## Highlights

- •We developed a Geant4-DNA application to reproduce cell survival of V79 cells.
- •The application reproduced DNA rejoining and cell survival of V79.
- •This is the first application for cell survival prediction with DNA simulations.

## Abstract

### Purpose:

### Methods:

### Results:

### Conclusion:

## Keywords

## 1. Introduction

*foci*) after gamma irradiation on a normal human fibroblast cell [

*foci*prediction functionality allows us to understand a portion of the radiobiological phenomena in fibroblast cells after irradiation.

Tang N. évaluation, à partir de modélisations nanodosimétriques, de l’influence de la compaction de la chromatine sur les effets radio-induits précoces et extension aux effets tardifs (réparation des dommages à l’adn et mort cellulaire). [phD thesis], Written in French from the University of Bordeaux France.

## 2. Materials and methods

### 2.1 Simulation configuration and initial DNA damage quantification

#### 2.1.1 Geometrical model

^{3}[

^{3}[

^{3}) is surrounded by an ellipsoid of water ($23.2\phantom{\rule{1em}{0ex}}\mathrm{\mu}\mathrm{m}\times 5\phantom{\rule{1em}{0ex}}\mathrm{\mu}\mathrm{m}\times 23.2\phantom{\rule{1em}{0ex}}\mathrm{\mu}\mathrm{m}$, $\sim 1409\phantom{\rule{1em}{0ex}}\mathrm{\mu}\mathrm{m}$

^{3}) modeling the cytoplasm.

#### 2.1.2 Particle transport model and chemistry diffusion–reaction model

#### 2.1.3 Initial DNA damage scoring and damage classification

### 2.2 Calculation of DNA rejoining kinetics and cell surviving fraction

Here ${L}_{1}\left(t\right)$ is the expected number of DSBs in fast repair per cell at the time from the start of irradiation $t$; similarly, ${L}_{2}\left(t\right)$ is the expected number of DSBs in slow repair per cell at time from the start of irradiation $t$. $\stackrel{\u0307}{D}\left(t\right)Y{\Sigma}_{1}$ and $\stackrel{\u0307}{D}\left(t\right)Y{\Sigma}_{2}$ are the lesion production terms for DSBs in fast and slow repair, respectively, which are proportional to the dose rate $\stackrel{\u0307}{D}\left(t\right)$ multiplied by number of lesions ($\Sigma $) per unit of dose and bp (Gy

^{−1}Gbp

^{−1}) and number of bp in a cell $Y$. In this work, the instantaneous lesions are defined as ${\Sigma}_{1}={\mathrm{N}}_{\mathrm{DSB}}$ and ${\Sigma}_{2}={\mathrm{N}}_{\mathrm{DSB+}+2{N}_{DSB++}}$ as classified by the definition of Nikjoo et al. [

^{−1}) for simple and complex DSBs, respectively. ${\eta}_{1}$, ${\eta}_{2}$ and ${\eta}_{1,2}$ are the DSB–DSB binary rejoining rates (h

^{−1}) for simple–simple, complex–complex and simple–complex rejoining combinations, respectively. Similarly, ${\u03f5}_{1}$ and ${\u03f5}_{2}$ account for the rates by physiochemical fixation (h

^{−1}for simple and complex DSBs, respectively).

where ${a}_{1}$ and ${a}_{2}$ represent the probabilities of correctly repaired damage in simple and complex DSBs, respectively. The probabilities ${\beta}_{1}$, ${\beta}_{2}$, ${\gamma}_{1}$, ${\gamma}_{2}$ and ${\gamma}_{1,2}$ describe the partitioning of misrepaired damage into lethal and nonlethal genetic alterations for each repair type. For example, ${\beta}_{1}=1$ means that if the DSB was not repaired correctly in the fast-repair process regarded as misrepair, the DSB always produces a lethal lesion. As in the original study by Stewart [

and

Finally, these yields are numerically integrated to calculate the SF,

The differential equation has been solved numerically by means of the fourth-order Runge–Kutta method in the boost/numerical C++ library.

where ${F}_{max}$ is the maximum fraction of the DNA that can enter the gel plug, ${M}_{0}$ is the average DNA length in a chromosome, and $K$ is the detection limit length. In this study, ${F}_{max}$ was set to 1, ${M}_{0}=180$ Mbp, and $K=4.9\phantom{\rule{1em}{0ex}}\mathrm{Mbp}$ as estimated by Belli et al. [

### 2.3 Protectable damage fraction

where SF

_{0}and S${\mathrm{F}}_{\infty}$ are the measured SF at 0 mol of DMSO and the assumed SF at infinite DMSO concentration, respectively. Moreover, the maximum DP can be obtained as the value at the point of intersection of the regression where the concentration of DMSO is infinite (1/$x$ =0), with the equation given by:

where $x$ is the density of DSMO, $k$ is the slope, and ${y}_{\infty}$ is the intersection (at the limit of infinite DMSO concentration). Similarly, the DP can be calculated with the SFs of the Geant4-DNA application as follows:

where S${\mathrm{F}}_{\mathrm{wChem}}$ and S${\mathrm{F}}_{\mathrm{woChem}}$ are the calculated SFs with the initial DSB yields, which were simulated with- and without- chemistry simulations, respectively. In this study, DP${}_{\mathrm{method1}}$ is calculated with ${\text{SF}}_{\mathrm{wChem}}$ and ${\text{SF}}_{\mathrm{woChem}}$ at 1 Gy, where it is not affected by the SF enhancement known as the stochastic effect [

where N${}_{{\mathrm{DSB}}_{dir}}$, N${}_{{\mathrm{DSB}}_{ind}}$,N${}_{{\mathrm{DSB}}_{mix}}$ and N${}_{{\mathrm{DSB}}_{hyb}}$ are the numbers of ${\mathrm{DSB}}_{dir}$, ${\mathrm{DSB}}_{ind}$, ${\mathrm{DSB}}_{mix}$ and ${\mathrm{DSB}}_{hyb}$, respectively. We neglected the contribution of ${\mathrm{DSB}}_{mix}$ to the protectable damage fraction, because it cannot be clearly classified as protectable DSB or not. Because, in the reference [

## 3. Results

### 3.1 Number of initial DSBs after irradiation

^{−1}Gy

^{−1}and was about 7.3 Gbp

^{−1}Gy

^{−1}at 7.0 MeV, although the geometry of the simulations was slightly different.

### 3.2 Optimized model parameters of the TLK model

^{−1}, and its half-repair time was about 35 min. Similarly, the repair rates were approximately $2.51\times 1{0}^{-3}$ and $3.62\times 1{0}^{-6}$ h

^{−1}, for the slow repair and binary repair, respectively. In addition, the corresponding half-lives were 12 days and 22 years, respectively. The probability of the misrepair in the slow repair leading to cell death was approximately 16 %. The probability for fast-repair (${\beta}_{1}$) was fixed at 0 % and that for binary-repair ($\gamma $) at 100 % at the maximum probability as the result of the optimization.

${\lambda}_{1}$ (h^{−1}) | ${\lambda}_{2}$ (h^{−1}) | $\eta $ (h^{−1}) | ${\beta}_{1}$ | ${\beta}_{2}$ | $\gamma $ |

1.19 | $2.51\times 1{0}^{-3}$ | $3.62\times 1{0}^{-6}$ | 0.0 | 0.16 | 1.0 |

### 3.3 DNA rejoining kinetics

### 3.4 Cell surviving fraction

### 3.5 Fraction of indirect damage (protectable damage fraction)

## 4. Discussion

## 5. Conclusion

## Acknowledgments

## Appendix. Model parameter optimization

where $F\left(x\right)$ is a matrix of an $n$-dimensional vector of variables (the number of data points), and $m$-dimensional function of $x$ (the number of optimized parameters), whereas $J\left(x\right)$ is the Jacobian. We select SPARSE_NORMAL_CHOLESKY as the algorithm of the Jacobian factorization, given that the optimization problem is usually sparse. The residual cost for each data point was calculated as ${V}_{calc}-{V}_{exp}$ with the same weight for all configurations of both the SF and relative unrejoined DSB, where ${V}_{calc}$ was calculated as the value with simulated DSBs.

## References

- Track structure in radiation biology: theory and applications.
*Int J Radiat Biol.*1998; 73: 355-364 - Perspectives in radiation biophysics: From radiation track structure simulation to mechanistic models of DNA damage and repair.
*Rad Phys Chem.*2016; 128: 3-10 - Radiation track, DNA damage and response—a review.
*Rep Progr Phys.*2016; 79116601 - Review of the Geant4-DNA simulation toolkit for radiobiological applications at the cellular and DNA level.
*Cancers.*2021; 14: 35 - Reactive oxygen species and oxidative DNA damage.
*Ind J Phys Phar.*1998; 42: 440-452 - Cross-section of water vapour for the Monte Carlo electrons track structure code from 10 eV to the MeV region.
*Phys Med Biol.*1993; 38: 1841-1858 - Computational modeling of low-energy electron-induced DNA damage by early physical and chemical events.
*Int J Radiat Biol.*1997; 71: 467-483 - Computational approach for determining the spectrum of DNA damage induced by ionizing radiation.
*Rad Res.*2001; 156: 577-583 - Monte Carlo simulation of the production of short DNA fragments by low-linear energy transfer radiation using higher-order DNA models.
*Rad Res.*1998; 150: 170-182 - Simulation of DNA damage after proton irradiation.
*Rad Res.*2003; 159: 401-410 - Track structures, DNA targets and radiation effects in the biophysical Monte Carlo simulation code PARTRAC.
*Mutat Res.*2011; 711: 28-40 - Comprehensive track-structure based evaluation of DNA damage by light ions from radiotherapy-relevant energies down to stopping.
*Sci Rep.*2017; 7: 45161 - Applications of Monte Carlo methods in biology.in: Medicine and other fields of science. Monte-carlo simulation of ionizing radiation tracks. InTech, 2011: 315-356
- Radiation physics and chemistry.in: 2017 considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations, Vol. 139. Elsevier Ltd, 2016: 157-172
- The Geant4–DNA project.
*Int J Model Simul Sci Comput.*2009; 1: 157-178 - Comparison of Geant4 very low energy cross section models with experimental data in water.
*Med Phys.*2010; 37: 4692-4708 - Track structure modeling in liquid water: A review of the Geant4–DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit.
*Phys Med.*2015; 31: 157-178 - Geant4–DNA example applications for track structure simulations in liquid water: a report from the Geant4–DNA project.
*Med Phys.*2018; 45: e722-e739 - Mechanistic DNA damage simulations in Geant4-DNA part 1: A parameter study in a simplified geometry.
*Phys Med.*2018; 48: 135-145 - Mechanistic DNA damage simulations in Geant4-DNA part 2: Electron and proton damage in a bacterial cell.
*Phys Med.*2018; 48: 146-155 - Evaluation of early radiation DNA damage in a fractal cell nucleus model using Geant4-DNA.
*Phys Med.*2019; 62: 152-157 - Fully integrated Monte Carlo simulation for evaluating radiation induced DNA damage and subsequent repair using Geant4-DNA.
*Sci Rep.*2020; 10: 20788 - Simulation of early DNA damage after the irradiation of a fibroblast cell nucleus using Geant4-DNA.
*Sci Rep.*2017; 7: 11923 - TOPAS: An innovative proton Monte Carlo platform for research and clinical applications.
*Med Phys.*2012; 39: 6818-6837 - TOPAS-nBio: An extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology.
*Rad Res.*2018; 191: 125-138 - Geometrical structures for radiation biology research as implemented in the TOPAS-nbio toolkit.
*Phys Med Biol.*2018; 63175018 - A quantitative model of the major pathways for radiation-induced DNA double-strand break repair.
*J Theoret Biol.*2015; 366: 115-130 - Rapid method for viable cell titration and clone production with HeLa cells in tissue culture: the use of X-irradiated cells to supply conditioning factors.
*Proc Natl Acad Sci.*1995; 41: 432-437 - Action of x rays on mammalian cells.
*J Exp Med.*1956; 103: 653-666 - In vitro RBE-LET dependence for multiple particle types.
*Acta Oncol.*2011; 50: 757-762 - Initial events in the cellular effects of ionizing radiations: clustered damage in DNA.
*Int J Radiat Biol.*1994; 65: 7-17 - Microdosimetry of low-energy electrons.
*Int J Radiat Biol.*2012; 88: 899-907 - Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models.
*Rad Res.*2012; 178: 341-356 - Two-lesion kinetic model of double-strand break rejoining and cell killing.
*Rad Res.*2001; 156: 365-378 Tang N. évaluation, à partir de modélisations nanodosimétriques, de l’influence de la compaction de la chromatine sur les effets radio-induits précoces et extension aux effets tardifs (réparation des dommages à l’adn et mort cellulaire). [phD thesis], Written in French from the University of Bordeaux France.

- RBE-LET relationships for cell inactivation and mutation induced by low energy protons in V79 cells: further results at the LNL facility.
*Int J Rad Biol.*1998; 74: 501-509 - DNA DSB induction and rejoining in V79 cells irradiated with light ions: a constant field gel electrophoresis study.
*Int J Rad Biol.*2000; 76: 1095-1104 - Dependence of the yield of DNA double-strand breaks in Chinese hamster V79-4 cells on the photon energy of ultrasoft X rays.
*Rad Res.*2001; 155: 440-448 - Radiobiological effects of tritiated water short-term exposure on V79 clonogenic cell survival.
*Int J Radiat Biol.*2018; 94: 157-165 - In CHEF electrophoresis a linear induction of DSB corresponds to a nonlinear fraction of extracted DNA with dose.
*Int J Radiat Biol.*1990; 57: 7-12 - DNA fragmentation in mammalian cells exposed to various light ions.
*Adv Space Res.*2001; 27: 393-399 - Inelastic cross-sections for electron transport in liquid water: a comparison of dielectric models.
*Radiat Phys Chem.*2003; 66: 373-385 - The impact of new Geant4-DNA cross section models on electron track structure simulations in liquid water.
*J Appl Phys.*2016; 119194902 - Technical note: Improvements in Geant4 energy-loss model and the effect on low-energy electron transport in liquid water.
*Med Phys.*2015; 42: 3870-3876 - Implementation of new physics models for low energy electrons in liquid water in Geant4–DNA.
*Phys Med.*2016; 32: 1833-1840 - Microdosimetry of electrons in liquid water using the low-energy models of Geant4.
*J Appl Phys.*2017; 122024303 - Stochastic modeling of fast kinetics in a radiation track.
*J Phys Chem.*1990; 94: 251-258 - MMEJ repair of double-strand breaks (director’s cut): deleted sequences and alternative endings.
*Tren Genet.*2008; 24: 529-538 - RBE–LET relationship for the survival of V79 cells irradiated with low energy protons.
*Int J Rad Biol.*1989; 55: 93-104 - Yeast [PSI+] prion aggregates are formed by small sup35 polymers fragmented by Hsp104.
*J Biol Chem.*2003; 278: 49636-49643 - Measurement of DNA double strand breaks in CHO cells at various stages of the cell cycle using pulse field gel electrophoresis: Calibrations by means of 125i decay.
*Int J Radiat Biol.*1991; 59: 343-357 - Analysis of DNA double strand breakage and repair using orthogonal field alternation gel electrophoresis.
*Yeast.*1987; 3: 71-76 - A quantitative model of DNA fragments generated by ionizing radiation, and possible experimental applications.
*Rad Res.*1991; 125: 102-106 - Contribution of indirect action to radiation-induced mammalian cell inactivation: Dependence on photon energy and heavy-ion LET.
*Rad Res.*2006; 165: 703-712 - Contributions of direct and indirect actions in cell killing by high-LET radiations.
*Rad Res.*2009; 171: 212-218 - Report 90: Key data for ionizing-radiation dosimetry: Measurement standards and applications.
*J Int Com Rad Units Meas.*2016; 14: 1 - Mechanistic modelling of DNA repair and cellular survival following radiation-induced DNA damage.
*Sci Rep.*2016; 6: 33290 - Cell survival computation via the generalized stochastic microdosimetric model (GSM2); part I: The theoretical framework.
*Rad Res.*2022; 197: 218-232 - Comparison of nonhomologous end joining and homologous recombination in human cells.
*DNA Rep (Amst).*2008; 7: 1765-1771

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