Modeling the Overproduction of Ribosomes when Antibacterial Drugs Act on Cells

Abstract

Bacteria that are subjected to ribosome-inhibiting antibiotic drugs show an interesting behavior: Although the drug slows down cell growth, it also paradoxically increases the cell's concentration of ribosomes. We combine our earlier nonlinear model of the energy-biomass balance in undrugged Escherichia coli cells with Michaelis-Menten binding of drugs that inactivate ribosomes. Predictions are in good agreement with experiments on ribosomal concentrations and synthesis rates versus drug concentrations and growth rates. The model indicates that the added drug drives the cell to overproduce ribosomes, keeping roughly constant the level of ribosomes producing ribosomal proteins, an important quantity for cell growth. The model also predicts that ribosomal production rates should increase and then decrease with added drug. This model gives insights into the driving forces in cells and suggests new experiments.

Figure 1

Minimal kinetic model of E. coli. The model expresses the dynamical fluxes (arrows) and concentrations of active ribosomes (R_act), nonribosomal proteins (P), and a lumped internal energy (ATP). The double arrow shows a positive feedback mechanism for ribosomal autosynthesis, a key controller of growth behavior. Antibiotic inhibitor molecules are represented by X. X binds reversibly with active ribosomes. While in the bound form, R_in, the ribosomes are inactivated, and they do not translate proteins. P degrades with rate constant γ. The cell grows exponentially, with a specific growth rate of λ.

Figure 2

E. coli physiological correlations. (A) Growth rate versus extracellular glucose concentration from a simulation for antibiotic (chloramphenicol) concentrations of 0, 2.1, and 6.4 μM. (B) Dependence of growth rate, λ, on antibiotic concentration, x. The line is the numerical solution of the ODE model, with G = 0.08 mM (red line). Red solid circles represent the experimental data (10) of E. coli grown on glucose + M63.

Figure 3

E. coli ribosomal protein fraction versus growth rates. Numerical solutions of the ODE model, with increasing glucose concentrations (in mM) G = 0.04 (blue), 0.05 (green), 0.08 (red), and 0.125 (purple), and antibiotic concentrations x = 0 → 25 μM (arrows). Circles represent the experimental data (10) for E. coli grown on glucose + M63 at different dosages of chloramphenicol (in μM). To get ϕ, the rRNA/protein ratio from Scott et al. (10) is scaled by a factor of 0.46 (20). The black line represents the prediction from theory (Eq. 18), with $f_{\text{p}}=f_{\text{p}}^{\infty }=0.7$, $k_{\text{p}}^{\text{'}}=9.65$ h⁻¹, γ = 0.1 h⁻¹, and α = 1 (absence of drugs).

Figure 4

Effect of ribosomal inhibitors on cellular homeostasis. Lines are scaled numerical solutions of the ODE model, with G = 0.08 mM. The orange line represents the active ribosomes, [α(x)/α(x = 0)], as a function of drug concentration, x. The red line represents the total ribosomes, [ϕ_tot(x)/ϕ_tot(x = 0)]. The black line represents the fraction of active ribosomes that are producing ribosomal proteins, [ϕ_rr(x)/ϕ_rr(x = 0)] (Eq. 19). Also see Figs. S2–S4.

Figure 5

Effect of ribosomal inhibitors on ribosomal activity. The symbols show the rate of ribosomal synthesis, J_fr = M_rJ_r/ρ, versus specific growth rate of E. coli converted from the experimental ϕ − k data. Chloramphenicol concentrations (in μM) are indicated inside the circles. Nutrients were M63 + glucose (red) at T = 37 C (10). Gray solid circles represent experimental data (10) in the absence of drugs. To get ϕ, the rRNA/protein ratio from Scott et al. (10) is scaled by a factor of 0.46 (20). The blue line represents the ODE model prediction at constant G = 0.04 mM with chloromaphenicol varied according to x = 0 → 15 μM (arrow). The black line represents the theoretical prediction (Eq. 21) in the absence of drugs, with $f_{\text{p}}=f_{\text{p}}^{\infty }=0.7$, $\gamma =0.1$ h⁻¹, and $k_{\text{p}}\text{'}=9.65$ h⁻¹. Also see Fig. S1.

Figure 6

Effect of ribosomal inhibitors on the rate of energy metabolism. Shown are predictions of the rate of energy metabolism versus growth rate, λ, from the ODE model with glucose varied, G = 0 − 1 mM, and no drugs (black line), and the prediction at G = 0.04 mM (red line), with the drug dosage varied according to x = 0 → 15 μM (arrow). An increase in drug concentration reduces both rates of growth and energy generation.