A model of the cell nucleus for DNA damage calculations

Modelling radiobiology

Radiotherapy has played an essential role in cancer treatment for over a century, and remains one of the best-studied methods of cancer treatment. Because of its close links with the physical sciences, it has been the subject of extensive quantitative mathematical modelling, but a complete understanding of the mechanisms of radiotherapy has remained elusive. In part this is because of the complexity and range of scales involved in radiotherapy-from physical radiation interactions occurring over nanometres to evolution of patient responses over months and years. This review presents the current status and ongoing research in modelling radiotherapy responses across these scales, including basic physical mechanisms of DNA damage, the immediate biological responses this triggers, and genetic- and patient-level determinants of response. Finally, some of the major challenges in this field and potential avenues for future improvements are also discussed.

Modelling DNA damage-repair and beyond

The paper presents a review of mechanistic modelling studies of DNA damage and DNA repair, and consequences to follow in mammalian cell nucleus. We hypothesize DNA deletions are consequences of repair of double strand breaks leading to the modifications of genome that play crucial role in long term development of genetic inheritance and diseases. The aim of the paper is to review formation mechanisms underlying naturally occurring DNA deletions in the human genome and their potential relevance for bridging the gap between induced DNA double strand breaks and deletions in damaged human genome from endogenous and exogenous events. The model of the cell nucleus presented enables simulation of DNA damage at molecular level identifying the spectrum of damage induced in all chromosomal territories and loops. Our mechanistic modelling of DNA repair for double stand breaks (DSB), single strand breaks (SSB) and base damage (BD), shows the complexity of DNA damage is responsible for the longer repair times and the reason for the biphasic feature of mammalian cells repair curves. In the absence of experimentally determined data, the mechanistic model of repair predicts the in vivo rate constants for the proteins involved in the repair of DSB, SSB, and of BD.

Modelling Cellular Response to Ionizing Radiation: Mechanistic, Semi-Mechanistic, and Phenomenological Approaches - A Historical Perspective

Radiation research is a multidisciplinary field, and among its many branches, mathematical and computational modelers have played a significant role in advancing boundaries of knowledge. A fundamental contribution is modelling cellular response to ionizing radiation as that is the key to not only understanding how radiation can kill cancer cells, but also cause cancer and other health issues. The invention of microdosimetry in the 1950s by Harold Rossi paved the way for brilliant scientists to study the mechanism of radiation at cellular and sub-cellular scales. This paper reviews some snippets of ingenious mathematical and computational models published in microdosimetry symposium proceedings and publications of the radiation research community. Among these are simulations of radiation tracks at atomic and molecular levels using Monte Carlo methods, models of cell survival, quantification of the amount of energy required to create a single strand break, and models of DNA-damage-repair. These models can broadly be categorized into mechanistic, semi-mechanistic, and phenomenological approaches, and this review seeks to provide historical context of their development. We salute pioneers of the field and great teachers who supported and educated the younger members of the community and showed them how to build upon their work.

Proton relative biological effectiveness for the induction of DNA double strand breaks based on Geant4

Uncertainties in the relative biological effectiveness (RBE) of proton remains a major barrier to the biological optimization of proton therapy. A large amount of experimental data suggest that proton RBE is variable. As an evolving Monte Carlo code toolkit, Geant4-DNA is able to simulate the initial DNA damage caused by particle beams through physical and chemical interactions at the nanometer scale over a short period of time. This contributes to evaluating the radiobiological effects induced by ionizing radiation. Based on the Geant4-DNA toolkit, this study constructed a DNA geometric model containing 6.32Gbp, simulated the relationship between radiochemical yields (G-values) and their corresponding chemical constructors, and calculated a detailed calculation of the sources of damage and the complexity of damage in DNA strand breaks. The damage model constructed in this study can simulate the relative biological effectiveness (RBE) in the proton Bragg peak region. The results indicate that: (1) When the electron energy is below 400 keV, the yield of OH·account for 18.1% to 25.3% of the total water radiolysis yields. (2) Under the influence of histone clearance function, the yield of indirect damage account for over 72.93% of the yield of DNA strand breaks (SBs). When linear energy transfer (LET) increased from 29.79 (keV/μm) to 64.29 (keV/μm), the yield of double strand breaks (DSB) increased from 17.27% to 32.65%. (3) By investigating the effect of proton Bragg peak depth on the yield of direct DSB (DSBdirect) and total DSB (DSBtotal), theRBEDSBtotandRBEDSBdirlevels of cells show that the RBE value of protons reaches 2.2 in the Bragg peak region.

Evaluation of the Yield of DNA Double-Strand Breaks for Carbon Ions Using Monte Carlo Simulation and DNA Fragment Distribution

PURPOSE

The aim of this work was to provide a method to evaluate the yield of DNA double-strand breaks (DSBs) for carbon ions, overcoming the bias in existing methods due to the nonrandom distribution of DSBs.

METHODS AND MATERIALS

A previously established biophysical program based on the radiation track structure and a multilevel chromosome model was used to simulate DNA damage induced by x-rays and carbon ions. The fraction of activity retained (FAR) as a function of absorbed dose or particle fluence was obtained by counting the fraction of DNA fragments larger than 6 Mbp. Simulated FAR curves for the 250 kV x-rays and carbon ions at various energies were compared with measurements using constant-field gel electrophoresis. The doses or fluences at the FAR of 0.7 based on linear interpolation were used to estimate the simulation error for the production of DSBs.

RESULTS

The relative difference of doses at the FAR of 0.7 between simulation and experiment was -8.5% for the 250 kV x-rays. The relative differences of fluences at the FAR of 0.7 between simulations and experiments were -17.5%, -42.2%, -18.2%, -3.1%, 10.8%, and -14.5% for the 34, 65, 130, 217, 2232, and 3132 MeV carbon ions, respectively. In comparison, the measurement uncertainty was about 20%. Carbon ions produced remarkably more DSBs and DSB clusters per unit dose than x-rays. The yield of DSBs for carbon ions, ranging from 10 to 16 Gbp-1Gy-1, increased with linear energy transfer (LET) but plateaued in the high-LET end. The yield of DSB clusters first increased and then decreased with LET. This pattern was similar to the relative biological effectiveness for cell survival for heavy ions.

CONCLUSIONS

The estimated yields of DSBs for carbon ions increased from 10 Gbp-1Gy-1 in the low-LET end to 16 Gbp-1Gy-1 in the high-LET end with 20% uncertainty.

Modeling of dose and linear energy transfer homogeneity in cell nuclei exposed to alpha particles under various setup conditions

PURPOSE

Different alpha exposure setups are often used to study the relation between biological responses and LET. This study aimed to estimate the dose heterogeneity and uncertainty in four exposure setups using Geant4 and PARTRAC codes. The importance of the irradiation system characteristics was shown in the context of reporting experimental results, especially in radiobiological studies at the molecular level.

MATERIALS AND METHODS

Geant4 was used to estimate the dose distributions in cells grown on a disk exposed to alpha particles penetrating from above and below. The latter setup was simulated without and with a collimator. PARTRAC was used for the validation of Geant4 simulations based on distributions of the number of alpha particles penetrating a round nucleus and the deposited energy.

RESULTS

The LET distributions obtained for simulated setups excluding the collimator were wide and non-Gaussian. Using a collimator resulted in a Gaussian LET distribution, but strongly reduced dose rate and dose homogeneity. Comparison between PARTRAC and Geant4 calculations for the cell nucleus exposed to alpha radiation showed an excellent agreement.

CONCLUSIONS

The interpretation of results from radiobiological experiments with alpha particles should always cover the characteristics of the experimental setup, which can be done precisely with computational methods.

Development and implementation of a metaphase DNA model for ionizing radiation induced DNA damage calculation

Objective. To develop a metaphase chromosome model representing the complete genome of a human lymphocyte cell to support microscopic Monte Carlo (MMC) simulation-based radiation-induced DNA damage studies.Approach. We first employed coarse-grained polymer physics simulation to obtain a rod-shaped chromatid segment of 730 nm in diameter and 460 nm in height to match Hi-C data. We then voxelized the segment with a voxel size of 11 nm per side and connected the chromatid with 30 types of pre-constructed nucleosomes and 6 types of linker DNAs in base pair (bp) resolutions. Afterward, we piled different numbers of voxelized chromatid segments to create 23 pairs of chromosomes of 1-5μm long. Finally, we arranged the chromosomes at the cell metaphase plate of 5.5μm in radius to create the complete set of metaphase chromosomes. We implemented the model in gMicroMC simulation by denoting the DNA structure in a four-level hierarchical tree: nucleotide pairs, nucleosomes and linker DNAs, chromatid segments, and chromosomes. We applied the model to compute DNA damage under different radiation conditions and compared the results to those obtained with G0/G1 model and experimental measurements. We also performed uncertainty analysis for relevant simulation parameters.Main results. The chromatid segment was successfully voxelized and connected in bps resolution, containing 26.8 mega bps (Mbps) of DNA. With 466 segments, we obtained the metaphase chromosome containing 12.5 Gbps of DNA. Applying it to compute the radiation-induced DNA damage, the obtained results were self-consistent and agreed with experimental measurements. Through the parameter uncertainty study, we found that the DNA damage ratio between metaphase and G0/G1 phase models was not sensitive to the chemical simulation time. The damage was also not sensitive to the specific parameter settings in the polymer physics simulation, as long as the produced metaphase model followed a similar contact map distribution.Significance. Experimental data reveal that ionizing radiation induced DNA damage is cell cycle dependent. Yet, DNA chromosome models, except for the G0/G1 phase, are not available in the state-of-the-art MMC simulation. For the first time, we successfully built a metaphase chromosome model and implemented it into MMC simulation for radiation-induced DNA damage computation.

Impact of the Lorentz force on electron track structure and early DNA damage yields in magnetic resonance-guided radiotherapy

Magnetic resonance-guided radiotherapy (MRgRT) has been developed and installed in recent decades for external radiotherapy in several clinical facilities. Lorentz forces modulate dose distribution by charged particles in MRgRT; however, the impact of Lorentz forces on low-energy electron track structure and early DNA damage induction remain unclear. In this study, we estimated features of electron track structure and biological effects in a static magnetic field (SMF) using a general-purpose Monte Carlo code, particle and heavy ion transport code system (PHITS) that enables us to simulate low-energy electrons down to 1 meV by track-structure mode. The macroscopic dose distributions by electrons above approximately 300 keV initial energy in liquid water are changed by both perpendicular and parallel SMFs against the incident direction, indicating that the Lorentz force plays an important role in calculating dose within tumours. Meanwhile, DNA damage estimation based on the spatial patterns of atomic interactions indicates that the initial yield of DNA double-strand breaks (DSBs) is independent of the SMF intensity. The DSB induction is predominantly attributed to the secondary electrons below a few tens of eV, of which energy deposition patterns are not considerably affected by the Lorentz force. Our simulation study suggests that treatment planning for MRgRT can be made with consideration of only changed dose distribution.

THE APPLICATION OF NEURAL NETWORK TECHNOLOGY BASED ON MEA-BP ALGORITHM IN THE PREDICTION OF MICRODOSIMETRIC QUALITIES

The most abundant products of the interaction between radiation and matter are low-energy electrons, and the collisions between these electrons and biomolecules are the main initial source of radiation-based biological damage. To facilitate the rapid and accurate quantification of low-energy electrons (0.1-10 keV) in liquid water at different site diameters (1-2000 nm), this study obtained ${\overline{y}}_{\mathrm{F}}$ and ${\overline{y}}_{\mathrm{D}}$data for low-energy electrons under these conditions. This paper proposes a back-propagation (BP) neural network optimized by the mind evolutionary algorithm (MEA) to construct a prediction model and evaluate the corresponding prediction effect. The results show that the ${\overline{y}}_{\mathrm{F}}$ and ${\overline{y}}_{\mathrm{D}}$ values predicted by the MEA-BP neural network algorithm reach a training precision on the order of ${10}^{-8}$. The relative error range between the prediction results of the validated model and the Monte Carlo calculation results is 0.03-5.98% (the error range for single-energy electrons is 0.1-5.98%, and that for spectral distribution electrons is 0.03-4.4%).

Nanoscale Calculation of Proton-Induced DNA Damage Using a Chromatin Geometry Model with Geant4-DNA

Monte Carlo simulations can quantify various types of DNA damage to evaluate the biological effects of ionizing radiation at the nanometer scale. This work presents a study simulating the DNA target response after proton irradiation. A chromatin fiber model and new physics constructors with the ELastic Scattering of Electrons and Positrons by neutral Atoms (ELSEPA) model were used to describe the DNA geometry and the physical stage of water radiolysis with the Geant4-DNA toolkit, respectively. Three key parameters (the energy threshold model for strand breaks, the physics model and the maximum distance to distinguish DSB clusters) of scoring DNA damage were studied to investigate the impact on the uncertainties of DNA damage. On the basis of comparison of our results with experimental data and published findings, we were able to accurately predict the yield of various types of DNA damage. Our results indicated that the difference in physics constructor can cause up to 56.4% in the DNA double-strand break (DSB) yields. The DSB yields were quite sensitive to the energy threshold for strand breaks (SB) and the maximum distance to classify the DSB clusters, which were even more than 100 times and four times than the default configurations, respectively.

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.

Evaluating Iodine-125 DNA Damage Benchmarks of Monte Carlo DNA Damage Models

A wide range of Monte Carlo models have been applied to predict yields of DNA damage based on nanoscale track structure calculations. While often similar on the macroscopic scale, these models frequently employ different assumptions which lead to significant differences in nanoscale dose deposition. However, the impact of these differences on key biological readouts remains unclear. A major challenge in this area is the lack of robust datasets which can be used to benchmark models, due to a lack of resolution at the base pair level required to deeply test nanoscale dose deposition. Studies investigating the distribution of strand breakage in short DNA strands following the decay of incorporated 125I offer one of the few benchmarks for model predictions on this scale. In this work, we have used TOPAS-nBio to evaluate the performance of three Geant4-DNA physics models at predicting the distribution and yield of strand breaks in this irradiation scenario. For each model, energy and OH radical distributions were simulated and used to generate predictions of strand breakage, varying energy thresholds for strand breakage and OH interaction rates to fit to the experimental data. All three models could fit well to the observed data, although the best-fitting strand break energy thresholds ranged from 29.5 to 32.5 eV, significantly higher than previous studies. However, despite well describing the resulting DNA fragment distribution, these fit models differed significantly with other endpoints, such as the total yield of breaks, which varied by 70%. Limitations in the underlying data due to inherent normalisation mean it is not possible to distinguish clearly between the models in terms of total yield. This suggests that, while these physics models can effectively fit some biological data, they may not always generalise in the same way to other endpoints, requiring caution in their extrapolation to new systems and the use of multiple different data sources for robust model benchmarking.

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.

Verification of KURBUC-based ion track structure mode for proton and carbon ions in the PHITS code

The particle and heavy ion transport code system (PHITS) is a general-purpose Monte Carlo radiation transport simulation code. It has the ability to handle diverse particle types over a wide range of energy. The latest PHITS development enables the generation of track structure for proton and carbon ions (¹H⁺, ¹²C⁶⁺) based on the algorithms in the KURBUC code, which is considered as one of the most verified track-structure codes worldwide. This ion track-structure mode is referred to as the PHITS-KURBUC mode. In this study, the range, radial dose distributions, and microdosimetric distributions were calculated using the PHITS-KURBUC mode. Subsequently, they were compared with the corresponding data obtained from the original KURBUC and from other studies. These comparative studies confirm the successful inclusion of the KURBUC code in the PHITS code. As results of the synergistic effect between the macroscopic and microscopic radiation transport codes, this implementation enabled the detailed calculation of the microdosimetric and nanodosimetric quantities under complex radiation fields, such as proton beam therapy with the spread-out Bragg peak.

Simulation of Proton-Induced DNA Damage Patterns Using an Improved Clustering Algorithm

Simulations of deoxyribonucleic acid (DNA) molecular damage use the traversal algorithm that has the disadvantages of being time-consuming, slowly converging, and requiring high-performance computer clusters. This work presents an improved version of the algorithm, "density-based spatial clustering of applications with noise" (DBSCAN), using a KD-tree approach to find neighbors of each point for calculating clustered DNA damage. The resulting algorithm considers the spatial distributions for sites of energy deposition and hydroxyl radical attack, yielding the statistical probability of (single and double) DNA strand breaks. This work achieves high accuracy and high speed at calculating clustered DNA damage that has been induced by proton treatment at the molecular level while running on an i7 quad-core CPU. The simulations focus on the indirect effect generated by hydroxyl radical attack on DNA. The obtained results are consistent with those of other published experiments and simulations. Due to the array of chemical processes triggered by proton treatment, it is possible to predict the effects that different track structures of various energy protons produce on eliciting direct and indirect damage of DNA.

A parameter sensitivity study for simulating DNA damage after proton irradiation using TOPAS-nBio

Monte Carlo (MC) track structure simulation tools are commonly used for predicting radiation induced DNA damage by modeling the physical and chemical reactions at the nanometer scale. However, the outcome of these MC simulations is particularly sensitive to the adopted parameters which vary significantly across studies. In this study, a previously developed full model of nuclear DNA was used to describe the DNA geometry. The TOPAS-nBio MC toolkit was used to investigate the impact of physics and chemistry models as well as three key parameters (the energy threshold for direct damage, the chemical stage time length, and the probability of damage between hydroxyl radical reactions with DNA) on the induction of DNA damage. Our results show that the difference in physics and chemistry models alone can cause differences up to 34% and 16% in the DNA double strand break (DSB) yield, respectively. Additionally, changing the direct damage threshold, chemical stage length, and hydroxyl damage probability can cause differences of up to 28%, 51%, and 71% in predicted DSB yields, respectively, for the configurations in this study.

Internal microdosimetry of alpha-emitting radionuclides

At the tissue level, energy deposition in cells is determined by the microdistribution of alpha-emitting radionuclides in relation to sensitive target cells. Furthermore, the highly localized energy deposition of alpha particle tracks and the limited range of alpha particles in tissue produce a highly inhomogeneous energy deposition in traversed cell nuclei. Thus, energy deposition in cell nuclei in a given tissue is characterized by the probability of alpha particle hits and, in the case of a hit, by the energy deposited there. In classical microdosimetry, the randomness of energy deposition in cellular sites is described by a stochastic quantity, the specific energy, which approximates the macroscopic dose for a sufficiently large number of energy deposition events. Typical examples of the alpha-emitting radionuclides in internal microdosimetry are radon progeny and plutonium in the lungs, plutonium and americium in bones, and radium in targeted radionuclide therapy. Several microdosimetric approaches have been proposed to relate specific energy distributions to radiobiological effects, such as hit-related concepts, LET and track length-based models, effect-specific interpretations of specific energy distributions, such as the dual radiation action theory or the hit-size effectiveness function, and finally track structure models. Since microdosimetry characterizes only the initial step of energy deposition, microdosimetric concepts are most successful in exposure situations where biological effects are dominated by energy deposition, but not by subsequently operating biological mechanisms. Indeed, the simulation of the combined action of physical and biological factors may eventually require the application of track structure models at the nanometer scale.

A new open-source GPU-based microscopic Monte Carlo simulation tool for the calculations of DNA damages caused by ionizing radiation - Part II: sensitivity and uncertainty analysis

PURPOSE

Calculations of deoxyribonucleic acid (DNA) damages involve many parameters in the computation process. As these parameters are often subject to uncertainties, it is of central importance to comprehensively quantify their impacts on DNA single-strand break (SSB) and double-strand break (DSB) yields. This has been a challenging task due to the required large number of simulations and the relatively low computational efficiency using CPU-based MC packages. In this study, we present comprehensive evaluations on sensitivities and uncertainties of DNA SSB and DSB yields on 12 parameters using our GPU-based MC tool, gMicroMC.

METHODS

We sampled one electron at a time in a water sphere containing a human lymphocyte nucleus and transport the electrons and generated radicals until 2 Gy dose was accumulated in the nucleus. We computed DNA damages caused by electron energy deposition events in the physical stage and the hydroxyl radicals at the end of the chemical stage. We repeated the computations by varying 12 parameters: (a) physics cross section, (b) cutoff energy for electron transport, (c)-(e) three branching ratios of hydroxyl radicals in the de-excitation of excited water molecules, (f) temporal length of the chemical stage, (g)-(h) reaction radii for direct and indirect damages, (i) threshold energy defining the threshold damage model to generate a physics damage, (j)-(k) minimum and maximum energy values defining the linear-probability damage model to generate a physics damage, and (l) probability to generate a damage by a radical. We quantified sensitivity of SSB and DSB yields with respect to these parameters for cases with 1.0 and 4.5 keV electrons. We further estimated uncertainty of SSB and DSB yields caused by uncertainties of these parameters.

RESULTS

Using a threshold of 10% uncertainty as a criterion, threshold energy in the threshold damage model, maximum energy in the linear-probability damage model, and probability for a radical to generate a damage were found to cause large uncertainties in both SSB and DSB yields. The scaling factor of the cross section, cutoff energy, physics reaction radius, and minimum energy in the linear-probability damage model were found to generate large uncertainties in DSB yields.

CONCLUSIONS

We identified parameters that can generate large uncertainties in the calculations of SSB and DSB yields. Our study could serve as a guidance to reduce uncertainties of parameters and hence uncertainties of the simulation results.

Microdosimetric calculations of the direct DNA damage induced by low energy electrons using the Geant4-DNA Monte Carlo code

To calculate the yield of direct DNA damage induced by low energy electrons using Monte Carlo generated microdosimetric spectra at the nanometer scale and examine the influence of various simulation inputs. The potential of classical microdosimetry to offer a viable and simpler alternative to more elaborate mechanistic approaches for practical applications is discussed. Track-structure simulations with the Geant4-DNA low-energy extension of the Geant4 Monte Carlo toolkit were used for calculating lineal energy spectra in spherical volumes with dimensions relevant to double-strand-break (DSB) induction. The microdosimetric spectra were then used to calculate the yield of simple and clustered DSB based on literature values of the threshold energy of DNA damage. The influence of the different implementations of the dielectric function of liquid water available in Geant4-DNA (Option 2 and Option 4 constructors), as well as the effect of particle tracking cutoff energy and target size are examined. Frequency- and dose-mean lineal energies in liquid-water spheres of 2, 2.3, 2.6, and 3.4 nm diameter, as well as, number of simple and clustered DSB/Gy/cell are presented for electrons over the 100 eV to 100 keV energy range. Results are presented for both the 'default' (Option 2) and 'Ioannina' (Option 4) physics models of Geant4-DNA applying several commonly used tracking cutoff energies (10, 20, 50, 100 eV). Overall, the choice of the physics model and target diameter has a moderate effect (up to ~10%-30%) on the DSB yield whereas the effect of the tracking cutoff energy may be significant (>100%). Importantly, the yield of both simple and clustered DSB was found to vary significantly (by a factor of 2 or more) with electron energy over the examined range. The yields of electron-induced simple and clustered DSB exhibit a strong energy dependence over the 100 eV-100 keV range with implications to radiation quality issues. It is shown that a classical microdosimetry approach for the calculation of DNA damage based on lineal energy spectra in nanometer-size targets predicts comparable results to computationally intensive mechanistic approaches which use detailed atomistic DNA geometries, thus, offering a relatively simple and robust alternative for some practical applications.

Mechanistic Modelling of Radiation Responses

Radiobiological modelling has been a key part of radiation biology and therapy for many decades, and many aspects of clinical practice are guided by tools such as the linear-quadratic model. However, most of the models in regular clinical use are abstract and empirical, and do not provide significant scope for mechanistic interpretation or making predictions in novel cell lines or therapies. In this review, we will discuss the key areas of ongoing mechanistic research in radiation biology, including physical, chemical, and biological steps, and review a range of mechanistic modelling approaches which are being applied in each area, highlighting the possible opportunities and challenges presented by these techniques.

A New Standard DNA Damage (SDD) Data Format

Our understanding of radiation-induced cellular damage has greatly improved over the past few decades. Despite this progress, there are still many obstacles to fully understand how radiation interacts with biologically relevant cellular components, such as DNA, to cause observable end points such as cell killing. Damage in DNA is identified as a major route of cell killing. One hurdle when modeling biological effects is the difficulty in directly comparing results generated by members of different research groups. Multiple Monte Carlo codes have been developed to simulate damage induction at the DNA scale, while at the same time various groups have developed models that describe DNA repair processes with varying levels of detail. These repair models are intrinsically linked to the damage model employed in their development, making it difficult to disentangle systematic effects in either part of the modeling chain. These modeling chains typically consist of track-structure Monte Carlo simulations of the physical interactions creating direct damages to DNA, followed by simulations of the production and initial reactions of chemical species causing so-called "indirect" damages. After the induction of DNA damage, DNA repair models combine the simulated damage patterns with biological models to determine the biological consequences of the damage. To date, the effect of the environment, such as molecular oxygen (normoxic vs. hypoxic), has been poorly considered. We propose a new standard DNA damage (SDD) data format to unify the interface between the simulation of damage induction in DNA and the biological modeling of DNA repair processes, and introduce the effect of the environment (molecular oxygen or other compounds) as a flexible parameter. Such a standard greatly facilitates inter-model comparisons, providing an ideal environment to tease out model assumptions and identify persistent, underlying mechanisms. Through inter-model comparisons, this unified standard has the potential to greatly advance our understanding of the underlying mechanisms of radiation-induced DNA damage and the resulting observable biological effects when radiation parameters and/or environmental conditions change.

Accounting for radiation-induced indirect damage on DNA with the Geant 4-DNA code

The use of Monte Carlo (MC) simulations remains a powerful tool to study the biological effects induced by ionizing radiation on living beings. Several MC codes are commonly used in research fields such as nanodosimetry, radiotherapy, radiation protection, and space radiation. This work presents an enhancement of an existing model [1] for radiobiological purposes, to account for the indirect DNA damage induced by ionizing particles. The Geant4-DNA simulation toolkit was used to simulate the physical, pre-chemical, and chemical stages of early DNA damage induced by protons and α-particles. Liquid water was used as the medium for simulations. Two phase-space files were generated, one containing the energy deposition events and another with the position of chemical species produced by water radiolysis from 0.1 ps up to 1 ns. These files were used as input in the radiobiological code that contains the genetic material model with atomic resolution, consisting of several copies of 30 nm chromatin fibers. The B-DNA configuration was used. This work focused on the indirect damage produced by the hydroxyl radical (OH) attack on the sugar-phosphate group. The approach followed to account for the indirect DNA damage was the same as those used by other radiobiological codes [2,3]. The critical parameter considered here was the reaction radius, which was calculated from the Smoluchowski's diffusion equation. Single, double, and total strand break yields produced by direct, indirect, and mixed mechanisms are reported. The obtained results are consistent with experimental and calculation data sets published in the literature.

Mechanistic DNA damage simulations in Geant4-DNA part 1: A parameter study in a simplified geometry

Mechanistic modelling of DNA damage in Monte Carlo simulations is highly sensitive to the parameters that define DNA damage. In this work, we use a simple testing geometry to investigate how different choices of physics models and damage model parameters can change the estimation of DNA damage in a mechanistic DNA damage simulation built in Geant4-DNA. The choice of physics model can lead to variations by up to a factor of two in the yield of physically induced strand breaks, and the parameters that determine scavenging, and physical and chemical single strand break induction can have even larger consequences. Using low energy electrons as primary particles, a variety of parameters are tested in this geometry in order to arrive at a parameter set consistent with past simulation studies. We find that the modelling of scavenging can play an important role in determining results, and speculate that high-scavenging regimes, where only chemical radicals within 1 nm of DNA are simulated, could provide a good means of testing mechanistic DNA simulations.

Radiation track, DNA damage and response-a review

The purpose of this paper has been to review the current status and progress of the field of radiation biophysics, and draw attention to the fact that physics, in general, and radiation physics in particular, with the aid of mathematical modeling, can help elucidate biological mechanisms and cancer therapies. We hypothesize that concepts of condensed-matter physics along with the new genomic knowledge and technologies and mechanistic mathematical modeling in conjunction with advances in experimental DNA (Deoxyrinonucleic acid molecule) repair and cell signaling have now provided us with unprecedented opportunities in radiation biophysics to address problems in targeted cancer therapy, and genetic risk estimation in humans. Obviously, one is not dealing with 'low-hanging fruit', but it will be a major scientific achievement if it becomes possible to state, in another decade or so, that we can link mechanistically the stages between the initial radiation-induced DNA damage; in particular, at doses of radiation less than 2 Gy and with structural changes in genomic DNA as a precursor to cell inactivation and/or mutations leading to genetic diseases. The paper presents recent development in the physics of radiation track structure contained in the computer code system KURBUC, in particular for low-energy electrons in the condensed phase of water for which we provide a comprehensive discussion of the dielectric response function approach. The state-of-the-art in the simulation of proton and carbon ion tracks in the Bragg peak region is also presented. The paper presents a critical discussion of the models used for elastic scattering, and the validity of the trajectory approach in low-electron transport. Brief discussions of mechanistic and quantitative aspects of microdosimetry, DNA damage and DNA repair are also included as developed by the authors' work.

Microdosimetry of DNA conformations: relation between direct effect of (60)Co gamma rays and topology of DNA geometrical models in the calculation of A-, B- and Z-DNA radiation-induced damage yields

In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models.

Physical Considerations for Understanding Responses of Biological Systems to Low Doses of Ionizing Radiation: Nucleosome Clutches Constitute a Heterogeneous Distribution of Target Volumes

Humans are exposed to low doses of ionizing radiation that arise from a variety of sources. The response of biological systems to low doses of ionizing radiation depend on many factors. Some of the physical factors include distribution of the radiation sources, radiation track structure, structure and dimensions of the biological targets, temporal patterns of radiation exposure(s), absorbed dose rate and total absorbed dose. Recent discoveries suggest that assumptions regarding the structure of an important biological target, namely chromatin, may not be correct. It is now believed that chromatin fiber consists of heterogeneous groups of nucleosomes called clutches, and the distribution of clutch sizes differs between somatic cells and stem cells. This shift in paradigm may have implications for radiation target theory and its explanation of observations of clustered DNA damage.

The quest to exploit the Auger effect in cancer radiotherapy - a reflective review

To identify the emergence of the recognition of the potential of the Auger effect for clinical application, and after tracing the salient milestones towards that goal, to evaluate the status quo and future prospects. It was not until 40 years after the discovery of Auger electrons, that the availability of radioactive DNA precursors enabled the biological power, and the clinical potential, of the Auger effect to be appreciated. Important milestones on the path to clinical translation have been identified and reached, but hurdles remain. Nevertheless the potential is still evident, and there is reasonable optimism that the goal of clinical translation is achievable.

Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit

Understanding the fundamental mechanisms involved in the induction of biological damage by ionizing radiation remains a major challenge of today's radiobiology research. The Monte Carlo simulation of physical, physicochemical and chemical processes involved may provide a powerful tool for the simulation of early damage induction. The Geant4-DNA extension of the general purpose Monte Carlo Geant4 simulation toolkit aims to provide the scientific community with an open source access platform for the mechanistic simulation of such early damage. This paper presents the most recent review of the Geant4-DNA extension, as available to Geant4 users since June 2015 (release 10.2 Beta). In particular, the review includes the description of new physical models for the description of electron elastic and inelastic interactions in liquid water, as well as new examples dedicated to the simulation of physicochemical and chemical stages of water radiolysis. Several implementations of geometrical models of biological targets are presented as well, and the list of Geant4-DNA examples is described.

On the consistency of Monte Carlo track structure DNA damage simulations

PURPOSE

Monte Carlo track structures (MCTS) simulations have been recognized as useful tools for radiobiological modeling. However, the authors noticed several issues regarding the consistency of reported data. Therefore, in this work, they analyze the impact of various user defined parameters on simulated direct DNA damage yields. In addition, they draw attention to discrepancies in published literature in DNA strand break (SB) yields and selected methodologies.

METHODS

The MCTS code Geant4-DNA was used to compare radial dose profiles in a nanometer-scale region of interest (ROI) for photon sources of varying sizes and energies. Then, electron tracks of 0.28 keV-220 keV were superimposed on a geometric DNA model composed of 2.7 × 10(6) nucleosomes, and SBs were simulated according to four definitions based on energy deposits or energy transfers in DNA strand targets compared to a threshold energy ETH. The SB frequencies and complexities in nucleosomes as a function of incident electron energies were obtained. SBs were classified into higher order clusters such as single and double strand breaks (SSBs and DSBs) based on inter-SB distances and on the number of affected strands.

RESULTS

Comparisons of different nonuniform dose distributions lacking charged particle equilibrium may lead to erroneous conclusions regarding the effect of energy on relative biological effectiveness. The energy transfer-based SB definitions give similar SB yields as the one based on energy deposit when ETH ≈ 10.79 eV, but deviate significantly for higher ETH values. Between 30 and 40 nucleosomes/Gy show at least one SB in the ROI. The number of nucleosomes that present a complex damage pattern of more than 2 SBs and the degree of complexity of the damage in these nucleosomes diminish as the incident electron energy increases. DNA damage classification into SSB and DSB is highly dependent on the definitions of these higher order structures and their implementations. The authors' show that, for the four studied models, different yields are expected by up to 54% for SSBs and by up to 32% for DSBs, as a function of the incident electrons energy and of the models being compared.

CONCLUSIONS

MCTS simulations allow to compare direct DNA damage types and complexities induced by ionizing radiation. However, simulation results depend to a large degree on user-defined parameters, definitions, and algorithms such as: DNA model, dose distribution, SB definition, and the DNA damage clustering algorithm. These interdependencies should be well controlled during the simulations and explicitly reported when comparing results to experiments or calculations.

Evaluation of the dose enhancement of combined ¹⁰B + ¹⁵⁷Gd neutron capture therapy (NCT)

An innovative molecule, GdBLDL, for boron neutron capture therapy (BNCT) has been developed and its effectiveness as a BNCT carrier is currently under evaluation using in vivo experiments on small animal tumour models. The molecule contains both (10)B (the most commonly used NCT agent) and (157)Gd nuclei. (157)Gd is the second most studied element to perform NCT, mainly thanks to its high cross section for the capture of low-energy neutrons. The main drawback of (157)Gd neutron capture reaction is the very short range and low-energy secondary charged particles (Auger electrons), which requires (157)Gd to be very close to the cellular DNA to have an appreciable biological effect. Treatment doses were calculated by Monte Carlo simulations to ensure the optimised tumour irradiation and the sparing of the healthy organs of the irradiated animals. The enhancement of the absorbed dose due to the simultaneous presence of (10)B and (157)Gd in the experimental set-up was calculated and the advantage introduced by the presence of (157)Gd was discussed.

Spectrum of Radiation-Induced Clustered Non-DSB Damage - A Monte Carlo Track Structure Modeling and Calculations

The aim of this report is to present the spectrum of initial radiation-induced cellular DNA damage [with particular focus on non-double-strand break (DSB) damage] generated by computer simulations. The radiation types modeled in this study were monoenergetic electrons (100 eV-1.5 keV), ultrasoft X-ray photons Ck, AlK and TiK, as well as some selected ions including 3.2 MeV/u proton; 0.74 and 2.4 MeV/u helium ions; 29 MeV/u nitrogen ions and 950 MeV/u iron ions. Monte Carlo track structure methods were used to simulate damage induction by these radiation types in a cell-mimetic condition from a single-track action. The simulations took into account the action of direct energy deposition events and the reaction of hydroxyl radicals on atomistic linear B-DNA segments of a few helical turns including the water of hydration. Our results permitted the following conclusions: a. The absolute levels of different types of damage [base damage, simple and complex single-strand breaks (SSBs) and DSBs] vary depending on the radiation type; b. Within each damage class, the relative proportions of simple and complex damage vary with radiation type, the latter being higher with high-LET radiations; c. Overall, for both low- and high-LET radiations, the ratios of the yields of base damage to SSBs are similar, being about 3.0 ± 0.2; d. Base damage contributes more to the complexity of both SSBs and DSBs, than additional SSB damage and this is true for both low- and high-LET radiations; and e. The average SSB/DSB ratio for low-LET radiations is about 18, which is about 5 times higher than that for high-LET radiations. The hypothesis that clustered DNA damage is more difficult for cells to repair has gained currency among radiobiologists. However, as yet, there is no direct in vivo experimental method to validate the dependence of kinetics of DNA repair on DNA damage complexity (both DSB and non-DSB types). The data on the detailed spectrum of DNA damage presented here, in particular the non-DSB type, provide a good basis for testing mechanistic models of DNA repair kinetics such as base excision repair.

Accurate Measurements of Dielectric and Optical Functions of Liquid Water and Liquid Benzene in the VUV Region (1-100 eV) Using Small-Angle Inelastic X-ray Scattering

Using a third-generation synchrotron source (the BL12XU beamline at SPring-8), inelastic X-ray scattering (IXS) spectra of liquid water and liquid benzene were measured at energy losses of 1-100 eV with 0.24 eV resolution for small momentum transfers (q) of 0.23 and 0.32 au with ±0.06 au uncertainty for q. For both liquids, the IXS profiles at these values of q converged well after we corrected for multiple scattering, and these results confirmed the dipole approximation for q ≤ ∼0.3 au. Several dielectric and optical functions [including the optical oscillator strength distribution (OOS), the optical energy-loss function (OLF), the complex dielectric function, the complex index of refraction, and the reflectance] in the vacuum ultraviolet region were derived and tabulated from these small-angle (small q) IXS spectra. These new data were compared with previously obtained results, and this comparison demonstrated the strong reproducibility and accuracy of IXS spectroscopy. For both water and benzene, there was a notable similarity between the OOSs of the liquids and amorphous solids, and there was no evidence of plasmon excitation in the OLF. The static structure factor [S(q)] for q ≤ ∼0.3 au was also deduced and suggests that molecular models that include electron correlation effects can serve as a good approximation for the liquid S(q) values over the full range of q.

Genome-based, mechanism-driven computational modeling of risks of ionizing radiation: The next frontier in genetic risk estimation?

Research activity in the field of estimation of genetic risks of ionizing radiation to human populations started in the late 1940s and now appears to be passing through a plateau phase. This paper provides a background to the concepts, findings and methods of risk estimation that guided the field through the period of its growth to the beginning of the 21st century. It draws attention to several key facts: (a) thus far, genetic risk estimates have been made indirectly using mutation data collected in mouse radiation studies; (b) important uncertainties and unsolved problems remain, one notable example being that we still do not know the sensitivity of human female germ cells to radiation-induced mutations; and (c) the concept that dominated the field thus far, namely, that radiation exposures to germ cells can result in single gene diseases in the descendants of those exposed has been replaced by the concept that radiation exposure can cause DNA deletions, often involving more than one gene. Genetic risk estimation now encompasses work devoted to studies on DNA deletions induced in human germ cells, their expected frequencies, and phenotypes and associated clinical consequences in the progeny. We argue that the time is ripe to embark on a human genome-based, mechanism-driven, computational modeling of genetic risks of ionizing radiation, and we present a provisional framework for catalyzing research in the field in the 21st century.

Future development of biologically relevant dosimetry

Proton and ion beams are radiotherapy modalities of increasing importance and interest. Because of the different biological dose response of these radiations as compared with high-energy photon beams, the current approach of treatment prescription is based on the product of the absorbed dose to water and a biological weighting factor, but this is found to be insufficient for providing a generic method to quantify the biological outcome of radiation. It is therefore suggested to define new dosimetric quantities that allow a transparent separation of the physical processes from the biological ones. Given the complexity of the initiation and occurrence of biological processes on various time and length scales, and given that neither microdosimetry nor nanodosimetry on their own can fully describe the biological effects as a function of the distribution of energy deposition or ionization, a multiscale approach is needed to lay the foundation for the aforementioned new physical quantities relating track structure to relative biological effectiveness in proton and ion beam therapy. This article reviews the state-of-the-art microdosimetry, nanodosimetry, track structure simulations, quantification of reactive species, reference radiobiological data, cross-section data and multiscale models of biological response in the context of realizing the new quantities. It also introduces the European metrology project, Biologically Weighted Quantities in Radiotherapy, which aims to investigate the feasibility of establishing a multiscale model as the basis of the new quantities. A tentative generic expression of how the weighting of physical quantities at different length scales could be carried out is presented.

Oxidatively generated base damage to cellular DNA by hydroxyl radical and one-electron oxidants: similarities and differences

Hydroxyl radical (OH) and one-electron oxidants that may be endogenously formed through oxidative metabolism, phagocytosis, inflammation and pathological conditions constitute the main sources of oxidatively generated damage to cellular DNA. It is worth mentioning that exposure of cells to exogenous physical agents (UV light, high intensity UV laser, ionizing radiation) and chemicals may also induce oxidatively generated damage to DNA. Emphasis is placed in this short review article on the mechanistic aspects of OH and one-electron oxidant-mediated formation of single and more complex damage (tandem lesions, intra- and interstrand cross-links, DNA-protein cross-links) in cellular DNA arising from one radical hit. This concerns DNA modifications that have been accurately measured using suitable analytical methods such as high performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry. Evidence is provided that OH and one-electron oxidants after generating neutral radicals and base radical cations respectively may partly induce common degradation pathways. In addition, selective oxidative reactions giving rise to specific degradation products of OH and one-electron oxidation reactions that can be used as representative biomarkers of these oxidants have been identified.

Calculation of the energy deposition in nanovolumes by protons and HZE particles: geometric patterns of initial distributions of DNA repair foci

The biological effects of high-linear energy transfer (LET) radiation are different from those caused by low-LET radiation due to the difference in the patterns of energy deposition in cells. In this work, we studied the role of the track structure in the spatial distribution of radiation-induced double-strand breaks (DSBs). In the first part, the irradiation of a cubic volume of 12 µm of side by 300 MeV protons (LET ∼0.3 keV µm(-1)) and by 1 GeV/amu iron ion particles (LET∼150 keV µm(-1)) was simulated with the Monte Carlo code RITRACKS (relativistic ion tracks) and the dose was calculated in voxels of different sizes. In the second part, dose calculations were combined with chromosomes simulated by a random walk (RW) model to assess the formation of DSBs. The number of DSBs was calculated as a function of the dose and particle fluence for 1 GeV protons, 293 MeV/u carbon, and 1 GeV/u iron particles. Finally, the DSB yield was obtained as a function of the LET for protons, helium, and carbon. In general, the number and distribution of calculated DSBs were similar to experimental DNA repair foci data. From this study, we concluded that a stochastic model combining nanoscopic dose calculations and chromosomes simulated by RWs is a useful approach to study radiation-induced DSBs.

Ionizing radiation and genetic risks. XVII. Formation mechanisms underlying naturally occurring DNA deletions in the human genome and their potential relevance for bridging the gap between induced DNA double-strand breaks and deletions in irradiated germ cells

While much is known about radiation-induced DNA double-strand breaks (DSBs) and their repair, the question of how deletions of different sizes arise as a result of the processing of DSBs by the cell's repair systems has not been fully answered. In order to bridge this gap between DSBs and deletions, we critically reviewed published data on mechanisms pertaining to: (a) repair of DNA DSBs (from basic studies in this area); (b) formation of naturally occurring structural variation (SV) - especially of deletions - in the human genome (from genomic studies) and (c) radiation-induced mutations and structural chromosomal aberrations in mammalian somatic cells (from radiation mutagenesis and radiation cytogenetic studies). The specific aim was to assess the relative importance of the postulated mechanisms in generating deletions in the human genome and examine whether empirical data on radiation-induced deletions in mouse germ cells are consistent with predictions of these mechanisms. The mechanisms include (a) NHEJ, a DSB repair process that does not require any homology and which functions in all stages of the cell cycle (and is of particular relevance in G0/G1); (b) MMEJ, also a DSB repair process but which requires microhomology and which presumably functions in all cell cycle stages; (c) NAHR, a recombination-based DSB repair mechanism which operates in prophase I of meiosis in germ cells; (d) MMBIR, a microhomology-mediated, replication-based mechanism which operates in the S phase of the cell cycle, and (e) strand slippage during replication (involved in the origin of small insertions and deletions (INDELs). Our analysis permits the inference that, between them, these five mechanisms can explain nearly all naturally occurring deletions of different sizes identified in the human genome, NAHR and MMBIR being potentially more versatile in this regard. With respect to radiation-induced deletions, the basic studies suggest that those arising as a result of the operation of NHEJ/MMEJ processes, as currently formulated, are expected to be relatively small. However, data on induced mutations in mouse spermatogonial stem cells (irradiation in G0/G1 phase of the cell cycle and DSB repair presumed to be via NHEJ predominantly) show that most are associated with deletions of different sizes, some in the megabase range. There is thus a 'discrepancy' between what the basic studies suggest and the empirical observations in mutagenesis studies. This discrepancy, however, is only an apparent but not a real one. It can be resolved by considering the issue of deletions in the broader context of and in conjunction with the organization of chromatin in chromosomes and nuclear architecture, the conceptual framework for which already exists in studies carried out during the past fifteen years or so. In this paper, we specifically hypothesize that repair of DSBs induced in chromatin loops may offer a basis to explain the induction of deletions of different sizes and suggest an approach to test the hypothesis. We emphasize that the bridging of the gap between induced DSB and resulting deletions of different sizes is critical for current efforts in computational modeling of genetic risks.

Absolute cross section for low-energy-electron damage to condensed macromolecules: a case study of DNA

Cross sections (CSs) for the interaction of low-energy electrons (LEE) with condensed macromolecules are essential parameters for accurate modeling of radiation-induced molecular decomposition and chemical synthesis. Electron irradiation of dry nanometer-scale macromolecular solid films has often been employed to measure CSs and other quantitative parameters for LEE interactions. Since such films have thicknesses comparable with electron thermalization distances, energy deposition varies throughout the film. Moreover, charge accumulation occurring inside the films shields a proportion of the macromolecules from electron irradiation. Such effects complicate the quantitative comparison of the CSs obtained in films of different thicknesses and limit the applicability of such measurements. Here, we develop a simple mathematical model, termed the molecular survival model, that employs a CS for a particular damage process together with an attenuation length related to the total CS, to investigate how a measured CS might be expected to vary with experimental conditions. As a case study, we measure the absolute CS for the formation of DNA strand breaks (SBs) by electron irradiation at 10 and 100 eV of lyophilized plasmid DNA films with thicknesses between 10 and 30 nm. The measurements are shown to depend strongly on the thickness and charging condition of the nanometer-scale films. Such behaviors are in accord with the model and support its validity. Via this analysis, the CS obtained for SB damage is nearly independent of film thickness and charging effects. In principle, this model can be adapted to provide absolute CSs for electron-induced damage or reactions occurring in other molecular solids across a wider range of experimental conditions.