Modelling rate and extent of resistance development against colistin in Klebsiella pneumoniae
A.D. Pham (1), J. G. C. van Hasselt (1)
1. Leiden University, Leiden, The Netherlands
Objectives: Klebsiella pneumonia is a gram-negative pathogen of concern due to widespread multidrug resistance [1]. Colistin is one of the last resorts antibiotics for treatment of multidrug resistant K. pneumoniae infections [2]. Emergence of colistin resistance is a global issue [3] and can develop during treatment of K. pneumoniae with colistin [4].
Quantitative characterization of the antibiotic pharmacodynamics and emergence of resistance using time kill experiments and mathematical modelling can guide design of treatment schedules to control emergence of resistance [5]. Most commonly, such in vitro time kill studies and in silico models consider the total number of colony forming units (CFUs). Quantifying the rate and extent of resistance, e.g., the specific antibiotic sensitivity of underlying bacterial sub-populations, is of relevance to unravel the pharmacodynamic principles associated with emergence of resistance, and can be experimentally studied using population analysis profiling (PAP). In PAP assays, samples from time kill study cultures are plated on antibiotic-containing plates at different antibiotic concentrations. However, PAP assays have not been commonly incorporated in mathematical pharmacodynamic models.
Here, we aimed to develop and demonstrate a pharmacodynamic model that incorporates quantitative PAP-derived time course and distribution of resistant bacterial sub-populations, for K. pneumoniae time kill studies with colistin.
Methods: Data: Static concentration time kill (SCTK) experiments were conducted for the K. pneumoniae strain ATCC BAA-1705. SCTKs were conducted with 20 mL cultures in Cation-adjusted Mueller Hinton broth for multiple colistin concentration ranging from 0.1 to 5 µg/mL. Samples were collected at 0, 1, 2, 4, 8 and 24 h. CFUs were quantified by plating on antibiotic free plates and for PAPs using plates containing 1, 5, 10 and 20 µg/mL of colistin.
Model development: A previous pharmacodynamic ordinary differential equation (ODE) model described the SCTK of colistin against Pseudomonas aeruginosa was used as the base model [5]. Briefly, this model consisted of drug-susceptible growing bacteria (S) and non-susceptible bacteria (R). The resistance development in this model is described by a transition from state of no resistance (ReOFF) to a state of resistance (ReON), according to a concentration dependent rate constant (Eq. 1):
kon = Kon.max*CAB/(Con.50+CAB) (1)
The colistin-mediated kill rate kkill was characterized using an Emax model with resistance development modelled according to resistance state ReON (Eq. 2):
kkill = (Emax*CAB/(EC50+CAB))*(1-ReONβ) (2)
The fraction (F) of bacteria on PAP plates (CFUPAP) that could survive at specific concentrations of colistin plates (CcolPAP) relative to the total number of bacteria (CFUtotal) was described according to Eq. 3-4:
log10(CFUPAP) = F*log10(CFUtotal) (3)
F=1-(CcolPAP/(F50(t)+CcolPAP)) (4)
where F50 is considered a time-varying variable, which was modelled as follows (Eq. 5):
d/dt(F50) =kfmax*ReONβ*F50 with F50(t=0) = EC50 (5)
here, kfmax reflects the rate at which 50% of the total population at time t and PAP plate concentration CcolPAP will survive.
The model was implemented in R, version 4.0.3 in combination with the nlmixr package, version 2.0.4 [6].
Results: The model adequately captured total CFU time kill profiles, with a maximum population density of 9.6 (RSE 1.79%) log10 CFU/ml and a natural growth rate of 1.9h-1 (RSE 16.1%). Colistin showed a rapid bactericidal effect with a maximum killing rate constant (Emax) of 378 h-1 (RSE 4.81%) and an EC50 of 2.36 µg/mL (RSE 7.96%). The concentration-dependent rate of development of resistance was konmax was estimated at 3.71 h-1 (RSE 7.08%), with the concentration needed to reach half of maximum rate (Cab_on50) was 2.23 µg/ml (RSE 17.8%), with a Hill parameter of 0.748 (RSE 8.88%). The power term β describing the proportion of resistance development was 0.158 (RSE 20.3%). PAP CFU data at different concentrations of colistin could be adequately captured, identifying a maximum rate of resistance development (kf.max) of 0.237 h-1 (RSE 26.8%).
Conclusions: Our modelling approach may be a relevant strategy to characterize the rate and extent of resistance as informed by time kill studies and PAP assays, as demonstrated for K. pneumoniae treated with colistin. The model can be applied to guide dose optimization to prevent the development of resistance.
References:
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