The pharmacodynamic inoculum effect from the perspective of bacterial population modeling

Abstract

1Efficacy assessment of antimicrobials is essential, both to determine the best 2 clinical use of the antimicrobial and as input for predictive mathematical mod-3 eling. The pharmacodynamic (PD) function is a tool to describe antimicrobial 4 efficacy and can be seen as an extension of the commonly used MIC. While the 5 PD function describes the efficacy of a given dose of antimicrobials, it is based 6 on one bacterial inoculum size only. Therefore, the PD function does not inform 7 us about the change in efficacy due to changes in the inoculum size, also known 8 as the inoculum effect. Here, we used mathematical modeling to quantify the 9 inoculum effect in terms of PD parameters. In particular, we used the multi-hit 10 model that describes the mechanism of action of antimicrobials: When a cer-11 tain number of antimicrobial molecules have hit a bacterial cell, it dies. This 12 framework allowed us to examine the effect of reversible binding and enzymatic 13 degradation of antimicrobials on the pharmacodynamics. A change in bacte-14 rial inoculum size resulted in a change of the PD parameter A 50 , M IC P D , and 15 therefore κ due to reversible binding. We determined an extended PD function 16 that captured the inoculum effect as change in the PD parameters. When we 17 allowed for degradation of antimicrobials by bacterial enzymes, the inoculum 18 effect was intensified. The extended PD function could mimic long term pop-19 ulation dynamics based on the multi-hit model with reversible binding only, 20 1 but deviated from long-term predictions based on a multi-hit model including 21 degradation. We then used the multi-hit framework to estimate outcomes of 22 competition experiments with a sensitive and resistant strain and compared it 23 to predictions of the PD function. When we do not take the inoculum effect into 24 account, our simulations underestimated the ability of the sensitive population 25 to survive for a given PK regime and the competitiveness of the sensitive strain 26 against the resistant strain. Our work emphasizes that the PD function -and 27 in general any efficacy measure -should, at least, include information about 28 the inoculum size and, ideally, account for the inoculum effect. 29 Introduction 30 Efficacy of antimicrobials against bacteria is quantified using time-kill curves 31 and is subsequently captured in so-called pharmacodynamic (PD) functions, 32 also known as E max and Zhi models (1 -3 ). A time-kill curve captures how 33 a bacterial population changes over time in presence of a given concentration 34 of an antimicrobial (fig. 1a). During exponential growth, time-kill curves are 35 approximately linear on a logarithmic scale. Thus, the slopes of these log-linear 36 time-kill curves describe the change of the bacterial population over time and 37 are a direct measure of the bacterial net growth rate. The PD function returns 38 the net growth rate for any given antimicrobial concentration. The parameters 39 of the PD function are estimated based on several time-kill curves with the...

Inoculum effect of antimicrobial peptides

“…It is interesting to note that considerations extremely similar to those presented here, regarding a drug-target binding equilibrium and a threshold number of bound drug molecules per cell to cause killing or growth inhibition, have been demonstrated to be valid also for the IE of traditional antibiotics (e.g., oxacillin, ciprofloxacin, or gentamicin), including ionophores such as vancomycin (14,15,87). In addition, a plateau for the MIC values for inocula lower than 10 5 to 10 6 CFU/mL has been observed also for traditional antibiotics, irrespective of their mode of action (14,91,92), and this limiting value has by some authors been termed the single-cell MIC (91,92).…”

The pharmacokinetic–pharmacodynamic modelling framework as a tool to predict drug resistance evolution

“…Furthermore, the susceptibility of a pathogen population to antimicrobials can depend on the number of bacterial cells [159–161]. For both ABs [162] and AMPs [89, 159, 163–165], the efficacy of an antimicrobial decreases with increasing bacterial starting inoculum (called the ‘inoculum effect’), meaning that a higher number of bacterial cells increases the probability of survival and the potential for resistance evolution (, see Text S3 for details). The inoculum effect can, for example, be caused by the uptake of AB molecules into bacterial cells, which depletes them extracellularly [159].…”

Multi-scale modeling of drug binding kinetics to predict drug efficacy

“…One explanation for this effect relates to the fact that the change in the drug availability after binding can be a function of the drug affinity. This effect can be explained by a kinetic model of binding-intuitively, drug molecules that are already bound to their targets cannot kill more bacteria [6,8].…”

“…Increased initial bacterial concentration can imply decreased antibiotic efficacy [6,8,43,44] Heterogeneous population The bacterial population can be heterogeneous, i.e. with different values in: [6]…”

“…Over the last 50 years, mathematical models describing drug pharmacokinetics (PK) and pharmacodynamics (PD) developed from the first concepts of simple relationships between drug concentration and its effects in the 1960 s [1][2][3][4][5] to advanced models that substantially improve our comprehension of the drug action mechanisms [6][7][8][9][10]. Advances in computational power and the improved accuracy and availability of experimental data have further fuelled model development.…”