Fig 1.
Barriers for quantitative monitoring of the growth of bacteria using microplate readers.
(A) Representative curves of optical density (OD–black circles) and fluorescence (FL–green squares) of bacterial culture measured with a multimode 96-well microplate reader. Multiple scattering is significant in microplate-reader measurements, resulting in deviations of the OD growth curves from traditional cuvette-based measurements, leading to failures in fitting the growth curve by sigmoid models (such as the Gompertz model, red dashed line). The fluorescent growth curve of the same bacterial culture, which does not show the standard sigmoid shape, is much less studied. (B) Representative OD curves of bacteria measured with a multimode 96-well microplate reader in the absence (black circles) and presence (blue squares) of AgNPs. The AgNPs in the bacterial culture scatter light and interact with growth media and/or bacteria, causing not only a vertical shift in the OD measurements but also elusive features (e.g., a high peak at short time) in the OD growth curve. Error bars (smaller than the symbols) stand for the standard error of the mean.
Fig 2.
Quantitative models and predictions for the cell number n and the number of expressed and matured fluorescent proteins pf.
(A) Sketch of the model for bacterial growth and proliferation: a bacterium recovers from a dormant state to an active reproduction state with an activation rate of α, while activated bacteria grow and reproduce at a maximum growth rate of k0. (B) Sketch of the model for the expression, maturation, and degradation of green fluorescent protein (GFP). Non-fluorescent GFP proteins (GFPn), expressed in bacteria with a generation rate of g, will mature into fluorescent ones (GFPf) with a maturation rate of km. Both GFPn and GFPf are degraded in bacteria, with a degradation rate of γ. (C-F) Predictions from the models in panels A and B (and Eqs 1 – 4) for the cell number (n), number of GFPf (pf), and their time derivatives (dn/dt, dpf/dt, and d2pf/dt2) as functions of growth time.
Fig 3.
Predictions of the models for the dependence of the cell number n the number of GFPf pf, and their time derivatives on the activation rate α. (A-D) Predicted curves of the models for the (A) n, (B) pf, (C) dn/dt, and (D) d2pf/dt2 as functions of time with increasing activation rates α ranging from 10−4 to 10+2 hr-1. (E) Predicted dependence of the peak locations (τp–black circles and –green triangles) of the dn/dt and d2pf/dt2 curves on the activation rate α, compared to that of the fitted lag time λ (blue squares). (F) Relation between the peak locations (τp–black circles and
–green triangles) and the fitted lag time λ. Blue dashed line and red dotted line are linear fittings.
Fig 4.
Predictions of the models for the dependence of the cell number n, the number of GFPf pf, and their time derivatives on the maximum growth rate k0.
(A-D) Predicted curves of the models for the (A) n, (B) pf, (C) dn/dt, and (D) d2pf/dt2 as functions of time with increasing growth rates k0 ranging from 0.50 to 2.00 hr-1. (E) Predicted dependence of the peak heights (ηp–black circles and –green triangles) of the dn/dt and d2pf/dt2 curves on the growth rate k0 in the model. Inset: predicted dependence of the fitted maximum specific growth rate μ on the growth rate k0 in the model. (F) Predicted dependence of the peak locations (τp–black circles and
–green triangles) of the dn/dt and d2pf/dt2 curves and the fitted lag time (λ –blue squares) on the growth rate k0. Blue dashed line and red dotted line are exponential fittings.
Fig 5.
Predictions of the models for the dependence of the cell number n, the number of GFPf pf, and their time derivatives on the GFP generation rate g and maturation rate km.
(A) Predicted curves of the models for pf and d2pf/dt2 (inset) as functions of time with increasing generation rate g ranging from 1 to 1.1×103 hr-1. (B) Predicted dependence of the peak height (–black circles) and peak location (
–blue triangles) of the d2pf/dt2 curve on the GFP generation rate g. (C) Predicted curves of the models for pf and d2pf/dt2 (inset) as functions of time with increasing maturation rate km ranging from 0.04 to 2.56 hr-1. (D) Predicted dependence of the peak height (
–black circles) and peak location (
–blue triangles) of the d2pf/dt2 curve on the GFP maturation rate km. Green solid line and red dashed line are fittings.
Fig 6.
Predictions of the models for the dependence of the cell number n, the number of GFPf pf, and their time derivatives on the GFP degradation rate γ and degradation capacity M.
(A) Predicted curves of the models for pf and d2pf/dt2 (inset) as functions of time with increasing degradation rate γ ranging from 100 to 2×1012 hr-1. (B) Predicted dependence of the peak height (–black circles) and peak location (
–blue triangles) of the d2pf/dt2 curve on the GFP degradation rate γ. Inset: a close-up look of the same data in the range of γ∈[1, 1010] hr-1. (C) Predicted curves of the models for pf and d2pf/dt2 (inset) as functions of time with increasing degradation capacity M ranging from 108 to 1015. (D) Predicted dependence of the peak height (
–black circles) and peak location (
–blue triangles) of the d2pf/dt2 curve on the GFP degradation capacity M.
Fig 7.
Application of the time-derivative based method for identifying the elongation of lag time in the growth of E. coli bacteria due to the treatment with Ag+ ions.
(A) OD growth curves of E. coli in the absence (-Ag+, blue circles) and presence (+Ag+, orange squares) of 40 μM Ag+ ions, measured with a multimode 96-well microplate reader. (B) FL growth curves of the same E. coli samples (-Ag+: green crosses; Ag+: red triangles). Error bars in panels A and B represent standard errors of the means (SEM). (C, D) Time derivatives of the corresponding growth curves in panels A and B. Vertical lines highlights the corresponding peaks. (E) Measured peak locations of ΔOD/Δt in the absence () and presence (
) of Ag+ ions. Error bars stand for the standard deviations of the peaks. (F) Measured peak locations of Δ2FL/Δt2 in the absence (
) and presence (
) of Ag+ ions. Error bars stand for the standard deviations of the peaks. (G) Comparison between the changes of the peak locations (Δτp and
) and the elongation of the fitted lag time (Δλ).
Fig 8.
Application of the time-derivative based method for identifying the effect of silver nanoparticles (AgNPs) at various concentrations on the growth of E. coli bacteria.
(A) FL growth curves of E. coli bacteria in the presence of AgNPs at 0 (control, blue circles), 20 (orange squares), 40 (green cross), 60 (red triangle), and 80 (purple triangle) μg/mL. Inset: the corresponding OD growth curves for the same samples. Error bars represent standard errors of the means (SEM). (B) Time derivatives of the FL growth curves (Δ2FL/Δt2) in panel A. Vertical lines highlight the peak locations. (C, D) Measured dependence of the (C) peak locations and (D) peak heights
on the concentration of AgNPs.