
==== Front
J Radiat Res
J Radiat Res
jrr
Journal of Radiation Research
0449-3060
1349-9157
Oxford University Press

39278665
10.1093/jrr/rrae071
rrae071
Fundamental Radiation Science
AcademicSubjects/MED00870
AcademicSubjects/SCI00960
Exploring the LET dependence of DNA DSB repair kinetics using the DR DNA database
Radstake Wilhelmina E Department of Radiation Oncology, Mayo Clinic, 4450 San Pablo Rd S, Jacksonville, FL 32224, USA

Parisi Alessio Department of Radiation Oncology, Mayo Clinic, 4450 San Pablo Rd S, Jacksonville, FL 32224, USA

Denbeigh Janet M Department of Radiation Oncology, Mayo Clinic, 4450 San Pablo Rd S, Jacksonville, FL 32224, USA

Beltran Chris J Department of Radiation Oncology, Mayo Clinic, 4450 San Pablo Rd S, Jacksonville, FL 32224, USA

Furutani Keith M Department of Radiation Oncology, Mayo Clinic, 4450 San Pablo Rd S, Jacksonville, FL 32224, USA

Corresponding author. Department of Radiation Oncology, Mayo Clinic, 4500 San Pablo Rd S, Jacksonville, FL 32224, USA. Email: radstake.wilhelmina@mayo.edu
9 2024
15 9 2024
15 9 2024
65 5 651657
28 5 2024
17 7 2024
15 8 2024
© The Author(s) 2024. Published by Oxford University Press on behalf of The Japanese Radiation Research Society and Japanese Society for Radiation Oncology.
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Abstract

The repair of DNA double-strand breaks is a crucial yet delicate process which is affected by a multitude of factors. In this study, our goal is to analyse the influence of the linear energy transfer (LET) on the DNA repair kinetics. By utilizing the database of repair of DNA and aggregating the results of 84 experiments, we conduct various model fits to evaluate and compare different hypothesis regarding the effect of LET on the rejoining of DNA ends. Despite the considerable research efforts dedicated to this topic over the past decades, our findings underscore the complexity of the relationship between LET and DNA repair kinetics. This study leverages big data analysis to capture overall trends that single experimental studies might miss, providing a valuable model for understanding how radiation quality impacts DNA damage and subsequent biological effects. Our results highlight the gaps in our current understanding, emphasizing the pressing need for further investigation into this phenomenon.

DNA double-strand breaks (DSBs)
DNA repair kinetics
linear energy transfer (LET)
ionizing radiation
random effects modeling
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pmcINTRODUCTION

Understanding the repair of DNA double strand breaks (DSBs), which are considered the most lethal form of DNA damage, is crucial for both radiotherapy and space applications. Breakage and disruption of the DNA strands, induced by traversal of the ionizing radiation through the cell nucleus, leads to a cascade of different repair proteins localizing at the side of damage called the DNA damage response (DDR) [1]. Failure to repair the break efficiently can result in chromosomal aberrations, and high levels of DNA DSBs can lead to cellular apoptosis [2, 3]. Compared with photon exposure, higher levels of cell killing are observed after cellular exposure to ions at the same radiation dose level. Due to their dense pattern of energy deposition, ions cause increased complexity of DNA DSBs. Therefore, the complexity of the DNA damage is potentially a deterministic factor for repair efficiency and cell survival [4–9].

Despite efforts to determine the linear energy transfer (LET) dependence on DNA DSB repair, studies are divided on how the DDR is precisely affected and how different spatial complexity of DNA damage direct DNA repair pathways [10]. Besides discrepancies in the number of unrepaired damages as function of LET, debates also consider the effects of the LET on the DNA repair rates. However, published studies report both a decrease in repair rates as well as no effects of LET on this process [5, 11–18].

We recently published a systematic review of DNA repair studies, encompassing a total of 285 published DNA repair curves in the database of repair of DNA (DR DNA) [10]. In this study, we use the DR DNA database to investigate the possible LET dependence of the DNA repair kinetics and uncover which hypothesis regarding the effect of LET on repair rates, repair fractions, and fractions of unrepaired damage is best supported by the data.

MATERIALS AND METHODS

The data set of DR DNA [10] was used for data analysis. To account for the large spread in the photon-exposed data, the photon data was filtered for photon source (γ-ray or X-rays with peak voltage of 200 kVp and higher) and only exposure times of less than 15 minutes were included. The denser energy deposition on the microscopic scale of low-energy photons can lead to a variety of biological effect. Besides, any exposure to radiation lasting longer than 15 minutes would result in a mixture of repair processes occurring at different stages. The effect of exclusion of this data has previously been published [10]. For both the photon dataset as well as the ion exposures, experiments performed with repair competent, asynchronized cells and measures obtained with immunocytochemistry were selected. In total, 84 individual experimental repair curves were included in this study.

Statistical analysis

All analysis and plots were done in R (version 4.2.2) [19]. The data was fitted with a non-linear mixed effect (NLME) model, using the NLME package [20]. This package is specifically designed for fitting and analysing mixed-effects models that accommodate both fixed and random effects in the data, thereby enabling accounting of variability at multiple levels. In other words, NLME models are a statistical tool that helps to understand complex relationships, such as DNA repair kinetics, by analysing general trends as well as differences between individual experiments. The DNA repair kinetics data were fitted by means of a biexponential decay function. This function is commonly used for describing the rejoining of DNA DSBs over time in a biphasic fashion and has been shown to perform better than other models [21].

The following equations were used to fit the data:

Biexponential model

(1) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*} N=f{e}^{-{k}_ft}+\left(1-f\right){e}^{-{k}_st} \end{equation*}\end{document}

Biexponential model with fraction of unrepaired damage

(2) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*} N=U+\left(1-U\right)\left(f{e}^{-{k}_ft}+\left(1-f\right){e}^{-{k}_st}\right) \end{equation*}\end{document}

Where N is the number of remaining DNA DSBs at time t normalized to the highest number of DNA DSBs. f is the fraction of DNA DSBs that is repaired with the fast decay rate kf. The fraction of cells that is not repaired with the fast decay rate (1 – f), is repaired with the slow decay rate ks. U represents the fraction of DSBs that is left unrepaired.

Fig. 1 Results for hypothesis 1. Values for fitted parameters of kf (a) and ks (b) as function of LET and different ions. Parameter f was kept constant across all experimental fits. An average LET value of 0.75 keV/μm was chosen for the photon data [22].

Using the biexponential function, we test the following hypotheses:

The decay rates (kf & ks) are dependent on the LET while the fraction of damage being repaired with either rate (f & 1-f) remains independent.

The fractions of damage repaired with either the fast decay rate f, or slow repair rate (1-f) are dependent on LET while the decay rates (kf & ks) remain independent.

The fraction of unrepaired damage (U) depends on LET, the other parameters f, 1-f, kf, & ks, remain independent.

Both the fraction of fast and slow repaired damage (f & 1-f) and the fraction of unrepaired damage (U) are dependent on LET, the decay rates (kf & ks) remain independent.

First, the data was grouped by factor experimental unit (eu), which is a unique identification number for each experiment, to partition the dataset into subsets based on each unique experimental curve included in the dataset. For the photon-exposed cells, the data was grouped together to obtain a general curve. Following the data partitioning, the nonlinear least squares method was employed to individually fit the specified biexponential model to each subset of the data. Finally, the NLME package was utilized to apply the nonlinear mixed-effects modeling. To test the different hypotheses, outline above, random effects for the parameter estimates were sequentially included to allow variation in one parameter while simultaneously fixing the estimates for the other parameters.

RESULTS

In the following section, we compare different NLME-models fitted to the in vitro data of photon and ion exposed cells. For this, we selected asynchronized, repair competent cells in which DNA DSBs were measured with immunocytochemistry.

First, we test the hypothesis 1, that is, the decay rates depend on the LET and the fraction of damage repaired with either rate remains stable. The value of f was estimated at 0.497, values of kf and ks as a function of LET are shown in Fig. 1. For the fast decay rate, kf, parameter estimates lay between ~0.3 and 0.7 h−1. For the slow decay rate, ks, for the lower LET values, the parameter estimates ranged from 0.06 to 0.12 h−1, while at higher LET, ~100 keV/μm and above values lowered and converted to zero. This indicates that for the higher LET values the fraction that would be repaired with the slower repair rate remained unrepaired.

Next, we test hypothesis 2; that the decay rates kf and ks are independent of LET, and the fraction of damage repaired with the fast decay rate, f, depends on the LET. Therefore, only random effects for f were included in the NLME-model. kf and ks were estimated to be 0.50 and 0.07 h−1, respectively. The fitted values for f as function of LET are shown in Fig. 2a. For the lower LET exposures (<50 keV/μm), the fitted values for f lay mostly slightly higher than the photon data, indicating that the majority of breaks are likely repaired with the faster repair rate. At higher LET (100 keV/μm and above), lower values for f were observed, suggesting an increased dependence on the slower repair rate.

Fig. 2 (a) Results for hypothesis 2. Values of fitted parameter coefficient f as function of LET and different ions. Decay rates kf and ks are kept constant across all experimental fits. (b) Results for hypothesis 3. Values of fitted parameter U as function of LET and different ions. Parameters f, kf, and ks are kept constant across all experimental fits. An average LET value of 0.75 keV/μm was chosen for the photon data [22].

Finally, we add the parameter U to the model which represents the fraction of unrepaired damage. To investigate whether the LET affects this parameter while all other parameters would remain independent (hypothesis 3), only a random effect for U was included in the NLME-model assuring that the parameters (f, kf and ks) were kept at the same values for all experiments. Parameter estimates for kf & ks were 0.6 and 0.1 h−1, respectively, while f was estimated at 0.53. The fitted values for U as function of LET are shown in Fig. 2b. Again, a difference was observed where for the lower LET exposures lower values for U were estimated, while at higher LET (100 keV/μm and above) values lay ~20–30%.

A fourth hypothesis is that both the fraction of fast repaired and the fraction of unrepaired DNA DSBs are changing depending on the LET while the repair rates remain unchanged. To test hypothesis 4, we included random effects for both the factors f and U. kf & ks were estimated at 0.52 and 0.05 h−1, respectively. The fitted values of f and U from this NLME-model are shown in Fig. 3. A similar pattern compared to the NLME analysis with random effects for either f or U was observed, although the estimated values were slightly different. f decreased with increasing LET while for the U variable, an opposite effect was observed.

Fig. 3 Results for hypothesis 4. Fitted parameter coefficients f (a) and U (b) as function of LET and different ions. Decay rates kf and ks are kept constant across all experimental fits while random effects were included for both f and U. An average LET value of 0.75 keV/μm was chosen for the photon data [22].

An overview of the different parameter estimates for the fixed effects of the different NLME-models can be found in Table 1. In addition to these fits, we conducted a global fit with shared parameters for the photon data with repair competent and deficient cell lines (See Supplementary Materials, Fig. S1). The outcome of these parameters are included in Table 1 as well.

Table 1 Parameter estimates for the different hypothesis as well as the parameter estimates of a global fit of photon-exposed repair competent and deficient cell lines

	f	kf (h−1)	ks (h−1)	U	
Hyp 1	0.50	Fig. 1a	Fig. 1b	-	
Hyp 2	Fig. 2a	0.50	0.07	-	
Hyp 3	0.53	0.60	0.10	Fig. 2b	
Hyp 4	Fig. 3a	0.52	0.05	Fig. 3b	
Glogal fit	0.47	0.54	0.08	-	
Global fit refers to the shared parameter fit of repair deficient cell lines exposed to photons as described in the supplementary materials (See Table S1).

Table 2 NLME-model fit goodness-of-fit comparison

	Hyp. 1:
kf & ks	Hyp. 2:
f	Hyp. 3:
U	Hyp. 4
f & U	df	AIC	RSS total	RSS ion	
Hyp. 1: kf & ks	-	-	-	-	6	−579	4.1	0.84	
Hyp. 2: f	Χ2 = 13.2,
P < 0.0001	-	-	-	5	−594	3.9	0.69	
Hyp. 3: U	-	Χ2 = 10.5,
P = 0.0012	-	-	6	−582	4.3	0.86	
Hyp. 4  f & U	Χ2 = 10.5,
P = 0.0012	Χ2 = 2.7,
P = 0.2586	Χ2 = 7.8,
P = 0.0051	-	7	−587	3.8	0.39	
Numbers show the results of the likelihood ratio test (χ2) with corresponding P-values for comparison of different model fits. kf & ks, f, U, f & U, represent the parameters for which random effects were included in the NLME-model, i.e. the different hypotheses (hyp.) that were tested. df = degree of freedom, AIC = Aikake Information Criterion, RSS total = residual sum of squares for the whole data set. RSS ion = residual sum of squares for the dataset excluding the photon data.

Fig. 4 Residual sum of squares (RSS) for the different NLME-models as function of LET and different ions (photon data excluded). RSS for the model with random effects for kf and ks (a), f, (b), U (c), and f and U (d).

Comparison of the different hypotheses

To identify the most suitable hypothesis for explaining the in vitro data, we compared the goodness-of-fit measures, including the Akaike information criterion (AIC), from the various NLME-models (Table 2). The AIC is a measure that balances the goodness of fit of a statistical model with the complexity of the model itself. A lower AIC value indicates a model that better accounts for both fit and complexity, suggesting it is likely to be a better explanation for the observed data patterns compared to a model with higher a AIC. The NLME-model including a random effect for f exclusively (hypothesis 2) showed the lowest AIC of −594, followed by the NLME-model including random effects for both f and U (−587, hypothesis 4). The likelihood ratio test between these two models indicated no statistically significant difference. Moreover, the NLME-model incorporating random effects for both parameters f and U had the lowest residual sum of squares (RSS) which was particularly evident upon exclusion of the RSS pertaining to the photon data. The NLME-models testing hypothesis 1 & 3 showed significantly higher AIC values, indicating a poor support from the data compared with the NLME-models testing hypothesis 2 & 4.

To better understand the performance of each model we then calculated the RRS for each combination of ion and LET (Fig. 4). The model incorporating both f and U as random effects, consistently demonstrated the lowest RSS for all included ions and LET values. Although the model containing solely f as random effect yielded similar results, a higher RSS for iron ions at ~150 keV/μ was observed. Finally, in Fig. 5, we compare the results of the NLME model fits with the in vitro data.

Fig. 5 Comparison of predicted repair curves based on NLME-models with random effects for kf & ks, f, U, and f & U for each individual experiment (photon data is grouped). Dots represent the in vitro data. The numbers represent the LET values in keV/μm. Plots are grouped by each individual experiment included in the database except for the photon data which is grouped together.

Fig. 6 Overview of RTR50 values as function of LET and different ions. RTR50 values were obtained by determining the ratio between ion and photon exposed cells for the time needed to repair 50% of the DNA DSBs. RTR50 values were calculated based on inclusion of random effect for the fraction of fast repaired DNA DSBs (f), i.e. hypothesis 2 (a) or, random effect for f, and the fraction of unrepaired DNA DSBs (U), hypothesis 4 (b).

RTR50 calculations

In the next section we aim to reflect the difference in repair speed as a function of LET and ion species. For this aim, we used the values for the estimated parameters for each individual experimental curve (i.e. experimental unit, or eu [see Methodology section]), obtained from the best fitting NLME-fits, to determine the duration for repair of 50% of the DNA DSBs. This value was then divided by the average time needed for the photon exposed cells to repair the same percentage of DSBs. The obtained value reflects the ratio between the radiation quality under investigation and the reference radiation (the photon data) for the time needed to repair 50% of the damage. Hence, we call this the Repair Time Ratio (RTR) at 50%, or RTR50.

For most repair curves, RTR50 values were close to 1 for the lower LET exposed cells (Fig. 6). The RTR50 started to rise at LET values >100 keV/μm. Most RTR50 values for higher LET groups reached highest values ~2–3, indicating that cells exposed to higher LET radiation were ~2–3 times slower in repairing 50% of the DSBs compared with photon exposed cells.

DISCUSSION

In this paper we used the DR DNA database [10] with the aim of improving our understanding of the effect of LET on the DNA DSB repair process. Through this approach, utilizing large data and pooling the experimental data of 84 studies, trends could be observed that may not be apparent from individual experimental studies alone. By using NLME-models including random effect for sequentially fitting of different parameters of the bi-exponential decay function, we found that LET tended to induce a shift towards reliance on slower repair mechanisms which could possibly be in combination with an increase in fraction of DNA DSBs remaining unrepaired. The hypotheses that LET only influences the number of unrepaired DNA DSBS (hypothesis 3), or that LET directly influences the repair rates or the fraction of unrepaired DNA DSBs (hypothesis 1) had lower support from the data. Furthermore, comparing fitted curves from ion experiments to those from photon exposed cells showed a more than 2-fold increase in the time needed to repair 50% of DNA DSBs at higher LET.

Unfortunately, the conclusions drawn in this paper are hindered by the large uncertainty and the unreported parameters in the experimental investigation (as discussed in [10]). Throughout our study, we encountered a significant challenge stemming from the scattered nature of the data. We therefore applied a data-selection procedure based on several criteria outlined in the methodology section. Regardless, a large variation in the photon-exposed cell lines persisted, possibly driven by differences in the cell line, cell typology, the species and tissue from which the cell line was isolated, and the cell class. However, with the aim of observing a general trend, we chose to pool the photon data, especially since no one unique cell type was available across all the conditions tested in this study.

In addition to filtering the dataset, we included a global fit on the photon exposed dataset including both repair competent and deficient cell lines and applying biological assumptions regarding the available repair pathways to determine the shared parameters for the fitting (see Supplementary Materials). This approach allows us to better account for the noise in the data. By estimating model parameters jointly from all conditions of repair competence, the number of fitting parameters is reduced, thereby enhancing the precision and reliability of the estimated parameters. Additionally, it leverages the full dataset to constrain parameter values and enhance statistical power [23]. The resulting parameter estimates based on the global fit of the photon exposed cells are in close proximity to those obtained with the NLME-model fits of the photon and ion dataset, supporting the validity of these parameters.

Nevertheless, the observed heterogeneity in the photon-exposed data underscores the necessity of investigating cell-type-specific effects on DNA double-strand break repair following radiation exposure, as these variations may have implications for cell survival outcomes [24, 25]. Future studies should include a variety of different cell types exposed to various LET values and ion species to further elucidate the effects of cell-type specific responses to radiation.

Although several publications have reported a decrease in DNA DSB repair rates with an increase in LET [5, 13–15], our findings provided less support for altered decay rates as result of exposure to higher LET. This aligns with other studies demonstrating the independence of repair rates from LET [16–18]. As previously mentioned, our analysis shows a potential shift towards more dependence on slower repair rates with increase in LET. This could possibly be attributed to the heightened complexity of DNA damage and potential alterations in repair pathway dependence [26, 27].

Comparing hypotheses 2 and 4, that is, the NLME-model which includes a random effect for f only, and the NLME-model with random effects for both f and U, we found no clear differences in goodness-of-fit between both models. Nevertheless, the latter model showed slightly improved RSS, especially at higher LET (Fig. 4d). Particularly for the later timepoints at higher LET, the NLME-model with random effect for f only, appeared to underestimate the remaining DNA DSBs while the model based on hypothesis 4 (f & U dependence on LET) captured these data points better (Fig. 5). Nevertheless, most in vitro data points do not extend past the 24 hours post-irradiation. Therefore, it remains unclear whether the DSBs persisting at 24 hours are indeed not undergoing repair. For a more definitive determination, further data points, especially at higher LET and later timepoints, are essential.

Furthermore, though the LET dependence on f seemed to appear as linear within the range of LETs included in the database (Figs 2a and 3a), for parameter U this dependence seemed non-linear (Fig. 2b and c). In the supplementary materials we included a nonlinear fit using the parameter estimates of U (Fig. S2). Yet, with the current dataset, this dependence cannot be clearly discerned. In addition, it is well-known that the relative biological effect of particle radiation reaches a maximum at LET values in the range between 100 and 200 keV/μm [9]. Likewise, the results discussed in this work show strongest effects on the fitted parameters, as well as the RTR50 calculations in the same LET range. However, due to the limited number of datapoints, clear LET- and ion dependent trends remain elusive. These observations underscore the necessity for more extensive data collection to discern the patterns in LET- and ion- dependent repair and its implications for the overkill effect.

Therefore, expanding the current dataset by performing experiments with a broader scope of ions species as well as including a wide range of LET values is essential to fully elucidate the relationship between LET and repair dynamics. Additionally, such studies are of clinical importance for determining timing-sensitive parameters for cell survival. Improving our understanding of the relationship between LET, repair kinetics, and cellular survival by incorporating a variety of ion species and ranges of LET in DNA DSB repair studies, is crucial for improving predictions of how accumulation of sublethal damage and its subsequent repair contribute to cellular radiosensitivity.

Conclusion

In conclusion, our study highlights the complex relationship between LET and DNA DSB repair dynamics. Our findings suggest a potential shift towards greater reliance on slower repair mechanisms with increasing LET, likely driven by the heightened complexity of DNA damage. Although the exact nature of this relationship, particularly regarding the increase in the number of unrepaired DSBs at later timepoints post-irradiation, remains unclear, this study provides a valuable model for understanding overall trends in DNA repair kinetics. Future research should include additional experimental observations at later time points, explore a broader range of ion species, and examine a wider spectrum of LET values. Addressing these areas will help refine experimental designs and enhance our understanding of DNA repair dynamics and its implications for cellular survival following radiation exposure.

Supplementary Material

20240903_supplementary_rrae071

20240524_supplementary_blinded_rrae071

CONFLICT OF INTEREST

The authors declare no conflict of interest.
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