A Monte Carlo model of DNA double-strand break clustering and rejoining kinetics for the analysis of pulsed-field gel electrophoresis data

Applications of nanodosimetry in particle therapy planning and beyond

This topical review summarizes underlying concepts of nanodosimetry. It describes the development and current status of nanodosimetric detector technology. It also gives an overview of Monte Carlo track structure simulations that can provide nanodosimetric parameters for treatment planning of proton and ion therapy. Classical and modern radiobiological assays that can be used to demonstrate the relationship between the frequency and complexity of DNA lesion clusters and nanodosimetric parameters are reviewed. At the end of the review, existing approaches of treatment planning based on relative biological effectiveness (RBE) models or dose-averaged linear energy transfer are contrasted with an RBE-independent approach based on nandosimetric parameters. Beyond treatment planning, nanodosimetry is also expected to have applications and give new insights into radiation protection dosimetry.

Impact of Hypoxia on Relative Biological Effectiveness and Oxygen Enhancement Ratio for a 62-MeV Therapeutic Proton Beam

This study uses the yields of double-strand breaks (DSBs) to determine the relative biological effectiveness (RBE) of proton beams, using cell survival as a biological endpoint. DSB induction is determined when cells locate at different depths (6 positions) along the track of 62 MeV proton beams. The DNA damage yields are estimated using Monte Carlo Damage Simulation (MCDS) software. The repair outcomes are estimated using Monte Carlo excision repair (MCER) simulations. The RBE for cell survival at different oxygen concentrations is calculated using the repair-misrepair-fixation (RMF) model. Using 60Co γ-rays (linear energy transfer (LET) = 2.4 keV/μm) as the reference radiation, the RBE for DSB induction and enzymatic DSB under aerobic condition (21% O2) are in the range 1.0-1.5 and 1.0-1.6 along the track depth, respectively. In accord with RBE obtained from experimental data, RMF model-derived RBE values for cell survival are in the range of 1.0-3.0. The oxygen enhancement ratio (OER) for cell survival (10%) decreases from 3.0 to 2.5 as LET increases from 1.1 to 22.6 keV/μm. The RBE values for severe hypoxia (0.1% O2) are in the range of 1.1-4.4 as LET increases, indicating greater contributions of direct effects for protons. Compared with photon therapy, the overall effect of 62 MeV proton beams results in greater cell death and is further intensified under hypoxic conditions.

Ionizing Radiation and Complex DNA Damage: From Prediction to Detection Challenges and Biological Significance

Biological responses to ionizing radiation (IR) have been studied for many years, generally showing the dependence of these responses on the quality of radiation, i.e., the radiation particle type and energy, types of DNA damage, dose and dose rate, type of cells, etc. There is accumulating evidence on the pivotal role of complex (clustered) DNA damage towards the determination of the final biological or even clinical outcome after exposure to IR. In this review, we provide literature evidence about the significant role of damage clustering and advancements that have been made through the years in its detection and prediction using Monte Carlo (MC) simulations. We conclude that in the future, emphasis should be given to a better understanding of the mechanistic links between the induction of complex DNA damage, its processing, and systemic effects at the organism level, like genomic instability and immune responses.

Induction of DNA Damage by Light Ions Relative to 60Co γ-rays

The specific types and numbers of clusters of DNA lesions, including both DNA double-strand breaks (DSBs) and non-DSB clusters, are widely considered 1 of the most important initiating events underlying the relative biological effectiveness (RBE) of the light ions of interest in the treatment of cancer related to megavoltage x-rays and 60Co γ-rays. This review summarizes the categorization of DNA damage, reviews the underlying mechanisms of action by ionizing radiation, and quantifies the general trends in DSB and non-DSB cluster formation by light ions under normoxic and anoxic conditions, as predicted by Monte Carlo simulations that reflect the accumulated evidence from decades of research on radiation damage to DNA. The significance of the absolute and relative numbers of clusters and the local complexity of DSB and non-DSB clusters are discussed in relation to the formation of chromosome aberrations and the loss of cell reproductive capacity. Clinical implications of the dependence of DSB induction on ionization density is reviewed with an eye towards increasing the therapeutic ratio of proton and carbon ion therapy through the explicit optimization of RBE-weighted dose.

New Insight into Quantitative Modeling of DNA Double-Strand Break Rejoining

Accurate and mechanistically plausible mathematical models of DNA double-strand break (DSB) rejoining kinetics are needed to correctly estimate the dependence of cell death and transformation on linear energy transfer, radiation dose and time. When integrated into more comprehensive risk estimation approaches, such models are potentially valuable tools in applications such as treatment planning for radiotherapy. In this study, we compared 10 DSB rejoining models based on data collected from 61 mammalian cell lines after high-dose-rate photon or heavy ion irradiation. The set of models included formalisms with: 1. one, two or three discrete first-order rejoining rates; 2. continuously distributed first-order rejoining rates; and 3. second-order rejoining rates. The Akaike information criterion was used to quantify the relative support for each model from the data, accounting for goodness of fit and model complexity. The best performance was exhibited by a bi-exponential model with two discrete rejoining rates and a model with gamma-distribution rejoining rates. Models with more than three free parameters overfitted the data and models with single DSB rejoining rates or with an inflexible distribution of rejoining rates lacked accuracy. Of special note is that the analyzed data provide little support for models that rely on pairwise interactions to describe DSB rejoining kinetics. Consequently, kinetic cell survival models reflecting bi-exponential DSB rejoining might be preferable to models based on the kinetics of intra- and inter-lesion rejoining.

A stochastic model of DNA fragments rejoining

When cells are exposed to ionizing radiation, DNA damages in the form of single strand breaks (SSBs), double strand breaks (DSBs), base damage or their combinations are frequent events. It is known that the complexity and severity of DNA damage depends on the quality of radiation, and the microscopic dose deposited in small segments of DNA, which is often related to the linear transfer energy (LET) of the radiation. Experimental studies have suggested that under the same dose, high LET radiation induces more small DNA fragments than low-LET radiation, which affects Ku efficiently binding with DNA end and might be a main reason for high-LET radiation induced RBE [1] since DNA DSB is a major cause for radiation-induced cell death. In this work, we proposed a mathematical model of DNA fragments rejoining according to non-homologous end joining (NHEJ) mechanism. By conducting Gillespie's stochastic simulation, we found several factors that impact the efficiency of DNA fragments rejoining. Our results demonstrated that aberrant DNA damage repair can result predominantly from the occurrence of a spatial distribution of DSBs leading to short DNA fragments. Because of the low efficiency that short DNA fragments recruit repair protein and release the protein residue after fragments rejoining, Ku-dependent NHEJ is significantly interfered with short fragments. Overall, our work suggests that inhibiting the Ku-dependent NHEJ may significantly contribute to the increased efficiency for cell death and mutation observed for high LET radiation.

Mathematical models of the generation of radiation-induced DNA double-strand breaks

The double-strand break (dsb) is one of the most critical lesions leading to a variety of radiobiological effects. In this paper, we reconsider the previously constructed and generally accepted mathematical models for dsb generation, and give a concrete mathematical basis for the generation of dsbs and the calculation of the number of induced dsbs, under the assumption of randomness in the break location in DNA and in the number of breaks. Using these models based on the Poisson distribution and the binomial distribution, we calculate the dose dependence of dsb generation. We deduced from our models that the dose dependence of the number of dsbs is described approximately as a quadratic form in both distribution models where dsb generation is accounted for by two ssbs. Previously reported experimental data on the dsb generation in phage DNA was found to be in good agreement with our models. Though the widely used model, the linear quadratic (LQ) model or the molecular theory of dsb formation based on the Poisson distribution, also gives the quadratic term, in spite of rough estimates or some mathematical incompleteness, a marked feature of our formulation is the absence of a parameter like the [Formula: see text] in the quadratic term that requires experimental data to determine. Thus in this study we provide mathematical validity to the generally accepted models of the number of dsb.

Stochastic simulation of DNA double-strand break repair by non-homologous end joining based on track structure calculations

A Monte Carlo simulation model for DNA repair via the non-homologous end-joining pathway has been developed. Initial DNA damage calculated by the Monte Carlo track structure code PARTRAC provides starting conditions concerning spatial distribution of double-strand breaks (DSBs) and characterization of lesion complexity. DNA termini undergo attachment and dissociation of repair enzymes described in stochastic first-order kinetics as well as step-by-step diffusive motion considering nuclear attachment sites. Pairs of DNA termini with attached DNA-PK enter synapsis under spatial proximity conditions. After synapsis, a single rate-limiting step is assumed for clean DNA ends, and step-by-step removal of nearby base lesions and strand breaks is considered for dirty DNA ends. Four simple model scenarios reflecting different hypotheses on the origin of the slow phase of DSB repair have been set up. Parameters for the presynaptic phase have been derived from experimental data for Ku70/Ku80 and DNA-PK association and dissociation kinetics. Time constants for the post-synaptic phase have been adapted to experimental DSB rejoining kinetics for human fibroblasts after (137)Cs gamma irradiation. In addition to DSB rejoining kinetics, the yields of residual DSBs, incorrectly rejoined DSBs, and chromosomal aberrations have been determined as a function of dose and compared with experimental data. Three of the model scenarios obviously overestimate residual DSBs after long-term repair after low-dose irradiation, whereas misrejoined DSBs and chromosomal aberrations are in surprisingly good agreement with measurements.

Distribution of DNA fragment sizes after irradiation with ions

Ionizing radiation is responsible for production of double-strand breaks (DSBs) in a DNA structure. In contrast to sparsely ionizing radiation, densely ionizing radiation produces DSBs that are non-randomly distributed along the DNA molecule and can form clusters of various size. The paper discusses minimalistic models that describe observable patterns of fragment length in DNA segments irradiated with heavy ions and applies the formalism to interpret the recent experimental data collected by use of atomic force microscope (AFM).

DNA DSB induced in human cells by charged particles and gamma rays: Experimental results and theoretical approaches

PURPOSE

To quantify the role played by radiation track structure and background fragments in modulating DNA fragmentation in human cells exposed to gamma-rays and light ions.

MATERIALS AND METHODS

Human fibroblasts were exposed in vitro to different doses (in the range from 40 - 200 Gy) of (60)Co gamma-rays and 0.84 MeV protons (Linear Energy Transfer, LET, in tissue 28.5 keV/microm). The resulting DNA fragments were scored under two electrophoretic conditions, in order to optimize separation in the size ranges 0.023 - 1.0 Mbp and 1.0 - 5.7 Mbp. In parallel, DNA fragmentation was simulated both with a phenomenological approach based on the "generalized broken-stick" model, and with a mechanistic approach based on the PARTRAC (acronym of PARticle TRACk) Monte Carlo code (1.32 MeV photons were used for the simulation of (60)Co gamma-rays).

RESULTS

For both gamma-rays and protons, the experimental dose response in the range 0.023 - 5.7 Mbp could be approximated as a straight line, the slope of which provided a yield of (5.3 +/- 0.4) x 10(-9) Gy(-1) bp(-1) for gamma-rays and (7.1 +/- 0.6) x 10(-9) Gy(-1) bp(-1) for protons, leading to a Relative Biological Effectiveness (RBE) of 1.3 +/- 0.2. From both theoretical analyses it appeared that, while gamma-ray data were consistent with double-strand breaks (DSB) random induction, protons at low doses showed significant deviation from randomness, implying enhanced production of small fragments in the low molecular weight part of the experimental range. The theoretical analysis of fragment production was then extended to ranges where data were not available, i.e. to fragments larger than 5.7 Mbp and smaller than 23 kbp. The main outcome was that small fragments (<23 kbp) are produced almost exclusively via non-random processes, since their number is considerably higher than that produced by a random insertion of DSB. Furthermore, for protons the number of these small fragments is a significant fraction (about 20%) of the total number of fragments; these fragments remain undetected in these experiments. Calculations for 3.3 MeV alpha particle irradiation (for which no experimental data were available) were performed to further investigate the role of fragments smaller than 23 kbp; in this case, besides the non-random character of their production, their number resulted to be at least as much as half of the total number of fragments.

CONCLUSION

Comparison between experimental data and two different theoretical approaches provided further support to the hypothesis of an important role of track structure in modulating DNA damage. According to the theoretical approaches, non-randomness of fragment production was found for proton irradiation for the smaller fragments in the experimental size range and, in a significantly larger extent, for fragments of size less than 23 kbp, both for protons and alpha particles.

Stochastic properties of radiation-induced DSB: DSB distributions in large scale chromatin loops, the HPRT gene and within the visible volumes of DNA repair foci

PURPOSE

We computed probabilities to have multiple double-strand breaks (DSB), which are produced in DNA on a regional scale, and not in close vicinity, in volumes matching the size of DNA damage foci, of a large chromatin loop, and in the physical volume of DNA containing the HPRT (human hypoxanthine phosphoribosyltransferase) locus.

MATERIALS AND METHODS

The model is based on a Monte Carlo description of DSB formation by heavy ions in the spatial context of the entire human genome contained within the cell nucleus, as well as at the gene sequence level.

RESULTS

We showed that a finite physical volume corresponding to a visible DNA repair focus, believed to be associated with one DSB, can contain multiple DSB due to heavy ion track structure and the DNA supercoiled topography. A corrective distribution was introduced, which was a conditional probability to have excess DSB in a focus volume, given that there was already one present. The corrective distribution was calculated for 19.5 MeV/amu N ions, 3.77 MeV/amu alpha-particles, 1000 MeV/amu Fe ions, and X-rays. The corrected initial DSB yield from the experimental data on DNA repair foci was calculated. The DSB yield based on the corrective function converts the focus yield into the DSB yield, which is comparable with the DSB yield based on the earlier PFGE experiments. The distribution of DSB within the physical limits of the HPRT gene was analyzed by a similar method as well.

CONCLUSION

This corrective procedure shows the applicability of the model and empowers the researcher with a tool to better analyze focus statistics. The model enables researchers to analyze the DSB yield based on focus statistics in real experimental situations that lack one-to-one focus-to-DSB correspondance.

Subtraction of background damage in PFGE experiments on DNA fragment-size distributions

The non-random distribution of DNA breakage in pulsed-field gel electrophoresis (PFGE) experiments poses a problem of proper subtraction of the background damage to obtain a fragment-size distribution due to radiation only. As been pointed out by various authors, a naive bin-to-bin subtraction of the background signal will not result in the right DNA mass distribution histogram, and may even result in negative values. Previous more systematic subtraction methods have been based mainly on random breakage, appropriate for low-LET radiation but problematic for high LET. Moreover, an investigation is needed whether the background breakage itself is random or non-random. Previously a new generalized formalism based on stochastic processes for the subtraction of the background damage in PFGE experiments for any LET and any background was proposed, and as now applied it to a set of PFGE data for Fe ions. We developed a Monte Carlo algorithm to compare the naïve subtraction procedure in artificial data sets to the result produced by the new formalism. The simulated data corresponded to various cases, involving non-random (high-LET) or random radiation breakage and random or non-random background breakage. The formalism systematically gives better results than naïve bin-by-bin subtraction in all these artificial data sets.

A Robust Procedure for Removing Background Damage in Assays of Radiation-Induced DNA Fragment Distributions

The non-random distribution of DNA breakage in PFGE (pulsed-field gel electrophoresis) experiments poses a problem of proper subtraction of the background DNA damage to obtain a fragment-size distribution due to radiation only. A naive bin-to-bin subtraction of the background signal will not result in the right DNA mass distribution histogram. This problem could become more pronounced for high-LET (linear energy transfer) radiation, because the fragment-size distribution manifests a higher frequency of smaller fragments. Previous systematic subtraction methods have been based on random breakage, appropriate for low-LET radiation. Moreover, an investigation is needed to determine whether the background breakage is itself random or non-random. We consider two limiting cases: (1) the background damage is present in all cells, and (2) it is present in only a small subset of cells, while other cells are not contributing to the background DNA fragmentation. We give a generalized formalism based on stochastic processes for the subtraction of the background damage in PFGE experiments for any LET and apply it to two sets of PFGE data for iron ions.

Chromatin loops are responsible for higher counts of small DNA fragments induced by high-LET radiation, while chromosomal domains do not affect the fragment sizes

PURPOSE

To apply a polymer model of DNA damage induced by high-LET (linear energy transfer) radiation and determine the influence of chromosomal domains and loops on fragment length distribution.

MATERIALS AND METHODS

The yields of DSB (double-strand breaks) induced by high-LET radiation were calculated using a track structure model along with a polymer model of DNA packed in the cell nucleus. The cell nucleus was constructed to include the chromosomal domains and chromatin loops. The latter were generated by the random walk method.

RESULTS AND CONCLUSIONS

We present data for DSB yields per track per cell, DNA fragment sizes, the radial distribution of DSB with respect to the track center, and the distribution of 0, 1, 2, and more DSB from a single particle. Calculations were carried out for a range of particles including He (40 keV/microm), N (225 keV/microm), and Fe ions (150 keV/mum). Situations relevant to PFGE (pulsed-field gel electrophoresis) and microbeam experiments with direct irradiation of the cell nucleus were simulated to demonstrate the applicability of the model. Data show that chromosomal domains do not have a significant influence on fragment-size distribution, while the presence of DNA loops increases the frequencies of smaller fragments by nearly 30% for fragment sizes in the range from 2 kbp (bp = base pair) to 20 kbp.

Evidence for complexity at the nanometer scale of radiation-induced DNA DSBs as a determinant of rejoining kinetics

The rejoining kinetics of double-stranded DNA fragments, along with measurements of residual damage after postirradiation incubation, are often used as indicators of the biological relevance of the damage induced by ionizing radiation of different qualities. Although it is widely accepted that high-LET radiation-induced double-strand breaks (DSBs) tend to rejoin with kinetics slower than low-LET radiation-induced DSBs, possibly due to the complexity of the DSB itself, the nature of a slowly rejoining DSB-containing DNA lesion remains unknown. Using an approach that combines pulsed-field gel electrophoresis (PFGE) of fragmented DNA from human skin fibroblasts and a recently developed Monte Carlo simulation of radiation-induced DNA breakage and rejoining kinetics, we have tested the role of DSB-containing DNA lesions in the 8-kbp-5.7-Mbp fragment size range in determining the DSB rejoining kinetics. It is found that with low-LET X rays or high-LET alpha particles, DSB rejoining kinetics data obtained with PFGE can be computer-simulated assuming that DSB rejoining kinetics does not depend on spacing of breaks along the chromosomes. After analysis of DNA fragmentation profiles, the rejoining kinetics of X-ray-induced DSBs could be fitted by two components: a fast component with a half-life of 0.9+/-0.5 h and a slow component with a half-life of 16+/-9 h. For alpha particles, a fast component with a half-life of 0.7+/-0.4 h and a slow component with a half-life of 12+/-5 h along with a residual fraction of unrepaired breaks accounting for 8% of the initial damage were observed. In summary, it is shown that genomic proximity of breaks along a chromosome does not determine the rejoining kinetics, so the slowly rejoining breaks induced with higher frequencies after exposure to high-LET radiation (0.37+/-0.12) relative to low-LET radiation (0.22+/-0.07) can be explained on the basis of lesion complexity at the nanometer scale, known as locally multiply damaged sites.