Using Chemical Reaction Kinetics to Predict Optimal Antibiotic Treatment Strategies

Abstract

Identifying optimal dosing of antibiotics has proven challenging—some antibiotics are most effective when they are administered periodically at high doses, while others work best when minimizing concentration fluctuations. Mechanistic explanations for why antibiotics differ in their optimal dosing are lacking, limiting our ability to predict optimal therapy and leading to long and costly experiments. We use mathematical models that describe both bacterial growth and intracellular antibiotic-target binding to investigate the effects of fluctuating antibiotic concentrations on individual bacterial cells and bacterial populations. We show that physicochemical parameters, e.g. the rate of drug transmembrane diffusion and the antibiotic-target complex half-life are sufficient to explain which treatment strategy is most effective. If the drug-target complex dissociates rapidly, the antibiotic must be kept constantly at a concentration that prevents bacterial replication. If antibiotics cross bacterial cell envelopes slowly to reach their target, there is a delay in the onset of action that may be reduced by increasing initial antibiotic concentration. Finally, slow drug-target dissociation and slow diffusion out of cells act to prolong antibiotic effects, thereby allowing for less frequent dosing. Our model can be used as a tool in the rational design of treatment for bacterial infections. It is easily adaptable to other biological systems, e.g. HIV, malaria and cancer, where the effects of physiological fluctuations of drug concentration are also poorly understood.

Drug-target binding quantitatively predicts optimal antibiotic dose levels

“…Qualitatively, this means that the MIC is linear with KD when keeping all other parameters constant. This is consistent with our previous finding when deriving the MIC from drug-target binding alone in a very simplified model [13].…”

“…To include this effect in our model, we modify the term of drug-target dissociation. In the equation describing antibiotic concentration, the unbinding rate kr=0, while, in the bacteria equation, we substitute the dissociation rate kr with the deacetylation rate ka, see [13].…”

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

“…Here, the assumption of equivalent receptors (assumption 6 on the list in "Traditional pharmacodynamic models") is invalid, because the same number of bound targets, combined differently, can have different outcomes. [7,34]). However, the modeling approach can be limited due to lack of knowledge on the specific mechanisms.…”

“…The unspecific binding rate is denoted as k u,f and the unspecific dissociation rate as k u,r . This model can be expressed as follows [7]:…”

“…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.…”