A fast Monte Carlo cell-by-cell simulation for radiobiological effects in targeted radionuclide therapy using pre-calculated single-particle track standard DNA damage data

Introduction

We developed a new method that drastically speeds up radiobiological Monte Carlo radiation-track-structure (MC-RTS) calculations on a cell-by-cell basis.

Methods

The technique is based on random sampling and superposition of single-particle track (SPT) standard DNA damage (SDD) files from a "pre-calculated" data library, constructed using the RTS code TOPAS-nBio, with "time stamps" manually added to incorporate dose-rate effects. This time-stamped SDD file can then be input into MEDRAS, a mechanistic kinetic model that calculates various radiation-induced biological endpoints, such as DNA double-strand breaks (DSBs), misrepairs and chromosomal aberrations, and cell death. As a benchmark validation of the approach, we calculated the predicted energy-dependent DSB yield and the ratio of direct-to-total DNA damage, both of which agreed with published in vitro experimental data. We subsequently applied the method to perform a superfast cell-by-cell simulation of an experimental in vitro system consisting of neuroendocrine tumor cells uniformly incubated with 177Lu.

Results and discussion

The results for residual DSBs, both at 24 and 48 h post-irradiation, are in line with the published literature values. Our work serves as a proof-of-concept demonstration of the feasibility of a cost-effective "in silico clonogenic cell survival assay" for the computational design and development of radiopharmaceuticals and novel radiotherapy treatments more generally.

Haptoglobin is an early indicator of survival after radiation-induced severe injury and bone marrow transplantation in mice

Background

Hematopoietic stem cell transplantation (HSCT) is the main treatment for acute radiation sickness, especially after fatal radiation. The determination of HSCT for radiation patients is mainly based on radiation dose, hemogram and bone marrow injury severity. This study aims to explore a better biomarker of acute radiation injury from the perspective of systemic immune response.

Methods

C57BL/6J female mice were exposed to total body irradiation (TBI) and partial body irradiation (PBI). Changes in haptoglobin (Hp) level in plasma were shown at different doses and time points after the exposure and treatment with amifostine or bone marrow transplantation. Student’s t-test/two tailed test were used in two groups. To decide the Hp levels as a predictor of the radiation dose in TBI and PBI, multiple linear regression analysis were performed. The ability of biomarkers to identify two groups of different samples was determined by the receiver operating characteristic (ROC) curve. The results were expressed as mean ± standard deviation (SD). Significance was set at P value < 0.05, and P value < 0.01 was set as highly significant. Survival distribution was determined by log-rank test.

Results

In this study, we found that Hp was elevated dose-dependently in plasma in the early post-irradiation period and decreased on the second day, which can be used as a molecular indicator for early dose assessment. Moreover, we detected the second increase of Hp on the 3rd and 5th days after the lethal irradiation at 10 Gy, which was eliminated by amifostine, a radiation protection drug, while protected mice from death. Most importantly, bone marrow transplantation (BMT) on the 3rd and 5th day after 10 Gy radiation improved the 30-days survival rate, and effectively accelerated the regression of secondary increased Hp level.

Conclusions

Our study suggests that Hp can be used not only as an early molecule marker of radiation injury, but also as an important indicator of bone marrow transplantation therapy for radiation injury, bringing new scientific discoveries in the diagnosis and treatment of acute radiation injury from the perspective of systemic immunity.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13287-022-03162-x.

Geometrical Properties of the Nucleus and Chromosome Intermingling Are Possible Major Parameters of Chromosome Aberration Formation

Ionizing radiation causes chromosome aberrations, which are possible biomarkers to assess space radiation cancer risks. Using the Monte Carlo codes Relativistic Ion Tracks (RITRACKS) and Radiation-Induced Tracks, Chromosome Aberrations, Repair and Damage (RITCARD), we investigated how geometrical properties of the cell nucleus, irradiated with ion beams of linear energy transfer (LET) ranging from 0.22 keV/μm to 195 keV/μm, influence the yield of simple and complex exchanges. We focused on the effect of (1) nuclear volume by considering spherical nuclei of varying radii; (2) nuclear shape by considering ellipsoidal nuclei of varying thicknesses; (3) beam orientation; and (4) chromosome intermingling by constraining or not constraining chromosomes in non-overlapping domains. In general, small nuclear volumes yield a higher number of complex exchanges, as compared to larger nuclear volumes, and a higher number of simple exchanges for LET < 40 keV/μm. Nuclear flattening reduces complex exchanges for high-LET beams when irradiated along the flattened axis. The beam orientation also affects yields for ellipsoidal nuclei. Reducing chromosome intermingling decreases both simple and complex exchanges. Our results suggest that the beam orientation, the geometry of the cell nucleus, and the organization of the chromosomes within are important parameters for the formation of aberrations that must be considered to model and translate in vitro results to in vivo risks.

BPIFA2 as a Novel Early Biomarker to Identify Fatal Radiation Injury After Radiation Exposure

Background

Current dosimeters cannot cope with the two tasks of medical rescue in the early stage of nuclear accident, the accurate determination of radiation exposure and the identification of patients with fatal radiation injury. As radiation can cause alterations in serum components, it is feasible to develop biomarkers for radiation injury from serum. This study aims to investigate whether serum BPIFA2 could be used as a potential biomarker of predicting fatal radiation injury in the early stage after nuclear accident.

Methods

A rabbit anti-mouse BPIFA2 polyclonal antibody was prepared to detect the expression of BPIFA2. C57BL/6J female mice were exposed to total body radiation (TBI) at different dose and Partial body radiation (PBI) at lethal dose to detect the dynamic changes of BPIFA2 in serum at different time points after irradiation by Western blot assay.

Results

BPIFA2 in mice serum were significantly increased at 1–12 h post-irradiation at .5–10 Gy, and increased again significantly at 3 d after 10 Gy irradiation with associated with mortality closely. It also increased rapidly after PBI and was closely related to injury degree, regardless whether the salivary glands were irradiated.

Conclusions

The increase of serum BPIFA2 is a novel early biomarker not only for identifying radiation exposure, but also for fatal radiation injury playing a vital role in rational use of medical resources, and greater efficiency of medical treatment to minimize casualties.

Impact of Radiation Quality on Microdosimetry and Chromosome Aberrations for High-Energy (>250 MeV/n) Ions

Studying energy deposition by space radiation at the cellular scale provides insights on health risks to astronauts. Using the Monte Carlo track structure code RITRACKS, and the chromosome aberrations code RITCARD, we performed a modeling study of single-ion energy deposition spectra and chromosome aberrations for high-energy (>250 MeV/n) ion beams with linear energy transfer (LET) varying from 0.22 to 149.2 keV/µm. The calculations were performed using cells irradiated directly by mono-energetic ion beams, and by poly-energetic beams after particle transport in a digital mouse model, representing the radiation exposure of a cell in a tissue. To discriminate events from ion tracks directly traversing the nucleus, to events from δ-electrons emitted by distant ion tracks, we categorized ion contributions to microdosimetry or chromosome aberrations into direct and indirect contributions, respectively. The ions were either ions of the mono-energetic beam or secondary ions created in the digital mouse due to interaction of the beam with tissues. For microdosimetry, the indirect contribution is largely independent of the beam LET and minimally impacted by the beam interactions in mice. In contrast, the direct contribution is strongly dependent on the beam LET and shows increased probabilities of having low and high-energy deposition events when considering beam transport. Regarding chromosome aberrations, the indirect contribution induces a small number of simple exchanges, and a negligible number of complex exchanges. The direct contribution is responsible for most simple and complex exchanges. The complex exchanges are significantly increased for some low-LET ion beams when considering beam transport.

Early Biomarkers Associated with P53 Signaling for Acute Radiation Injury

Accurate dose assessment within 1 day or even 12 h after exposure through current methods of dose estimation remains a challenge, in response to a large number of casualties caused by nuclear or radiation accidents. P53 signaling pathway plays an important role in DNA damage repair and cell apoptosis induced by ionizing radiation. The changes of radiation-induced P53 related genes in the early stage of ionizing radiation should compensate for the deficiency of lymphocyte decline and γ-H2AX analysis as novel biomarkers of radiation damage. Bioinformatic analysis was performed on previous data to find candidate genes from human peripheral blood irradiated in vitro. The expression levels of candidate genes were detected by RT-PCR. The expressions of screened DDB2, AEN, TRIAP1, and TRAF4 were stable in healthy population, but significantly up-regulated by radiation, with time specificity and dose dependence in 2–24 h after irradiation. They are early indicators for medical treatment in acute radiation injury. Their effective combination could achieve a more accurate dose assessment for large-scale wounded patients within 24 h post exposure. The effective combination of p53-related genes DDB2, AEN, TRIAP1, and TRAF4 is a novel biodosimetry for a large number of people exposed to acute nuclear accidents.

Track Structure Components: Characterizing Energy Deposited in Spherical Cells from Direct and Peripheral HZE Ion Hits

To understand the biological effects of radiation, it is important to determine how ionizing radiation deposits energy in micrometric targets. The energy deposited in a target located in an irradiated tissue is a function of several factors such as the radiation type and the irradiated volume size. We simulated the energy deposited by energetic ions in spherical targets of 1, 2, 4, and 8 µm radii encompassed in irradiated parallelepiped volumes of various sizes using the stochastic radiation track structure code Relativistic Ion Tracks (RITRACKS). Because cells are usually part of a tissue when they are irradiated, electrons originating from radiation tracks in neighboring volumes also contribute to energy deposition in the target. To account for this contribution, we used periodic boundary conditions in the simulations. We found that the single-ion spectra of energy deposition in targets comprises two components: the direct ion hits to the targets, which is identical in all irradiation conditions, and the contribution of hits from electrons from neighboring volumes, which depends on the irradiated volume. We also calculated an analytical expression of the indirect hit contributions using the local effect model, which showed results similar to those obtained with RITRACKS.

A Mechanistic DNA Repair and Survival Model (Medras): Applications to Intrinsic Radiosensitivity, Relative Biological Effectiveness and Dose-Rate

Variations in the intrinsic radiosensitivity of different cells to ionizing radiation is now widely believed to be a significant driver in differences in response to radiotherapy. While the mechanisms of radiosensitivity have been extensively studied in the laboratory, there are a lack of models which integrate this knowledge into a predictive framework. This paper presents an overview of the Medras model, which has been developed to provide a mechanistic framework in which different radiation responses can be modelled and individual responses predicted. This model simulates the repair of radiation-induced DNA damage, incorporating the overall kinetics of repair and its fidelity, to predict a range of biological endpoints including residual DNA damage, mutation, chromosome aberration, and cell death. Validation of this model against a range of exposure types is presented, including considerations of varying radiation qualities and dose-rates. This approach has the potential to inform new tools to deliver mechanistic predictions of radiation sensitivity, and support future developments in treatment personalization.

Cellular Response to Proton Irradiation: A Simulation Study with TOPAS-nBio

The cellular response to ionizing radiation continues to be of significant research interest in cancer radiotherapy, and DNA is recognized as the critical target for most of the biologic effects of radiation. Incident particles can cause initial DNA damages through physical and chemical interactions within a short time scale. Initial DNA damages can undergo repair via different pathways available at different stages of the cell cycle. The misrepair of DNA damage results in genomic rearrangement and causes mutations and chromosome aberrations, which are drivers of cell death. This work presents an integrated study of simulating cell response after proton irradiation with energies of 0.5-500 MeV (LET of 60-0.2 keV/µm). A model of a whole nucleus with fractal DNA geometry was implemented in TOPAS-nBio for initial DNA damage simulations. The default physics and chemistry models in TOPAS-nBio were used to describe interactions of primary particles, secondary particles, and radiolysis products within the nucleus. The initial DNA double-strand break (DSB) yield was found to increase from 6.5 DSB/Gy/Gbp at low-linear energy transfer (LET) of 0.2 keV/µm to 21.2 DSB/Gy/Gbp at high LET of 60 keV/µm. A mechanistic repair model was applied to predict the characteristics of DNA damage repair and dose response of chromosome aberrations. It was found that more than 95% of the DSBs are repaired within the first 24 h and the misrepaired DSB fraction increases rapidly with LET and reaches 15.8% at 60 keV/µm with an estimated chromosome aberration detection threshold of 3 Mbp. The dicentric and acentric fragment yields and the dose response of micronuclei formation after proton irradiation were calculated and compared with experimental results.

Determination of Chromosome Aberrations in Human Fibroblasts Irradiated by Mixed Fields Generated with Shielding

To better study biological effects of space radiation using ground-based facilities, the NASA Space Radiation Laboratory (NSRL) at the Brookhaven National Laboratory has been upgraded to rapidly switch ions and energies. This has allowed investigators to design irradiation protocols comprising a mixture of ions and energies more indicative of the galactic cosmic ray (GCR) environment. Despite these advancements, beam selection and delivery schemes should be optimized against facility and experimental constraints and validated to ensure such irradiations are a suitable representation of the space environment. Importantly, since experiments are time consuming and expensive, models capable of predicting biological outcomes over a range of irradiation conditions (single ion, sequential multi ion or mixed fields) are needed to support such efforts. In this work, human fibroblasts were placed behind 20 g/cm2 aluminum and 10.345 g/cm2 polyethylene and irradiated separately by 344 MeV hydrogen, 344 MeV/n helium, 450 MeV/n oxygen and 950 MeV/n iron ions at various doses. The fluorescence in situ hybridization (FISH) whole chromosome painting technique was then used to assess the cells for chromosome aberrations (CAs), notably simple exchanges. A multi-scale modeling approach was also developed to predict the formation of chromosome aberrations in these experiments. The Geant4 simulation toolkit was used to determine the spectra of particles and energies produced by interactions between the incident beams and shielding. The simulated mixed field generated by shielding was then transferred into the track structure code, RITRACKS (relativistic ion tracks), to generate three-dimensional (3D) voxelized dose maps at the nanometer scale. Finally, these voxel dose maps were input into the new damage and repair model, RITCARD (radiation-induced tracks, chromosome aberrations, repair and damage), to predict the formation of various CAs. The multi-scale model described herein is a significant advancement for the computational tools used to predict biological outcomes in cells exposed to highly complex, mixed ion fields related to the GCR environment. Results show that the simulation and experimental data are in good agreement for the complex radiation fields generated by all ions incident on shielding for most data points. The differences between model predictions and measurements are discussed. Although improvements are needed, the model extends current capabilities for evaluating beam selection and delivery schemes at the NSRL ground-based GCR simulator and for informing NASA risk projection models in the future.

Radiation Track Structure: How the Spatial Distribution of Energy Deposition Drives Biological Response

Ionising radiation is incredibly effective at causing biological effects. This is due to the unique way energy is deposited along highly structured tracks of ionisation and excitation events, which results in correlation with sites of DNA damage from the nanometre to the micrometre scale. Correlation of these events along the track on the nanometre scale results in clustered damage, which not only results in the formation of DNA double-strand breaks (DSB), but also more difficult to repair complex DSB, which include additional damage within a few base pairs. The track structure varies significantly with radiation quality and the increase in relative biological effectiveness observed with increasing linear energy transfer in part corresponds to an increase in the probability and complexity of clustered DNA damage produced. Likewise, correlation over larger scales, associated with packing of DNA and associated chromosomes within the cell nucleus, can also have a major impact on the biological response. The proximity of the correlated damage along the track increases the probability of miss-repair through pairwise interactions resulting in an increase in probability and complexity of DNA fragments/deletions, mutations and chromosomal rearrangements. Understanding the mechanisms underlying the biological effectiveness of ionising radiation can provide an important insight into ways of increasing the efficacy of radiotherapy, as well as the risks associated with exposure. This requires a multi-scale approach for modelling, not only considering the physics of the track structure from the millimetre scale down to the nanometre scale, but also the structural packing of the DNA within the nucleus, the resulting chemistry in the context of the highly reactive environment of the nucleus, together with the subsequent biological response.

A Bi-Exponential Repair Algorithm for Radiation-Induced Double-Strand Breaks: Application to Simulation of Chromosome Aberrations

Background: Radiation induces DNA double-strand breaks (DSBs), and chromosome aberrations (CA) form during the DSBs repair process. Several methods have been used to model the repair kinetics of DSBs including the bi-exponential model, i.e., N(t) = N₁exp(−t/τ₁) + N₂exp(−t/τ₂), where N(t) is the number of breaks at time t, and N₁, N₂, τ₁ and τ₂ are parameters. This bi-exponential fit for DSB decay suggests that some breaks are repaired rapidly and other, more complex breaks, take longer to repair. Methods: The bi-exponential repair kinetics model is implemented into a recent simulation code called RITCARD (Radiation Induced Tracks, Chromosome Aberrations, Repair, and Damage). RITCARD simulates the geometric configuration of human chromosomes, radiation-induced breaks, their repair, and the creation of various categories of CAs. The bi-exponential repair relies on a computational algorithm that is shown to be mathematically exact. To categorize breaks as complex or simple, a threshold for the local (voxel) dose was used. Results: The main findings are: i) the curves for the kinetics of restitution of DSBs are mostly independent of dose; ii) the fraction of unrepaired breaks increases with the linear energy transfer (LET) of the incident radiation; iii) the simulated dose–response curves for simple reciprocal chromosome exchanges that are linear-quadratic; iv) the alpha coefficient of the dose–response curve peaks at about 100 keV/µm.

RITCARD: Radiation-Induced Tracks, Chromosome Aberrations, Repair and Damage

Chromosome aberrations (CAs) are one of the effects of radiation exposure and can have implications for human health in the space environment, since they are related to cancer risk. In radiation research, chromosome aberrations are a convenient biomarker for carcinogenesis. To shed light on the formation and quality of chromosome aberrations in the space environment, many experiments and simulations have been performed using chromosome aberrations in human cells, induced by heavy ions, which are present in galactic cosmic rays (GCRs). In this work, the new simulation program, radiation-induced tracks, chromosome aberrations, repair and damage (RITCARD), is presented. This software program is based on the algorithm used in the NASA Radiation Track Image (NASARTI) model with some improvements. NASARTI and RITCARD are both comprised of four parts: a random walk (RW) algorithm for simulating chromosomes in a nucleus; a deoxyribonucleic acid (DNA) damage algorithm; a break repair process; and a function to assess and count chromosome aberrations. Prior to running RITCARD, the code, relativistic ion tracks (RITRACKS), is used to simulate detailed radiation track structure and calculate time-dependent differential voxel dose maps in a parallelepiped centered on a cell nucleus. The RITCARD program reads the pre-calculated voxel dose and locates the intersections between the voxels and the chromosomes that were simulated by random walk. Radiation-induced breaks occur strictly at these intersections with a probability that is a function of the voxel dose. When a break occurs in the random walk, the corresponding chromosome piece is cut into two fragments where each has a free end at the position of the break. RITCARD generates a collection of all fragments, free ends, and enlists free end pairs. In the next step, the algorithm simulates the time-dependent rejoining of free end pairs, using different probabilities for pairs originating from a given break (proper) or from different breaks (improper), which results in the formation of fragment sequences. By grouping these sequences, the program determines the number and types of aberrations, based on the same criteria used in our experiment. The new program is used to assess the yields of various types of chromosome aberrations in human fibroblast cells for several ions (¹H⁺, ⁴He²⁺, ¹²C⁶⁺, ¹⁶O⁸⁺, ²⁰Ne¹⁰⁺, ²⁸Si¹⁴⁺, ⁴⁸Ti²²⁺ and ⁵⁶Fe²⁶⁺) with energies varying from 10 to 1,000 MeV/n. The results show linear and linear-quadratic dose dependence for most chromosome aberrations types. The calculation results were compared with those obtained by fluorescence in situ hybridization (FISH) experiments that were performed by our group. The simulations and experiments are in better agreement at lower LET. Regarding the simulation results, the coefficient of the linear part of the dose-dependence curve also peaks at an LET value of approximately 100 keV/lm, which evokes a relative biological effectiveness (RBE) peak found by other researchers.

Track to the future: historical perspective on the importance of radiation track structure and DNA as a radiobiological target

PURPOSE

Understanding the mechanisms behind induced biological response following exposure to ionizing radiation is not only important in assessing the risk associated with human exposure, but potentially can help identify ways of improving the efficacy of radiotherapy. Over the decades, there has been much discussion on what is the key biological target for radiation action and its associated size. It was already known in the 1930s that microscopic features of radiation significantly influenced biological outcomes. This resulted in the development of classic target theory, leading to field of microdosimetry and subsequently nanodosimetry, studying the inhomogeneity and stochastics of interactions, along with the identification of DNA as a key target.

CONCLUSIONS

Ultimately, the biological response has been found to be dependent on the radiation track structure (spatial and temporal distribution of ionization and excitation events). Clustering of energy deposition on the nanometer scale has been shown to play a critical role in determining biological response, producing not just simple isolated DNA lesions but also complex clustered lesions that are more difficult to repair. The frequency and complexity of these clustered damage sites are typically found to increase with increasing LET. However in order to fully understand the consequences, it is important to look at the relative distribution of these lesions over larger dimensions along the radiation track, up to the micrometer scale. Correlation of energy deposition events and resulting sites of DNA damage can ultimately result in complex gene mutations and complex chromosome rearrangements following repair, with the frequency and spectrum of the resulting rearrangements critically dependent on the spatial and temporal distribution of these sites and therefore the radiation track. Due to limitations in the techniques used to identify these rearrangements it is likely that the full complexity of the genetic rearrangements that occur has yet to be revealed. This paper discusses these issues from a historical perspective, with many of these historical studies still having relevance today. These can not only cast light on current studies but guide future studies, especially with the increasing range of biological techniques available. So, let us build on past knowledge to effectively explore the future.

Radiation quality and intra-chromosomal aberrations: Size matters

The shift from plant to mammalian cell models in radiation cytogenetics hastened the development of methods suitable for the analysis of chromosome-type aberrations. These included methods to detect interchanges that take place between different chromosomes (dicentrics and translocations), and intrachanges occurring within a given chromosome (rings, interstitial deletions and inversions). In this review we consider the relationship between chromosome-type interchanges and intrachanges in response to changes in ionization density (linear energy transfer; LET). In that context, we discuss advantages and disadvantages of more modern methods used to measure intrachanges, and the implications that their increased resolution of measurement may have on the inter-to-intrachange fraction (i.e., the F-ratio). We conclude that the premise of the F-ratio is supported by its biophysical assumptions, but its intended use as an LET-dependent measure of prior radiation exposure is hampered mainly by our inability to accurately assess, on a cell-by-cell basis, inversions and interstitial deletions whose small sizes are below the detection limits of conventional cytogenetic techniques.

Proximity effects in chromosome aberration induction: Dependence on radiation quality, cell type and dose

It is widely accepted that, in chromosome-aberration induction, the (mis-)rejoining probability of two chromosome fragments depends on their initial distance, r. However, several aspects of these "proximity effects" need to be clarified, also considering that they can vary with radiation quality, cell type and dose. A previous work performed by the BIANCA (BIophysical ANalysis of Cell death and chromosome Aberrations) biophysical model has suggested that, in human lymphocytes and fibroblasts exposed to low-LET radiation, an exponential function of the form exp(-r/r₀), which is consistent with free-end (confined) diffusion, describes proximity effects better than a Gaussian function. Herein, the investigation was extended to intermediate- and high-LET. Since the r₀ values (0.8 μm for lymphocytes and 0.7 μm for fibroblasts) were taken from the low-LET study, the results were obtained by adjusting only one model parameter, i.e. the yield of "Cluster Lesions" (CLs), where a CL was defined as a critical DNA damage producing two independent chromosome fragments. In lymphocytes, the exponential model allowed reproducing both dose-response curves for different aberrations (dicentrics, centric rings and excess acentrics), and values of F-ratio (dicentrics to centric rings) and G-ratio (interstitial deletions to centric rings). In fibroblasts, a good correspondence was found with the dose-response curves, whereas the G-ratio (and, to a lesser extent, the F-ratio) was underestimated. With increasing LET, F decreased and G increased in both cell types, supporting their role as "fingerprints" of high-LET exposure. A dose-dependence was also found at high LET, where F increased with dose and G decreased, possibly due to inter-track effects. We therefore conclude that, independent of radiation quality, in lymphocytes an exponential function can describe proximity effects at both inter- and intra-chromosomal level; on the contrary, in fibroblasts further studies (experimental and theoretical) are needed to explain the strong bias for intra-arm relative to inter-arm exchanges.

Proximity effects in chromosome aberration induction by low-LET ionizing radiation

Although chromosome aberrations are known to derive from distance-dependent mis-rejoining of chromosome fragments, evaluating whether a certain model describes such "proximity effects" better than another one is complicated by the fact that different approaches have often been tested under different conditions. Herein, a biophysical model ("BIANCA", i.e. BIophysical ANalysis of Cell death and chromosome Aberrations) was upgraded, implementing explicit chromosome-arm domains and two new models for the dependence of the rejoining probability on the fragment initial distance, r. Such probability was described either by an exponential function like exp(-r/r₀), or by a Gaussian function like exp(-r²/2σ²), where r₀ and σ were adjustable parameters. The second, and last, parameters was the yield of "Cluster Lesions" (CL), where "Cluster Lesion" defines a critical DNA damage producing two independent chromosome fragments. The model was applied to low-LET-irradiated lymphocytes (doses: 1-4Gy) and fibroblasts (1-6.1Gy). Good agreement with experimental yields of dicentrics and centric rings, and thus their ratio ("F-ratio"), was found by both the exponential model (with r₀=0.8μm for lymphocytes and 0.7μm for fibroblasts) and the Gaussian model (with σ=1.1μm for lymphocytes and 1.3μm for fibroblasts). While the former also allowed reproducing dose-responses for excess acentric fragments, the latter substantially underestimated the experimental curves. Both models provided G-ratios (ratio of acentric to centric rings) higher than those expected from randomness, although the values calculated by the Gaussian model were lower than those calculated by the exponential one. For lymphocytes the calculated G-ratios were in good agreement with the experimental ones, whereas for fibroblasts both models substantially underestimated the experimental results, which deserves further investigation. This work suggested that, although both models performed better than a step model (which previously allowed reproducing the F-ratio but underestimated the G-ratio), an exponential function describes proximity effects better than a Gaussian one.

Mechanistic Modelling of DNA Repair and Cellular Survival Following Radiation-Induced DNA Damage

Characterising and predicting the effects of ionising radiation on cells remains challenging, with the lack of robust models of the underlying mechanism of radiation responses providing a significant limitation to the development of personalised radiotherapy. In this paper we present a mechanistic model of cellular response to radiation that incorporates the kinetics of different DNA repair processes, the spatial distribution of double strand breaks and the resulting probability and severity of misrepair. This model enables predictions to be made of a range of key biological endpoints (DNA repair kinetics, chromosome aberration and mutation formation, survival) across a range of cell types based on a set of 11 mechanistic fitting parameters that are common across all cells. Applying this model to cellular survival showed its capacity to stratify the radiosensitivity of cells based on aspects of their phenotype and experimental conditions such as cell cycle phase and plating delay (correlation between modelled and observed Mean Inactivation Doses R(2) > 0.9). By explicitly incorporating underlying mechanistic factors, this model can integrate knowledge from a wide range of biological studies to provide robust predictions and may act as a foundation for future calculations of individualised radiosensitivity.

Chromosome aberration model combining radiation tracks, chromatin structure, DSB repair and chromatin mobility

The module that simulates the kinetics and yields of radiation-induced chromosome aberrations within the biophysical code PARTRAC is described. Radiation track structures simulated by Monte Carlo methods are overlapped with multi-scale models of DNA and chromatin to assess the resulting DNA damage. Spatial mobility of individual DNA ends from double-strand breaks is modelled simultaneously with their processing by the non-homologous end-joining enzymes. To score diverse types of chromosome aberrations, the joined ends are classified regarding their original chromosomal location, orientation and the involvement of centromeres. A comparison with experimental data on dicentrics induced by gamma and alpha particles shows that their relative dose dependence is predicted correctly, although the absolute yields are overestimated. The critical model assumptions on chromatin mobility and on the initial damage recognition and chromatin remodelling steps and their future refinements to solve this issue are discussed.

The BIANCA model/code of radiation-induced cell death: application to human cells exposed to different radiation types

This paper presents a biophysical model of radiation-induced cell death, implemented as a Monte Carlo code called BIophysical ANalysis of Cell death and chromosome Aberrations (BIANCA), based on the assumption that some chromosome aberrations (dicentrics, rings, and large deletions, called ‘‘lethal aberrations’’) lead to clonogenic inactivation. In turn, chromosome aberrations are assumed to derive from clustered, and thus severe, DNA lesions (called ‘‘cluster lesions,’’ or CL) interacting at the micrometer scale; the CL yield and the threshold distance governing CL interaction are the only model parameters. After a pilot study on V79 hamster cells exposed to protons and carbon ions, in the present work the model was extended and applied to AG1522 human cells exposed to photons, He ions, and heavier ions including carbon and neon. The agreement with experimental survival data taken from the literature supported the assumptions. In particular, the inactivation of AG1522 cells was explained by lethal aberrations not only for X-rays, as already reported by others, but also for the aforementioned radiation types. Furthermore, the results are consistent with the hypothesis that the critical initial lesions leading to cell death are DNA cluster lesions having yields in the order of *2 CL Gy-1 cell-1 at low LET and*20 CL Gy-1 cell-1 at high LET, and that the processing of these lesions is modulated by proximity effects at the micrometer scale related to interphase chromatin organization. The model was then applied to calculate the fraction of inactivated cells, as well as the yields of lethal aberrations and cluster lesions, as a function of LET; the results showed a maximum around 130 keV/lm, and such maximum was much higher for cluster lesions and lethal aberrations than for cell inactivation.

Generalized time-dependent model of radiation-induced chromosomal aberrations in normal and repair-deficient human cells

We have developed a model that can simulate the yield of radiation-induced chromosomal aberrations (CAs) and unrejoined chromosome breaks in normal and repair-deficient cells. The model predicts the kinetics of chromosomal aberration formation after exposure in the G₀/G₁ phase of the cell cycle to either low- or high-LET radiation. A previously formulated model based on a stochastic Monte Carlo approach was updated to consider the time dependence of DNA double-strand break (DSB) repair (proper or improper), and different cell types were assigned different kinetics of DSB repair. The distribution of the DSB free ends was derived from a mechanistic model that takes into account the structure of chromatin and DSB clustering from high-LET radiation. The kinetics of chromosomal aberration formation were derived from experimental data on DSB repair kinetics in normal and repair-deficient cell lines. We assessed different types of chromosomal aberrations with the focus on simple and complex exchanges, and predicted the DSB rejoining kinetics and misrepair probabilities for different cell types. The results identify major cell-dependent factors, such as a greater yield of chromosome misrepair in ataxia telangiectasia (AT) cells and slower rejoining in Nijmegen (NBS) cells relative to the wild-type. The model's predictions suggest that two mechanisms could exist for the inefficiency of DSB repair in AT and NBS cells, one that depends on the overall speed of joining (either proper or improper) of DNA broken ends, and another that depends on geometric factors, such as the Euclidian distance between DNA broken ends, which influences the relative frequency of misrepair.

From DNA damage to chromosome aberrations: joining the break

Despite many years of experimental studies on radiation-induced chromosomal aberrations, and the recent progress in elucidating the molecular mechanisms of the DNA damage response, the link between DNA double-strand break repair and its expression as microscopically visible chromosomal rearrangements remains, in many ways, obscure. Some long standing controversies have partially been resolved to the satisfaction of most investigators, including the linearity of the dose-response for DNA double-strand break induction, the necessity of pairwise interaction of radiogenic damaged sites in the formation of exchange aberrations, and the importance of proximity between lesions in misrejoining. However, the contribution of different molecular DNA repair mechanisms (e.g., alternative end-joining pathways) and their impact on the kinetics of aberration formation is still unclear, as is the definition of "complex" radiogenic damaged sites - in either the chemical or spatial sense - which ostensibly lead to chromosome rearrangements. These topics have been recently debated by molecular biologists and cytogeneticists, whose opinions are summarized in this paper.

Biological effectiveness of accelerated particles for the induction of chromosome damage: track structure effects

We have investigated how radiation quality affects the induction of chromosomal aberrations in human cells. Human lymphocytes were irradiated in vitro with various energies of accelerated high charge and energy (HZE) particles including oxygen, neon, silicon, titanium and iron. Chromosome damage was assessed using three-color FISH chromosome painting in chemically induced premature chromosome condensation samples collected at first cell division after irradiation. The LET values for these particles ranged from 30 to 195 keV/μm, and their energies ranged from about 55 MeV/u to more than 1,000 MeV/u. The 89 and 142 MeV/u neon particles produced the most simple-type reciprocal exchanges per unit dose. For complex-type exchanges, 64 MeV/u neon and 450 MeV/u iron were equally effective and induced the greatest amount of complex damage. Track structure models predict that at a fixed value of LET, particles with lower charge number (Z) will have a higher biological effectiveness compared to particles with a higher Z, and that a saturation cross section will be observed for different radiation qualities. Our results are consistent with model expectations within the limitation of experimental error, and provide the most extensive data that have been reported on the radiation quality dependences of chromosomal aberrations.