiotic exposure, i.e., in terms of the fraction of bacteria which can survive at specific antibiotic concentration, has typically not been considered in modelling. This could be particularly relevant when heteroresistance occurs.
In this work we extend an established mathematical model for antibiotic PD with a model to characterize the heterogeneity in antibiotic sensitivity/resistance, focusing on colistin pharmacodynamics in KP and PA strains, as proof-of-concept example.
Methods:
KP strain ATCC BAA-1705 and the PA strain PAO1 was exposed to various colistin concentrations (0.05- 25 µg/mL) in 20 mL broth cultures up to 24h, followed by plating on colistin PAP plates (0 - 50 µg/mL) for colony forming units (CFUs) quantification.
A previous PD ordinary differential equation model described the TK of colistin against PA was used5. This model consisted of drug-susceptible growing bacteria (S) and non-susceptible resting bacteria (R). Under antibiotic pressure, the resistance developed by a transition of resistance states (ReOFF -ReON), according to a concentration dependent rate constant (Eq. 1).
(1) kon = Kon.slope*CAB
The colistin-mediated kill rate kkill was characterized using an mononomial relation drug concentration and resistance development according to resistance state ReON (Eq. 2).
(2) kkill = = kkill.slope* CAB pow*(1-ReON)
The fraction (fractionpap) of bacteria on PAP plates (CFUPAP) that could survive at specific concentrations of colistin plates (CAB.PAP) relative to the total number of bacteria (CFUtotal) was described according to Eq. 3-4.
(3) fractionpap = CAB.PAP hill / (CAB.PAP hill + EC50.PAP hill)
(4) log10(CFUPAP) = log10(CFUtotal – CFUtotal * fractionpap )
EC50.PAP is considered a time-varying variable, which was modelled as follows (Eq. 5)
(5) EC50.PAP = EC50.PAP.t0 * exp(kon.pap.slope *CAB *time)
A published popPK model 7 was used to simulate the population dynamics of PA and KP under various dosing scheme for treatment with colistin in patient.
Estimation was performed using NONMEM 7.4.36. Simulations were implemented in R with RxODE8
Results:
The model adequately captured total CFU time kill profiles of both pathogens, with a maximum population density of 9.67(3.4%) and 8.79(1.2%) log10 CFU/ml and a natural growth rate of 0.943h-1 (11.3%) and 1.03 (5.9%) for KP and PA respectively. Colistin showed a stronger bactericidal effect on KP with a killing rate of 42.1 h-1 (39%) 10 times higher than PA 4.05 h-1 (14.5%). The concentration dependence rate of resistance development was estimated at 1.84h-1 (48%), 7 times higher than PA at 0.268(15.3%). Similarly, the rate of HR development is 8 time higher for KP 0.59(28.6%) than PA 0.0734(13.3%). HR distribution was described with 2 parameters EC50 and hill. KP is more sensitive toward colistin with lower EC50 of 1.22 (13.6%) compared to PA 3.62(4.4%). In contrast, KP possessed broader heterogeneity, lower hill function 6.6 (9.1%) vs 14.2(6.1%). That explains the faster resistance development as a higher fraction of population can survive at high concentration. Simulation of different dosing regimens illustrate how dosing schedules that appear to show a similar total CFU time profile can show pronounced differences in the population heterogeneity of antibiotic sensitivity.
Conclusions:
Our modelling approach is of relevance to characterize the rate and extent of resistance as informed by time kill studies and PAP assays. Our simulations moreover demonstrate how the use of PAP data to account of population heterogeneity can be of interest to further optimize dosing schedules to prevent the emergence of high-level resistance.
Acknowledgment: This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 861323.
References:
1 WHO. WHO priority pathogens list for R&D of new antibiotics (2017)
2 Petrosillo, N. et al. Expert Review of Anti-Infective Therapy 11, 159–177 (2013)
3 Olaitan, A. O. et al. Int J Antimicrob Agents 44, 500–507 (2014)
4 Aulin, L. B. S. et al. Journal of Antimicrobial Chemotherapy 76, 533–535 (2021)
5 Mohamed, A. F. et al. Journal of Antimicrobial Chemotherapy 69, 1350–1361 (2014)
6 Beal SL et al. in Hanover, MD.: ICON Development Solutions (2018)
7 Matthieu, B. et al. Antimicrob Agents Chemother 58, 7331–7339 (2014)
8 Wang, W. et al. CPT Pharmacometrics Syst Pharmacol 5, 3–10 (2016)