Abstract
During exposure to ionizing radiation, sublethal damage repair (SLDR) competes with DNA damage induction in cultured cells. By virtue of SLDR, cell survival increases with decrease of doserate, socalled doserate effects (DREs). Here, we focused on a wide doserate range and investigated the change of cellcycle distribution during Xray protracted exposure and doseresponse curves via hybrid analysis with a combination of in vitro experiments and mathematical modelling. In the course of flowcytometric cellcycle analysis and clonogenic assays, we found the following responses in CHOK1 cells: (1) The fraction of cells in S phase gradually increases during 6 h exposure at 3.0 Gy/h, which leads to radioresistance. (2) Slight cell accumulation in S and G_{2}/M phases is observed after exposure at 6.0 Gy/h for more than 10 hours. This suggests that an increase of SLDR rate for cells in S phase during irradiation may be a reproducible factor to describe changes in the doseresponse curve at doserates of 3.0 and 6.0 Gy/h. By reevaluating cell survival for various doserates of 0.186–60.0 Gy/h considering experimentalbased DNA content and SLDR, it is suggested that the change of S phase fraction during irradiation modulates the doseresponse curve and is possibly responsible for some inverse DREs.
Introduction
The impact of ionizing radiation on mammalian cells depends significantly on the particle fluence of radiation per unit of time, so called doserate effects (DREs)^{1}. During protracted irradiation at lower doserates, induction of toxic DNA lesions along the particle track competes with DNA damage repair, which leads to reduced cellkilling^{2}. However, in recent decades, increased induction of mutation or chromosomal aberrations^{3,4} and enhancement of cellkilling in a lower doserate range of 10–100 cGy/h^{5} have been reported, socalled “inverse doserate effects (IDREs)”. Under lowdose exposure, mammalian cells exhibit hyper radiosensitivity (HRS) to doses with <30 cGy which is believed to result from failure to arrest in G_{2}^{6,7}, whilst intercellular signalling has also been reported to have the potential capacity to enhance cellkilling^{8,9}. Although the involvement of the cellular signalling in IDREs has been presumed, the underlying mechanism of IDREs remains unclear. Reevaluation of the DREs on cell survival including IDREs is a crucial issue from the standpoints of radiation therapy and radiation protection^{10}.
The sparing effects of cellkilling under a lower doserate can be explained by sublethal damage repair (SLDR) during irradiation^{2}. SLDR during exposure also contributes to a decrease of the quadratic component in highdose ranges^{2}. Under the confluent condition of cells represented as plateau phase (similar to conditions in tissue)^{11}, the cellcycle distribution is mainly composed of cells in G_{1} phase. There have been some reports that the fraction of cells in G_{2}/M phase gradually increases during protracted irradiation, i.e., at 60 cGy/h in tumour cell line of T98G (derived from human glioblastoma multiforma) and U373MG (derived from human glioblastoma astrocytoma) and at 100 cGy/h in CHOK1 (derived from Chinese Hamster ovary)^{5,12}. As reported in our previous study, the fractionated regimen of 1 Gy per fraction at every 1 h time interval, which is similar to continuous exposure at 1.0 Gy/h, was used to discuss the cellcycle change^{12}. In such an irradiation, the accumulation in G_{2}/M phase under lower doserate may be associated with higher radiosensitivity^{12}. In this regard, radiosensitivity during exposure can be potentially modulated by not only intercellular signalling as suspected recently but also changes in cellcycle distribution^{13,14} including cell multiplication^{15,16}. Thus, it is necessary to investigate the change for various doserates at the level of in vitro experiments.
From the viewpoint of estimating doseresponse curves, the curves can be described in general by taking account of SLDR rate deduced from a splitdose cell recovery^{17,18}. According to the previous reports^{2,17,18}, the repair halftime of SLD is cell type and cell condition specific, e.g., 0.985 h in CHO cells in plateau phase. The linearquadratic (LQ) model with LeaCatcheside time factor^{19} or microdosimetrickinetic (MK) model^{17} have been used to analyse cell survival considering SLDR during irradiation at the level of cell populations. However, recent model analysis using the MK model suggests that rate of SLDR depends on doserate, in which the SLDR rate decreases as doserate lowers^{20}. This interpretation may be linked to cellcycle changes, but there is currently no report with evidence to support that SLDR changes depending on doserate. Thus, the interest in this study is directed to the consideration of SLDR depending on doserate associated with experimentally determined cellcycle distribution during irradiation.
In this study, we used the Chinese Hamster Ovary (CHO)K1 cell line that does not exhibit lowdose HRS^{21} and newly observed the doserate dependence of cell survival in relation to the change of cellcycle distribution during irradiation at 3.0 Gy/h (1.5 Gy per fraction at every 30 min interval, 24 fractions) and 6.0 Gy/h (2.0 Gy per fraction at every 20 min interval, 36 fractions) in addition to our previous data at 1.0 Gy/h (1.0 Gy/fr at every 1 h time interval, 12 fractions). Combined with previous cell responses for 0.186, 1.0, 1.5, 10.8, 18.6, 60.0 Gy/h, here we reevaluated the radiosensitivity at the endpoint of cell survival and mean inactivation dose. Finally we show that the changes of radiosensitivity in doseresponse curves under continuous irradiation can be explained by changes of SLDR rate due to an increase of cells in S phase.
Model Overview
Methodology of CellKilling Model
In order to determine a fractionated regimen equivalent to a longterm continuous exposure and to predict DREs on cell survival, we used the microdosimetrickinetic (MK) model for continuous irradiation^{17}. The MK model has been developed based on microdosimetry^{22} and popular theory of damage behaviour^{23,24} by comparing with several experimental data so far^{2,12,17,18,20,25,26,27,28,29}. In this study, we further developed the MK model so as to consider change of DNA amount per nucleus and SLDR rate during irradiation, hereafter called the “integrated microdosimetrickinetic (IMK) model”.
Briefly, the MK model^{17} subdivides the cell nucleus into a lot of microorder territories (socalled domains) so as to incorporate microdosimetry^{22}. The shape of the domains is for simplicity defined as a sphere with radius from 0.5 to 1.0 μm^{17,20} and the local energy deposition along radiation particle track can be evaluated in terms of tissue equivalent proportional counter (TEPC) measurements^{27} or Monte Carlo simulations^{27,30}. DNA damage which may be toxic to the cell is represented as a potentially lethal lesion (PLL), induced in a domain packaging DNA amount of g (kg) along the particle track with local dose deposition (as in Gy) per domain z. The DNA lesion (PLL) can gradually transform into lethal lesion (LL) or be repaired until no PLL remain:

(i)
A PLL may transform into a lethal lesion (LL) via a firstorder process at a constant rate a (h^{−1})

(ii)
Two PLLs may interact and transform into a lethal lesion (LL) via a secondorder process at a constant rate b_{d} (h^{−1})

(iii)
A PLL may be repaired via a firstorder process at constant rate c (h^{−1}).
The rate equation for the number of PLLs per domain after acute exposure x_{d}(t) is given by
This can be solved as exponential function expressed by
where k_{d} is the PLL induction coefficient per DNA amount and imparted energy in the domain.
Let us consider a continuous exposure to a cell population with dosedelivery time T (h) and doserate \(\dot{D}\) (Gy/h). To model this, during the dosedelivery, specific energy (z_{1}, z_{2}, …, z_{N}) is discontinuously deposited in a domain with amount of DNA (g_{1}, g_{2}, …, g_{N}) at each subsection of dosedelivery time ([0, ΔT), [ΔT, 2ΔT), …, [(N − 1)ΔT, NΔT)), thus we obtain the relation of T = NΔT, where N is the number of sub sections in total dosedelivery time T^{12,17}. In this study, we newly assumed that the rate of SLDR (c_{1}, c_{2}, …, c_{N}) changes at each subsection of T ([0, ΔT), [ΔT, 2ΔT), …, [(N − 1)ΔT, NΔT)). Thus, the number of PLLs per domain x_{ d }(t) can be expressed based on Eq. (2) as
Whilst PLLs’ induction competes with SLDR during dosedelivery, LLs gradually increase according to the next rate equation as
where w_{d} is the number of LLs per domain. Solving Eq. (4) for the time dependent repair in Eq. (3), we can obtain the accumulated number of LLs per domain as,
where
In Eq. (6), the value of a is a few percent of c_{ n }^{17,20}, thus (a + c_{ n }) can be simply approximated by c_{ n }. Let <w_{d}> and <w>_{T} be the average number of lethal lesions per domain and the average number of LLs per nucleus, respectively. Considering the mean dose per nucleus <z_{ n }> and the mean amount of DNA per nucleus <G_{ n }> at the timing of t = (n − 1)ΔT and assuming that the absorbed dose rate is constant (<z_{1}> = <z_{2}> = , …, = <z_{ n }> = \(\dot{D}\)ΔT), <w>_{T} is expressed as
where
p is the mean number of domains contained in a cell nucleus, f_{ z }(z_{ n }) is the probability density of the z_{ n }, f_{ g }(g_{ n }) is the probability density of the DNA amount per domain g_{ n }, 〈G_{ n }〉 = p〈g_{ n }〉 is the mean amount of DNA per cell nucleus. For simplicity, we define:
It is assumed that the cells with no LLs (〈w_{T}〉 = 0) have clonogenic ability. Assuming that the number of LLs per nucleus follows the Poisson distribution, the clonogenic cell survival (S) can be expressed by S = exp(−〈w〉_{T}). Thus we obtain the following formula
It should be noted that Eq. (10) represents the relationship between accumulated absorbed dose and surviving fraction of cells (doseresponse curve) in consideration of cell cycle (not only the change in amount of DNA, 〈G_{1}〉, 〈G_{2}〉, …, 〈G_{ n }〉 as previously publised^{12} but also the change in the rate of SLDR, c_{1}, c_{2}, …, c_{ N } as newly introduced) (see Fig. 1A).
Link to the LQ model with or without LeaCatcheside time factor
The present model can be linked to the LQ model with the classic LeaCatcheside time factor^{19}. Here, we assume a special case that cell condition (amount of DNA and SLDR rate) does not change during irradiation, i.e., 〈G_{1}〉 = 〈G_{2}〉 = … = 〈G_{ N }〉 = 〈G〉 = constant, c_{1} = c_{2} = … = c_{ N } = c = constant, α_{ n } = α_{0} = constant and β_{ n } = β_{ nm } = β_{0} = constant. Eq. (10) can be expressed by
Taking the limit N to infinity (hence, ΔT → 0), Eq. (11) is approximately expressed by
Thus we can obtain a simple SF formula considering constant dose rate as
where
Eq. (13) is the cellkilling model including the LeaCatcheside time factor including SLDR rate. Further if we consider the acute exposure (\(T\to {\rm{0}}\)), the following formula of surviving fraction is obtained as
Thus, the traditional linearquadratic (LQ) model approximates this model for the case of acute exposure without considering dosedelivery time^{2,19}. In this study, in comparison between doseresponse curves described by Eq. (11) and by Eq. (13), we planned a fractionated regimen equivalent to the continuous exposure with a constant dose rate (Fig. 1B) as previously described^{12}.
Materials and Methods
Cell Culture and Irradiation Condition
A mammalian cell line, Chinese Hamster Ovary (CHO)K1 was obtained from RIKEN Bio Resource Center, Japan (RBC0285). This type of cell line was selected because it does not exhibit HRS^{21}. The cells were maintained in Dulbecco’s modified Eagle’s (DMEM, Sigma Life Science) supplemented with 10% fetal bovine serum (FBS, EquitechBio Inc.) and 1% penicillin/streptomycin (Sigma Life Science) at 37 °C in humidified 95% air and 5% CO_{2}.
To investigate cell responses after a longterm exposure, five days prior to irradiation 4 × 10^{5} cells were seeded onto the cell culture dish with 60 mm diameter (Nippon Genetics) to obtain the cells under plateau phase. In parallel, to quantify the dependence of SLDR rates on cellcycle distribution, we prepared two cellcycle distributions for plateau phase and logarithmic growth phase five days and one day after seeding, respectively.
Irradiation Condition
Standard radiation, 250 kVp Xrays (Stabilipan, Siemens, Concord, CA), was used to irradiate the cultured cells. The dose rate in air at the surface of cell culture was measured by using Farmertype ionizing radiation chamber (model NE2581, Nuclear Enterprises Ltd) and was converted to the dose rate in water (4.31 Gy/min) according to the dose protocol TRS277^{31}. From the comparison between Eqs (11) and (13), the practical fractionation regimens equivalent to the average dose rates of 3.0 Gy/h and 6.0 Gy/h were newly determined at a visual level (the R^{2} value is found to be 0.999), which were 1.5 Gy per fraction at 30 min interval for 3.0 Gy/h and 2.0 Gy at 20 min interval for 6.0 Gy/h (Fig. 1B).
FlowCytometric Analysis of CellCycle Distribution
For each doserate exposure, 1 × 10^{6} cells were harvested at 0, 2, 4, 6, 8, 10, 12 h after the start of irradiation and fixed with 70% ethanol, and then kept at 4 °C for at least 2 h. After a centrifugation, the cells were resuspended in 1 ml phosphatebuffered saline (PBS) (−). After a centrifugation again, the DNA was stained with 0.5 ml FxCycle^{TM} propidium iodide (PI)/RNase staining solution (Life Technologies) including 0.2% v/v triton X for 15 min in the dark at room temperature. Cellcycle distribution was then obtained by using the Attune acoustic focusing flow cytometer (Applied Biosystems by Life Technologies TM).
The fluorescence intensity emitted from the DNA in a nucleus was normalized by that from the DNA contained in a cell in G_{0}/G_{1} phase. The cellcycle distribution (fractions of the cells in G_{0}/G_{1}, S and G_{2}/M) was then obtained from the DNA profile. All sets of cellcycle study were performed three times. By using the TukeyKramer method^{32}, we evaluated if there is significant difference in the change of cellcycle distribution from the control group (before irradiation at t = 0 (h)).
Clonogenic Survival Assay
After exposure to the regimen equivalent to 3.0 and 6.0 Gy/h, irradiated cells were trypsinized immediately and the appropriate number of cells was reseeded into a cell culture dish with 60 mm diameter (Nippon Genetics). Culture medium was exchanged every two days and the cells were cultured for 10–14 days. The colonies were fixed with methanol and were stained with 2% Giemsa solution (Kanto Chemical Co. Inc.) Survival fraction was obtained from the ratio of colony number of irradiated cells to that of nonirradiated cells (control cells). The plating efficiency for control cells was 38.8 ± 9.2% (mean ± standard deviation), which was given by 27 dishes (the assay was performed three times for each doserate, and three dishes were used in one assay).
Determination of SLDR Rate from a SplitDose Cell Recovery Curve
The constant rate of SLDR was obtained from cell recovery curve of cell survival in a splitdose experiment. Let us consider a case of exposing a cell population to equal acute doses with D_{1} (=<z_{1}>) (Gy) and D_{2} (=<z_{2}>) (Gy) at the interval of τ (=ΔT) (h). The surviving fraction for a splitdose exposure is given by
The SLDR rate can be deduced by using the surviving fractions taking the limits of period of exposure interval (\({\tau }\to {\rm{0}},\,\,{\tau }\to \infty \)). Based on Eq. (16), S(0) and S(\(\infty \)) can be given by
On one hand, subtracting Eq. (18) from Eq. (17) gives
On the other hand, taking the derivative of Eq. (16) and taking the limit of dS/dτ as τ tends to 0, we have
Thus we can deduce the cellspecific parameter of SLDR rate by using the following equation,
Cell recovery curves for a splitdose experiment are always influenced by redistribution and cell proliferation^{17,18}. Based on the previous reports to deduce (a + c) value^{17,18}, to avoid the influences of redistribution and repopulation, the initial slope dS/dτ and S(\(\infty \)) were determined from experimental surviving fraction by taking the gradient from 0 to 1 h, and maximum survival was taken at the 2 h time interval. Because the value of a is a few percent of c^{17,20}, thus the rate of SLDR can be approximated by c value. Whilst the SLDR rate for plateau phase of CHOK1 was taken from our previous report^{12}, that for logarithmic growth phase was deduced by Eq. (21) and a cell recovery curve reported in the literature^{33}.
Change of DNA Amount and SLDR Rate During Irradiation
Experimentally determined changes of relative DNA amount per nucleus during irradiation 〈G_{ n }〉/〈G_{1}〉 were input into Eq. (10) as previously described^{12}. Additionally, in this study we assumed that SLDR rate represented by c_{ n } (h^{−1}) changes during irradiation depending on fraction of cells in S phase, which has a high repair efficiency^{34} leading to lower radiosensitivity^{14,35}. We estimated the differential rate of SLDR, and then deduced the change of SLDR rate per fraction of cells in S phase during exposure from experimental cellcycle distributions using the following equation
where t is the time after the start of irradiation (h), c_{0} is the SLDR rate at t = 0, dc/dN_{ S } is the differential rate of SLDR per fraction of cells in S phase, and N_{ S } is the fraction of cells in S phase. In this study, dc/dN_{ S } was determined from the subtractions of SLDR and fraction of cells in S phase for plateau and logarithmic growth phases, and the change of cell fraction in S phase ΔN_{ S } was obtained from cellcycle study during fractionated exposures.
Comparison Between Model and Measured Cell Survival
To investigate the influence of change of repair rate associated with cellcycle distribution on cell survival curve, we compared the doseresponse curves estimated by Eq. (10) with measured clonogenic cell survival data. We used model parameters for the CHOK1 cell line after exposure with 250 kVp Xrays which have been already published^{12}. The values of the parameters are summarized in Table 1. In the set of parameters, DNA contents represented by 〈G〉 and 〈G^{2}〉 were obtained within the performed cellcycle experiment, and the set of physical parameters (γ, y_{ D }, r_{d}, ρ) was taken from the previous reports^{12}. Here, we assumed that the constant rates of a (h^{−1}) and b_{d} (h^{−1}) are cellspecific parameters independent of the cellcycle distribution for simplicity, and the cell survival curve was calculated considering the change of mean DNA amount per nucleus and SLDR rate during the exposure at various doserates.
To test the assumption of fixed a and b_{d} values, we compared the estimated survival curve with experimental one for two cell conditions of plateau and logarithmic growth phases. Whilst the set of parameters (α_{0}, β_{0}, a + c) for plateau phase is summarized in the left side of Table 1, the set for logarithmic growth phase is given by the ratios of DNA amount measured in this work and SLDR rate deduced by Eq. (21).
The fit quality of the model used in this study was evaluated from reduced chisquare value expressed by
where S_{exp} is measured cell survival, S_{model} is cell survival estimated by the present model, σ_{exp} is the standard deviation of measured cell survival.
Mean Inactivation Doses
To investigate survival curves of the CHOK1 cells, we further used the concept of the mean inactivation dose \(\bar{D}\)^{36}, which is recommended by ICRU Report 30^{37}. In this quantity, doseresponse curve is treated as a probability distribution of cell killing with absorbed dose. Considering the survival probability S(D) as an integral probability distribution, the mean dose necessary to inactivate cells (socalled mean inactivation dose) \(\bar{D}\) is given as,
The \(\bar{D}\) values for various doserates of 18.6–60.0 Gy/h were calculated for experimental survival data, model prediction at constant SLDR of c \(\cong \) (a + c) = 0.704 (h^{−1}) based on Eq. (13), and the prediction considering changes of mean DNA contents per nucleus and Sphase dependent SLDR rate based on Eq. (10). The \(\bar{D}\) values predicted by the model were compared with the experimental data by using R^{2} value given by
where exp and est represent the experimental value and the estimated value by the model, respectively, and n is the number of data.
Results
Change in CellCycle Distribution during Exposure for Various Dose Rates
Two fractionated regimens equivalent to the continuous exposures with 3.0 and 6.0 Gy/h were used to investigate DREs on cellcycle distribution during exposure. Figure 2 shows the change in cellcycle distribution during the exposure for various doserates, in which data at 3.0 Gy/h and 6.0 Gy/h were newly measured in this study. The data at 0.0 Gy/h, 0.186 Gy/h and 1.0 Gy/h were obtained from our previous investigation^{12}.
During the exposure with lower doserates such as 1.0 Gy/h and 0.186 Gy/h, the fraction of the cells in G_{2}/M phase gradually and slightly increased with increasing fractions. During the exposure with 3.0 Gy/h, significant increases of cell fraction in S phase were observed up to 6 h after the start of fractionated irradiation, whilst the subtle accumulation of the cells in G_{2}/M phase was observed. During the exposure with the highest dose rate, 6.0 Gy/h, there is no change in cellcycle distribution until 8 h after the start of irradiation. However, at 10 h after the start of irradiation, significant increases of cell fraction in S phase and G_{2}/M phase were observed.
SLDR Rate during Exposure and Prediction of Cell Survival
To investigate the influence of the change in cellcycle distribution on cell survival, we obtained the change of mean DNA amount per nucleus and the SLDR rate during exposure from flowcytometric analysis of DNA profiles. In the upper panels of Fig. 3, the DNA profile for plateau phase and for logarithmic growth phase (Fig. 3A) and the procedure to deduce the SLDR rate for logarithmic growth phase from Eq. (21) with a splitdose cell recovery^{33} (Fig. 3B) are presented. The details of cellcycle distribution for both phases and SLDR rates c_{1} were also listed in Table 1. The SLDR rate for logarithmic growth phase (1.782 ± 0.441 h^{−1}) is in good agreement with that of the previous report (1.72 (1.27–2.59) h^{−1}) by Hawkins^{17}. Based on the cellcycle study (Fig. 2) and the rate of SLDR via cellkilling model (Fig. 3B), we obtained the change of mean DNA amount per nucleus (Fig. 3C) and estimated the Sphase dependent SLDR rate during exposure according to Eq. (22), as shown in Fig. 3D. From the experimental data about fraction of cells in S phase and SLDR rate for plateau and logarithmic growth phases (Table 1), we deduced the value of dc/dN_{ S } = 0.0287 ± 0.0128 (h^{−1}/%).
Figure 4 shows the comparison between the cell survival curve described by the present model (IMK model) and the clonogenic survival data for various doserates of 0.186–60.0 Gy/h. This includes both newly obtained doseresponse curves after the exposure with 3.0 and 6.0 Gy/h (Fig. 4D,E) and reanalysed curves in comparison with reference data (Fig. 4A–C and F–H)^{38}. In Fig. 4, dotted lines and solid lines represent respectively the model prediction according to Eq. (13) with a constant rate of (a + c) = 0.704 (h^{−1}) and Eq. (10) with the experimentalbased variable SLDR rate during exposure as well as DNA amount changing shown in Fig. 3C,D, whilst symbols denote the experimental cell survival including reference data^{38}. In Fig. 4D for 3.0 Gy/h, unexpected radioresistance (increase of cell survival) was observed compared to the curve predicted by Eq. (13). This is attributable to both the change of SLDR rate and DNA amount per nucleus during exposure (Fig. 3C,D). The cell survival curves (in Fig. 4B,D and E) described by the IMK model for 1.0, 3.0 and 6.0 Gy/h with the both factors were in better agreement with experimental data (Table 2). Applying the time course of DNA contents and SLDR rate under 6.0 Gy/h into the model prediction of cell survival for a higher dose rate of 10.8 Gy/h, the surviving fraction estimated by the IMK model is slightly higher than that by the previous model (Fig. 4F). Figure 4G,H represent the cases in higher dose rates (18.6 and 60.0 Gy/h), where the dosedelivery time is relatively short. We applied the cellcycle kinetics under higher doserate of 6.0 Gy/h to predict the doseresponse curve for 18.6 and 60.0 Gy/h.
Figure 4I shows the collection of all of the parts of doseresponse curve estimated by the present model (following Eq. (10) and change of cell conditions given by Fig. 3C,D) in comparison with the experimental data. The cell survival increases as the doserate decreases by virtue of SLDR during dosedelivery time. However, focusing on the doserate range of 1.0–3.0 Gy/h, the inverse doserate effects (IDREs) can be observed, in which a radioresistance resulted from cell accumulation in S phase for 3.0 Gy/h whilst a higher radiosensitivity induced by cell accumulation in G_{2}/M phase for around 1.0 Gy. These results suggest that the cellcycle dynamics during exposure may modulate the cell survival curve, whilst it is shown that the cellkilling model with traditional LeaCatcheside time factor (Eq. (13)) is a special case for no cellcycle change during exposure.
Evaluation of DoseRate Effects on Mean Inactivation Dose
The DREs on cell survival shown in Fig. 4 were next evaluated by means of the mean inactivation dose \(\bar{D}\)^{35}, which is recommended by ICRU Report 30^{37}. Figure 5 shows the relationship between the absorbed dose rate in Gy/h and mean inactivation dose \(\bar{D}\), in which experimental \(\bar{D}\) was represented as red symbol. In this study, we predicted the DREs by using two SLDR approach, one for a constant (a + c) value of 0.704 (h^{−1}) and the other for the variable (a + c) values during irradiation shown in Fig. 3D. In Fig. 5, whilst the \(\bar{D}\) value predicted with (a + c) = 0.704 (h^{−1}) becomes higher as the doserate is lower (green symbols and dotted line), the predicted \(\bar{D}\) with variable SLDR rate (blue symbols and dotted line) agrees better with the experimental \(\bar{D}\). In comparison between the experimental and model predicted values, it was shown that the IMK model with variable (a + c) leads to a peak of resistance at doserates around 1.5–3.0 Gy/h in agreement with the experimental result. The experimental \(\bar{D}\) value at 10.8 Gy/h is higher than that by the model, suggesting a higher radioresistance. However, the experimental data is calculated from just one data set result taken from ref.^{38}. Regarding the about 5% inherent uncertainties of \(\bar{D}\) value^{36} and the possibility of experimental outliers, we cannot clearly judge if there is a reversal in radiosensitivity at doserates around 10.8 Gy/h.
Testing the Assumption of CellSpecific Model Parameters Independent of the Cell Cycle
Testing the Assumption of CellSpecific Model Parameters Independent of the Cell Cycle. Here we assumed that the constant rates of a (h^{−1}) and b_{d} (h^{−1}) are cellspecific parameters independent of the cellcycle distribution. To check if this assumption is correct or not, we further compared Eq. (15) with measured cell survival after acute exposure under two cell phases, plateau phase and logarithmic growth phase (Fig. 6A). The set of parameters (α_{0}, β_{0}) for plateau phase was converted to those in logarithmic growth phase by using the ratios of DNA amount and SLDR rate, which is listed in Table 1. In Fig. 6B, we also compared the cell surviving fractions for both phases^{2,38,39,40,41,42,43,44} with the estimation by using the converted model parameters for logarithmic growth phase. In this comparison, the difference between doseresponse curves in plateau phase and logarithmic growth phase is explainable by taking account of the mean DNA amount per nucleus and SLDR rate, which validates partly the interpretation that the values of a (h^{−1}) and b_{d} (h^{−1}) don’t depend on the cell condition.
Discussion
CHOK1 cells show the following responses: (i) accumulation of cells in G_{2} during exposure with 1.0 Gy/h^{12}, (ii) delay of DNA synthesis and accumulation of the cells in S and G_{2} during exposure with 3.0 Gy/h and (iii) no significant change of cellcycle distribution until 8 h after the start of exposure to 6.0 Gy/h (Fig. 2). The increase of cells in S phase during the exposure to 3.0 Gy/h might be attributed to the DNA damage response in S phase checkpoint^{45}. In contrast, according to previous investigations^{46}, the threshold dose for blocking cell cycle progression at the G_{1}/S checkpoint is considerably higher than G_{2}/M checkpoint. For the case of CHO cells, Lee et al. reported a p53independent damagesensing checkpoint which operates to prevent late G_{1} or early Sphase^{47}. In this regard, we interpreted that whilst the G_{1}/S checkpoint system was not activated under exposure with 3.0 Gy/h, it was activated under exposure with 6.0 Gy/h (Fig. 2A).
From the measured cellcycle distribution (Fig. 2), we estimated Sphase dependent SLDR rates (Fig. 3D) and subsequently described cell survival curves in comparison with the MK model with a constant SLDR rate of (a + c) = 0.704 (h^{−1}) (dotted line in Fig. 4) and also with a changing rate of SLDR (solid line in Fig. 4). From the statistical evaluation by using the model (Table 2), the changing rate of repair c plays an important role for describing not only the DREs on cell survival curve with reduction of chisquare value (Fig. 4 and Table 2) but also mean inactivation dose with reasonable R^{2} value (Fig. 5). This suggests that the magnitude of DNA damage might trigger the series of repair proteins activation, depending on dose rate^{48}. Here, the misrepair rates, a (h^{−1}) and b_{d} (h^{−1}) were assumed to be constant cellspecific parameters not depending on cell condition. On this basis, we converted the set of parameters for plateau phase to that for logarithmic growth phase (Table 1), to reproduce the surviving fraction under the both phases in the methodology of the IMK model (Fig. 6B). According to the previous model assessment by Hawkins, the value of (a + c) is mainly composed of nonhomologous end joining (NHEJ)^{20}. However, it is known that Homologous Recombination (HR), a more accurate repair process, becomes more important in S phase, which may contribute to the observed increased resistance in S phase. Traditionally, there are two types of definition for repair kinetics, i.e., SLDR for dose fractionation and potentially lethal damage repair (PLDR) for treatment such as hypertonic saline. Several attempts have been made to understand whether or not SLDR and PLDR are the same^{49}. To this subject, the present model study (Figs 4 and 6B) may support that SLDR and PLDR are similar to each other.
The model proposed in this study follows the linearquadratic (LQ) formalism, which is convenient for calculating α/β and biological effective dose (BED)^{50} considering the LeaCatcheside time factor^{19,51}. The modelling approach for predicting cellcycle dependent survival of V79 cells was also presented in a similar manner to that with a small set of parameters by Hufnagl et al.^{53}. In comparison to their model, the present IMK model enables us to describe cellcycle dependent doseresponse curve (Fig. 4) for not only acute exposure but also longterm exposure (Fig. 6B). However, the DNA damage repair kinetics is complex and is generally quantified by two exponential components for rejoining of the broken ends of DNA^{52}. If the complex repair kinetics is essential, more detailed mechanistic modelling such as the computational modelling by McMahon et al.^{54,55} may be more suitable to understand the underlying radiation biology. As for clarifying the underlying mechanism of damage repair system, further investigation about the relation between SLDR and repairs function (NHEJ, HR, etc.) is necessary in various cell lines.
The model and data exhibit IDREs in the doserate range of 1.0–3.0 Gy/h, attributable to increases in SLDR during irradiation. According to the previous investigation about dependence of cell phase on cell killing^{14}, S phase (including late S phase) is the most radioresistant. This tendency was found in the comparison between the experiment and the model in Fig. 4D–F. In addition, the accumulation of cells in the relatively more radiosensitive phase of G_{2}/M^{12,14,56} contributes to the modulation of cell survival curve, leading to the reversal of DREs as shown in Fig. 4I. Supported by the doseresponse curve in Fig. 4I, the mean inactivation dose in Fig. 5 indicates the existence of IDREs as well. Considering these results, the combination of the accumulations of cells in S phase and G_{2}/M phase is possibly responsible for IDREs.
IDREs on cell killing have been previously observed in doserate range of below 1.0 Gy/h^{5,57}, and other reports have shown higher mutant frequencies at doserates lower than 0.1–1 cGy/min^{58}. This previously observed doserate range is different from that we observed in this study. Other potential mechanisms, such as cumulative lowdose HRS after fractionated exposures has a possibility to induce this reversal in radiosensitivity^{57,58,59,60}, however the CHOK1 cell line does not exhibit this behaviour^{21}. From the present study and the previous reports, it is likely that the doserate range for IDREs related to cellcycle effects is higher than that related with lowdose HRS. Further model development for the cumulative lowdose HRS based on more detailed mechanistic evidence about the time course of the HRS is necessary.
In summary, we investigated the radiosensitivity after the protracted exposure for various dose rates. Focusing on cellcycle distribution, the experimental results suggested that the CHOK1 cells show following responses: (1) an accumulation of the cells in G_{2} during exposure with lower dose rate (e.g., 1.0 Gy/h), (2) the delay of DNA synthesis and an accumulation of the cells in S/G_{2} during the exposure with intermediate dose rates (e.g., 3.0 Gy/h), and (3) the blocks of cell cycle progressing in whole checkpoints (G_{1}/S and G_{2}/M checkpoints) and the delay of DNA synthesis during the exposure with higher dose (e.g., 6.0 Gy/h). A greater radioresistance after the exposure with 3.0 Gy/h was observed and this tendency was interpreted as increases in SLDR rate associated with the fraction of cells in S phase. Taking account of both higher radiosensitivity under 1.0 Gy/h exposure and the radioresistance after exposure to 3.0 Gy/h, the changes in cellcycle distribution during exposure modulate the cell survival curve and are possibly responsible for IDREs. This study would contribute to a quantitative understanding of radiosensitivity after longterm exposure to ionizing radiation as well as general characteristics of DNA repair and dose response, which can be of help to radiation protection and radiation therapy.
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 16J07497.
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Y.M. designed the study, Y.M., K.T., R.M. and J.O. performed the experiments, Y.M., S.M., K.S., Y.Y. and G.O. developed model and performed the model analysis. Y.M., S.M., H.D. and K.P. wrote the manuscript, K.T., H.D. and K.P. supervised the study. All authors reviewed the manuscript.
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Matsuya, Y., McMahon, S.J., Tsutsumi, K. et al. Investigation of doserate effects and cellcycle distribution under protracted exposure to ionizing radiation for various doserates. Sci Rep 8, 8287 (2018). https://doi.org/10.1038/s41598018265565
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DOI: https://doi.org/10.1038/s41598018265565
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