Radiation-induced DNA damage by proton, helium and carbon ions in human fibroblast cell: Geant4-DNA and MCDS-based study

Background. Radiation-induced DNA damages such as Single Strand Break (SSB), Double Strand Break (DSB) and Complex DSB (cDSB) are critical aspects of radiobiology with implications in radiotherapy and radiation protection applications. Materials and Methods. This study presents a thorough investigation into the effects of protons (0.1–100 MeV/u), helium ions (0.13–100 MeV/u) and carbon ions (0.5–480 MeV/u) on DNA of human fibroblast cells using Geant4-DNA track structure code coupled with DBSCAN algorithm and Monte Carlo Damage Simulations (MCDS) code. Geant4-DNA-based simulations consider 1 μm × 1 μm × 0.5 μm water box as the target to calculate energy deposition on event-by-event basis and the three-dimensional coordinates of the interaction location, and then DBSCAN algorithm is used to calculate yields of SSB, DSB and cDSB in human fibroblast cell. The study investigated the influence of Linear Energy Transfer (LET) of protons, helium ions and carbon ions on the yields of DNA damages. Influence of cellular oxygenation on DNA damage patterns is investigated using MCDS code. Results. The study shows that DSB and SSB yields are influenced by the LET of the particles, with distinct trends observed for different particles. The cellular oxygenation is a key factor, with anoxic cells exhibiting reduced SSB and DSB yields, underscoring the intricate relationship between cellular oxygen levels and DNA damage. The study introduced DSB/SSB ratio as an informative metric for evaluating the severity of radiation-induced DNA damage, particularly in higher LET regions. Conclusions. The study highlights the importance of considering particle type, LET, and cellular oxygenation in assessing the biological effects of ionizing radiation.


Introduction
Recent research has placed a significant focus on the impact of ionizing particles on living cells, with applications spanning the medical field, particularly in cancer treatment through radiotherapy, as well as in space science and radioprotection for astronauts (Francis and Stypczynska 2013, Lee 2017, Manalad 2022).When highly energetic particles traverse biological tissue, they can induce various effects, including excitations, ionizations, and alterations in molecules within the medium (Nickoloff et al 2020).Among these effects, the most critical modifications are believed to occur in the deoxyribonucleic acid (DNA), as this molecule governs cellular functions, and any changes to it can disrupt the cell cycle, leading to cell death.Typically, endogenously induced lesions are evenly distributed throughout the cell, whereas clustered damage sites, characterized by the presence of multiple damage events in close proximity, are a characteristic feature of ionizing radiation (Lomax et al 2013).Upon detecting DNA damage, cells initiate repair processes.However, the effectiveness of these repair mechanisms is heavily dependent on the type of damage and the complexity of the damage pattern.Notably, repair processes take place within the cell nucleus following irradiation, assuming that single-strand breaks (SSBs) can be repaired (Chapman et al 2012).Repairing double-strand breaks (DSBs) is a more challenging task, and the repair of complex damages, characterized by the presence of more than two SSBs within a relatively small proximity, poses the greatest challenge for repair activities (Chapman et al 2012, Nickoloff et al 2020).The poor repair process of clustered DSBs (cDSB) at least in part, reflects inhibition of canonical NHEJ (nonhomologous end-joining) by short DNA fragments (Chapman et al 2012, Nickoloff et al 2020).This shifts repair toward HR (homologous recombination) and perhaps alternative NHEJ, and can result in chromothripsis-mediated genome instability or cell death (Nickoloff et al 2020).In various circumstances, the success of the repair process can vary, potentially leading to either successful restoration or, in some cases, an erroneous repair that results in mutations (Francis and Stypczynska 2013).Mutations are a significant concern as they can contribute to the development of long-term cancers or even lead to cell death.This aspect is particularly relevant in the context of radiotherapy, where the primary treatment itself can induce secondary cancers due to radio-induced mutations.
Currently, in therapeutic contexts, a widely used approximation relies on the linear quadratic (LQ) model, which has been extensively analysed by Brenner (Brenner et al 1998).This model approximates the cell death rate as being related to the energy delivered to the biological medium.However, the LQ model is constructed based on observations of cell survival following irradiation.As a result, it doesn't provide insight into the internal processes occurring within the cell or nucleus, nor does it offer information about the intricacies of cellular repair activities or the resulting DNA mutations (Brenner et al 1998).Furthermore, the predictions made by the LQ model may be limited to relatively short-term cellular responses, as its parameters are typically adjusted to match cell death within a specific time frame after irradiation (Brenner et al 1998).It's worth noting that the effects of radiation on the human body can manifest over an extended period, sometimes several years after the initial exposure.Therefore, to precisely quantify the effects of radiation on biological tissue and predict the resulting reactions, it is imperative to gain a detailed understanding of what transpires at the DNA level during irradiation and throughout the subsequent repair phase.This deeper insight can provide a more comprehensive and accurate assessment of the longterm consequences of radiation exposure.
Monte Carlo method is a powerful tool to model a particle's track as it traverses a target volume, while considering its interactions with the medium's molecules and yielding both the positions and the amount of energy deposition at each interaction point.Numerous analytical approaches are subsequently disseminated to gauge the ultimate impact of such a particle trajectory on cellular behaviour, including the probability of cell survival.One approach to investigate this matter involves investigating the yields of energy deposition clusters, which can give rise to complex DNA damage, often referred to as clustered lesions, proven to be fatal for the cell.
Several studies have been conducted to estimate the yields of DNA damages, shedding light on the nature and complexity of these lesions under different radiation conditions.Nikjoo et al (1998) analysed DNA damage utilizing the K-means algorithm.Garty et al (2010) conducted a study focusing on counting the number of interactions occurring inside small nanometer-sized cylinders ( - ~3 8 nm) randomly placed along the particle track.Friedland et al (2003) described the spatial coordinates of the whole genome inside a human cell and calculated proton induced DNA damage yields using PARTRAC code.Leloup et al (2005) Zhu et al (2020) quantified the proportion of proton-induced direct and indirect DNA damages in fibroblast cell nucleus using TOPAS-nBio code.The details on the physical and chemical processes responsible for DNA damage and the use of Geant4-DNA toolkit for simulating direct and indirect DNA damages are discussed by Bordeaux (2021).In a recent study by Hosseini et al (2022), they utilized the Geant4-DNA code and DNA PDB format to compute the damages caused by 0.1-20 MeV protons.Their investigation focused on assessing the effects of high-Z nanoparticles on radiation induced DNA damage.Zhu et al (2022) estimated proton-induced early DNA damages in a solenoid chromatin fiber model using Geant4-DNA.The MCDS-calculated DNA damage yields are published in several published literatures (Semenenko and Stewart 2004, Semenenko and Stewart 2006, Stewart and Semenenko 2008, Stewart et  The current study bridges a gap in the existing body of published literatures.While numerous studies explored the effects of ionizing radiation on DNA damage, they have often been focused on specific energy ranges and types of particles, using various clustering algorithms to correlate Monte Carlo track structure code outputs with DNA damage probabilities.The present study extends this research by providing a comprehensive investigation across a wide range of kinetic energies of protons (0.1-100 MeV/u), helium ions (0.13-100 MeV/u), and carbon ions (0.5-480 MeV/u).The study employs the Geant4-DNA code coupled with an adapted DBSCAN clustering algorithm to estimate yields of SSB, DSB, and complex Double-Strand Breaks (cDSB) induced by these particles.Note that energy domain considered in the study for protons and carbon ions has relevance in cancer therapy whereas study on helium ions is of theoretical interest.In addition, MCDS (Monte Carlo Damage Simulations) code is employed, and the results are compared against those obtained from the Geant4-DNA code.Moreover, the study goes beyond existing research by exploring the impact of tissue oxygenation levels on DNA damage using MCDS code.

Materials and methods
Geant4-DNA calculations Geant4-DNA A small 1 μm × 1 μm × 0.5 μm box filled with liquid water is considered as target volume.The particle beam is incident perpendicularly on the 1 μm × 1 μm surface of the target volume.The simulation geometry is consistent with that used by Francis et al (2011b).The box target is placed within a WORLD volume which is vacuum.Present study considered (a) Proton beams ranging from 0.1-100 MeV/u, (b) helium ion beams ranging from 0.13-100 MeV/u (i.e.0.5-400 MeV) and (c) carbon ion beams ranging from 0.5-480 MeV/u.Geant4-DNA track structure code is used to score energy deposited in the target volume on event-by-event basis.Geant4-DNA is low energy extension of Geant4 toolkit.The present study used Geant4 version 10.06.p03 (Agostinelli et al 2003).The details of Geant4-DNA physics are described elsewhere (Incerti et al 2016, Kyriakou et al 2021).'G4EmDNAPhysics' physical constructor is used for the simulations.It can simulate electrons (up to 1 MeV), protons (100 eV-100 MeV), helium ions (1 keV-400 MeV) and heavy ions (0.5-10 6 MeV/u) (Incerti et al 2016, Kyriakou et al 2021).The physics interactions taken into account are: (a) ionisation, excitation and elastic collisions for electrons, (b) ionisation, excitation and charge transfer for protons and helium ions, and (c) ionisation for heavy ions (Incerti et al 2016, Kyriakou et al 2021).Depending on the kinetic energy, 5 × 10 4 to 10 5 primary particle tracks are simulated in multi-threaded mode for each charged particle/ion.As guided by Francis et al (2011b), the incident charged particle should have sufficient kinetic energy to cross the target thickness of 0.5 μm and accordingly the lower limit of the kinetic energy of protons, helium ions and carbon ions are selected for this study.

DBSCAN algorithm
The DBSCAN clustering algorithm is described in details elswhere (Francis et al 2011b, Francis andStypczynska 2013).This algorithm uses output data file of Geant4-DNA simulations along with userdefined input parameters such as SPointsProb, EMin-Damage, EMaxDamage, Minpts and eps.The output data file of Geant4-DNA simulations contains the particles event number, the three-dimensional coordinates of the interaction location and its energy deposit.Note that an event corresponds to a primary particle track with all its secondaries.For every event and for every interaction, a random sampling is carried out using SpointsProb and the linear damage induction function.The first step is to identify damage coordinates and strand locations.In the second step, the clustering DBSCAN (Sander et al 1998) algorithm is used to identify the potential clusters of damages in the medium.At this step, the algorithm uses two userdefined parameters; eps and MinPts.Present study considered, MinPts = 2 since at least 2 SSBs are required to form a DSB and eps = 3.2 nm which represents approximately 10 DNA base pairs distance.Note that, in radiobiology two SSBs are considered a DSB if they are separated by less than 10 base pairs corresponding distance∼3.2 nm.As the DNA molecule has 2 strands, each damage is randomly assigned to one strand with equal probability.The obtained clusters of damages were classified into different types as follows: • SSB: isolated damages with no neighbours, • DSB: Clusters containing 2 or more SSBs located within 10 bp corresponding distance (∼3.2 nm) and at least one SSB is located on an opposite strand.
• Complex or clustered DSB: formed by at least one DSB and one SSB located within the mentioned maximum distance (∼3.2 nm), they can get more complex with increasing concentration of any damage within the mentioned area.
The parameter, SPointsProb represents the uniform probability that an interaction point is situated in a sensitive region capable of directly or indirectly affecting DNA.SPointsProb is an adjustable parameter and is essentially the ratio of the volume occupied by these sensitive areas within the medium to the total volume of the medium itself.DBSCAN approach does not take into account the full chemical diffusion and DNA geometry modelling.However, they are accounted for through different parameters (Francis and Stypczynska 2013).It is considered that the DNA is homogenously occupying 11% of the nucleus volume and any energy deposition sufficiently close to DNA can cause indirect damage through the diffusion of free radicals.Thus, DBSCAN considers a geometrical cross section that an energy deposition could fall in a sensitive area.This cross section is assumed to occupy about 5% of the nucleus volume and is known as an 'aura' around the DNA.Finally, 16% of the irradiated nucleus (SPointsProb = 16%) is considered as sensitive volume (Francis and Stypczynska 2013).
In the present study, a linear damage induction function similar to the one used by Friedland et al (2008)  Taking into account that not every particle-DNA interaction leads to DNA damage, the probability of damage induction is taken as a linear function increasing with the energy deposit value at the considered interaction locations.It's worth noting that the induction of damage resulting from relatively low-energy deposits (less than 5 eV) is still a subject of ongoing debate (Francis et al 2011b).The reason for this debate lies in the fact that, theoretically, energy deposits of such small magnitudes do not correspond to ionizing collisions but instead represent different modes of excitation.In some instances, when a water molecule becomes excited, it can break down into chemically reactive species, which may indirectly cause damage to DNA molecules (Francis et al 2011b, Francis andStypczynska 2013).However, there is currently no definitive evidence to establish the impact of these low-energy deposits on DNA strands.

Calculation of DNA damage yield
The yield, Y of DNA damage per Gy per Giga base pair (Gy −1 Gbp −1 ) in terms of SSB, DSB or cDSB is calculated as per the equation given below: Where, N bp and D tot are total number of base pairs in the target volume and total absorbed dose in Gy, respectively.N eff is the effective number of SSB or DSB or cDSB and is given by: Spoints Prob total number of SSB or DSB or cDSB 3 eff Note that The Geant4-DNA in combination with DBSCAN algorithm provides histogram of SSB, DSB and cDSB clusters.The area under these SSB, DSB and cDSB histogram is the total number of SSB, DSB and cDSB, respectively.To achieve optimal results, we set the value of SPointsProb = 0.16 (16% of the primary clusters are used for calculating yield), as used by Francis et al (2011b).
The present study calculated yields of DNA damages in human fibroblast cell which is a diploid cell.The number of base pairs in typical human fibroblast cell is around 6.4 Gbp within a nucleus volume of ∼ 500 μm 3 (Sakata et al 2020, Kalospyros et al 2021).Thus, the base pair density (r bp ) = 1.28 × 10 −2 Gbp/μm 3 .The volume of the target is 0.5/μm 3 .Thus, N bp = 6.4 ×10 −3 Gbp.Hereafter, yields of SSB, DSB and cDSB will be denoted as Y SSB , Y DSB and Y cDSB , respectively.

MCDS calculation
The present study utilized MCDS VERSION 3.10A (December 5, 2011).The MCDS algorithm is very fast compared to other Monte Carlo track-structure simulations and it is described in detail elsewhere (Semenenko andStewart 2004, Semenenko andStewart 2006).The MCDS generates spatial maps of the damaged nucleotides forming many types of clustered DNA lesion, including SSB, DSB as well as individual and clustered base damages.This code implicitly account for both direct and indirect DNA damage mechanisms.This code neglects the DNA damage due to bystander effect.The code has the capability to simulate damage induction for neutral particles (photons and neutrons), electrons, and charged particles with atomic number, Z = 1 -26 (Hsiao and Stewart 2007).It can simulate damage induction for arbitrary mixtures of charged particles.MCDS can simulate the effects of oxygen on the induction of clustered DNA lesions (Stewart et al 2011b).The minimum allowed kinetic energy depends on the particle type (faculty.washington.edu/trawets/mcds/table1.html).The minimum allowed kinetic energy for protons, helium ions and carbon ions are 6.47 keV, 0.294 MeV and 14.8 MeV, respectively.
MCDS-based calculation was carried out to estimate yields of SSB and DSB for monoenergetic protons (0.1-100 MeV), helium ions (0.5-400 MeV) and carbon ions (1.25-480 MeV u −1 ).To investigate the effect of oxygen on the yields of DNA damage, O 2 concentrations of 100%, 21% and 2% were considered.Note that O 2 concentrations of 100%, 21% and 2% represent fully oxic, normoxic and anoxic cells, respectively.Both the parameters AD (absorbed dose) and DNA (DNA content of cell nucleus in Gbp) were set as 1 to obtain the yield of DNA damage in units of clusters per Gy per Gbp.The present MCDS-based calculations used the default parameter values: s sb = 217 Gy −1 Gbp −1 , f = 3, n min = 9 bp and n dsb = 10 bp, where σ Sb is the number of individual strand breaks per unit dose per amount of DNA in the cell, f is the ratio of base damage to strand breaks, n min is minimum distance between clusters (in bp) of undamaged DNA from neighbouring elementary damages and n dsb is maximum distance between two SSB to compose a DSB (Stewart et al 2015, Kalospyros et al 2021).σ Sb and f relates absorbed dose to the number of individual lesions (strand breaks).The parameter n seg denotes DNA segment length in the unit of (bp Gy −1 cell −1 ).n seg is calculated using the following relation (Stewart et al 2011b): is the number of lesions to be distributed within the segments (Stewart et al 2011b).Finally, the grouping of the lesions into SSB and DSB clusters is determined by the paramener n min .
The algorithm for simulating the effect of oxygen on the formation of individual and clustered DNA lesions is described in details elsewhere (Stewart et al 2011b).The main steps are listed below: Step 1: Based on the above-mentioned algorithm, initial location of DNA radicals, the radicals and lesion clustering effects were simulated depending on the structure of individual particle tracks.
Step 2: This step determines the probability with which a DNA radical is reduced by a thiol group within the cellular environment rather than fixed by O 2 (oxygen fixation hypothesis).The fraction of the initial DNA radicals removed through the above-mentioned chemical repair process is determined as below: M x is modelled based on the empirical formula as given below: Here, M 0 determines the maximum fraction of DNA radicals that can be removed through chemical repair and ( ) / q x r corrects the changes in the effectiveness of the chemical repair with radiation quality (Stewart et al 2011b).When ( )  q x M x , approaches the asymptotic value M .
0 With the increase in LET, / q x decreases, ( ) M x approaches unity and oxygen fixation is maximized.The default values of M , 0 q, K and r are 1.740, 946.10, 0.3372 and 2.15, respectively.
Step 3: It is assumed that all the DNA radicals created in Step 1 are equally likely to be removed through the chemical repair process.

Results
Kinetic energy versus LET For assessing the biological impact of charged particles, LET proves to be a more accurate measure compared to their kinetic energy.Figure 1 illustrates how LET of different particles such as protons, helium ions, and carbon ions in water varies as a function of their kinetic energy.It is evident that, for a specific type of particle, LET decreases as its kinetic energy increases.Furthermore, when comparing charged particles with different Z and same kinetic energy, it becomes apparent that charged particles with high Z consistently exhibit higher LET values than their low Z counterparts.In this context, carbon ions have the highest LET, while protons have the lowest.
In the present study, the LET as a function of kinetic energy of each charged particle is calculated using MCDS code at the entrance surface of the target geometry.Thus, the LET represents the linear electronic stopping power of the charged particle in water medium.This study considered a unique geometry setup for both high-and low-energy ions where charged particle beam is directly incident on the sensitive volume.Auxiliary simulations have been carried out in MCDS to investigate the change of LET between the entrance of the fibroblast cell and entrance of its nucleus.The results show that the difference between the LET at the entrance of cell and that at the entrance of nucleus goes up to 19% for 0.1 MeV protons and 0.5 MeV helium ions.However, LET at the entrance of cell is comparable (within 4%) to that at the entrance of the nucleus for 0.5 MeV protons, 1 MeV helium ions and 6 MeV carbon ions.Above these energies, change in LET at the nucleus surface with respect to the entrance of the cell is negligible.Thus, linear electronic stopping power may be considered as a good approximation of track-averaged LET for protons above 0.5 MeV, helium ion above 1 MeV and carbon ion above 6 MeV.

Variation of SSB, DSB and cDSB clusters with particle type
The DBSCAN linked with Geant4-DNA generates histograms of SSBs, DSBs and cDSBs.The area under a given histogram represents the total number of corresponding events (SSBs or DSBs or cDSBs).In the present study, normalized cluster distributions for SSB, DSB, and cDSB are obtained by normalizing the number of events in each bin with respect to the total number of corresponding events.Thus, the cluster distribution is the plot of number of events (SSB or DSB or cDSB) along X-axis and normalised frequency along Y-axis.
Figure 2 shows Geant4-DNA-calculated normalized cluster distributions for SSB, DSB, and cDSB for protons, helium ions, and carbon ions having kinetic energy of 5 MeV/u.Despite having the same kinetic energy, these particles exhibit distinct characteristics in the shape of their cluster distributions, including both peak height and peak position.One noteworthy trend is that the cluster distributions for all types of DNA damage (SSB, DSB, and cDSB) are consistently shifted towards higher values when heavier charged particles, such as carbon ions, are involved.Furthermore, there is a clear reduction in the peak height of these cluster distributions as the charge of the particle increases.Thus, figure 2 underscores the substantial differences in DNA damage patterns caused by particles with the same kinetic energy but varying charges.Note that in both Geant4-DNA and MCDS codes, the charge states for proton, helium ion and carbon ion are 1 H 1+ , 4 He 2+ and 12 C 6+ , respectively.Specifically, heavy charged particles are shown to have a heightened ability to induce DNA damage when compared to their lighter counterparts with same kinetic energy.Thus, although the LET of proton, helium ions and carbon ions are comparable, the incident kinetic energies (K.E) of these particles are different (K.E of proton < K.E of helium ion < K.E of carbon ions).This difference in the initial kinetic energy of these particles leads to differences in the delta electron frequency distribution.Auxiliary simulations were carried out to investigate the frequency distribution of delta electrons in water produced by 2 MeV/u protons, 12.5 MeV/u helium and 200 MeV/u carbon ions.Figure 4 presents the normalised frequency distributions of delta electrons (normalised with respect to total frequency) produced by protons, helium ions and carbon ions with comparable LET values within 1 μm × 1 μm × 0.5 μm water-filled target box.The figure shows that the frequency of delta electrons in the energy range of 30 eV-1 keV is higher in the case of 2 MeV/u protons when compared with that produced by 12.5 MeV/u helium and 200 MeV/ucarbon ions.In the case of helium and carbon ions, frequency of delta electrons is comparable up to 100 eV and thereafter bin-wise yield of helium ions is marginally higher as compared to those with carbon ions.The differences in the frequency distribution of delta electrons as discussed above leads to the differences in the particlespecific SSB, DSB and cDSB cluster distributions.
Variation of yields of SSB and DSB with LET Figure 5 displays the changes in yields of DSB and SSB in human fibroblast cells, calculated using the Geant4-DNA model for protons with different LET.This figure also incorporates DSB and SSB yields calculated by MCDS for fully-oxic, normoxic and anoxic cells.Figures 6 and 7 present analogous data, but for helium and carbon ions, respectively.The key findings are as below: • Protons (figure 5): (i) Y DSB is relatively insensitive to the change in LET in the range of 0.7-5 keV/μm, (ii) above 5 keV/μm Y DSB exhibits an increase as the LET increases, and (iii) Y SSB remains insensitive to LET in the range of 0.7-5 keV/μm and then starts decreasing in the range of 5-80 keV/μm.Cellular survival is significantly affected by high LET radiation in contrast to low-LET radiation.High-LET radiation is characterized by its condensed energy deposition pattern, which results in closely spaced DSBs (Roobol et al 2020).The high frequency of multiple DSBs occurring in close proximity within the cell nucleus offers a explanation for the higher biological effectiveness of high-LET radiation when compared to low-LET radiation (Roobol et al 2020).
In the case of protons and helium ions the MCDScalculated Y DSB consistently exhibits lower values when compared to the corresponding yields calculated by the Geant4-DNA model.This trend is also observed in Y DSB induced by carbon ions up to = 300 keV/μm.However, in the case of Y SSB for proton, helium ions and carbon ions, an interesting pattern emerges (figures 5-7).The Geant4-DNA-calculated Y SSB are higher than the corresponding MCDS-based yields for oxic and anoxic cells in the LET range of 0.7-40 keV/μm, 2-80 keV/μm and 10-40 keV/μm, respectively.Beyond these ranges, the trend reverses, and the Geant4-DNA-calculated Y SSB become lower than the corresponding yields.

Variation of DNA damage yields with tissue oxygenation
The MCDS-calculated values consistently demonstrate that, for all investigated particles (protons, helium ions, and carbon ions), the Y DSB is lower for anoxic cells when compared to the corresponding yield for oxic cells (see figures 5-7).Y SSB are lower in anoxic cells as compared to oxic cells in the LET range of 0.7-40 keV/μm for protons, 2.8-90 keV/μm for     helium ions and 10-100 keV/μm for carbon ions.Beyond the above-mentioned LET range for a given particle, the yields for both anoxic and oxic cells become comparable (see figures 5(b)-7(b)).
Many tumors contain poorly oxygenated hypoxic regions that exhibit resistance to radiotherapy (Thomlinson and Gray 1955).Patients with highly hypoxic tumors generally have worse prognoses compared to those with well-oxygenated tumors (Nordsmark et al 2005, Lomax et al 2013).Favaudon et al (Favaudon et al 2022) discussed on the role of tissue oxygenation in FLASH radiotherapy.The radiosensitizing impact of oxygen (O 2 ) can be partly elucidated by its rapid reaction, occurring within milliseconds, with radiation-induced DNA radicals.Ionizing radiation causes DNA damage through indirect and direct damage mechanisms (Chang et al 2021, Chan et al 2021, Favaudon et al 2022).In indirect damage, ionizing radiation interacts with water molecules in the cellular environment and produces ROS (Reactive Oxygen Species) and free radicals which can damage DNA.Normally cells have repair mechanism to fix DNA damage.However, if oxygen is present, it reacts with these free radicals before the cell is repaired and creates even more damaging molecules like peroxyl radicals which can cause permanent DNA damage.With the increase of the concentration of oxygen, the yield of peroxyl radicals increases.This mechanism is called oxygen fixation hypothesis (Chan et al 2021, Chang et al 2021).Direct damage occurs when ionizing radiation directly interacts with the DNA molecules, causing alteration to its structure.The contribution of indirect damage mechanism is more in the case of low LET radiation and with the increase of LET, relative contribution from direct damage mechanism increases as compared to indirect damage.As direct damage is independent of oxygen concentration of the cell, the relative differences of the yields of DSB and SSB between anoxic and oxic cells become smaller with increasing LET.

Variation of cDSB yield with LET
Figure 8 shows the yields of Geant4-DNA-calculated cDSB in human fibroblast cells, illustrating their relationship with the LET of proton, helium ions, and carbon ions.For both protons and helium ions, Y cDSB remains almost insensitive to changes in LET when LET is below 5 keV/μm.Within 5-80 keV/μm, Y cDSB for proton, helium ions, and carbon ions exhibits an increase as LET increases.In the case of helium and carbon ions, the trend is slightly different.For helium and carbon ions, the Y cDSB increases with LET up to the LET range of 90 and 161 keV/μm, respectively.However, beyond that ion-specific LET range, there is a decrease in the yield as LET continues to increase.The proton-induced Y cDSB is systematically higher than that induced by helium and carbon ions.The proton induced cDSB cluster distribution is significantly different from the corresponding distribution induced by helium and carbon ions with comparable LET to that of protons (see figure 3).The increased frequency of lower energy electrons produced by protons as compared to helium and carbon ions with comparable LET (see figure 4) causes more damage closer to the track.Thus, for a given LET, the proton-induced Y cDSB is systematically higher than that induced by helium and carbon ions.The introduction of ion therapy, utilizing ions such as 12 C 6+ , necessitates the consideration of cDSB which pose greater challenges for repair (Lomax et al 2013).Thus, consideration of cDSB in ion therapy may lead to an increased relative biological effectiveness (RBE) (Lomax et al 2013).

Mathematical form of DNA damage yields
The Geant4-DNA calculated yields of DNA damage such as SSB and DSB as a function of LET for protons, helium ions, and carbon ions are fitted using the nonlinear least squares method based on the Levenberg-Marquardt algorithm.The resulting fitted equations for these particles are as follows: The Geant4-DNA calculated yields of cDSB for protons, helium ions and carbon ions as a function of their LET are represented by the following equations: p H e and so on, represent the yields of SSB, DSB and cDSB for the respective particles.Note that, in the equations (7)-( 15), suffix 'p', 'He' and 'C' represents protons, helium ions and carbon ions, respectively.
The goodness of fit parameters (R 2 ) for equations (7)-( 9) are 0.999, 0.999, and 0.988, respectively.Similarly, for equations (10)-( 12), the R 2 values are 0.998, 0.994, and 0.999, respectively.In the case of equations ( 13)-( 15), the R 2 values for equations are 0.996, 0.998 and 0.988, respectively.Table 1 presents a comparison of Y SSB , Y DSB and Y cDSB obtained from the above equations and corresponding Geant4-DNA simulated values.According table 1, particle-specific maximum deviation between the equationderived and Geant4-DNA simulated values are: (a) 6% in 0.85 keV/μm proton-induced Y DSB , (b) 7% in 3.59 keV/μm helium ion-induced Y DSB and (c) 5% in 19.46 keV/μm carbon ion-induced Y SSB .These high R 2 values and the comparison shown in table 1 indicate that the fitted equations provide reasonably good representation of relationship between LET and Y SSB , Y DSB and Y cDSB for within the investigated range of LET values.

Ratio of DSB to SSB
Figure 9 presents Geant4-DNA-based ratio DSB/SSB for protons, helium ions and carbon ions as a function of LET.The figure also includes DSB/SSB ratio calculated using MCDS for both fully-oxic, normoxic and anoxic cells.The DSB/SSB ratio remains relatively insensitive to LET within specific LET ranges: (a) 0.7-10 keV/μm for protons, (b) 2-30 keV/μm for helium ions, and (c) 9-30 keV/μm for carbon ions.Beyond these LET range, the ratio increases with LET for protons and helium ions.Beyond 9-30 keV/μm of carbon ions, MCDS-calculated DSB/SSB increases with LET, and Geant4-DNA-calculated DSB/SSB increases up to 271 keV/μm and then decreases with increasing LET.In terms of kinetic energy, protons above 60 MeV/u, helium ions above 12 MeV/u, and carbon ions above 100 MeV/u exhibit comparable DSB/SSB ratios.In essence, in the high-energy region, DNA damage induced by protons, helium ions, and carbon ions shows similar characteristics.The Geant4-DNA-and MCDS-based DSB/SSB ratios demonstrate good agreement up to: (a) LET of 40 keV/μm for protons and helium ions, and (b) LET of 20 keV/μm for carbon ions.Beyond the above-mentioned particle-specific LET values, a notable deviation in the ratio is observed between these codes.The figure also shows that the cellular oxygenation level does not affect the ratio significantly.Note that the DSB/SSB ratio provides more insight of the Table 1.Comparison between the DNA damage yields (Y SSB , Y DSB , Y cDSB ) calculated using equations ( 7)-( 15) and the corresponding Geant4-DNA-calculated values.

Discussions
Simulating DNA damage with a detailed consideration of the DNA double-helix structure can provide exceptionally precise and accurate descriptions of the underlying events.However, it is worth noting that these simulations can be computationally intensive and time-consuming, often necessitating complex computing clusters to execute effectively (Francis and Stypczynska 2013).In response to these challenges, alternative approaches have been explored to simplify DNA damage simulations.Some of these approaches involve statistical methods (Garty et al 2010), while others utilize data mining clustering algorithms (Francis et al 2011a).These methods depart from the detailed geometric configuration of DNA and instead rely on approximate statistical analyses, which can still yield relatively good results.In such simulations, water is frequently employed as an approximation for biological tissue.This choice is based on the fact that water is the primary component of living organisms, and calculations of interaction cross sections are relatively simpler for water compared to the more complex bio-compounds found in living systems (Francis and Stypczynska 2013).This simplification allows for more computationally efficient simulations while still providing valuable insights into the radiation-induced effects on DNA and biological tissues.Table 2 provides a comparison between the yields of DSB and SSB for protons and helium ions in human fibroblast cells as calculated by the Geant4-DNA model and published data (Francis et al 2011b, Friedland et al 2003, de la Fuente Rosales et al 2018, Sakata et al 2020, Nikjoo et al 2016).The overall agreement between the two sets of data is reasonably good.It is important to note that slight discrepancies may arise due to variations in the codes used, different DNA models employed by various authors, and the utilization of distinct cross-section libraries of different codes in these calculations.Table 2 shows that the deviation between Geant4-DNA-calculated yields with the corresponding PARTRAC-based yields reported by Friedland et al (Friedland et al 2003) is relatively higher at lower proton energies (0.5-2 MeV) as compared to higher proton energies.This may be due to the fact that Friedland et al (Friedland et al 2003) tracked protons down to 1 keV whereas in the present study the protons are tracked down to 100 eV kinetic energy.Additionally, the low energy proton produces secondary electrons in the range of few eV at which excitation and vibration of water molecules are the important interactions.The code-wise variation of cross-sections and physics models of these two interactions may also contribute to larger deviations at lower proton energies.Comparison with published data reaffirmed the reliability of the computational models and methods employed in this study.In the present study, the Geant4-DNA-calculated Y DSB for carbon ions increases with LET, reaching a maximum value of 31 Gy −1 Gbp −1 at ∼ 200 keV/μm, and then it a decreasing trend, with value of about 12 Gy −1 Gbp −1 at ∼ 836 keV/μm.A similar trend is observed for helium and carbon ions-induced Y cDSB .Both the Geant4-DNA coupled with DBSCANestimated yield of DNA damage arises from the combined effect of direct and indirect damage mechanisms.At low and medium LET, the majority of Strand Breaks (SB) arises from indirect effects and at high LET direct effects become dominant.The reduction in indirect effects with increasing LET occurs because of mutual reactions among the byproducts of water radiolysis (recombination of free radicals) within the condensed tracks of low-energy (i.e.high LET) ions (Friedland et al 2017, de la Fuente Rosales et al 2018, Bordeaux 2021).Similarly, the decrease in DSB or cDSB from direct effects at high LET (> 200 keV/μm) is due to the delivery of energy to the DNA molecules, or its hydration shell, at a density surpassing the threshold required for the breakage (Friedland et al 2017).Consequently, the extra energy is wasted which is known as overkill effect.Thus, the dip in carbon ioninduced Y DSB after 200 keV/μm, and dip in Y cDSB induced by helium and carbon ions beyond 90 and 120 keV/μm, respectively is due to the combined effect of recombination of free radicals and overkill effect.Friedland et al (Friedland et al 2017) calculated Y DSB induced by proton, helium, carbon, oxygen and neon ions having kinetic energies 0.25-256 MeV/u using Monte Carlo track structure code PARTRAC.The observed variations in Y DSB with the LET of protons and helium and carbon ions in the present study align closely with those demonstrated by Friedland et al (Friedland et al 2017).In addition to Geant4-DNA coupled with the DBSCAN algorithm, present study used MCDS code to calculate the yields of DSB and SSB within the nuclei of human fibroblast cells.The MCDS code is used because of its simplicity and its results production swiftness (Kalospyros et al 2021).This code has been developed to predict the initial yield and types of DNA damage formed by a given ionising radiation.In addition to easy-to-use algorithm, MCDS is much faster compared to conventional track structure simulations (it can give results within seconds to minutes) (Semenenko and Stewart 2004).It does not have the accuracy of other Monte Carlo-based track structure (MCTS) codes, but it can yield major trends in the spectrum of DNA damage predicted by other detailed MCTS simulations (Kalospyros et al 2021).The DSB and SSB yields obtained through MCDS for oxic cells exhibit reasonably good agreement with the Geant4-DNA based calculations.However, some deviations are observed depending on the energy and particle type.For DSB yields, deviations range between 4%-18% for protons, 6%-22% for helium ions and 15%-25% for carbon ions.Similarly, for SSB yields, deviations fall within the range of 4%-7% for protons, 2%-11% for helium ions and 1%-14% for carbon ions.These variations may be attributed to the dissimilarities in the calculation algorithms employed by both codes.Unlike Geant4-DNA, MCDS does not reproduce the dip in Y DSB of carbon ions beyond 200 keV/μm.Note that Friedland et al (Friedland et al 2017) also showed that the MCDS-based Y DSB for low energy (i.e.high LET) ions differs significantly from that calculated using Monte Carlo-based PARTRAC code.It is important to note that Geant4-DNA operates as a Monte Carlo track structure code, while MCDS utilizes quasi-phenomenological models for its calculations (Kalospyros et al 2021).These distinctions in calculation methodologies may be the reasons for the observed differences in the computed DSB and SSB yields, across particle energy and particle types.

Conclusion
The present study provides valuable insights into the complex relationship between ionizing radiation such as protons (0.1-100 MeV/u), helium ions (0.13-100 MeV/u) and carbon ions (0.5-480 MeV/u), its LET, and the resulting DNA damage in human fibroblast cells.Using Geant4-DNA model coupled with the DBSCAN algorithm and MCDS code, the study sheds light on the impact of protons, helium ions, and carbon ions on DNA damage induction within cellular nuclei.The study reveals that the LET of the charged particles is a critical factor influencing the type and extent of DNA damage.The study also shows that Y SSB , Y DSB and Y cDSB are influenced by the LET of the incident particles, with distinct trends observed for different particles.Carbon ion-induced Y DSB increases with LET, reaching a maximum value of 31 Gy −1 Gbp −1 at ∼ 200 keV/μm, and then it decreases to 12 Gy −1 Gbp −1 at ∼ 836 keV/μm.A similar trend is observed for helium and carbon ionsinduced Y cDSB .The maximum value of Y cDSB is about 18 Gy −1 Gbp −1 at ∼ 90 keV/μm of helium ions and 17 Gy −1 Gbp −1 at ∼ 161 keV/μm of carbon ions.Proton-induced Y DSB and Y cDSB continuously increases with LET up to about 77 keV/μm.The study also highlights the oxygen sensitivity of DNA damage, with anoxic cells exhibiting lower yields of both DSB and SSB compared to oxic cells.Furthermore, this study introduces the concept of cDSB which shows that the carbon ions yielded lesser number of cDSBs compared to protons having comparable LET.
Overall, present study contributes to understand the radiation-induced DNA damage and its dependence on particle type, LET, and cellular oxygenation.Such knowledge is crucial for applications in radiation therapy, radiobiology, and radiation protection, as it helps in optimizing treatment strategies and assessing the potential risks (mutations and chromosomal aberrations) associated with exposure to ionizing radiation.
measured yields of SSB and DSB after irradiating a plasmid DNA with 1.03, 19.3 and 249 MeV protons, 26 MeV helium nuclei and γ-rays ( 137 Cs or 60 Co).Francis et al (2011b) focused on calculating DNA damage clusters resulting from proton irradiation in the energy range of 0.5 -50 MeV.(Dos Santos et al 2013) conducted an evaluation of how chromatin density influences the formation of clustered damages caused by protons within the nuclei of fibroblast and endothelium cells in the G0/G1 phase.Villagrasa et al (2017) investigated the correlation between the number of radiationinduced DSB in DNA molecules and the probability of detecting nuclear foci after targeted microbeam irradiation of cells with protons (23 keV/μm) and alpha particles (37, 90, and 160 keV/μm).Francis et al (2011b), Dos Santos et al (2013) and Villagrasa et al (2017) used Geant4-DNA code coupled with adapted Density Based Spatial Clustering Algorithm with Noise (DBSCAN) algorithm.Friedland et al (2017) evaluated DNA damages induced by light ions (0.25-256 MeV/u) using PAR-TRAC track structure code.de la Fuente Rosales et al (2018) assessed the physical, pre-chemical, and chemical phases of damage to calculate the early DNA damage induced by protons (0.5-30 MeV) and α-particles (2-10 MeV) in liquid water.Moeini et al (2020) focused on studying damage in the form of SSBs and DSBs by simulating the transportation of primary alpha particles (2-20 MeV) and the resulting secondary particles in liquid water using Geant4-DNA code.Mokari et al (2020) investigated direct and indirect DNA damage caused by electrons in the energy range of 0.011-100 keV using Geant4-DNA code.Sakata et al (2020) developed a Geant4-DNA based 'fully integrated' Monte Carlo simulation framework that calculates both early DNA damage and subsequent biological responses over time.This unique platform also incorporates a Biological repair model (Sakata et al 2020).
al 2011a, Stewart et al 2011b, Wang et al 2012, Frese et al 2012, Hsiao et al 2014, Kalospyros et al 2021).Chan et al (Chan et al 2021) used MCDS-calculated DSB yields to determine RBE of 62 MeV therapeutic proton beams along the central axis depths in water using cell survival as biological end-point.The author also estimated the cell repair outcomes using Monte Carlo Excision Repair (MCER) code.The role of tissue or cellular oxygenation on DNA damage and biological effectiveness of ionizing radiation is discussed by Lomax et al (2013), Chan et al (2021), Chang et al (2021) and Favaudon et al (2022).
is considered.As per this function, damage probability is 0 for energies below EMinDamage and increases linearly, reaching a probability of 1 at energies equal to or exceeding EMaxDamage.Present study used values of EMinDamage and EMaxDamage as 5 and 37.5 eV, respectively(Francis et al 2011b).The linear damage induction function ( ( )) P E dep is shown below(Zhu et al 2022) where E dep is energy deposited within the cell

Figure 3
Figure 3 presents Geant4-DNA-calculated cluster distributions for SSB, DSB, and cDSB for particles with comparable LET.Specifically, the LET values for these particles are as follows: protons with LET = 16.2 keV/μm (2 MeV/u), helium ions with LET = 15.1 keV/μm (12.5 MeV/u), and carbon ions with LET = 16.1 keV/μm (200 MeV/u).The noteworthy observations from figure 3 are: (a) the cluster distributions for protons are significantly different from that of helium and carbon ions although their LET values are comparable.and (b) for helium and carbon ions with comparable LET, the helium ions induced SSB, DSB, and cDSB cluster shows slight difference in the bin-wise yield as compared to the corresponding cluster produced by carbon ions.Thus, although the LET of proton, helium ions and carbon ions are comparable, the incident kinetic energies (K.E) of these particles are different (K.E of proton < K.E of helium ion < K.E of carbon ions).This difference in the initial kinetic energy of these particles leads to differences in the delta electron frequency distribution.Auxiliary simulations were carried out to investigate the frequency distribution of delta electrons in water produced by 2 MeV/u protons, 12.5 MeV/u helium and 200 MeV/u carbon ions.Figure4presents the normalised frequency distributions of delta electrons (normalised with respect to total frequency) produced by protons, helium ions and carbon ions with comparable LET values within 1 μm × 1 μm × 0.5 μm water-filled target box.The figure shows that the frequency of delta electrons in the energy range of 30 eV-1 keV is higher in the case of 2 MeV/u protons when compared with that produced by 12.5 MeV/u helium and 200 MeV/ucarbon ions.In the case of helium and carbon ions, frequency of delta

Figure 1 .
Figure 1.MCDS-calculated LET values of protons, helium ions and carbon ions as a function of their kinetic energy.

Figure 4 .
Figure 4. Normalised delta electron fluence spectrum produced by protons, helium ions and carbon ions with comparable LET within 1 μm × 1 μm × 0.5 μm water filled target box.Fluence in each bin is normalised with respect to the total fluence.

Figure 5 .
Figure 5. Geant4-DNA-and MCDS-calculated DNA damage yields in human fibroblast cells as a function of LET of protons: (a) DSB; (b) SSB.In the case of MCDS the yields are presented for fully oxic, normoxic and anoxic cells.

Figure 6 .
Figure 6.Geant4-DNA-and MCDS-calculated DNA damage yields in human fibroblast cells shown as a function of LET of helium ions: (a) DSB; (b) SSB.In the case of MCDS the yields are presented for fully oxic, normoxic and anoxic cells.

Figure 7 .
Figure 7. Geant4-DNA-and MCDS-calculated DNA damage yields in human fibroblast cells shown as a function of LET of carbon ions: (a) DSB; (b) SSB.In the case of MCDS the yields are presented for fully oxic, normoxic and anoxic cells.

Figure 8 .
Figure 8. Geant4-DNA model-based cDSB yields in human fibroblast cells as a function of LET of protons, helium ions and carbon ions.
details of radiation induced DNA damage(Sakata et al 2020).Higher DSB/SSB ratios, especially above: (a) 10 keV/μm for protons, (b) 15 keV/μm helium ions, and (c) 30 keV/μm for carbon ions, as observed in the present study, signify a more significant impact of radiation-induced DNA damage due to an increase in DSB yield.
Figure 10 compares Geant4-DNA calculated proton-induced Y SSB and Y DSB values with the corresponding published values (Zhu et al 2020, Sakata et al 2020, Zhu et al 2022).It should be noted that the data points from the mentioned published literatures are digitized using online Webplot digitizer software for comparison purpose.Although, there are differences in the absolute values which may be attributed to the differences in the simulated geometries, the trend is similar to those observed in the published literatures (Zhu et al 2020, Sakata et al 2020, Zhu et al 2022).Sakata et al (Sakata et al 2020) modelled realistic double helix structure of Human skin fibroblast cell DNA which was folded compactly by spherical histones and calculated early DNA damage due to protons using Geant4-DNA based realistic fully integrated code.Zhu et al (Zhu et al 2020) modelled a whole fibroblast cell nucleus with fractal DNA geometry using

Figure 9 .
Figure 9. Geant4-DNA-based DSB/SSB ratio as a function of LET for: (a) protons, (b) helium ions and (c) carbon ions.Also included MCDS-based DSB/SSB ratio for the above particles in fully oxic, normoxic and anoxic cells.

Figure 10 .
Figure 10.Comparison of proton induced DNA damage yields obtained from Geant4-DNA simulations with the data adapted from Zhu et al (Zhu et al 2020, Zhu et al 2022) and Sakata et al (2020).(a) Y SSB and (b) Y DSB . -1

Table 2 .
Description of published studies and comparison of Geant4-DNA calculated yields of SSB and DSB in the present study with the published data.Francis et al (2011b) estimated Y SSB and Y DSB for 0.5-50 MeV protons are comparable with that of present study (maximum deviation for Y DSB is about 10% at 1 MeV).Friedland et al (2003) calculated Y SSB and Y DSB for protons (0.5-50 MeV) using PARTRAC code.They used high order DNA target model for genome of a human fibroblast in its interphase for the calculations of yields.Friedland et al (2003) estimated proton induced Y SSB and Y DSB are comparable with the corresponding values in the present study.