Correlating Drug-Target Residence Time and Post-antibiotic Effect: Insight into Target Vulnerability

Abstract

Target vulnerability correlates the level of drug-target engagement required to generate a pharmacological response. High vulnerability targets are those that require only a relatively small fraction of occupancy to achieve the desired pharmacological outcome, whereas low vulnerability targets require high levels of engagement. Here, we demonstrate that the slope of the correlation between drug-target residence time and the post-antibiotic effect (PAE) can be used to define the vulnerability of bacterial targets. For macrolides, a steep slope is observed between residence time on the E. coli ribosome and the PAE, indicating that the ribosome is a highly vulnerable drug target. The analysis of the residence time-PAE data for erythromycin, azithromycin, spiramycin, and telithromycin using a mechanistic pharmacokinetic-pharmacodynamic model that integrates drug-target kinetics into predictions of drug activity lead to the successful prediction of the cellular PAE for tylosin, which has the longest residence time (7.1 h) and PAE (5.8 h). Although the macrolide data support a connection between residence time, PAE, and bactericidality, many bactericidal β-lactam antibiotics do not give a PAE, illustrating the role of factors such as protein resynthesis in the expression of target vulnerability.

Keywords: antibiotic; macrolide; post-antibiotic effect; residence time; ribosome; target vulnerability; β-lactam.

Figure 1.. The two-step induced-fit binding mechanism.

K_i is the inhibition constant for the first rapid equilibrium step and k₅, k₆ are the association and dissociation rate constants, respectively, for the second slow step.

Figure 2.. Correlation between residence time and PAE.

Experimental data are shown by solid symbols and the dashed-line is a linear fit to the data with a slope of 0.76 (R² 0.96). The reported residence-times were determined at 25°C while the PAEs were measured at 37°C against the E. coli ΔacrAB strain. Tylosin is included in the data fitting although the results of simulating and measuring the PAEs for tylosin are presented later in the results and discussion. The curve has not been constrained to pass through 0,0 as it is possible that a compound with no residence time could lead to an appreciable PAE as observed for inhibitors of LpxC.

Figure 3.. Fitting of the PAE data to the kinetics-driven mathematical model.

The experimental data are shown as squares and the lines represent the results of fitting to Equation 1. Input and output values for each parameter are given in Table 2. The decrease in CFUs at 1 h is due to a 1000-fold dilution of the bacterial culture into fresh media (see Figure S1).

Figure 4.. Simulation of the PAE for tylosin.

The experimental data are shown as squares and the lines represent the best simulation of the data by Equation 1 (R² = 0.95) when the input values were allowed to float between the boundary factors. Input values for the parameters were as follows with the output values in parentheses: k₅ 1.36 (0.68) min⁻¹, k₆ 0.0023 (0.0046) min⁻¹, k_growth 2.0 (1.9) log₁₀ h⁻¹, k_kill 2.6 (2.4) log₁₀ h⁻¹, p_m/K_i 0.01 (0.0027), and K_m/[S] 0.31 (0.62). The decrease in CFUs at 1 h is due to a 1000-fold dilution of the bacterial culture into fresh media (see Figure S1).