Comprehensive database of track-structure simulations on DNA damage by H–Fe ions up to 1 GeV/u for space radiation biology

Abstract

Understanding biological effects of high-charge, high-energy (HZE) particles is critical for evaluating health risks of long-duration deep-space missions. To complement the scarce experimental data, PARTRAC track-structure simulations are reported on DNA damage induction by magnesium, silicon, calcium, titanium and iron ions with energies from 1 MeV/u to 1 GeV/u, abundant in space radiation. In addition, previous simulations for hydrogen to neon ions are extended to 1 GeV/u. The simulation results reproduce reference stopping power data. Simulated DNA damage yields agree with pulsed-field gel electrophoresis results and extend them to species and energies not directly addressed experimentally. The simulations also explain the large variability in experimental data by tracing it to detection limits and data analysis methods. With increasing ionisation density, the simulations predict an enhanced production of difficult-to-repair clustered lesions, short DNA fragments, and DNA damage response foci containing multiple DNA double-strand breaks. The simulations also indicate a shift from scattered to streaks or continuous foci along HZE tracks, reflecting a substantial increase in damage complexity and severity. The findings highlight the potential of PARTRAC as a valuable tool for mechanistic modelling and risk assessment in radiobiology for space research and other applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-55264-8.

Introduction

As space technologies advance, human missions are extending beyond the low Earth orbit, resulting in a prolonged exposure to ionizing radiation, including galactic cosmic rays (GCR)¹. GCR comprise high-charge, high-energy (HZE) particles, such as Fe and Ti ions, which are largely shielded by the Earth’s magnetic field but pose a significant biological hazard in deep space². HZE particles are particularly biologically effective due to their high ionization density and enhanced induction of clustered, difficult-to-repair DNA damage³. Exposure to GCR may lead to long-term health effects such as carcinogenesis or degenerative diseases^4–6. However, studies on GCR-induced biological effects are limited by challenges in replicating the full GCR spectrum and spatial damage complexity in terrestrial experiments⁷.

Computational approaches such as PARTRAC provide a complementary strategy, enabling detailed mechanistic modelling of DNA damage induction under simulated space radiation conditions. PARTRAC is a Monte Carlo track-structure simulation code developed to model the interactions of ionizing radiation at nanoscopic and microscopic scales⁸. The tool integrates knowledge from radiation physics, chemistry and biology. It has been extensively benchmarked against corresponding experimental data. It has been widely utilized to simulate the induction of DNA damage by diverse types of ionizing radiation. Although PARTRAC has mainly focused on radiation qualities relevant to radiotherapy and radiation protection under terrestrial conditions, its detailed modelling capabilities also make it a promising tool for advancing our understanding of radiation risks in space environments⁹.

This work aims to fill gaps in experimental data and knowledge on radiation biology of HZE particles, with emphasis on applications and implications in space research. To this end, PARTRAC was employed to simulate heavy ion tracks and the induced DNA damage for Mg, Si, Ca, Ti, and Fe as key species for space radiation research, across a wide range of energies, 1 MeV/u to 1 GeV/u. The previously published comprehensive database of simulations covering light ions from H to Ne^10,11 was extended herein to 1 GeV/u, also to cover the higher energy range relevant in the space radiation environment. The simulated stopping powers agree with ICRU data^12,13 and SRIM calculations¹⁴, providing a key radiation physics benchmark. The predicted yields of DNA double-strand breaks (DSBs) are in line with published pulsed-field gel electrophoresis (PFGE) data^15–18. The simulations serve as a means of extending the experimental results to ions, energies and/or damage types not directly addressed yet. HZE particles are predicted to induce high yields of DSBs located densely along the track, frequently producing very short DNA fragments, below typical detection thresholds of PFGE experiments. At the level of radiation-induced foci, formed by accumulation of DNA damage response proteins, this enhanced clustering of DSBs leads to merging of elementary foci into elongated ones and/or streaks; this is illustrated by a few exemplary tracks over a range of ionization densities. Finally, simulation results are shown on the yields of DNA single-strand breaks (SSBs), DSBs, their sites and DSB clusters. To facilitate applications across diverse fields, the results are presented in terms of three alternative descriptors used to capture radiation quality in space radiation protection, radiation biology, clinical radiotherapy and other applications, namely (starting) energy, linear energy transfer (LET), and effective charge over velocity squared, (Z_eff/β)².

Methods

To extend PARTRAC capabilities for space research and related applications, the previously published database of simulations^10,11,19 on initial DNA damage induced by light ions (H – Ne) was expanded herein to cover energies up to 1 GeV/u and to include five key heavy ions in GCR: Mg, Si, Ca, Ti, and Fe. As done standardly in track-structure simulations^8,10, first the physics processes were simulated, i.e. individual interactions of the primary particles as well as of all their secondary and higher-generation electrons. Then, the pre-chemical and chemical stages were modelled, namely the production of reactive species, their diffusion and mutual reactions. The induction of DNA damage was simulated, accounting for both energy depositions to DNA and radical attacks on DNA (leading to so-called direct and indirect effects of radiation, respectively). Finally, the resulting damage patterns were analysed. While also damage repair may be addressed in PARTRAC^20–22, this was not done in the present work, focusing on initial DNA damage only. The key methodological aspects are described below; additional details on PARTRAC methods are provided elsewhere^8,10.

Irradiation setup

Two different setups were used herein, a large-scale, liquid-water one for stopping power and a microscopic one for DNA damage simulations. The setup for stopping power simulations is illustrated in Fig. 1a. Ions were generated at the origin and propagated through liquid water until they lost 1% of their starting energy, at which point their tracking was stopped. The value of 1% energy loss was taken as a compromise between a sufficiently high value to assure reasonable statistics (i.e., a high-enough number of inelastic interactions) on the one hand, and a small-enough value not to largely reduce the energy and significantly affect the stopping power on the other hand. Due to the stochastic and discrete nature of radiation interactions, the actual energy loss slightly varied among individual ions tracked and slightly exceeded the targeted 1% of the starting energy. For each simulated track, the ratio of the actual energy loss to the actual track length was scored, giving the particle’s stopping power. The stopping power for a given ion species and starting energy was calculated as the mean across all simulated tracks, with its uncertainty assessed by the relative standard deviation (RSD; standard deviation divided by the mean). Per ion species and energy, simulations were performed in batches of 100 tracks, with further batches added until the RSD of the stopping power dropped below 1%. The resulting stopping power values were benchmarked against ICRU data^12,13. Since Ca and Fe ions are not included in the ICRU dataset, the corresponding simulations were compared to SRIM (version 2013)¹⁴ calculations; for lighter ions where the two reference datasets overlap, stopping powers from SRIM do agree with the ICRU data (not shown).

Fig. 1.

Simulation setup. Panel a: Stopping power assessment. Ions were started perpendicularly towards a liquid water layer and their tracks recorded until losing 1% of their starting energy. For each track, the actual stopping power was obtained as the ratio of the actual energy loss and the actual penetrated depth. The ion species- and energy-dependent stopping power was calculated as the mean over these values. Panel b: Setup for DNA damage simulations. Ions were started from a circular source tangential to the model cell nucleus (10 μm diameter sphere), perpendicularly to the source plane (arrows). Ions and secondary electrons leaving the world region (14.22 μm diameter sphere concentric with the nucleus) were no longer tracked. DNA damage was assessed by overlapping the tracks modelled in liquid water with a multi-scale 6.6 Gbp DNA model within the nucleus sphere (different chromosomes indicated by diverse colours).

The setup for DNA damage simulations was identical to that used for generating the previous database¹⁰ for light ions (H – Ne); it is schematically sketched in Fig. 1b. A human lymphocyte nucleus in G1/G0 cell cycle phase was modelled as a spherical volume with a diameter of 10 μm, containing 6.6 Gbp DNA in a multi-scale DNA model described below. Ions were started from randomly sampled positions within a circular source with a diameter of 10.09 μm tangential to the nucleus surface. Their direction was perpendicular to the source plane. Primary ions and all their secondary and higher-generation electrons were tracked. The total simulation world was defined as a larger sphere with a diameter of 14.22 μm, concentric with the cell nucleus and filled with liquid water. Particles leaving the world volume were no longer followed. However, especially low-energy electrons might have left the target volume (cell nucleus sphere) and re-enter it after experiencing large-angle scattering in the outer part of the world region. To avoid artefacts from an alignment of particle tracks and axes of chromatin building blocks, the ion source was randomly rotated, as done previously¹⁰. It should be noted that under this configuration, electronic equilibrium was not fully established. Furthermore, given the source size, some ions hit the nucleus by their penumbra regions only; however, ions were not included with impact parameter > 5.05 μm, though even they would induce some (low LET-like) DNA damage via secondary electrons.

Simulated were ²⁴Mg, ²⁸Si, ⁴⁰Ca, ⁴⁸Ti, and ⁵⁶Fe ions in energy-dependent equilibrium charge states, started at discrete energies of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1000 MeV/u. In addition, the previously reported results^10,11 for light ions (¹H, ⁴He, ⁷Li, ⁹Be, ¹¹B, ¹²C, ¹⁴N, ¹⁶O, and ²⁰Ne) with the same setup were extended by simulations for 1 GeV/u. With that, the extended database includes 14 ion species at 11 log-equidistant starting energies (154 data points).

To match the existing database of light ion-induced DNA damage^10,11 and its statistical power, the number of tracks simulated per ion species and starting energy ranged from 320 primary particles in the case of 1 MeV/u Fe ions to 4 × 10⁵ particles in the case of 1 GeV protons. Diverse DNA damage classes (specified below) were scored, and the simulated dose was calculated from total energy deposition to the model cell nucleus. Yields of DNA damage classes were calculated by dividing the scored numbers of lesions with the applied dose and the genomic content of the nucleus. Means and relative standard deviations were calculated.

Interaction cross sections for ions

The interaction between radiation and biological materials is simulated in PARTRAC by approximating these materials as liquid water⁸ (for photons, atomic composition of the material may be considered). For H and He, PARTRAC explicitly accounts for charge-changing processes using charge state-specific cross sections⁸, i.e. dedicated sets of cross sections for H⁺ and H⁰, and He²⁺, He⁺ and He⁰. For ions heavier than He, the cross sections are scaled from those of H (energy-dependent mixture of H⁺ and H⁰) at the same energy per unit mass, using the energy-dependent effective charge^10,23. The actual charge transfer processes for ions heavier than He are not explicitly simulated, but are reflected by their effective charge. Nuclear interactions and lateral scattering of ions are neglected. Only electronic interactions are considered for ions, and ion tracks are modelled as straight lines in PARTRAC⁸; due to their masses much larger than that of electrons, this straight-line approximation is not critical for ions, especially HZE particles. On the other hand, electron scattering is considered, leading to their tortuous paths.

Multiple ionizations play a significant role in the interaction of high-LET ions with biological matter. These ions may deposit substantial amounts of energy over very short distances, potentially leading to the ejection of multiple electrons from a single water molecule. Compared with single ionizations, this may result in an increased energy deposition, an altered spectrum of secondary electrons, and different molecular dissociation patterns^24–26. The studied heavy ions possess high LET values across their entire energy range, suggesting that multiple ionization might be a key factor influencing the resulting DNA damage. PARTRAC deals with multiple ionization events in an approximate way¹⁰, redistributing additional ionizations among neighbouring water molecules (‘delocalization’): As soon as the inelastic mean free path drops below 1 nm (a value sufficiently larger than the mean distance between molecules in liquid water, approx.²⁷ 0.3 nm), ionizations are laterally shifted and randomly distributed within a cylindrical volume whose radius is adjusted so that the mean ionization density is 1 per molecule. For instance, for 1 MeV/u Fe ions with a simulated LET of approximately 4000 keV/µm and inelastic mean free path of 0.013 nm, ionizations are laterally shifted by up to 0.86 nm. These redistributed ionizations are then processed using the pre-chemical and chemical modules for single ionization events²⁸.

DNA damage induction and classification

The existing multi-scale chromatin model in PARTRAC⁸ was used. Briefly, it includes an atomic model of DNA double helix, its winding over histones to form nucleosomes, further compaction into a 30 nm fibre, its loops within 1 Mbp spherical chromatin domains, arrangement of these domains into chromosomes, and of chromosomes into a lymphocyte nucleus in the G1/G0 phase of the cell cycle.

DNA damage was assessed by overlapping this DNA model with particle tracks simulated in liquid water as done standardly^8,10. The tracks included interactions of primary ions and their secondary and higher-generation electrons, as well as time-dependent distributions of reactive species from water radiolysis. Standard assumptions for both direct and indirect damage were used^8,10: For direct effects, the probability of inducing a strand break (SB) increased linearly from 0 to 1 with the energy deposited in a single sugar-phosphate group increasing from 5 eV to 37.5 eV. For indirect effects, the probability of SB was set at 65% per hydroxyl radical (^•OH) attack on the deoxyribose, with no other species assumed to cause indirect SBs. To mimic cellular environment such as glutathione, additional ^•OH scavenging was included⁸. Further, any reactive species hitting the histones was assumed to be scavenged. Radical attacks on DNA were integrated till 10⁻⁷ s post ion traversal.

DNA damage was classified according to the standard scheme^8,10: A double-strand break (DSB) was assumed to occur if both strands were broken within 10 base pairs. A DSB cluster was defined as two or more DSBs within 25 base pairs (an isolated DSB is not called a cluster). An isolated DSB or a cluster was treated as a single DSB site. Single-strand breaks (SSBs) were counted separately, resulting from SBs that were not a part of a DSB. Base damage was not included in the analysis.

The damage was evaluated on a track-by-track basis, without accounting for inter-track effects, such as separate SBs merging to form a DSB or DSBs induced by two or more tracks forming a DSB cluster. The results are expressed as the numbers of damage events per unit dose, as well as per-track yields. The assumption of a linear damage induction with dose holds true unless independent tracks overlap both spatially (at the nanometer scale) and temporally (at the nanosecond scale). Such overlaps occur at very high doses and/or very high dose rates, as potentially seen under FLASH conditions^29–31 but far from being relevant in the space radiation scenario investigated in this study.

Characterizing ion tracks by starting energy, LET, or (Z_eff/β)²

To maximize the applicability of this work across diverse fields, including space radiation protection, radiation biology, and clinical radiotherapy, the results are presented using three alternative descriptors widely used to capture radiation quality, namely the (starting) energy, linear energy transfer (LET), and effective charge over velocity squared, (Z_eff/β)². Particle type (atomic number Z) and energy (or their distributions for mixed fields such as GCR) are the primary quantities describing the radiation field. They are straightforward to simulate with general-purpose Monte Carlo codes for both simple and mixed fields, without or with shielding by diverse materials. On the other hand, in radiotherapy and radiobiology, it is LET (and lineal energy, its microdosimetry analogue) that is widely used to assess biological effectiveness of diverse radiation types and fields. The parameter (Z_eff/β)² serves as an important parameter for estimating cancer risk, as adopted by the U.S. National Aeronautics and Space Administration (NASA)^32,33.

In this study, LET was determined from the simulation results by dividing the total energy deposited within the nucleus by the mean chord length of the nucleus, which is equivalent to calculating it from the dose deposited to the nucleus and the ion fluence as done previously^8,10. This LET definition closely aligns with the concept of fluence-mean lineal energy in microdosimetry, with a target sphere of 10 μm diameter³⁴. It also shares similarities with restricted LET, which includes only secondary electrons below a certain energy threshold, and spatially restricted LET, which confines energy depositions to a cylindrical region of a specified radius around the ion track. These restricted forms of LET have been proposed to correlate with biological effects better than the traditional, unrestricted LET³⁵. For simplicity, the term LET is used throughout this work to refer to this specific, cell nucleus-centred definition. It is important to note that this LET does not assume electronic equilibrium due to the geometry and positioning of the radiation source. Moreover, for high-energy ions, this LET may differ significantly from the ion’s stopping power, which is defined solely by the particle’s energy loss, as high-energy secondary electrons may deposit considerable fractions of their energy outside the nucleus, both longitudinally and laterally.

This cell nucleus-based LET may be challenging to measure experimentally or simulate using other codes, in particular macroscopic radiation transport codes. Thus, for their broader applicability the results are also presented in dependence on the particle’s starting energy or (Z_eff/β)². The starting energy E refers to the energy at the tangential plane of the nucleus (entrance plane, Fig. 1b). The parameter (Z_eff/β)² is derived from the starting energy, where Z_eff is effective charge calculated by the Barkas formula³⁶,

1

and is ion’s velocity v relative to the speed of light c; it is related to the particle (kinetic) energy by , with m denoting particle mass. Note that, for simplicity, throughout this work the energy and hence also (Z_eff/β)² refer to the source (i.e., starting) plane. As the ion penetrates into the cell nucleus, its energy decreases, and (Z_eff/β)² increases; these variations are especially notable for low-energy ions.

Comparison of simulated DNA damage with PFGE experiments

The simulation outcomes on DNA damage were compared with experimental DSB data. A classical technique for assessing DSBs is pulsed-field gel electrophoresis (PFGE). It allows for the quantification of DNA damage by measuring the number of DNA fragments in specific size ranges. However, various approaches that somewhat differ in their outcomes exist for interpreting PFGE data, including the random breakage model^37,38, the generalized broken stick model³⁹, and methods based on analysing the fragmentation spectrum by counting fragments within specific size bins⁴⁰. Previous studies have shown that the assumption of randomly distributed DSBs does not hold for high-LET radiation, as their dense and localized energy deposition leads to clustered, non-random DNA breaks that deviate significantly from the assumptions of randomness^41–43. Therefore, in this study, the simulations were primarily benchmarked against PFGE results for human cells evaluated using the methods based on analysing the fragmentation spectrum, specifically by counting DNA fragments within defined size bins^15–18. These studies provide detailed information, including that on the lower and upper detection thresholds used. These thresholds were applied to the simulations as well. Specifically, the PARTRAC fragmentation analysis module^8,44, run after having simulated the DNA damage induction, scans each chromosome to score DNA fragment lengths between successive DSBs. Thresholds on fragment lengths were applied, i.e., fragments either shorter or longer than detectable in the experiments were not included in the respective comparisons. It was the simulated DSB sites (rather than total DSBs or DSB clusters) that were compared with experiments, since the experiments with the lower detection threshold of 1 kbp or longer (see below) could not have distinguished multiple DSBs within a cluster predicted by the simulations. In separate evaluations, total DSB yields including fragments outside the PFGE detection limits were scored.

The reported PFGE data^15–18 were gathered for human fibroblast cells (GM5787 or AG1522) irradiated by He, B, N, Ne, Ti, and Fe ions, detecting DNA fragments of either 1–5700 kbp, 5–5700 kbp, or 23–5700 kbp. Several experiments used unshielded beams as provided by the respective accelerators. However, in most cases, to reduce the ion energy the beam was shielded, e.g. by polymethylmethacrylate (PMMA, Lucite) blocks of various thicknesses. This led to nuclear reactions that produced considerable amounts of lighter (fragment) ions; for instance, for 1 GeV/u Fe ions passing through 23 g cm⁻² (20 cm, 1.16 g cm⁻³) PMMA, Fe ions (Z = 26) represented only about half of the transmitted particles⁴⁵, the other half being formed by fragments from Z = 1 up to 25. The fragment ions typically possess lower LET than the primary heavy ions. The reported experimental LET values correspond to dose-averaged LET stated in the respective studies. Since the majority of the dose is delivered by the primary ions, the dose-averaged LET tends to be close to that of the primaries. The reported simulations considered only the primary ion species, i.e. neglected the contribution to DNA damage from lighter fragments. The limited differences between unshielded and shielded data suggest that the contribution of primary ions is dominant and this approximation is acceptable. Differences between the simulated fluence-averaged and dose-averaged LET values were neglected, as they were much smaller than this shift in LET by fragments.

Comparison of PFGE results based on different evaluation methods

A number of PFGE studies were evaluated by their authors using the random breakage model. This model assumes that DSBs are randomly distributed along the DNA strand, and the relationship between DSB yield and the Fraction of Activity Released (FAR) is described by the formula³⁷:

2

where D is the radiation dose, k denotes the maximal detectable fragment size, Y_DSB is the DSB yield (DSB number per unit dose and Gbp), and M is the number of base pairs in the chromosome.

To extend our benchmarking of PARTRAC simulations to these studies and to help address the question how far the PFGE outcomes are affected by the specific evaluation method used, the random breakage evaluation was applied to the simulation results with known fragment sizes as follows. The fraction of DNA fragments within the detectable size range calculated with PARTRAC was divided by the total DNA content, and used as the simulated FAR in Eq. (2) to obtain Y_DSB, which was then compared with the published experimental data. The maximal fragment size k was set to 5.7 Mbp, a commonly used probe size in PFGE experiments⁴⁶. The value of M was set to 164 Mbp, representing the average size of a human chromosome⁴⁷. The commonly used irradiation dose of 100 Gy was adopted for the calculations. Ideally, the DSB yield (i.e., DSB number per unit dose) should remain constant regardless of dose, if inter-track effects are negligible and sufficient fragmentation occurs. The selected dose of 100 Gy is sufficiently high to produce detectable fragments smaller than the threshold of 5.7 Mbp but not too high to cause DSB yields to become dose-dependent, as discussed above. Exploratory simulations validated that varying the dose did not notably affect the model results. It was not possible to retrospectively evaluate the experimental data in more detail for more accurate comparisons, since most studies report DSB yields calculated solely from a single FAR value rather than the full fragmentation spectrum. A direct comparison of FAR values was not suitable either, because irradiation settings (in particular, applied doses) varied among the experiments and the reported DSB yields might have been derived from multiple dose points.

Relative biological effectiveness (RBE) for DSB induction

In addition to absolute DSB yields by the given species and energy, presented are also results on relative biological effectiveness for DSB induction (RBE_DSB values), using ⁶⁰Co photons as the reference radiation. Though less relevant for space applications, the RBE is included herein for its wide use in radiation biology. The RBE is defined as the ratio of doses by the reference and test radiations needed to produce the same effect. For endpoints exhibiting non-linear dose-response relationships (e.g. cell survival), modelling the data with an assumed relationship (e.g. the linear-quadratic model) and inverting the model formula to assess the dose leading to the given effect (e.g. 10% cell survival) is needed to derive the RBE. For effects directly proportional to radiation dose, such as DSB induction at dose levels considered here, this RBE definition reduces to the ratio of DSB yields by the test and reference radiations at the same dose. The results reported herein take advantage of this computationally simpler approach.

The simulations for ⁶⁰Co photons used the same setup as for ions described above, but all interactions of photons and secondary electrons were mirrored into the world region to save computational time⁴⁸. This also ensured electronic equilibrium conditions.

Radiation-induced foci

The performed DNA damage simulations were related to radiation-induced foci using a previously proposed simplistic approach^49,50, assuming that the initial DNA damage directly translates into the presence of DNA damage response foci. Around each DSB induced, an accumulation sphere with the diameter of 0.5 μm was assumed to be formed, corresponding to an area of approximately 0.2 µm², frequently reported for γH2AX foci^51,52 (H2AX histone variant phosphorylated upon the presence of a DSB). Note that other DNA damage response proteins may exhibit different sizes of accumulation regions; e.g., 140 and 600 nm were reported previously⁵⁰ for the assembly of pDNA-PKcs (DNA-dependent protein kinase catalytic subunit phosphorylated at threonine 2609) and 53BP1 (p53-binding protein 1), respectively. These DSB-centred spheres were then merged into foci: For well separated DSBs, each focus contained a single DSB and was identical in size and shape to the DSB-centred assembly sphere, but for less separated ones, larger and typically elongated or irregular foci resulted, corresponding to a union of multiple DSB-centred spheres. Linking foci directly to the initial DNA damage induction, rather than considering their relation to ongoing repair⁵³, tremendously reduced the complexity and computational costs of the simulations.

Results

PARTRAC stopping power and LET values agree with ICRU and SRIM data

In Fig. 2, PARTRAC results for stopping power (solid circles) and LET (open triangles) for selected ions are compared with the stopping power values recommended by the ICRU^12,13 (dashed lines) or resulting from SRIM¹⁴ calculations (dotted lines). Overall, the stopping powers from PARTRAC simulations show good agreement with the ICRU and SRIM data; in their overlap region, the two reference datasets match each other very well (not shown). PARTRAC results are slightly higher than these reference values in the high-energy region for all ions, with a typical difference of about 5%. In the low energy region, the stopping power for lighter ions (up to neon) is slightly underestimated, while that for heavier ions is slightly overestimated; the differences remain within 10%.

Fig. 2.

Stopping power and LET comparison. Stopping powers (filled circles) and cell nucleus-based LET (empty triangles) resulting from the performed track-structure simulations are compared with stopping powers from the ICRU data^12,13 (dashed lines) or SRIM¹⁴ calculations (dotted lines), for hydrogen, helium, carbon, neon, magnesium, silicon, calcium, and iron ions (diverse colours). The simulated LET values for 1–512 MeV/u H – Ne ions are taken from previous studies^10,11,19.

Generally, the simulated cell nucleus-based LET closely follows the stopping power because most secondary electrons deposit their energy locally. However, at high energies, secondary electrons frequently escape from the cell nucleus, laterally and/or longitudinally, causing the LET to fall below the stopping power. This difference becomes increasingly pronounced with increasing energy, as the maximal energy of secondary electrons increases accordingly. For instance, for 1 GeV/u ions, the nucleus-based LET is about 27% smaller than the stopping power across all ion species. On the other hand, at low energies, notably for H to Ne at 1 MeV/u, the LET is higher than the (initial) stopping power, as the ion energy considerably decreases and the stopping power increases along the ion path through the cell nucleus, and the nucleus-based LET basically corresponds to the average stopping power then.

Predicted DSB yields correspond to PFGE experiments

In Fig. 3, simulated yields of DSB sites in dependence on LET (lines) are compared to data from PFGE experiments evaluated using the fragment counting method^15–18 (large symbols) as well as using the random breakage model^47,54–60 (small symbols), for various ions (diverse colours). Figure 3a-b presents absolute yields, while Fig. 3c shows relative biological effectiveness for DSB induction (RBE_DSB values) with ⁶⁰Co photons as the reference radiation.

Fig. 3.

Predicted yields of DSB sites compared to PFGE experiments. Large symbols show data on DSB induction in human cells from PFGE studies^15–18 that counted DNA fragments in size ranges of 1–5700 kbp, 5–5700 kbp, or 23–5700 kbp, respectively. Also presented are data from PFGE studies^47,54–60 evaluated using the random breakage model (small symbols). Simulation results for alternative evaluation methods and detection limits are depicted by lines. The results for 1–512 MeV/u H, He and C ions are in part taken from previous studies^10,11,19. Diverse ions are presented in diverse colours, identically for experiments and simulations. Panel a: Yields of DSB sites corresponding to fragments in the 5–5700 kbp size range (solid lines) correspond to the bulk of PFGE data with fragment scoring (large symbols). Also the notably lower yields derived from random breakage analysis (small symbols) are reproduced by the corresponding simulations (long-dashed lines). Simulations that include very short (< 1 kbp) fragments are depicted too (dash-dotted lines). For clarity, simulations are presented for H, He and Fe ions only. Panel b: Closer look to the role of analysis method and detection limits in PFGE, for a single representative ion species (C ions, blue lines). Improving the PFGE lower detection limit from 5 to 1 kbp leads to a notable increase in DSB yields and a slight shift of the peak position towards higher LET (dotted vs. solid lines). Further increase and shift to higher LET occur when also fragments < 1 kbp are scored (dash-dotted line). The results for 23–5700 kbp are almost identical to those for 5–5700 kbp (not shown). Regarding the random breakage evaluation, some experimental studies assumed that only about 80% of the total DNA might get released at all in the experiments^55,61. Simulations without (long-dashed lines) or with (short-dashed line) this assumption largely capture the variability among PFGE data evaluated with the random breakage model (small symbols). Panel c: Relative biological effectiveness (RBE) with ⁶⁰Co photons as the reference radiation.

To avoid an overly busy figure, in Fig. 3a simulation results are shown only for H (red), He (green), and Fe ions (grey lines). These species cover the full studied LET range and were selected as representative ones: While H ions (protons) are notably more effective in inducing DSBs than He ions (alpha particles) and He is more effective than heavier ions in the overlapping LET regions, the variations among heavier ions are less pronounced. In Fig. 3b-c, focused on differences among alternative PFGE analyses methods and detection thresholds, simulation results are shown only for C ions (blue lines). Overall (Fig. 3a, b), with increasing LET the PFGE data show a general trend of DSB yields increasing towards a broad maximum at 30–200 keV/µm and then decreasing. However, there is a large scatter in the PFGE data. The simulations trace this scatter primarily to different PFGE evaluation methods: The results based on the fragment counting method and detecting fragments from 5 or 23 kbp to 5700 kbp are depicted by squares (experiments) and solid lines (simulations for 5–5700 kbp; results for 23–5700 kbp differed only by about 5%, not shown). DSB yields derived from evaluations assuming the random breakage model are shown by small circles (experimental data) and dashed lines (simulations). Specifically, long-dashed lines additionally assume that only approximately 80% of the nuclear DNA may be released into the gel at all^55,61, while short-dashed lines are free of this assumption (Fig. 3b). Interestingly, while this correction largely affects the absolute DSB yields at lower LET (< 100 keV/µm), its impact is limited at higher LET (Fig. 3b), and virtually diminishes in RBE plot throughout the studied LET values (Fig. 3c). In general, experiments assuming the random breakage model provided notably lower DSB yields than those using the fragment scoring method. The reduction corresponded roughly to a factor of two below 100 keV/µm and could exceed a factor of three above 100 keV/µm. The simulations capture this difference.

The simulations also highlight the crucial role of the bottom detection threshold (Fig. 3b): PFGE with the fragment counting evaluation detecting fragments as short as 1 kbp (dotted lines) are predicted to provide notably higher DSB yields than those limited to fragments longer than 5 kbp (solid lines). The predicted difference is comparable to the one that could be inferred, though with a large uncertainty, from diverse experiments with Fe ions (grey triangles vs. squares). Even higher yields are predicted for the total DSB numbers (dash-dotted lines), including those associated with very short (< 1 kbp) fragments. DSBs associated with < 1 kbp fragments are predicted to be induced especially for radiations with LET > 100 keV/µm; at 500 keV/µm, these fragments account for about 50% of all DSBs. With increasing sensitivity to short fragments, the LET at which maximal DSB yields occur are predicted to shift towards higher values, from about 70 keV/µm for the threshold of 5 kbp (solid lines) over 100 keV/µm for 1 kbp (dotted lines) to about 200 keV/µm if all fragments are resolved (dash-dotted lines).

HZE particles form streaks of DSBs and foci

To illustrate the role of track structure and damage clustering for biological effects, exemplary tracks of 128 MeV/u C, 32 MeV/u Mg, 8 MeV/u Si, and 2 MeV/u Fe ions are presented in Fig. 4. All these tracks cross the lymphocyte nuclei with chord lengths close to the mean one (6.7 μm). Their LET amounted to approximately 19, 240, 990, and 4200 keV/µm, and the doses deposited to the cell nucleus were about 0.039, 0.49, 2.0, and 8.6 Gy, respectively.

Fig. 4.

HZE particles tend to produce DSB and foci streaks or even contiguous columns along their tracks. Four exemplary tracks of ions with increasing LET are shown, in two nuclei: 128 MeV/u carbon (green), 32 MeV/u magnesium (orange), 8 MeV/u silicon (blue), and 2 MeV/u iron ions (red). They all travelled from bottom to top and crossed the cell nucleus (10 μm sphere) along chords of about identical length, corresponding to the mean chord length of 6.67 μm. Dots depict ionizations by the primary ion (very dense, hence forming straight lines of their trajectories) or by their secondary electrons (some visibly separated; forming curly trajectories). Differences in electron ranges (due to variations in their energies) and densities can be seen. Circles depict 0.5 μm-sized elementary regions centred on the induced DSBs, in which DNA damage response proteins such as γH2AX or 53BP1 are assumed to accumulate and manifest as radiation-induced foci. With increasing LET, these accumulation regions tend to overlap and form prolonged foci or even their streaks or a contiguous column (with increased intensity in the overlap regions, up to saturation), contrary to isolated, scattered foci from well-separated DSBs induced by low-LET radiation. Brackets and numbers indicate separate foci. See text for details.

Already the lowest-LET track shown (C ion, green) produces a dense core along the primary particle trajectory, with about 26,000 ionizations by the ion (typically separated by < 1 nm). In addition to the core, several branches formed by ionizations by secondary electrons (curly tracks) can be seen. Despite the rather dense track core, only two DSBs are formed by this track, yielding two well separated foci.

The plotted 32 MeV/u Mg ion track (orange) includes over 300,000 ionizations by the primary ion. Additional ionizations were induced by its secondary electrons. Their tracks formed curly branches, the highest-energy ones travelling through large parts of or the whole cell nucleus. With about 12-times increased density of the track core compared with the shown C ion, the Mg track induced 56 DSBs. These DSBs form 5 foci, which include (along the track direction, i.e. from bottom to top) 1, 3, 35, 16, and 1 DSB, respectively.

The 8 MeV/u Si track (blue) possesses an even higher core density, with almost 1.2 million ionizations. Due to its lower energy per nucleon, secondary electrons possess lower maximum energy and hence shorter ranges than for the Mg case (note that the C ion can produce longest-range electrons but their total number was not sufficient to include rather exceptional high-energy ones). There are in total 229 DSBs for the shown Si track, which form 2 elongated foci on the core (including 152 and 76 DSBs for foci labelled with 1 and 3, respectively) and a spherical focus that is well separated from the core (label 2, 1 DSB).

The > 4000 keV/µm Fe ion track (red) illustrates an extreme case, with almost 5.6 million ionizations by the primary ion. Due to its low energy (2 MeV/u), secondary electron tracks are confined to a close vicinity of the ion’s path. The simulations yielded 819 DSBs, which would form a single focus, basically a contiguous column of γH2AX along the track.

Predicted LET-dependent trends in DNA damage

Figure 5 shows in detail the predicted LET- and species-dependent DNA damage yields across 1–1000 MeV/u, for SSBs, DSBs, DSB sites, and DSB clusters, and also presents the mean multiplicity of the DSB clusters. For clarity, only H, He, C, Ne, Si, and Fe are shown; the results for the full range of ions are reported in Supplementary Material. In addition to the total yields (solid lines), also contributions from direct effects (dashed lines) are presented. Overall, the predicted trends are consistent with previously reported results for light ions^10,11. SSB yields (Fig. 5a) decrease with increasing LET, as higher ionization density leads to more closely spaced SBs that are more likely to form DSBs. Up to about 100 keV/µm, direct SSB yields remain approximately constant, indicating that this decrease is mainly driven by the decrease in indirect (radical-mediated) SSBs, due to radical recombination within the tracks. Above 100 keV/µm, both direct and total SSB yields decrease. While the fraction of direct to total SSBs is only about a third (i.e., indirect SSBs are almost twice more frequent than direct ones) at low LET, it is about a half (i.e., the two types contribute almost equally) at the highest LET values (i.e., lowest energies) for each ion.

Fig. 5.

Predicted trends in DNA damage induction (yields per unit dose and genomic content) in dependence on ions’ LET. Panel a: SSBs, panel b: total DSBs, panel c: DSB sites, panel d: DSB clusters, panel e: cluster multiplicity. Simulation results for 11 log-equidistant energies from 1 to 1000 MeV/u per ion connected by lines, showing total yields (solid lines) and contributions from direct effects (dashed lines). To avoid overly busy plots, the results are presented for selected six ions only, namely H, He, C, Ne, Si and Fe (diverse colours). The results for 1–512 MeV/u H – Ne ions are taken from previous studies^10,11,19. Data for the full set of 14 ions are available in Supplementary Material. Damage yields at low energies (high LET values) show some ion-specific behaviour, forming ‘whiskers’ in the plots. Except these whiskers, SSBs (panel a) gradually decrease with LET, relatively slowly up to 50–100 keV/µm and faster above these values. DSB damage classes (total DSBs, their sites and clusters; panels b-d) increase with increasing LET up to a maximum at 100–500 keV/µm and then decrease due to overkill effects. These common trends show that the LET serves as a useful though not perfect descriptor of radiation quality.

The yields of all three DSB categories (total DSBs, DSB sites, and DSB clusters; Fig. 5b-d) first increase with LET, then reach maxima, and eventually decline. The decline is due to overkill effects, which can be traced to the ionization density (and hence also the density of radical attacks) being higher than necessary for inducing these types of DNA damage. For DSB yields (Fig. 5b), there are notable variations among diverse ions of the same LET, lighter particles being somewhat more effective than heavier ones; overall, DSB yields are maximal at LET around 100–300 keV/µm. Also the yields of DSB sites (Fig. 5c) somewhat vary with Z, especially for light particles, but the variability is reduced compared to total DSBs; the peak occurs around 200 keV/µm. DSB cluster yields (Fig. 5d) peak near 400 keV/µm, with high-LET values approximately 20–50 times greater than those at low LET. The average DSB multiplicity per cluster increases with LET, starting to rise at around 100 keV/µm from values close to the minimal 2 DSBs per cluster, increasing rapidly beyond 1000 keV/µm where an average cluster contains ~ 4 DSBs, and reaching ~ 16 DSBs per mean cluster for 1 MeV/u (~ 4000 keV/µm) Fe ions. This highlights the significantly enhanced DNA damage complexity under very densely ionizing conditions. It is this sharply increasing DSB multiplicity per cluster at low energies (high LET values), which depends on Z, that leads to the increasing total DSB yields seen in Fig. 5b.

Indirect effects are predicted to be responsible even at low LET only for a minor part of DSBs, their sites and clusters (not shown). A notable fraction of DSB classes is due to hybrid (mixed) effects (not shown), where e.g. a DSB is composed of an SB induced by direct energy deposition and an SB on the opposite strand due to an ^•OH attack. The largest contribution, throughout the studied LET range, is from direct effects (dashed lines). In particular, the fractions of direct effects exceed 50% at LET > 100 keV/µm for all DSB classes, especially for DSB clusters.

While yields per unit dose (and genomic content) are commonly used in radiation biology, fluence-based reporting is more common in space research. Therefore, the same data is presented as per-track yields in Fig. 6. The yields of all damage types massively increase with particle LET. For instance, while only 36% and 1.5% of 1 GeV (0.17 keV/µm) proton tracks induce an SSB and a DSB, respectively, for a single Fe ion of 2 MeV/u (4200 keV/µm) there are > 2300 SSB and 740 DSB on average.

Fig. 6.

Predicted per-track yields of DNA damage in dependence on ions’ LET. Panel a: SSBs, panel b: total DSBs, panel c: DSB sites, panel d: DSB clusters. Simulation results for 11 log-equidistant energies from 1 to 1000 MeV/u per ion connected by lines, showing total per-track yields (solid lines) and contributions from direct effects (dashed lines). For ease of read, only the results for H, He, C, Ne, Si and Fe ions are shown (diverse colours). The results for 1–512 MeV/u H–Ne ions are taken from previous studies^10,11,19. Data for the full set of 14 ions are available in Supplementary Material.

In Supplementary Material, the same data are presented in dependence on (Z_eff/β)² and the starting energy. Numerical values are provided in Supplementary Material, Table S1. Overall, (Z_eff/β)² (Figure S1) does not capture the results much better than the LET (Fig. 5). With (Z_eff/β)², the scatter among ions is slightly reduced for SSBs (panels ‘a’ of Fig. 5 and Figure S1, respectively), very similar for total DSBs (b), slightly reduced for DSB sites (c), reduced in ascending parts (before peak) but increased in descending, beyond-peak parts for DSB clusters (d), and the effect for DSB multiplicity in clusters (e) is very small again. A principal difference is that, similarly to energy, (Z_eff/β)² is a unique descriptor of radiation type and quality, while LET not, i.e., as the ion slows down, two distinct energies correspond to a single LET value. This leads to hooks in LET-dependent plots for some of the results; plots dependent on (Z_eff/β)² and energy are free of this issue.

The statistical uncertainties of the simulations were on average 1.1% for SSBs and 1.4% (1.6% for direct effects) for DSBs and their sites; maximal uncertainties across the simulated database were 4.4%. For DSB clusters, the uncertainty was on average 4.2% (6.8% for direct effects) but reached up to 15% (for direct effects exceptionally 45%) for high-energy (low-LET) light ions, for which DSB clusters are very rare. The uncertainties are not depicted as error bars to avoid overly busy figures.

Discussion

PARTRAC simulations on heavy ion-induced DNA damage were reported, extending the previously published light-ion database^10,11 to Mg, Si, Ca, Ti, and Fe ions as the key species in GCR relevant to space radiation biology and risk assessment. The previously published data were extended to 1 GeV/u, since particles of such energies are the most abundant ones in GCR. The simulation results were successfully benchmarked against stopping powers in liquid water recommended by the ICRU and resulting from SRIM calculations as well as against available PFGE experimental data on DSB yields in human cells. The simulations provide detailed mechanistic understanding of processes running on diverse temporal and spatial scales. They highlight the key role of DSBs and their clustering on various scales, from nanometres to micrometres. In particular, with increasing LET, an increasing fraction of DSBs are predicted to be associated with very short DNA fragments, even < 1 kbp (Fig. 3). While such fragments are likely very detrimental biologically, they are below the detection thresholds of existing gold-standard PFGE experiments. With increasing LET, individual radiation-induced foci are predicted to contain increasing numbers of DSBs, and to form streaks or even merge into contiguous foci along the ion tracks (Fig. 4).

The performed simulations trace the high biological effectiveness of HZE particles solely to the patterns of their tracks. Throughout this work, model assumptions and parameters on radiation physics, chemistry and DNA damage induction were applied as previously derived from the effects of other radiation types⁸. No simulation parameter was specifically adjusted in the present HZE study.

The reported simulations used ion interaction cross sections scaled from hydrogen as proposed previously^10,23. For high-energy ions, the resulting stopping powers are approximately 5% higher than those reported by the ICRU^12,13 or calculated by the SRIM code¹⁴. For low-energy ions, the differences may reach up to 10%. These slight deviations are consistent with previous observations and likely may be attributed to the scaling of ion cross sections from H⁺/H⁰ data¹⁰.

A limitation of the reported simulations is that they do not explicitly account for multiple ionizations of water molecules. With increasing ionization density, the ions’ mean free path becomes comparable to or even smaller than inter-molecular distances in liquid water. Consequently, multiple ionizations of the same water molecule occur. This, in fact, is the case of almost all heavy ions and energies reported herein. The approximation employed in PARTRAC¹⁰ and used in this work shifts additional ionizations laterally to neighbouring water molecules. This avoids the need to account for the largely unknown processes related to multiple ionizations. Indeed, the research on multiple ionization effects on DNA damage is still in its infancy; existing studies have focused on the physical and chemical stages^24–26, with no clear insight into how DNA damage may be affected.

In the physical stage, first, ionization energy of an already ionized water molecule is higher than for a neutral molecule²⁵. Although PARTRAC does not explicitly model this effect, the overall energy deposition is conserved, and the ions’ stopping power is modelled correctly. Essentially, rather than producing fewer higher-energy ionization events, the energy is distributed into a higher number of lower-energy events locally. Second, electrons liberated from multiply ionized molecules may carry higher kinetic energies²⁵. This may broaden the radial dose distribution and increase the production of reactive chemical species, shifting the patterns of radiation interactions towards those typical of lower-LET radiation, producing less clustered DNA damage. These effects were neglected in this work, using the secondary electron spectrum for single ionizations.

In the physicochemical stage, a comparison of dissociation channels assumed for singly and multiply ionized water molecules^24,26 shows that multiple ionizations lead to fewer hydroxyl radicals (^•OH) and instead generate ground-state atomic oxygen, O(³P), which is also highly reactive. O(³P) quickly reacts with itself or with ^•OH, forming molecular oxygen (O₂) or hydroperoxyl radicals (HO₂^•). These reactions result in a decrease in hydrogen peroxide (H₂O₂) production and an increase in superoxide anion (O₂^•−) levels²⁶. The reduction in ^•OH production may decrease DNA damage. However, the estimated reduction in ^•OH yields is relatively small, reported²⁴ as approximately 10% for Ar ions at 5 MeV/u. Thus, its impact on overall DNA damage is likely limited. On the other hand, the increased production of O₂ and other reactive oxygen species (ROS), such as HO₂^• and O₂^•−, may enhance DNA damage. These two effects may largely compensate each other, supporting the present approximation. Furthermore, potential contribution by oxygen and ROS other than ^•OH is neglected in most radiation track structure codes. While some codes simulate their production and chemical interactions, their effects on DNA are typically not considered^62,63. The present approach may limit the model’s ability to fully capture the biological effects and the underpinning mechanisms, but it likely remains adequate for many applications; future work may aim at extending it by the above-discussed factors.

The reported DNA damage simulations highlighted the impact of the PFGE detection limits and evaluation methods on the scored DSB yields. Various data evaluation approaches have been established in PFGE, including the random breakage model^37,38, the generalized broken stick model³⁹, and analysing the fragmentation spectrum by counting fragments within defined size intervals^16,42. As illustrated in Fig. 3, DSB yields resulting from diverse evaluation methods may largely vary, by factors as high as 2–3. The reported simulations that account in silico for the diverse evaluation procedures do reproduce the outputs of both random breakage and fragment counting methods, helping explain the divergence observed across experimental datasets. To facilitate accurate comparisons with simulations and with experimental data from other groups, it is recommended that PFGE measurements be evaluated using fragmentation spectrum analysis, with fragment counts in each size bin considered and reported. Further, size bins should be sufficiently narrow, especially for the shortest fragments, to minimize the uncertainty of the mean fragment size in the given bin; as actual fragment size distributions largely differ from uniform ones, the mean fragment size deviates from the bin midpoint⁶⁴. Obviously, reducing the PFGE detection limit is important for high-LET irradiation, as for instance for 500–600 keV/µm Fe ions, two thirds of the fragments are predicted to be shorter than 5 kbp, a half even shorter than 1 kbp (Fig. 3).

The analysed PFGE experiments (Fig. 3) include a fragment yield of 15.2 Gy^− 1 Gbp^− 1 reported by Dini et al.¹⁷ for Ti ions at an LET of approximately 100 keV/µm, which is notably higher than values typically observed for lighter ions such as He and N at similar LETs (around 8–10 Gy^− 1 Gbp^− 1). The authors proposed that differences in track structure could account for this variation. However, the present simulations suggest that lighter ions are in general more effective than heavier ones. Furthermore, Esposito et al.¹⁸ reported a fragment yield of about 9 Gy^− 1 Gbp^− 1 for Fe ions at a comparable LET, and nearly identical effects are expected for heavy ions such as Ti and Fe at the same LET according to the present simulations. In fact, Ti data from Dini et al.¹⁷ obtained with PFGE threshold of 1 kbp are close to simulations of total fragment yields including shorter ones, while their Fe data are in line with other studies (Fig. 3). The reason for the reported high DNA fragmentation by Ti ions thus remains unclear.

Compared with the absolute fragment yields (Fig. 3a-b), the agreement of the simulations with experimental data is slightly worse in the RBE plot (Fig. 3c). This may be largely traced to the differing effectiveness of the reference low-LET irradiation used in the RBE calculation. According to the present simulations, the yield of DSB sites by ⁶⁰Co photons is approximately 7.5 Gy^{− 1} Gbp^{− 1}. The analysed experimental studies^15–18 reported values close to 6 Gy^{− 1} Gbp^{− 1}, shifting RBE to higher values compared with the simulations. Another experiment⁶⁵ resulted in 7.4 Gy^{− 1} Gbp^{− 1}, close to the present results and also previous simulations using Geant4-DNA⁶⁶ and an earlier version of PARTRAC^67–69 that reported yields of about 8 Gy^{− 1} Gbp^{− 1}. Also, the RBE results somewhat differ from our previous analysis, where high-energy protons were used as the reference radiation instead of photons¹⁰, since ⁶⁰Co gamma rays induce slightly more DNA damage per unit dose than high-energy protons.

The present DNA damage simulations were performed for human lymphocytes, while most PFGE data used in the reported comparison (Fig. 3) were gathered using human fibroblasts. However, when normalized per dose and DNA content as done here, very similar initial DSB yields were simulated for these two cell types¹⁰. Also experimentally, rather similar initial DSB or foci yields were observed across diverse cells, e.g. with 5.4–6.6 DSB or γH2AX foci per Gy per Gbp in yeast, CHO-K1 and human fibroblast cells exposed to low-LET photon irradiation^70–73. This suggests that the initial DNA damage (per unit dose and DNA content) is largely cell-type independent, so that the present simulations may approximate initial DNA damage induction not only in lymphocytes but also in other cell types in G1/G0 phase, including fibroblasts. However, subsequent biological endpoints such as the induction of chromosome aberrations or cell killing may largely differ, in particular due to variations in repair capacity among cell types.

The reported simulations on radiation-induced foci were based on the simplistic assumption⁵⁰ that each induced DSB triggers an immediate assembly of DNA damage response proteins (repair proteins or H2AX histone phosphorylation to γH2AX) within a sphere, whose size is protein-specific and may also depend on microscopy technique and image resolution. By linking foci with initial DNA damage induction directly, the temporal evolution of foci was not considered, namely the kinetics of their appearance and disappearance in relation to ongoing DSB repair⁵³. HZE particles possess high LET and induce complex DNA lesions difficult to repair, justifying the applied approximation. Although its assumptions are less appropriate for lighter ions, this approximation did reproduce foci numbers observed in high-resolution microscopy following irradiation by Li or C ions, visualizing pDNA-PKcs or 53BP1 repair protein foci with 140–600 nm sizes of the elementary accumulation regions⁵⁰.

The foci visualizations in Fig. 4 assumed that the level of response proteins and hence fluorescence in each accumulation region is homogeneous and identical, and well below the saturation level of the imaging technique. Thus, rather faint foci resulted from isolated DSBs, as opposed to intense prolonged foci, streaks or columns from densely spaced multiple DSBs along high-LET tracks. The actual accumulation of response proteins may hardly show such step-like profiles across the accumulation region; Gaussian distributions or even stochastic patterns and/or irregularities given e.g. by the local chromatin structure appear more realistic. Furthermore, the accumulation of response proteins may be limited by their local availability, which may reduce the difference in intensity between faint foci from isolated DSBs and dense ones from clustered DSBs. Thresholds, saturation and other non-linearities of the imaging may also modify the resulting picture. These effects may be accounted for in future simulation studies. Nevertheless, the present results highlight qualitative and quantitative changes in foci patterns; qualitatively similar transitions from isolated foci to their streaks were observed experimentally⁷⁴.

Throughout this work, only the initial DNA damage was considered. Future lines of research shall extend the present results by simulating cellular repair processes²⁰ and the induction of chromosome aberrations^22,75, with benchmarking against respective experimental data. Likewise, extending the present foci formalism to the kinetics of their appearance and disappearance in relation to ongoing repair processes shall be attempted.

Recently, a multiscale modelling framework using Geant4-DNA has been employed to simulate DNA damage by H and He ions in a realistic lunar radiation environment, incorporating human phantoms to reflect anatomical exposure scenarios⁷⁶. In contrast, our study focuses on a broad range of ion species and energies, aiming to provide generalized DNA damage predictions across space-relevant conditions, but is limited spatially to a cell nucleus. Very recently, interaction cross sections in Geant4-DNA have been extended to HZE particles⁷⁷. Building on DNA damage datasets such as the present one, approaches to account for effects of mixed radiation fields have been proposed using PARTRAC^34,78 and Geant4-DNA⁷⁹. Primarily developed for neutron-induced charged-particle mixed fields, such tools are of utmost importance in mixed fields abundant in space. Their potential direct applications include secondary neutrons generated by primary GCR or solar protons interacting with habitat walls, planetary atmosphere or soil. Together with previous publications^9,80,81, these studies illustrate the increasing use and value of track-structure approaches in space radiation research, supporting risk assessment and countermeasure development.

In conclusion, this study demonstrates the utility of the PARTRAC simulation framework in characterizing DNA damage induced by heavy ions relevant to space radiation. The model predictions were successfully benchmarked against stopping power data and against PFGE data on DNA DSB induction in human cells. The simulations explain the reported variability in PFGE data by identifying the key roles of detection limits and evaluation techniques in these experiments. The results highlight the enhanced complexity of DNA damage induced by HZE particles. With increasing ionization density, progressively shorter DNA fragments are predicted, increasingly deviating from a one-to-one correspondence between DSB and foci. Qualitative changes in foci patterns with increasing LET are predicted, from scattered foci to their streaks or even continuous columns along HZE tracks, leaving the cell with virtually no chance of proper repair. More generally, this work supports the application of PARTRAC as a predictive tool for evaluating the biological impact of space radiation, contributing to long-term efforts in risk assessment for extended human spaceflights.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

GB and PK designed the research. CWH performed the simulations. CWH, PK and GB interpreted the results. CWH drafted and PK edited the manuscript. All authors critically read and reviewed the manuscript.

Funding

This work was supported by institutional funding of the Nuclear Physics Institute of the Czech Academy of Sciences, Czech Technical University in Prague, and by funding of the University of Pavia granted by the Italian Space Agency (ASI) through the program-agreement: “On board payloads: Gestione scientifica di LIDAL e Mini-EUSO” n. 2020-26-HH.0 e Addendum 2020-26-HH.1-2024.

Data availability

The simulated data are available in Supplementary Table S1.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval

This simulation study does not include human or animal subjects.