# Repair Kinetics of DSB-Foci Induced by Proton and α-Particle Microbeams of Different Energies

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cell Culture

^{®}and supplements) (Lonza, Basel, Switzerland) containing 4.72% (v/v) fetal bovine serum (Lonza), hydrocortisone, hFGF-B, VEGF, R3-IGF-1, ascorbic acid, HEGF, gentamicin and amphotericin-B (EGM-2BulletKit; Lonza). They were maintained at a temperature of 37 °C in a humidified incubator in an atmosphere containing 5% CO

_{2}(v/v) in air.

#### 2.2. Microbeam Irradiations

_{2}. The dishes were then filled with fresh culture medium and remained in the incubator overnight. On the irradiation day, cells were stained with a 150 nM solution of Hoechst 33,342 dye (AAT Bioquest Inc., Sunnyvale, CA, USA) for 30 min.

#### 2.3. Immunostaining and Microscopy

^{®}-X (1/1000, Invitrogen, Waltham, MA, USA, T-6391). Finally, the cells were washed three times more with PBS, incubated for 5 min with 4′,6-Diamidino-2-Phenylindole, Dihydrochloride (14.3 μM, Invitrogen, D1306) and mounted with anti-fade Prolong

^{®}Gold (Invitrogen, P36930). Cells were analyzed at 64× magnification in a fluorescence microscope. Image analysis of 53BP1 foci was performed by the freeware CellProfiler [25].

#### 2.4. Data Analysis

- The expected number of foci per nucleus and the respective uncertainty for a radiation condition were estimated, respectively, as the mean and the sample standard deviation of the mean values found in the three replicate experiments.
- The possibility of indistinguishable foci in case of tracks passing the nucleus in proximity was taken into account using a development of the approach of Gonon et al. [15]: The mean number of tracks in proximity (leading to indistinguishable foci) were determined by a simulation of the irradiation, separately for each possible number of ions in such a track “cluster”. The positions of the points of ion passage through the image plane as well as the lengths of the main axes and orientation of the ellipse representing a cell nucleus were randomly sampled. (Supplementary Tables S1 and S2).
- In addition, the possibility that several foci are formed within an ion track and are indistinguishable is taken into account. The number of foci formed in an ion track is assumed to be Poisson distributed.
- It is assumed that radiation-induced foci and foci induced by non-radiation causes occur statistically independently.
- Sham irradiated foci are assumed to be always repairable whereas for radiation-induced foci it is possible that foci are persistent.
- The repair of foci is assumed to be below the saturation point and to follow first order kinetics with a repair rate independent of radiation quality. The first assumption seems justified because even at the highest LET values, the dose to the nucleus from the five passing ion tracks is less than 1 Gy.

## 3. Results

#### 3.1. 53BP1 Foci Background

#### 3.2. 53BP1 Foci in HUVEC Cells Targeted with 5 Ions

#### 3.3. Kinetics of the Decay of 53BP1 Foci

#### 3.4. Robustness Analysis

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the targeted irradiation positions for ions in the cell nucleus. The pattern was fixed in space and not adjusted to the nuclei orientation.

**Figure 2.**Characterization of 53BP1 foci background. Relative frequency distribution of the number of 53BP1 foci per nucleus for three replicate experiments of control dishes. The mean number of foci per nucleus, m

_{Control}, represents the mean of the means between the three replicate experiments and its associated standard deviation (SD) computed as the square root of the sample variance between the means.

**Figure 3.**Time dependence of the mean number of foci per nucleus as a function of the post-irradiation time for the sham-treated cells. Points represent the mean of means obtained between three replicate experiments for each time point, and error bars represent the SD between the means computed as the square root of the sample variance. The dashed line is the best-fit curve of a regression of only the sham-treated data using Equation (2). The solid line is the best-fit curve obtained by simultaneous regression of all data sets; the shaded area indicates the range of results obtained with the different options investigated in the robustness analysis. (See text for details).

**Figure 4.**Time dependence of the mean number of foci per nucleus for all radiation beams as a function of post-irradiation time (in hours). Points represent the mean of means obtained between three replicate experiments for each time point, and error bars represent the SD between the means computed as the square root of the sample variance.

**Figure 5.**Kinetics of the disappearance of 53BP1 foci in HUVEC cells targeted with 3 MeV protons (

**A**) and 8, 10 and 20 MeV α-particle beams (

**B**–

**D**). Symbols represent the mean number of foci per nucleus for each time point. The lines are the best-fit curves when the datasets are fitted independently (dotted lines) and when a simultaneous regression of all datasets is performed according to Equations (1) to (4) with ${\beta}_{0}$ as a free parameter (solid line) or with ${\beta}_{0}={\beta}_{1}$ (dashed lines). The gray shaded areas indicate the range of values obtained from the robustness analysis.

Particle Type and Beam Energy | Estimated Energy at Cell Nucleus Center (MeV) | Estimated LET at Cell Nucleus Center (keV/µm) |
---|---|---|

α-particles | ||

20 MeV | 17.8 ± 0.2 | 36 ± 1 |

10 MeV | 5.5 ± 0.4 | 85 ± 4 |

8 MeV | 1.9 ± 0.6 | 170 ± 40 |

Protons | ||

3 MeV | 1.6 ± 0.2 | 19 ± 2 |

**Table 2.**Results of the model parameters obtained by simultaneous non-linear regression of all datasets: Mean number of radiation-induced foci per track ${\overline{n}}_{Q}$, fraction of persistent radiation-induced foci ${p}_{Q}$, mean number of persistent radiation-induced foci per track ${\overline{p}}_{Q},$ repair rates ${\beta}_{1}$ and ${\beta}_{2}$, and respective standard errors (SE) obtained from the fit of the non-linear model (Equations (1)–(3)) to the ensemble of datasets for all radiation qualities and the sham-irradiated cells. The values are from the regression performed using MPfit procedure of GDL using ${\beta}_{0}$ in Equation (2) as a free parameter. The upper and lower values in the cells in columns 3 through 7 are the fit results obtained by using Equation (4) and Equation (5), respectively, in conjunction with Equations (1)–(3). The values given in italics in columns 4 and 5 have been calculated from the values in the respective other column. The resulting ratios ${\chi}^{2}/{f}^{}$ of the weighted sum of squared residuals ${\chi}^{2}$ (summed over all datasets) to the degrees of freedom $f$ are about 5.4 and 6.2, respectively. In columns 6 and 7 only one value is given, since in the simultaneous fit these parameters were kept the same for all radiation qualities.

(1) Radiation Beam | (2) LET (keV/µm) |
(3) Mean Number of Foci Per Track, $\text{}{\overline{\mathit{n}}}_{\mathit{Q}}$ |
(4) Proportion of Persistent Foci, ${\mathit{p}}_{\mathit{Q}}$ |
(5) Mean Number of Persistent Foci Per Track, $\text{}{\overline{\mathit{p}}}_{\mathit{Q}}$ |
(6) Repair Rate, $\text{}{\mathit{\beta}}_{1}\text{}\left({\mathbf{h}}^{-1}\right)$ |
(7) Repair Rate, $\text{}{\mathit{\beta}}_{2}\text{}\left({\mathbf{h}}^{-1}\right)$ |
---|---|---|---|---|---|---|

Protons 3 MeV | 19 ± 2 | 0.37 ± 0.02 0.37 ± 0.02 | 0.17 ± 0.12 0.28 ± 0.12 | 0.06 ± 0.04 0.10 ± 0.04 | 0.27 ± 0.05 0.32 ± 0.07 | 0.01 ± 0.03 0.04 ± 0.02 |

α—particles 20 MeV | 36 ± 1 | 0.63 ± 0.04 0.63 ± 0.04 | 0.10 ± 0.07 0.16 ± 0.08 | 0.06 ± 0.04 0.11 ± 0.05 | ||

10 MeV | 85 ± 4 | 1.08 ± 0.06 1.09 ± 0.07 | 0.11 ± 0.08 0.21 ± 0.10 | 0.12 ± 0.08 0.23 ± 0.11 | ||

8 MeV | 170 ± 40 | 1.66 ± 0.18 1.68 ± 0.18 | 0.11 ± 0.08 0.21 ± 0.10 | 0.19 ± 0.14 0.33 ± 0.16 |

**Table 3.**Results of the model parameters obtained by simultaneous non-linear regression of all datasets: Number of radiation-induced foci per track ${\overline{n}}_{Q}$, fraction of persistent radiation-induced foci ${p}_{Q}$, mean number of persistent radiation-induced foci per track ${\overline{p}}_{Q},$ repair rates ${\beta}_{1}$ and ${\beta}_{2}$, and respective standard errors (SE) obtained from the fit of the non-linear model (Equations (1)–(3)) to the ensemble of datasets for all radiation qualities and the sham-irradiated cells. The values are from the regression performed using the GDL MPfit procedure imposing ${\beta}_{0}={\beta}_{1}$. The upper and lower values in the cells in columns 3 through 7 are the fit results obtained by using Equation (4) and Equation (5), respectively, in conjunction with Equations (1)–(3). The values given in italics in columns 4 and 5 have been calculated from the values in the respective other column. The resulting ratio ${\chi}^{2}/{f}^{}$ of the weighted sum of squared residuals ${\chi}^{2}$ (summed over all datasets) to the degrees of freedom $f$ is about 4.8 in both cases. In columns 6 and 7, only one value is given, since these parameters were kept the same for all radiation qualities in the simultaneous fit.

(1) Radiation Beam | (2) LET (keV/µm) |
(3) Mean Number of Foci Per Track, $\text{}{\overline{\mathit{n}}}_{\mathit{Q}}$ |
(4) Proportion of Persistent Foci, ${\mathit{p}}_{\mathit{Q}}$ |
(5) Mean Number of Persistent Foci Per Track, $\text{}{\overline{\mathit{p}}}_{\mathit{Q}}$ |
(6) Repair Rate, $\text{}{\mathit{\beta}}_{1}\text{}\left({\mathbf{h}}^{-1}\right)$ |
(7) Repair Rate, $\text{}{\mathit{\beta}}_{2}\text{}\left({\mathbf{h}}^{-1}\right)$ |
---|---|---|---|---|---|---|

Protons 3 MeV | 19 ± 2 | 0.37 ± 0.02 0.37 ± 0.02 | 0.42 ± 0.06 0.38 ± 0.05 | 0.15 ± 0.02 0.14 ± 0.02 | 0.43 ± 0.01 0.41 ± 0.01 | 0.06 ± 0.01 0.05 ± 0.01 |

α—particles 20 MeV | 36 ± 1 | 0.69 ± 0.04 0.69 ± 0.04 | 0.25 ± 0.06 0.22 ± 0.05 | 0.38 ± 0.08 0.34 ± 0.06 | ||

10 MeV | 85 ± 4 | 1.13 ± 0.06 1.13 ± 0.06 | 0.33 ± 0.06 0.30 ± 0.05 | 0.38 ± 0.08 0.34 ± 0.06 | ||

8 MeV | 170 ± 40 | 1.68 ± 0.18 1.68 ± 0.18 | 0.31 ± 0.08 0.27 ± 0.07 | 0.52 ± 0.15 0.47 ± 0.10 |

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**MDPI and ACS Style**

Belchior, A.; Canhoto, J.F.; Giesen, U.; Langner, F.; Rabus, H.; Schulte, R.
Repair Kinetics of DSB-Foci Induced by Proton and α-Particle Microbeams of Different Energies. *Life* **2022**, *12*, 2040.
https://doi.org/10.3390/life12122040

**AMA Style**

Belchior A, Canhoto JF, Giesen U, Langner F, Rabus H, Schulte R.
Repair Kinetics of DSB-Foci Induced by Proton and α-Particle Microbeams of Different Energies. *Life*. 2022; 12(12):2040.
https://doi.org/10.3390/life12122040

**Chicago/Turabian Style**

Belchior, Ana, João F. Canhoto, Ulrich Giesen, Frank Langner, Hans Rabus, and Reinhard Schulte.
2022. "Repair Kinetics of DSB-Foci Induced by Proton and α-Particle Microbeams of Different Energies" *Life* 12, no. 12: 2040.
https://doi.org/10.3390/life12122040