The interaction between a β-lactam and a bacterial population expressing a Bla can be simplified to the interactions between four main components: population density, antibiotic concentration, nutrient level, and Bla concentration. To model bacteria that constitutively produce Bla and lyse due to antibiotics degrading the cell wall, we modified Tanouchi et al.’s ordinary differential equation model (41) for the nondimensional dynamics of bacterial density (n), extracellular Bla concentration (b), nutrient level (s), and β-lactam concentration (a).Embedded Image(3)Embedded Image(4)Embedded Image(5)Embedded Image(6)Embedded Image(7)Embedded Image(8)

Initial conditions of n(0) = 0.4, b(0) = 0, a(0) = 0:300, and s(0) = 4 were used for all the simulations. We assume that the growth rate of cells (g) is limited by s, following the Monod kinetics. We assume the lysis rate (l) can reach a maximum of γ and depends on a following the Hill kinetics and g. dB and dA are the natural decay rates of extracellular Bla and antibiotic, respectively. κb is the rate at which Bla degrades the antibiotic. ξ is a weighting factor for how much nutrients are recycled upon cell lysis, and h is the Hill coefficient. See the Supplementary Materials for parameter values and full model development.

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