Time-dose reciprocity mechanism for the inactivation of Escherichia coli using X-ray irradiation

Abstract

The time-dose reciprocity has long been a cornerstone in understanding ultraviolet (UV) sterilization. However, recent studies have demonstrated significant deviations from this law, attributed to complex mechanisms involving reactive oxygen species (ROS). This study investigates whether similar deviations occur at much shorter wavelengths of electromagnetic radiation than UV, specifically in the X-ray region, with a focus on the dose-rate dependence of bacterial inactivation. Using Escherichia coli as a model organism, it is found that dose-rate effects were highly dependent on the bacterial growth phase. In the stationary phase, lower dose rates with prolonged irradiation resulted in greater inactivation efficacy. The inactivation ratio obtained by the dose rate of 15.3 mGy/s shows more than 3 times larger than that obtained by the dose rate of 147 mGy/s at the dose of 200 Gy, which is consistent with findings from previous UV studies. On the other hand, in the exponential phase, higher dose rates with shorter irradiation durations were more effective. The inactivation ratio obtained by the dose rate of 147 mGy/s shows 40 times larger than that obtained by the dose rate of 15.3 mGy/s at the dose of 200 Gy. These results can be effectively explained by a stochastic multi-hit model that accounts for three terms of linearly proportional to dose, nonlinearly proportional to dose, and binary fission. This work bridges fundamental physical biology with practical applications, such as gamma sterilization, offering a robust framework for optimizing dose-rate strategies across diverse fields.

Keywords: Escherichia coli; Exponential phase; Inactivation; Multi hit model; Stationary phase; Time-dose reciprocity; X-ray.

Fig. 1

(a) Inactivation ratio of E. coli O1 in the stationary phase as a function of dose for dose rates of 147 mGy/s (red circles), 35.2 mGy/s (green circles), and 15.3 mGy/s (blue circles). Solid lines represent theoretical fits obtained using the stochastic model with parameters: (Gy⁻¹), (Gy^−1/2s^−1/2), and (s⁻¹). (b) Inactivation ratio as a function of irradiation duration. Red, green, and blue markers indicate inactivation ratios for dose rates of 147 mGy/s, 35.2 mGy/s, and 15.3 mGy/s, respectively. Solid triangles, rhombuses, squares, and circles denote results for doses of 50 Gy, 100 Gy, 150 Gy, and 200 Gy, respectively. Broken lines represent theoretical curves as a function of irradiation duration derived from Eq. (11) for P = 147 mGy/s (red), 35.2 mGy/s (green), and 15.3 mGy/s (blue). Dotted-dash lines represent theoretical curves for D = 50 Gy (purple), 100 Gy (blue), 150 Gy (green), and 200 Gy (red). Intersections between broken lines and dotted-dash lines correspond to the theoretically evaluated inactivation ratios.

Fig. 2

Inactivation ratio of E. coli O1 in the exponential phase as a function of dose for dose rates of 147 mGy/s (red circles), 35.2 mGy/s (green circles), and 15.3 mGy/s (blue circles). (a) Solid lines represent the theoretical fits obtained with the nonlinear mutual destruction term, using parameters (Gy⁻¹), (Gy^−1/2s^−1/2), and (s⁻¹). (b) Broken lines are the theoretical fits without the nonlinear mutual destruction term, using parameters (Gy⁻¹) and (s⁻¹).

Fig. 3

(a) Stochastic model in which the inactivation occurs by the hit of targets. N_ij (t) is the number of bacteria where j targets are hit on the total number of i targets. λ_j, µ_j, and ν₁ represent the hit rate, recovery rate, and replication rate, respectively. (b) Schematic of DNA inactivation. Γ₀ represents the rate of linearly dose rate dependent term, Γ₁ is the rate of the nonlinearly dose rate dependent term, and Γ₂ is the rate of replication by binary fission at the N_ij (t) state.

Fig. 4

3D plots of the theoretical inactivation ratios as a function of replication terms (0 ≤ Γ₂ ≤ 2.0 × 10⁻⁴) for various dose rates. The red, green, and blue meshes correspond to dose rates P_L, P_M, and P_H, respectively. The boundaries defining the effectiveness of dose rates are indicated by the curves XL1 (broken grey line), XL2 (solid line), and XL3 (dotted broken grey line).