First steps towards systems radiation biology studies concerned with DNA and chromosome structure within living cells

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.

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

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

An inter-comparison between radiobiological characteristics of a commercial low-energy IORT system by Geant4-DNA and MCDS Monte Carlo codes

INTRODUCTION

The need for accurate relative biological effectiveness (RBE) estimation for low energy therapeutic X-rays (corresponding to 50 kV nominal energy of a commercial low-energy IORT system (INTRABEAM)) is a crucial issue due to increased radiobiological effects, respect to high energy photons. Modeling of radiation-induced DNA damage through Monte Carlo (MC) simulation approaches can give useful information. Hence, this study aimed to evaluate and compare RBE of low energy therapeutic X-rays using Geant4-DNA toolkit and Monte Carlo damage simulation (MCDS) code.

MATERIALS AND METHODS

RBE calculations were performed considering the emitted secondary electron spectra through interactions of low energy X-rays inside the medium. In Geant4-DNA, the DNA strand breaks were obtained by employing a B-DNA model in physical stage with 10.79 eV energy-threshold and the probability of hydroxyl radical's chemical reactions of about 0.13%. Furthermore, RBE estimations by MCDS code were performed under fully aerobic conditions.

RESULTS

Acquired results by two considered MC codes showed that the same trend is found for RBEDSB and RBESSB variations. Totally, a reasonable agreement between the calculated RBE values (both RBESSB and RBEDSB) existed between the two considered MC codes. The mean differences of 9.2% and 1.8% were obtained between the estimated RBESSB and RBEDSB values by two codes, respectively.

CONCLUSION

Based on the obtained results, it can be concluded that a tolerable accordance is found between the calculated RBEDSB values through MCDS and Geant4-DNA, a fact which appropriates both codes for RBE evaluations of low energy therapeutic X-rays, especially in the case of RBEDSB where lethal damages are regarded.

Effects of Differing Underlying Assumptions in In Silico Models on Predictions of DNA Damage and Repair

The induction and repair of DNA double-strand breaks (DSBs) are critical factors in the treatment of cancer by radiotherapy. To investigate the relationship between incident radiation and cell death through DSB induction many in silico models have been developed. These models produce and use custom formats of data, specific to the investigative aims of the researchers, and often focus on particular pairings of damage and repair models. In this work we use a standard format for reporting DNA damage to evaluate combinations of different, independently developed, models. We demonstrate the capacity of such inter-comparison to determine the sensitivity of models to both known and implicit assumptions. Specifically, we report on the impact of differences in assumptions regarding patterns of DNA damage induction on predicted initial DSB yield, and the subsequent effects this has on derived DNA repair models. The observed differences highlight the importance of considering initial DNA damage on the scale of nanometres rather than micrometres. We show that the differences in DNA damage models result in subsequent repair models assuming significantly different rates of random DSB end diffusion to compensate. This in turn leads to disagreement on the mechanisms responsible for different biological endpoints, particularly when different damage and repair models are combined, demonstrating the importance of inter-model comparisons to explore underlying model assumptions.

Radiation-induced double-strand breaks by internal ex vivo irradiation of lymphocytes: Validation of a Monte Carlo simulation model using GATE and Geant4-DNA

This study describes a method to validate a radiation transport model that quantifies the number of DNA double-strand breaks (DSB) produced in the lymphocyte nucleus by internal ex vivo irradiation of whole blood with the radionuclides 90Y, 99mTc, 123I, 131I, 177Lu, 223Ra, and 225Ac in a test vial using the GATE/Geant4 code at the macroscopic level and the Geant4-DNA code at the microscopic level.

METHODS

The simulation at the macroscopic level reproduces an 8 mL cylindrical water-equivalent medium contained in a vial that mimics the geometry for internal ex vivo blood irradiation. The lymphocytes were simulated as spheres of 3.75 µm radius randomly distributed, with a concentration of 125 spheres/mL. A phase-space actor was attached to each sphere to register all the entering particles. The simulation at the microscopic level for each radionuclide was performed using the Geant4-DNA tool kit, which includes the clustering example centered on a density-based spatial clustering of applications with noise (DBSCAN) algorithm. The irradiation source was constructed by generating a single phase space from the sum of all phase spaces. The lymphocyte nucleus was defined as a water sphere of a 3.1 µm radius. The absorbed dose coefficients for lymphocyte nuclei (dLymph) were calculated and compared with macroscopic whole blood absorbed dose coefficients (dBlood). The DBSCAN algorithm was used to calculate the number of DSBs. Lastly, the number of DSB∙cell-1∙mGy-1 (simulation) was compared with the number of radiation-induced foci per cell and absorbed dose (RIF∙cell-1∙mGy-1) provided by experimental data for gamma and beta emitting radionuclides. For alpha emitters, dLymph and the number of α-tracks∙100 cell-1∙mGy-1 and DBSs∙µm-1 were calculated using experiment-based thresholds for the α-track lengths and DBSs/track values. The results were compared with the results of an ex vivo study with 223Ra.

RESULTS

The dLymph values differed from the dBlood values by -1.0% (90Y), -5.2% (99mTc), -22.3% (123I), 0.35% (131I), 2.4% (177Lu), -5.6% (223Ra) and -6.1% (225Ac). The number of DSB∙cell-1∙mGy-1 for each radionuclide was 0.015 DSB∙cell-1∙mGy-1 (90Y), 0.012 DSB∙cell-1∙mGy-1 (99mTc), 0.014DSB∙cell-1∙mGy-1 (123I), 0.012 DSB∙cell-1∙mGy-1 (131I), and 0.016 DSB∙cell-1∙mGy-1 (177Lu). These values agree very well with experimental data. The number of α-tracks∙100 cells-1∙mGy-1 for 223Ra and 225Ac where 0.144 α-tracks∙100 cells-1∙mGy-1 and 0.151 α-tracks∙100 cells-1∙mGy-1, respectively. These values agree very well with experimental data. Moreover, the linear density of DSBs per micrometer α-track length were 11.13 ± 0.04 DSB/µm and 10.86 ± 0.06 DSB/µm for 223Ra and 225Ac, respectively.

CONCLUSION

This study describes a model to simulate the DNA DSB damage in lymphocyte nuclei validated by experimental data obtained from internal ex vivo blood irradiation with radionuclides frequently used in diagnostic and therapeutic procedures in nuclear medicine.

The Cellular Response to Complex DNA Damage Induced by Ionising Radiation

Radiotherapy (ionising radiation; IR) is utilised in the treatment of ~50% of all human cancers, and where the therapeutic effect is largely achieved through DNA damage induction. In particular, complex DNA damage (CDD) containing two or more lesions within one to two helical turns of the DNA is a signature of IR and contributes significantly to the cell killing effects due to the difficult nature of its repair by the cellular DNA repair machinery. The levels and complexity of CDD increase with increasing ionisation density (linear energy transfer, LET) of the IR, such that photon (X-ray) radiotherapy is deemed low-LET whereas some particle ions (such as carbon ions) are high-LET radiotherapy. Despite this knowledge, there are challenges in the detection and quantitative measurement of IR-induced CDD in cells and tissues. Furthermore, there are biological uncertainties with the specific DNA repair proteins and pathways, including components of DNA single and double strand break mechanisms, that are engaged in CDD repair, which very much depends on the radiation type and associated LET. However, there are promising signs that advancements are being made in these areas and which will enhance our understanding of the cellular response to CDD induced by IR. There is also evidence that targeting CDD repair, particularly through inhibitors against selected DNA repair enzymes, can exacerbate the impact of higher LET, which could be explored further in a translational context.

Mechanistic modelling of oxygen enhancement ratio of radiation via Monte Carlo simulation-based DNA damage calculation

Objective.Oxygen plays an important role in affecting the cellular radio-sensitivity to ionizing radiation. The objective of this study is to build a mechanistic model to compute oxygen enhancement ratio (OER) using a GPU-based Monte Carlo (MC) simulation package gMicroMC for microscopic radiation transport simulation and DNA damage calculation.Approach.We first simulated the water radiolysis process in the presence of DNA and oxygen for 1 ns and recorded the produced DNA damages. In this process, chemical reactions among oxygen, water radiolysis free radicals and DNA molecules were considered. We then applied a probabilistic approach to model the reactions between oxygen and indirect DNA damages for a maximal reaction time oft0. Finally, we defined two parametersP0andP1, representing probabilities for DNA damages without and with oxygen fixation effect not being restored in the repair process, to compute the final DNA double strand breaks (DSBs). As cell survival fraction is mainly determined by the number of DSBs, we assumed that the same numbers of DSBs resulted in the same cell survival rates, which enabled us to compute the OER as the ratio of doses producing the same number of DSBs without and with oxygen. We determined the three parameters (t0,P0andP1) by fitting the OERs obtained in our computation to a set of published experimental data under x-ray irradiation. We then validated the model by performing OER studies under proton irradiation and studied model sensitivity to parameter values.Main results.We obtained the model parameters ast0= 3.8 ms,P0= 0.08, andP1= 0.28 with a mean difference of 3.8% between the OERs computed by our model and that obtained from experimental measurements under x-ray irradiation. Applying the established model to proton irradiation, we obtained OERs as functions of oxygen concentration, LET, and dose values, which generally agreed with published experimental data. The parameter sensitivity analysis revealed that the absolute magnitude of the OER curve relied on the values ofP0andP1, while the curve was subject to a horizontal shift when adjustingt0.Significance.This study developed a mechanistic model that fully relies on microscopic MC simulations to compute OER.

Computational modelling of γ-H2AX foci formation in human cells induced by alpha particle exposure

In cellular experiments, radiation-induced DNA damage can be quantified by counting the number of γ-H2AX foci in cell nucleus by using an immunofluorescence microscope. Quantification of DNA damage carries uncertainty, not only due to lack of full understanding the biological processes but also limitations in measurement techniques. The causes of limited certainty include the possibility of expressing foci in varying sizes responding individual DSBs and the overlapping of foci on the two-dimensional (2D) immunofluorescence microscopy image of γ-H2AX foci, especially when produced due to high-LET radiation exposure. There have been discussions on those limitations, but no successful studies to overcome them. In this paper, a practical modelling has been developed to simulate the occurrences of double-strand breaks (DSBs) and the formations of γ-H2AX foci in response to individual DSB formations, in cell nucleus due to exposure to alpha particles. Cell irradiation and DSB production were simulated using a user-written code that utilizes Geant4-DNA physics models. A C +  + code was used to simulate the formation γ-H2AX foci, which were spatially correlated to the loci of DBSs, and to calculate the number of individual foci from the observed 2D image of the cell nucleus containing the overlapping γ-H2AX foci. The average size of focal images was larger from alpha particle exposure than that from X-ray exposure, whereas the number of separate focal images were comparable except at doses up to 0.5 Gy. About 40% of separate focal images consisted of overlapping γ-H2AX foci at 1 Gy of alpha particle exposure. The foci overlapping ratios were obtained by simulation for individual size groups of focal images at varying doses. The size distributions of foci at varying doses were determined with experimentally obtained separate focal images. The correction factor for foci number was calculated using the foci overlapping ratio and foci size distribution, which are specific to dose from alpha particle exposure. The number of individual foci formations induced by applying the correction factor to the experimentally observed number of focal images better reflected the quality of alpha particles in causing DNA damage. Consequently, the conventional γ-H2AX assay can be better implemented by employing this computational modelling of γ-H2AX foci formation.

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.

Dosimetry of heavy ion exposure to human cells using nanoscopic imaging of double strand break repair protein clusters

The human body is constantly exposed to ionizing radiation of different qualities. Especially the exposure to high-LET (linear energy transfer) particles increases due to new tumor therapy methods using e.g. carbon ions. Furthermore, upon radiation accidents, a mixture of radiation of different quality is adding up to human radiation exposure. Finally, long-term space missions such as the mission to mars pose great challenges to the dose assessment an astronaut was exposed to. Currently, DSB counting using γH2AX foci is used as an exact dosimetric measure for individuals. Due to the size of the γH2AX IRIF of ~ 0.6 µm, it is only possible to count DSB when they are separated by this distance. For high-LET particle exposure, the distance of the DSB is too small to be separated and the dose will be underestimated. In this study, we developed a method where it is possible to count DSB which are separated by a distance of ~ 140 nm. We counted the number of ionizing radiation-induced pDNA-PKcs (DNA-PKcs phosphorylated at T2609) foci (size = 140 nm ± 20 nm) in human HeLa cells using STED super-resolution microscopy that has an intrinsic resolution of 100 nm. Irradiation was performed at the ion microprobe SNAKE using high-LET 20 MeV lithium (LET = 116 keV/µm) and 27 MeV carbon ions (LET = 500 keV/µm). pDNA-PKcs foci label all DSB as proven by counterstaining with 53BP1 after low-LET γ-irradiation where separation of individual DSB is in most cases larger than the 53BP1 gross size of about 0.6 µm. Lithium ions produce (1.5 ± 0.1) IRIF/µm track length, for carbon ions (2.2 ± 0.2) IRIF/µm are counted. These values are enhanced by a factor of 2–3 compared to conventional foci counting of high-LET tracks. Comparison of the measurements to PARTRAC simulation data proof the consistency of results. We used these data to develop a measure for dosimetry of high-LET or mixed particle radiation exposure directly in the biological sample. We show that proper dosimetry for radiation up to a LET of 240 keV/µm is possible.

Chromosome Folding Promotes Intrachromosomal Aberrations under Radiation- and Nuclease-Induced DNA Breakage

The long-standing question in radiation and cancer biology is how principles of chromosome organization impact the formation of chromosomal aberrations (CAs). To address this issue, we developed a physical modeling approach and analyzed high-throughput genomic data from chromosome conformation capture (Hi-C) and translocation sequencing (HTGTS) methods. Combining modeling of chromosome structure and of chromosomal aberrations induced by ionizing radiation (IR) and nuclease we made predictions which quantitatively correlated with key experimental findings in mouse chromosomes: chromosome contact maps, high frequency of cis-translocation breakpoints far outside of the site of nuclease-induced DNA double-strand breaks (DSBs), the distinct shape of breakpoint distribution in chromosomes with different 3D organizations. These correlations support the heteropolymer globule principle of chromosome organization in G1-arrested pro-B mouse cells. The joint analysis of Hi-C, HTGTS and physical modeling data offers mechanistic insight into how chromosome structure heterogeneity, globular folding and lesion dynamics drive IR-recurrent CAs. The results provide the biophysical and computational basis for the analysis of chromosome aberration landscape under IR and nuclease-induced DSBs.

Destabilizing Effects of Ionizing Radiation on Chromosomes: Sizing up the Damage

For long-term survival and evolution, all organisms have depended on a delicate balance between processes involved in maintaining stability of their genomes and opposing processes that lead toward destabilization. At the level of mammalian somatic cells in renewal tissues, events or conditions that can tip this balance toward instability have attracted special interest in connection with carcinogenesis. Mutations affecting DNA (and its subsequent repair) would, of course, be a major consideration here. These may occur spontaneously through endogenous cellular processes or as a result of exposure to mutagenic environmental agents. It is in this context that we discuss the rather unique destabilizing effects of ionizing radiation (IR) in terms of its ability to cause large-scale structural rearrangements to the genome. We present arguments supporting the conclusion that these and other important effects of IR originate largely from microscopically visible chromosome aberrations.

Multi-scaled Monte Carlo calculation for radon-induced cellular damage in the bronchial airway epithelium

Radon is a leading cause of lung cancer in indoor public and mining workers. Inhaled radon progeny releases alpha particles, which can damage cells in the airway epithelium. The extent and complexity of cellular damage vary depending on the alpha particle's kinetic energy and cell characteristics. We developed a framework to quantitate the cellular damage on the nanometer and micrometer scales at different intensities of exposure to radon progenies Po-218 and Po-214. Energy depositions along the tracks of alpha particles that were slowing down were simulated on a nanometer scale using the Monte Carlo code Geant4-DNA. The nano-scaled track histories in a 5 μm radius and 1 μm-thick cylindrical volume were integrated into the tracking scheme of alpha trajectories in a micron-scale bronchial epithelium segment in the user-written SNU-CDS program. Damage distribution in cellular DNA was estimated for six cell types in the epithelium. Deep-sited cell nuclei in the epithelium would have less chance of being hit, but DNA damage from a single hit would be more serious, because low-energy alpha particles of high LET would hit the nuclei. The greater damage in deep-sited nuclei was due to the 7.69 MeV alpha particles emitted from Po-214. From daily work under 1 WL of radon concentration, basal cells would respond with the highest portion of complex DSBs among the suspected progenitor cells in the most exposed regions of the lung epithelium.

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.

Cellular S-value evaluation based on real human cell models using the GATE MC package

Exploring the spatial distribution of the energy loss of ionising radiation at the subcellular level is indispensable for evaluating the radiobiological effects of targeted radionuclide therapy accurately. Believing that S-values are important for obtaining the target dose, the Committee on Medical Internal Radiation Dose (MIRD) proposed a method to obtain the cellular dosimetric parameter. However, most available data on cellular S-values were calculated based on simple geometric models, such as ellipsoids or spheres, which do not accurately reflect biological reality. To investigate the influence of the cellular model on S-values, calculations were performed for two kinds of polygon-surface phantom models of realistic, individual human cells, the lung epithelial cell model (the B2B Phantom model) and the hepatocyte model (the Liver Phantom model), using the Monte Carlo (MC) software package GATE. To analyse the influence of cell geometry on the final S-value, the differences in the S-values between the realistic cell models and simple geometric sphere and ellipsoid models with similar volumes were calculated and compared for six different combinations of source and target regions. The irradiation conditions were 0.01-1.10 MeV monoenergetic electron sources and the Auger electronic therapy nuclides Ga-67, Tc-99m, In-111, I-125 and Tl-201, which are commonly used in nuclear medicine. The S-values calculated in this study are different from the results of the simple geometry models proposed by previous researchers. Two more precise polygon-surface phantom models of realistic, individual human cells were used, which provided more accurate information about the cell dose and will be very useful for the diagnostic application of radiotherapy in the future.

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.

Mixed secondary chromatin structure revealed by modeling radiation-induced DNA fragment length distribution

Spatial chromatin structure plays fundamental roles in many vital biological processes including DNA replication, transcription, damage and repair. However, the current understanding of the secondary structure of chromatin formed by local nucleosome-nucleosome interactions remains controversial, especially for the existence and conformation of 30 nm structure. Since chromatin structure influences the fragment length distribution (FLD) of ionizing radiation-induced DNA strand breaks, a 3D chromatin model fitting FLD patterns can help to distinguish different models of chromatin structure. Here, we developed a novel "30-C" model combining 30 nm chromatin structure models with Hi-C data, which measured the spatial contact frequency between different loci in the genome. We first reconstructed the 3D coordinates of the 25 kb bins from Hi-C heatmaps. Within the 25 kb bins, lower level chromatin structures supported by recent studies were filled. Simulated FLD patterns based on the 30-C model were compared to published FLD patterns induced by heavy ion radiation to validate the models. Importantly, the 30-C model predicted that the most probable chromatin fiber structure for human interphase fibroblasts in vivo was 45% zig-zag 30 nm fibers and 55% 10 nm fibers.

Ionizing Radiation and Complex DNA Damage: Quantifying the Radiobiological Damage Using Monte Carlo Simulations

Ionizing radiation is a common tool in medical procedures. Monte Carlo (MC) techniques are widely used when dosimetry is the matter of investigation. The scientific community has invested, over the last 20 years, a lot of effort into improving the knowledge of radiation biology. The present article aims to summarize the understanding of the field of DNA damage response (DDR) to ionizing radiation by providing an overview on MC simulation studies that try to explain several aspects of radiation biology. The need for accurate techniques for the quantification of DNA damage is crucial, as it becomes a clinical need to evaluate the outcome of various applications including both low- and high-energy radiation medical procedures. Understanding DNA repair processes would improve radiation therapy procedures. Monte Carlo simulations are a promising tool in radiobiology studies, as there are clear prospects for more advanced tools that could be used in multidisciplinary studies, in the fields of physics, medicine, biology and chemistry. Still, lot of effort is needed to evolve MC simulation tools and apply them in multiscale studies starting from small DNA segments and reaching a population of cells.

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.

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.

Predicting DNA damage foci and their experimental readout with 2D microscopy: a unified approach applied to photon and neutron exposures

The consideration of how a given technique affects results of experimental measurements is a must to achieve correct data interpretation. This might be challenging when it comes to measurements on biological systems, where it is unrealistic to have full control (e.g. through a software replica) of all steps in the measurement chain. In this work we address how the effectiveness of different radiation qualities in inducing biological damage can be assessed measuring DNA damage foci yields, only provided that artefacts related to the scoring technique are adequately considered. To this aim, we developed a unified stochastic modelling approach that, starting from radiation tracks, predicts both the induction, spatial distribution and complexity of DNA damage, and the experimental readout of foci when immunocytochemistry coupled to 2D fluorescence microscopy is used. The approach is used to interpret γ-H2AX data for photon and neutron exposures. When foci are reconstructed in the whole cell nucleus, we obtain information on damage characteristics "behind" experimental observations, as the average damage content of a focus. We reproduce how the detection technique affects experimental findings, e.g. contributing to the saturation of foci yields scored at 30 minutes after exposure with increasing dose and to the lack of dose dependence for yields at 24 hours.

TRACKING DOWN ALPHA-PARTICLES: THE DESIGN, CHARACTERISATION AND TESTING OF A SHALLOW-ANGLED ALPHA-PARTICLE IRRADIATOR

Human exposure to α-particles from radon and other radionuclides is associated with carcinogenesis, but if well controlled and targeted to cancer cells, α-particles may be used in radiotherapy. Thus, it is important to understand the biological effects of α-particles to predict cancer risk and optimise radiotherapy. To enable studies of α-particles in cells, we developed and characterised an α-particle automated irradiation rig that allows exposures at a shallow angle (70° to the normal) of cell monolayers in a 30 mm diameter dish to complement standard perpendicular irradiations. The measured incident energy of the α-particles was 3.3 ± 0.5 MeV (LET in water = 120 keV μm-1), with a maximum incident dose rate of 1.28 ± 0.02 Gy min-1, which for a 5 μm cell monolayer corresponds to a mean dose rate of 1.57 ± 0.02 Gy min-1 and a mean LET in water of 154 keV μm-1. The feasibility of resolving radiation-induced DNA double-strand breaks (DSB) foci along the track of α-particles was demonstrated using immunofluorescent labelling with γH2AX and 53BP1 in normal MRC-5 human lung cells.

From Energy Deposition of Ionizing Radiation to Cell Damage Signaling: Benchmarking Simulations by Measured Yields of Initial DNA Damage after Ion Microbeam Irradiation

Advances in accelerator technology, which have enabled conforming radiotherapy with charged hadronic species, have brought benefits as well as potential new risks to patients. To better understand the effects of ionizing radiation on tumor and surrounding tissue, it is important to investigate and quantify the relationship between energy deposition at the nanometric scale and the initial biological events. Monte Carlo track structure simulation codes provide a powerful tool for investigating this relationship; however, their success and reliability are dependent on their improvement and development accordingly to the dedicated biological data to which they are challenged. For this aim, a microbeam facility that allows for fluence control, down to one ion per cell nucleus, was used to evaluate relative frequencies of DNA damage after interaction between the incoming ion and DNA according to radiation quality. Primary human cells were exposed to alpha particles of three different energies with respective linear energy transfers (LETs) of approximately 36, 85 or 170 keV·µm^-1 at the cells' center position, or to protons (19 keV·µm^-1). Statistical evaluation of nuclear foci formation (53BP1/γ-H2AX), observed using immunofluorescence and related to a particle traversal, was undertaken in a large population of cell nuclei. The biological results were adjusted to consider the factors that drive the experimental uncertainties, then challenged with results using Geant4-DNA code modeling of the ionizing particle interactions on a virtual phantom of the cell nucleus with the same mean geometry and DNA density as the cells used in our experiments. Both results showed an increase of relative frequencies of foci (or simulated DNA damage) in cell nuclei as a function of increasing LET of the traversing particles, reaching a quasi-plateau when the LET exceeded 80-90 keV·µm^-1. For the LET of an alpha particle ranging from 80-90 to 170 keV·µm^-1, 10-30% of the particle hits did not lead to DNA damage inducing 53BP1 or γ-H2AX foci formation.

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.

Comprehensive track-structure based evaluation of DNA damage by light ions from radiotherapy-relevant energies down to stopping

Track structures and resulting DNA damage in human cells have been simulated for hydrogen, helium, carbon, nitrogen, oxygen and neon ions with 0.25–256 MeV/u energy. The needed ion interaction cross sections have been scaled from those of hydrogen; Barkas scaling formula has been refined, extending its applicability down to about 10 keV/u, and validated against established stopping power data. Linear energy transfer (LET) has been scored from energy deposits in a cell nucleus; for very low-energy ions, it has been defined locally within thin slabs. The simulations show that protons and helium ions induce more DNA damage than heavier ions do at the same LET. With increasing LET, less DNA strand breaks are formed per unit dose, but due to their clustering the yields of double-strand breaks (DSB) increase, up to saturation around 300 keV/μm. Also individual DSB tend to cluster; DSB clusters peak around 500 keV/μm, while DSB multiplicities per cluster steadily increase with LET. Remarkably similar to patterns known from cell survival studies, LET-dependencies with pronounced maxima around 100–200 keV/μm occur on nanometre scale for sites that contain one or more DSB, and on micrometre scale for megabasepair-sized DNA fragments.

An Expanded Multi-scale Monte Carlo Simulation Method for Personalized Radiobiological Effect Estimation in Radiotherapy: a feasibility study

A novel and versatile "bottom-up" approach is developed to estimate the radiobiological effect of clinic radiotherapy. The model consists of multi-scale Monte Carlo simulations from organ to cell levels. At cellular level, accumulated damages are computed using a spectrum-based accumulation algorithm and predefined cellular damage database. The damage repair mechanism is modeled by an expanded reaction-rate two-lesion kinetic model, which were calibrated through replicating a radiobiological experiment. Multi-scale modeling is then performed on a lung cancer patient under conventional fractionated irradiation. The cell killing effects of two representative voxels (isocenter and peripheral voxel of the tumor) are computed and compared. At microscopic level, the nucleus dose and damage yields vary among all nucleuses within the voxels. Slightly larger percentage of cDSB yield is observed for the peripheral voxel (55.0%) compared to the isocenter one (52.5%). For isocenter voxel, survival fraction increase monotonically at reduced oxygen environment. Under an extreme anoxic condition (0.001%), survival fraction is calculated to be 80% and the hypoxia reduction factor reaches a maximum value of 2.24. In conclusion, with biological-related variations, the proposed multi-scale approach is more versatile than the existing approaches for evaluating personalized radiobiological effects in radiotherapy.

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.

An empirical method for deriving RBE values associated with electrons, photons and radionuclides

There is substantial evidence to justify using relative biological effectiveness (RBE) values of >1 for low-energy electrons and photons. But, in the field of radiation protection, radiation associated with low linear energy transfer has been assigned a radiation weighting factor wR of 1. This value may be suitable for radiation protection but, for risk considerations, it is important to evaluate the potential elevated biological effectiveness of radiation to improve the quality of risk estimates. RBE values between 2 and 3 for tritium are implied by several experimental measurements. Additionally, elevated RBE values have been found for other similar low-energy radiation sources. In this work, RBE values are derived for electrons based upon the fractional deposition of absorbed dose of energies less than a few kiloelectron volts. Using this empirical method, RBE values were also derived for monoenergetic photons and 1070 radionuclides from ICRP Publication 107 for which photons and electrons are the primary emissions.

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.

Fishing for radiation quality: chromosome aberrations and the role of radiation track structure

The yield of chromosome aberrations is not only dependent on dose but also on radiation quality, with high linear energy transfer (LET) typically having a greater biological effectiveness per unit dose than those of low-LET radiation. Differences in radiation track structure and cell morphology can also lead to quantitative differences in the spectra of the resulting chromosomal rearrangements, especially at low doses associated with typical human exposures. The development of combinatorial fluorescent labelling techniques (such as mFISH and mBAND) has helped to reveal the complexity of rearrangements, showing increasing complexity of observed rearrangements with increasing LET but has a resolution limited to ∼10 MBp. High-LET particles have not only been shown to produce clustered sites of DNA damage but also produce multiple correlated breaks along its path resulting in DNA fragments smaller than the resolution of these techniques. Additionally, studies have shown that the vast majority of radiation-induced HPRT mutations were also not detectable using fluorescent in situ hybridisation (FISH) techniques, with correlation of breaks along the track being reflected in the complexity of mutations, with intra- and inter-chromosomal insertions, and inversions occurring at the sites of some of the deletions. Therefore, the analysis of visible chromosomal rearrangements observed using current FISH techniques is likely to represent just the tip of the iceberg, considerably underestimating the extent and complexity of radiation induced rearrangements.

Variation in RBE for Survival of V79-4 Cells as a Function of Alpha-Particle (Helium Ion) Energy

High linear energy transfer (LET) α particles are important with respect to the carcinogenic risk associated with human exposure to ionizing radiation, most notably to radon and its progeny. Additionally, the potential use of alpha-particle-emitting radionuclides in radiotherapy is increasingly being explored. Within the body the emitted alpha particles slow down, traversing a number of cells with a range of energies and therefore with varying efficiencies at inducing biological response. The LET of the particle typically rises from between ~70-90 keV μm(-1) at the start of the track (depending on initial energy) to a peak of ~237 keV μm(-1) towards the end of the track, before falling again at the very end of its range. To investigate the variation in biological response with incident energy, a plutonium-238 alpha-particle irradiator was calibrated to enable studies with incident energies ranging from 4.0 MeV down to 1.1 MeV. The variation in clonogenic survival of V79-4 cells was determined as a function of incident energy, along with the relative variation in the initial yields of DNA double-strand breaks (DSB) measured using the FAR assay. The clonogenic survival data also extends previously published data obtained at the Medical Research Council (MRC), Harwell using the same cells irradiated with helium ions, with energies ranging from 34.9 MeV to 5.85 MeV. These studies were performed in conjunction with cell morphology measurements on live cells enabling the determination of absorbed dose and calculation of the average LET in the cell. The results show an increase in relative biological effectiveness (RBE) for cell inactivation with decreasing helium ion energy (increasing LET), reaching a maximum for incident energies of ~3.2 MeV and corresponding average LET of 131 keV μm(-1), above which the RBE is observed to fall at lower energies (higher LETs). The effectiveness of single alpha-particle traversals (relevant to low-dose exposure) at inducing cell inactivation was observed to increase with decreasing energy to a peak of ~68% survival probability for incident energies of ~1.8 MeV (average LET of 190 keV μm(-1)) producing ~0.39 lethal lesions per track. However, the efficiency of a single traversal will also vary significantly with cell morphology and angle of incidence, as well as cell type.

The polymorphisms of the chromatin fiber

In eukaryotes, the genome is packed into chromosomes, each consisting of large polymeric fibers made of DNA bound with proteins (mainly histones) and RNA molecules. The nature and precise 3D organization of this fiber has been a matter of intense speculations and debates. In the emerging picture, the local chromatin state plays a critical role in all fundamental DNA transactions, such as transcriptional control, DNA replication or repair. However, the molecular and structural mechanisms involved remain elusive. The purpose of this review is to give an overview of the tremendous efforts that have been made for almost 40 years to build physiologically relevant models of chromatin structure. The motivation behind building such models was to shift our representation and understanding of DNA transactions from a too simplistic 'naked DNA' view to a more realistic 'coated DNA' view, as a step towards a better framework in which to interpret mechanistically the control of genetic expression and other DNA metabolic processes. The field has evolved from a speculative point of view towards in vitro biochemistry and in silico modeling, but is still longing for experimental in vivo validations of the proposed structures or even proof of concept experiments demonstrating a clear role of a given structure in a metabolic transaction. The mere existence of a chromatin fiber as a relevant biological entity in vivo has been put into serious questioning. Current research is suggesting a possible reconciliation between theoretical studies and experiments, pointing towards a view where the polymorphic and dynamic nature of the chromatin fiber is essential to support its function in genome metabolism.

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.

Etiology and treatment of hematological neoplasms: stochastic mathematical models

Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.

Modeling dose deposition and DNA damage due to low-energy β(-) emitters

One of the main issues of low-energy internal emitters concerns the very short ranges of the beta particles, versus the dimensions of the biological targets. Depending on the chemical form, the radionuclide may be more concentrated either in the cytoplasm or in the nucleus of the target cell. Consequently, since in most cases conventional dosimetry neglects this issue it may overestimate or underestimate the dose to the nucleus and hence the biological effects. To assess the magnitude of these deviations and to provide a realistic evaluation of the localized energy deposition by low-energy internal emitters, the biophysical track-structure code PARTRAC was used to calculate nuclear doses, DNA damage yields and fragmentation patterns for different localizations of radionuclides in human interphase fibroblasts. The nuclides considered in the simulations were tritium and nickel-63, which emit electrons with average energies of 5.7 (range in water of 0.42 μm) and 17 keV (range of 5 μm), respectively, covering both very short and medium ranges of beta-decay products. The simulation results showed that the largest deviations from the conventional dosimetry occur for inhomogeneously distributed short-range emitters. For uniformly distributed radionuclides selectively in the cytoplasm but excluded from the cell nucleus, the dose in the nucleus is 15% of the average dose in the cell in the case of tritium but 64% for nickel-63. Also, the numbers of double-strand breaks (DSBs) and the distributions of DNA fragments depend on subcellular localization of the radionuclides. In the low- and medium-dose regions investigated here, DSB numbers are proportional to the nuclear dose, with about 50 DSB/Gy for both studied nuclides. In addition, DSB numbers on specific chromosomes depend on the radionuclide localization in the cell as well, with chromosomes located more peripherally in the cell nucleus being more damaged by short-ranged emitters in cytoplasm compared with chromosomes located more centrally. These results illustrate the potential for over- or underestimating the risk associated with low-energy emitters, particularly for tritium intake, when their distribution at subcellular levels is not appropriately considered.

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.

Chromatin structure and radiation-induced DNA damage: from structural biology to radiobiology

Genomic DNA in eukaryotic cells is basically divided into chromosomes, each consisting of a single huge nucleosomal fiber. It is now clear that chromatin structure and dynamics play a critical role in all processes involved in DNA metabolism, e.g. replication, transcription, repair and recombination. Radiation is a useful tool to study the biological effects of chromatin alterations. Conversely, radiotherapy and radiodiagnosis raise questions about the influence of chromatin integrity on clinical features and secondary effects. This review focuses on the link between DNA damage and chromatin structure at different scales, showing how a comprehensive multiscale vision is required to understand better the effect of radiations on DNA. Clinical aspects related to high- and low-dose of radiation and chromosomal instability will be discussed. At the same time, we will show that the analysis of the radiation-induced DNA damage distribution provides good insight on chromatin structure. Hence, we argue that chromatin "structuralists" and radiobiological "clinicians" would each benefit from more collaboration with the other. We hope that this focused review will help in this regard.

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.

Monte Carlo role in radiobiological modelling of radiotherapy outcomes

Radiobiological models are essential components of modern radiotherapy. They are increasingly applied to optimize and evaluate the quality of different treatment planning modalities. They are frequently used in designing new radiotherapy clinical trials by estimating the expected therapeutic ratio of new protocols. In radiobiology, the therapeutic ratio is estimated from the expected gain in tumour control probability (TCP) to the risk of normal tissue complication probability (NTCP). However, estimates of TCP/NTCP are currently based on the deterministic and simplistic linear-quadratic formalism with limited prediction power when applied prospectively. Given the complex and stochastic nature of the physical, chemical and biological interactions associated with spatial and temporal radiation induced effects in living tissues, it is conjectured that methods based on Monte Carlo (MC) analysis may provide better estimates of TCP/NTCP for radiotherapy treatment planning and trial design. Indeed, over the past few decades, methods based on MC have demonstrated superior performance for accurate simulation of radiation transport, tumour growth and particle track structures; however, successful application of modelling radiobiological response and outcomes in radiotherapy is still hampered with several challenges. In this review, we provide an overview of some of the main techniques used in radiobiological modelling for radiotherapy, with focus on the MC role as a promising computational vehicle. We highlight the current challenges, issues and future potentials of the MC approach towards a comprehensive systems-based framework in radiobiological modelling for radiotherapy.

Track structure, radiation quality and initial radiobiological events: considerations based on the PARTRAC code experience

PURPOSE

The role of track structures for understanding the biological effects of radiation has been the subject of research activities for decades. The physics that describes such processes is the core Monte Carlo codes, such as the biophysical PARTRAC (PARticle TRACks) code described in this review, which follow the mechanisms of radiation-matter interaction from the early stage. In this paper a review of the track structure theory (and of its possible extension concerning non-DNA targets) is presented.

MATERIALS AND METHODS

The role of radiation quality and track structure is analyzed starting from the heavy ions results obtained with the biophysical Monte Carlo code PARTRAC (PARticles TRACks). PARTRAC calculates DNA damage in human cells based on the superposition of simulated track structures in liquid water to an 'atom-by-atom' model of human DNA.

RESULTS

Calculations for DNA fragmentation compared with experimental data for different radiation qualities are illustrated. As an example, the strong dependence of the complexity of DNA damage on radiation track structure, and the very large production of very small DNA fragments (lower than 1 kbp (kilo base pairs) usually not detected experimentally) after high LET (high-Linear Energy Transfer) irradiation is shown. Furthermore the possible importance of non-nuclear/non-DNA targets is discussed in the particular case of cellular membrane and mitochondria.

CONCLUSIONS

The importance of the track structure is underlined, in particular the dependence of a given late cellular effect on the spatial distribution of DNA double-strand breaks (DSB) along the radiation track. These results show that the relative biological effectiveness (RBE) for DSB production can be significantly larger than 1. Moreover the cluster properties of high LET radiation may determine specific initial targets and damage evolution.

Simulation of DNA damage clustering after proton irradiation using an adapted DBSCAN algorithm

In this work the "Density Based Spatial Clustering of Applications with Noise" (DBSCAN) algorithm was adapted to early stage DNA damage clustering calculations. The resulting algorithm takes into account the distribution of energy deposit induced by ionising particles and a damage probability function that depends on the total energy deposit amount. Proton track simulations were carried out in small micrometric volumes representing small DNA containments. The algorithm was used to determine the damage concentration clusters and thus to deduce the DSB/SSB ratios created by protons between 500keV and 50MeV. The obtained results are compared to other calculations and to available experimental data of fibroblast and plasmid cells irradiations, both extracted from literature.