The mathematical model presented here can qualitatively and quantitatively describe two processes thought to be important for survival of bacteria at high doses of ionizing radiation: DNA double strand break (DSB) repair and protein oxidation. The interactions of these processes under conditions of severe radiation-induced oxidative stress are analyzed. Model predictions using some parameter values estimated from the literature and using freely-adjusted values for the remaining parameters () were consistent with the observed survival curve of D. radiodurans
exposed to acute γ-radiation (Daly et al., 2004
) (), and with the ability of D. radiodurans
to grow under constant dose rates of 0.05 or 0.06 kGy/h (Brim et al., 2006
; Daly et al., 2004
; Lange et al., 1998
) by preventing excessive accumulation of DNA and protein damage (, ). As more information becomes available to estimate model parameters, the formalism can be tested more rigorously.
Local model sensitivity to varying the value of each parameter one at a time, keeping all other parameters at default values, was performed for colony-forming unit survival (Scfu) after acute irradiation (), for equilibrium number of DSBs per cell (DSBeq) under chronic irradiation () and for normalized equilibrium concentration of active protein (PReqF) under chronic irradiation (). The parameters were varied by a factor of 5 in and , so that changes in the predictions would be easily noticeable visually. In a smaller factor of 1.5 was sufficient because the survival curve (Scfu), which has an approximately exponential dependence on the number of DSBs, is logically more sensitive to changes in parameter values than is the number of DSBs.
Fig. 7 Parameter sensitivities – effect on colony-forming unit survival after acute irradiation. Black curve = default parameter values from . Blue curve = increasing the selected parameter by a factor of 1.5, while keeping all other parameters (more ...)
Fig. 8 Parameter sensitivities – effect on equilibrium number of DSBs during chronic irradiation. Black curve = default parameter values from . Blue curve = increasing the selected parameter by a factor of 5, while keeping all other parameters (more ...)
Fig. 9 Parameter sensitivities – effect on equilibrium active protein concentration (normalized relative to the background equilibrium c5/c6) during chronic irradiation. Black curve = default parameter values from . Blue curve = increasing the (more ...)
, local sensitivity was also assessed numerically () by estimating the effects of varying each parameter on the radiation dose required to reduce Scfu
to 90% (Dose90
), and on the Log10
decrease in Scfu
at a dose of 20 kGy (Slope20
is a measure of the length of the “shoulder” of the survival curve, and Slope20
is a measure of the “terminal slope” of the survival curve. Additionally, global model sensitivity to each parameter was also estimated for DSBeq
, with more details provided in the Appendix
Table 2 Effects of varying parameter values on the shape of the survival curve for colony-forming units (Scfu). Dose90 refers to the acute radiation dose (in kGy) required to reduce Scfu to 90%; it is an estimate of the length of the “shoulder” (more ...)
As expected, sensitivity to a given parameter can be modulated by what outcome variable is tested (e.g. DSBeq vs. Scfu) and by radiation dose and dose rate. Globally, both DSBeq and Scfu were most sensitive to: DSB production and repair constants (c8 and c9, respectively), DSB repair protein production and degradation constants (c5 and c6, respectively), and the time available for DSB repair (Trep). Sensitivity of DSBeq to ROS production by radiation (c1) and protein inactivation by ROS (c7) was, as expected, relatively low at low dose rates, but increased at higher dose rates (). Local sensitivity studies support this (, ). Such behavior can be attributed to the fact that, given our model parameters, at low dose rates ROS concentrations are relatively low, in part due to antioxidant protection, and DSBs at these dose rates are mostly generated directly by radiation. At high dose rates, however, ROS concentrations become high, and ROS-induced DSBs make an important contribution to DSBeq.
The local sensitivity analysis ( and -) also largely confirmed the intuitive role of each parameter in the model. For example, it showed that the constants for ROS production by radiation (c1), ROS removal by first-order kinetics (c3), protein inactivation by ROS (c7), and DSB induction by radiation (c8) predominantly affect the slope of the survival curve at high doses. In contrast, the parameters for protein production and degradation (c5 and c6, respectively), the DSB repair constant (c9), and the time available for DSB repair (Trep) strongly affect both the high-dose slope, and the low-dose shoulder of the survival curve.