Mathematical Model for Growth and Rifampicin-Dependent Killing Kinetics of Escherichia coli Cells

Antibiotic resistance is a global health threat. We urgently need better strategies to improve antibiotic use to combat antibiotic resistance. Currently, there are a limited number of antibiotics in the treatment repertoire of existing bacterial infections. Among them, rifampicin is a broad-spectrum antibiotic against various bacterial pathogens. However, during rifampicin exposure, the appearance of persisters or resisters decreases its efficacy. Hence, to benefit more from rifampicin, its current standard dosage might be reconsidered and explored using both computational tools and experimental or clinical studies. In this study, we present the mathematical relationship between the concentration of rifampicin and the growth and killing kinetics of Escherichia coli cells. We generated time-killing curves of E. coli cells in the presence of 4, 16, and 32 μg/mL rifampicin exposures. We specifically focused on the oscillations with decreasing amplitude over time in the growth and killing kinetics of rifampicin-exposed E. coli cells. We propose the solution form of a second-order linear differential equation for a damped oscillator to represent the mathematical relationship. We applied a nonlinear curve fitting solver to time-killing curve data to obtain the model parameters. The results show a high fitting accuracy.