Abstract
Chromosome aberrations (CAs) are large scale structural rearrangements to the genome that have been used as a proxy endpoint of mutagenic and carcinogenic potential. And yet, many types of CAs are incapable of causing either of these effects simply because they are lethal. Using 24-color multi-fluor combinatorial painting (mFISH), we examined CAs in normal human lymphocytes exposed to graded doses of 1 GeV/nucleon accelerated 56Fe ions and 662 keV 137Cs gamma rays. As expected, the high-linear energy transfer (LET) heavy ions were considerably more potent per unit dose at producing total yields of CAs compared to low-LET gamma rays. As also anticipated, the frequency distribution of aberrations per cell exposed to 56Fe ions was significantly overdispersed compared to the Poisson distribution, containing excess numbers of cells devoid of aberrations. We used the zero-inflated negative binomial (ZINB) distribution to model these data. Based on objective cytogenetic criteria that are subject to caveats we discuss, each cell was individually evaluated in terms of likely survival (i.e., its ability to transmit to daughter cell progeny). For 56Fe ion irradiations, the frequency of surviving cells harboring complex aberrations represented a significant portion of aberration-bearing cells, while for gamma irradiation no survivable cells containing complex aberrations were observed. When the dose responses for the two radiation types were compared, and the analysis was limited to surviving cells that contained aberrations, we were surprised to find the high-LET 56Fe ions only marginally more potent than the low-LET gamma rays for doses less than 1 Gy. In fact, based on dose-response modeling, they were predicted to be less effective than gamma rays at somewhat higher doses. The major implication of these findings is that measures of relative biological effectiveness that fail to account for coincident lethality will tend to overstate the impact of transmissible chromosomal damage from high-LET particle exposure.
INTRODUCTION
For the better part of a century investigators have known that some types of ionizing radiation are more effective than others at causing various biological effects. Initial attempts to quantify this increased effectiveness centered around experimental model systems developed in plant species. It was here that the phrase “relative biological effectiveness” makes its first appearance in the literature with respect to the growth rates of irradiated seedlings (1) — and also where the concept of using the ratio of doses required to produce an equivalent biological effect was first suggested as a means for comparing the relative potency of radiation types. Later advances in mammalian cell culture saw the construction of in vitro dose responses for clonogenic survival (2). Over the decades that followed, measurements of relative biological effectiveness (RBE) for cell survival were expanded to include a variety of cell types and radiations encompassing a wide range of ionization densities (3).
In the context of monotonically changing (e.g., exponential) dose responses like cell survival, comparing radiations based on isoeffective dose ratios makes perfect sense, as it does for radiotherapy, where the objective is to achieve equal effects after exposure. However, while RBE remains the universally accepted approach for such comparisons, that was not always the case. The first quantitative comparisons of radiation with disparate ionization densities (LET) involved chromosome aberrations in Tradescantia after exposure to neutrons versus X rays, where the ratio of effects at a given dose was used instead as the metric of choice (4, 5). Some eighty years forward, we find a similar metric — the radiation effects ratio (RER) — proposed in connection with radiation risk estimates for dose response shapes that are non-linear and/or non-monotonic (6). For reasons that will become clear later, this is the measure of a radiation potency that we adopt for the present study.
Radiation protection standards are, to an overwhelming extent, based around cancer incidence in human populations exposed to sparsely ionizing radiation. This presents a problem for assessing risk connected with radiations of much higher ionization densities (LET), where reliable epidemiological data are sparse, or nonexistent. Various surrogate measures of risk have been developed to help fill this gap. On the in vitro side of such efforts, this includes large-scale structural damage to the genome that takes the form of microscopically visible chromosome aberrations (CAs). The relationship between CAs and cell killing is well established, as is their connection to cancer, either as the direct cause, or as mutagenic drivers of the carcinogenic process. Here, attention naturally falls on those types of aberrations which do not kill cells, but instead transmit to future cell progeny.
In a prior publication we described how cells at their first mitosis after exposure to gamma rays may be examined for the types of chromosome aberrations likely to transmit to clonal descendants of the affected cell (7). On that basis we derived a dose response model for the frequency of transmissible aberrations in human lymphocytes. As opposed to the monotonically-increasing linear-quadratic dose response typical of mean aberration frequencies per cell induced by low-LET radiations, this dose response reached a peak and became concave-downward (crescent-shaped) with a maximum transmissibility occurring at approximately 2 Gy, consistent with the conclusions of others for X rays (8). As a consequence of this basic shape, it is not possible to express a radiation’s relative potency in terms of dose-ratios for a given isoeffect (RBE), because using a horizontal iso-effective scaling approach for RBE calculation will not produce a unique solution. In situations like this, the ratio of biological effects at a given isodose (RER) is the preferable metric.
The purpose of this study is to determine the dose response curve for cells containing only nonlethal chromosome aberrations induced by high-LET accelerated 56Fe ions. By comparing this curve to the corresponding curve for 137Cs gamma rays we seek to characterize a dose-dependent RER relationship for these two radiation types.
MATERIALS AND METHODS
Details regarding cell irradiations, culture conditions and cytogenetic methodology can be found in our earlier published work (7, 9, 10). A core principle driving the analysis of this current work was proposed many years ago by Gray (11) and later employed by Elkind and coworkers (12). Translated for use in the present context, it makes the assumption of causal independence between the dose response representing the frequency of cells containing nonlethal aberrations and the dose response for cells having sustained lethal damage in terms of predicted clonogenic survival at a given dose. In such case, the probability of a surviving cell containing ≥1 nonlethal CAs and zero lethal CAs is given by the product of these two dose response relationships.
Aberration Scoring Criteria
The specific criteria for judging a cell’s ability to survive a given type of aberration were as follows. Any cell containing an acentric fragment was judged as having sustained a lethal event. This included true terminal deletions, incomplete exchanges and any acentric element associated with complex exchanges. Of course, dicentric chromosomes would also be considered lethal, although scoring them separately would be redundant since their formation (by definition) involves the simultaneous production of at least one acentric fragment. So-called “one-way exchanges” not associated with acentric fragment production were not considered lethal, as supported by arguments made by others (13). Neither were the occasional chromatid break since, singly by themselves, they lack the ability to inactivate reproductive integrity (i.e., the ability to form colonies). Minor changes in euploidy such as the odd “missing chromosome” were considered artifacts of metaphase preparation and were therefore not considered lethal. All other cells containing rearrangements, irrespective of complexity or the number of breakpoints involved, were considered viable. No provision was made for inversions in this analysis, as they are not generally detectable by mFISH.
Analysis of Probability Distributions of Lethal and Nonlethal Aberrations
Each cell was individually scored by the criteria listed above. We examined and analyzed the probability distributions of lethal and nonlethal CAs per cell, separately for each radiation dose. Previously published data for 0, 0.25, 0.5, 1, 2, 4 and 6 Gy doses of gamma rays (7) was incorporated into the analysis, together with new data corresponding to 0, 0.1, 0.2, 0.4, 0.7, 1.0, 1,4 and 1.5 Gy doses of 56Fe ions. Summary statistics (mean, median, 1st and 3rd quartiles, minimum and maximum) and histograms were calculated for each distribution (lethal or nonlethal CAs) at each radiation type and dose. Each distribution was also fitted by the Poisson and Negative binomial (NB) distribution functions using the fitdistrplus package (https://cran.r-project.org/web/packages/fitdistrplus/index.html) in R 4.2.0 software. Fitting was performed by maximum likelihood techniques, and relative fit qualities of the Poisson and NB distributions were compared using the Akaike information criterion (AIC).
Mathematical Modeling of Radiation Dose Responses for Lethal and Nonlethal Aberrations
The analysis of probability distributions of lethal and nonlethal CAs described above showed that the Poisson distribution was adequate for describing gamma-ray data, but for heavy ions the Poisson distribution provided a poor fit. Instead, the heavy ion data were decently described by the zero-inflated negative binomial (ZINB) distribution (14). This distribution is frequently used to model integer data that exhibit overdispersion and excess zeros, such as chromosome aberrations. According to ZINB distribution, the probability distribution PZINB of aberrations (k) in a cell is described by two separate functions: one for the case where k≥1, and the other for the case where k = 0. These functions are shown in the equation below, where F(d) is a dose response function of radiation dose d:
(1) |
where Q = F(d) + 1/r, Γ is the Gamma function, r is the “overdispersion” parameter, and p0 is the fraction of “extra” zero events.
The dose response function F(d) structure is based on the standard linear-quadratic formalism with a linear term α and a quadratic term β, and a baseline constant c. Based on radiobiological knowledge, the quadratic term was neglected (assumed to be zero) for 56Fe ions but is retained for gamma rays. As reported in our previous publication (7), we found that the CA data could be reasonably described by a simplified assumption where the shapes of the dose responses for lethal and nonlethal CAs are the same, and that their magnitudes differ only by a multiplicative proportionality constant P. This resulting model is described by the following equations, where the subscript l indicates lethal CAs, n indicates nonlethal CAs, γ indicates gamma rays, and Fe indicates 56Fe ions:
(2) |
This model formalism was fitted to the data by maximum likelihood using the sequential quadratic programming (SQP) algorithm in Maple 2021 software. Profile likelihood was used to estimate the 95% confidence intervals (CI) for each model parameter.
Since some cells carrying nonlethal CAs have the potential to become the ancestors of malignant clones, we were interested in estimating the joint probability distribution for cells containing ≥1 nonlethal CAs, but zero lethal CAs. We assumed that the lethal and nonlethal CA probability distributions are independent, and that the joint probability distribution of interest is given by their product.
(3) |
This approach was applied to gamma-ray data using the Poisson distribution and to 56Fe-ion data using the ZINB distribution.
RESULTS
Table 1 shows a tally of normal unaffected cells (i.e., nulls), lethal and nonlethal aberrations for the eight doses of 56Fe ions used in this study. For comparative purposes it is instructive to consider the dose responses for total aberration frequencies (nonlethal + lethal) per cell resulting from exposure to the two radiation types as expressed in the usual way, meaning that no assessment is made regarding individual cell survivability (Fig. 1). The figure serves also to help put into context the 18 individual dose data points used in subsequent modeling. Note the characteristic upward curvature after exposure to low-LET gamma rays, and the more linear dose response curve for 56Fe ions typical of damage produced by high-LET radiations.
TABLE 1.
Summary Data for the Incidences of Normal (Unaffected), Lethal and Nonlethal Aberrations for each Indicated Dose of 56Fe Accelerated Heavy Ions
Dose (Gy) | Sum of all cells | Sum of unaffected (normal) cells | Sum of lethal aberrations | Sum of nonlethal aberrations | Mean lethals per cell | Mean nonlethals per cell |
---|---|---|---|---|---|---|
0.00 | 231 | 216 | 16 | 4 | 0.069 | 0.017 |
0.10 | 292 | 260 | 29 | 11 | 0.099 | 0.038 |
0.20 | 413 | 332 | 116 | 18 | 0.281 | 0.044 |
0.40 | 277 | 197 | 118 | 24 | 0.426 | 0.087 |
0.70 | 350 | 195 | 257 | 57 | 0.734 | 0.163 |
1.00 | 189 | 88 | 162 | 39 | 0.857 | 0.206 |
1.40 | 111 | 42 | 141 | 25 | 1.270 | 0.225 |
1.50 | 217 | 65 | 298 | 75 | 1.373 | 0.346 |
FIG. 1.
Dose responses for total chromosome aberrations. Symbols represent observed data, and lines represent model fits. The green symbols and curves represent the response for 137Cs gamma rays. The black symbols and curves represent the response for 56Fe ion exposure.
Best-fit parameter values for our model formalism on 56Fe-ion data are provided in Table 2. The corresponding parameters for 137Cs gamma rays, which were also reported in our previous paper (7), were: were: clγ = 0.046 (95% CI: 0.015, 0.092), αlγ = 0.230 (0.139, 0.315) Gy–1, βlγ = 0.056 (0.039, 0.074) Gy–2, Pγ = 0.326 (0.284, 0.373). The gamma-ray data were described reasonably by the Poisson distribution with no overdispersion or extra zeros. The α parameters were clearly different for the two radiation types. Also, the p-value for 56Fe ions is somewhat lower than the corresponding gamma-ray value, perhaps suggesting that ions induce a larger fraction of lethal aberrations.
TABLE 2.
Best-Fit Model Parameter Values for 56Fe Ion Data
Parameter | Best-fit value | 95% confidence intervals | |
---|---|---|---|
Baseline dose response parameter for lethal aberrations, clFe | 0.657 | 0.475 | 0.845 |
Linear dose response term for lethal aberrations, αlFe (Gy−1) | 0.650 | 0.470 | 0.827 |
Proportionality constant for nonlethal/lethal aberration yield, P | 0.223 | 0.193 | 0.250 |
Fraction of “extra” zero events, p0 | 0.885 | 0.814 | 0.936 |
Overdispersion parameter, r | 0.294 | 0.175 | 0.442 |
We used these parameter values to calculate the RBE and RER metrics for 56Fe ions. At both the lowest and the highest doses considered, RER and RBE metrics yielded similar results. At low doses, where the dose responses for both radiations are close to linear, RBE and RER are asymptotically the same, and both estimates returned values of approximately 3. This value is based on the ratio of α dose response parameters for 56Fe ions/137Cs gamma rays. By extrapolation of the models used to fit the data, both RBE and RER tended toward unity at very high doses (Fig. 2). However, between these two dose extremes the two methods yielded rather different results. The RER for 56Fe ions remained rather high (~3) and relatively constant over the low dose region, falling sharply for doses in excess of about 0.5 Gy; conversely, this transition occurred more gradually for values of RBE. The basic shapes of both curves are not unexpected, as they are a direct consequence of the continuous dose-dependent upward curvature exhibited by the response to gamma rays in comparison to the quasi-linear response produced by high-LET 56Fe ions (Fig. 1).
FIG. 2.
Visual comparison of RBE (orange line) and RER (purple line) radiation quality metrics for 1.0 GeV 56Fe accelerated ions as a function of dose. Solid lines correspond to fits over the range of doses for which experimental measurements were made. Dashed lines indicate model-based extrapolations.
Central to the main thrust of this investigation is the dose response for aberrations among surviving cells. To qualify for inclusion into this data set we specify that individual cells must contain a visible chromosome aberration, and that the aberration(s) in question is not lethal (e.g., a simple reciprocal translocation). Figure 3 shows separate dose responses for the frequencies of lethal versus nonlethal aberrations per cell induced after exposure to 56Fe ions. Note the linear shape for both aberration types, suggesting that nonlethals represent a fixed fraction of lethal aberrations, a result we also previously observed for gamma rays (7).
FIG. 3.
Visual comparison of best-fit dose responses for the mean frequencies of lethal (red) and nonlethal (blue) aberrations after exposure to 56Fe ions.
The frequency of cells containing nonlethal aberrations is a more complicated function dose (Fig. 4). Both radiation types produce crescent-shaped dose response curves (concave downward) that are the obligatory result of their formation being the product of induction and survival processes (Eq. 3). While this is most clearly demonstrated in response to gamma irradiation, where data corresponding to doses up to 6 Gy are available, qualitatively similar results are produced by model fits to the 56Fe-ion data (Fig. 5). As previously noted, the basic shapes of the two curves, which peak and decrease as function of dose, precludes comparing the relative potency of 56Fe ions against that of gamma rays on the basis of dose ratios required for an isoeffect (i.e., RBE), because nonunique values exist for any given level of isoeffect. This, in fact, was the initial impetus for choosing RER instead as a measure of radiation potency.
FIG. 4.
Best-fit model predictions for the fraction of cells with no lethal and ≥1 nonlethal aberrations after 56Fe ion (brown curve) or gamma ray (yellow curve) exposures.
FIG. 5.
Dose-dependent model predictions for the frequency of cells carrying only nonlethal chromosome aberrations. 56Fe ion = brown curve, gamma rays = yellow curve. Solid curves indicate the range of doses where actual experimental data were available and thin dashed curves indicate model-derived extrapolations to higher doses.
The main objective of this investigation culminates with the results shown in Figure 6. The RER for cells sustaining transmissible chromosome damage after high-LET 56Fe ions is a complicated function of dose. It presents as a relatively stable metric over the low dose region up to roughly 0.2 Gy. A rather important yet unexpected result is that with increasing dose past about 0.8 Gy, the RER function actually returns values below unity! We should emphasize that this occurs over a dose range corresponding to actual measurements (solid lines of the figure). Model predictions at higher doses have the RER reaching a nadir at about 4 Gy, followed by a subsequent upturn at still higher doses. It is worth noting that the maximum RER (and RBE) values based on total chromosome aberrations (Fig. 2) are in excess of twice that observed when the consideration of chromosome damage is confined to only surviving cells (Fig. 6).
FIG. 6.
Radiation effects ratio (RER, purple curve) estimated based on best-fit model predictions for the fraction of cells with no lethal and ≥1 nonlethal aberrations after 56Fe ion (brown curve) or gamma ray (yellow curve) exposures. Solid curves indicate the range of doses where actual experimental data were available and thin dashed curves indicate model-derived extrapolations to higher doses. The x axis represents dose on a logarithmic scale for easier visualization of both low and high doses. The y axis is not labeled because RER (purple curve) is unitless. The 56Fe-ion and gamma-ray dose responses (brown and yellow curves, respectively) are shown in units of 20-fold that of the actual predicted probability. This was done for the sake of better visualization, by making it possible for both measurements to use a common scale.
DISCUSSION
Radiation quality involves the use of a low-LET reference standard, in this case 662 keV gamma rays from 137Cs. As expected, 56Fe ions produced a higher yield of total aberrations per unit dose compared to gamma rays. Additionally, we observed that the distribution of CAs among 56Fe-irradiated cells was clearly overdispersed, meaning the variance to mean ratio exceeded unity which, on the basis of earlier published work (15), was also expected. Overdispersion has long been associated with the production of chromosome aberrations produced by densely ionizing radiations and various non Poissonian distributions have been utilized to deal with the problems this creates for modeling (16–18). While the ZINB distribution has been applied to cytogenetic data (14), to our knowledge this is the first time it has been used in conjunction with multi-flour combinatorial chromosome painting mFISH.
While the quantitative relationship between asymmetrical aberrations and clonogenic cell survival (19, 20) justifies the criteria we and others (8) have used to predict transmissibility in these studies, we freely admit these criteria fall short of perfection. For example, there are instances where interstitial deletions large enough to be seen under the microscope do not kill the cell (21–24). Conversely, we imagine that certain submicroscopic deletions of this type can be lethal, depending on their relationship to essential flanking genes (22). Similar concerns are associated with the production of symmetrical interchanges (i.e., inversions), which are not detected by mFISH, especially since there is evidence that high-LET charged particles are more effective at producing them compared to gamma rays (25). These considerations will have a confounding influence on the absolute values of predicted transmissibility, although we rather doubt, they will change the fundamental shape of the curves shown in Fig. 5. Admittedly, our conclusions would benefit from the inclusion of data associated with higher doses of 56Fe ions. Unfortunately, the highest dose of 56Fe ions used in this study (1.8 Gy) produced such widespread damage — especially complex rearrangements involving a myriad of exchange breakpoints — that it pushes the upper limits of what we can accurately scored by mFISH.
One of the more intriguing results of these experiments relates to the transmissibility of complex aberrations after low- vs. high-LET radiation exposures. As reported previously (24), we and others (8) found virtually no viable cells containing complex aberrations after gamma-ray exposures. Interestingly, this was not because the complex aberrations themselves were necessarily lethal (many were not). Instead, it was because essentially all cells containing complex exchanges also contained one or more lethal simple lethal aberrations (e.g., dicentrics, terminal deletions, etc.). In stark contrast to these results for low-LET photons, we found that more than a quarter of the damaged cells surviving exposure to high-LET HZE particles contained complex exchanges. We are not entirely sure why this happens, though likely it is partly due to the fact that high-LET radiations produce a higher ratio of complex/simple exchanges compared to x- or gamma rays (9, 26, 27). Hence a random sample of aberration-bearing cells — which will contain both viable and nonviable cells — is bound to exhibit an LET-dependent bias favoring cells with complex exchanges.
Another curious finding has to do with the degree of complexity found within cells judged destined to survive. Irrespective of radiation quality, the dose response inclusive of all types of aberrations (lethal plus nonlethal) is dominated by simple two-breakpoint exchanges (i.e., CA2). This is followed in frequency order by CA3> CA4>> CA5… for the complex aberrations. As one would expect, simple CA2 exchanges found within surviving cells outnumbered all classes of complex rearrangements by a large margin. However, we were initially surprised to find that the most prominent class of transmissible complex aberrations was not the 3-way CA3 exchange; it was the 4-way (CA4) class of exchanges! Our proposed explanation for this result requires a rudimentary understanding of exchange cycle structure (8, 28, 29). Suffice it to say that the majority of CA4 aberrations could be imagined having been formed from two independent simple exchange reactions whose breakpoint junctions happen to involve a common chromosome (i.e., CA4; 2c2).
This discussion of complex exchanges is noteworthy for the following reason. When essentially all the exchange aberrations in surviving cells are simple (as we found for gamma rays) then the number of breakpoint junctions is merely twice the number of exchanges. By contrast, a three-way exchange (CA3) has three such junctions; a four-way (CA4) has four of them, and so on. It is the inappropriate recombination between broken chromosome ends that produces such junctions comprising the types of chromosomal anomalies long recognized as drivers of carcinogenic and mutagenic processes. Since complex exchanges, by definition, contain more breakpoint junctions than simple exchanges, it follows that they should be given more weight as a measure of mutagenic/carcinogenic potential. In that case breakpoint junctions rather than “exchange events” would seem to be the appropriate metric. The point being made is this: not only do complex aberrations after high-LET exposures transmit at unexpectedly high rates, but they also carry with them increased risk because of their higher number of exchange breakpoints. Consequently, it may be advisable to consider the number of exchange breakpoints rather than the number of exchange events themselves in (among surviving cells) future analyses.
Any implications the current study might have regarding radiation protection standards should be tempered by the assumption that HZE particles are suitably representative of high-LET radiation in general. HZE radiations are unquestionably relevant to deep space environments. However, whereas such particles have average LET’s comparable to those of more common sources of high-LET radiation like alpha particles, the two radiation types have radically different track structures. Nevertheless, our results are in broad agreement with other cytogenetic studies that used different experimental approaches, but also concluded that the transmissible cytogenetic damage after high-LET particle exposure was unexpectedly low compared to after X- or gamma ray exposures (8, 30). Regardless of this fact, we think it wise to consider a wider range of particle types before making wide-sweeping judgments based solely on this work.
ACKNOWLEDGMENTS
The authors are indebted to Amanda Mareth and Sheri Brackman for their expert technical support, and Stephen Kunkel for careful proofing of the manuscript. We further dedicate this work to Dr. Bradford Loucas, whose hard work and commitment to excellence over the span many years made this and many other investigations possible. This investigation was funded grants from the National Aeronautics and Space Administration, Human Research Program, NASA HRP grant 80NSSC21K0679 (MC) and by the National Institute of Allergy and Infectious Diseases grant number U19-AI067773(IS).
REFERENCES
- 1.Failla G, Henshaw PS, The Relative Biological Effectiveness of X-Rays of Gamma Rays. Radiology 1931; 17, 1–43. [Google Scholar]
- 2.Puck TT, Marcus P, Action of X-Rays on Mammalian Cells. J Exp Med 1956; 103, 653–66. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 3.Blakely EA, Chang PY, Biology of Charged Particles. Cancer Journal 2009; 15, 271–84. [DOI] [PubMed] [Google Scholar]
- 4.Giles N, The Effect of Fast Neutrons on The Chromosomes of Tradescantia. Proc Natl Acad Sci USA 1940; 26, 567–75. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Giles N, Comparative Studies of The Cytogenetical Effects of Neutrons of X-Rays. Genetics 1943; 28, 398–418. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6.Shuryak I, fornace AJ Jr., Datta K, Suman S, Kumar S, Sachs RK, et al. , Scaling Human Cancer Risks From Low LET to High LET When Dose-Effect Relationships are Complex. Radiat Res 2017; 187, 476–82. [DOI] [PubMed] [Google Scholar]
- 7.Loucas BD, Shuryak I, Kunkel SR, Cornforth MN, Dose-Dependent Transmissibility of Chromosome Aberrations at First Mitosis after Exposure to Gamma Rays. I. Modeling of Implications Related To Risk assessment. Radiat Res 2022; 197, 376–83. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Hartel C, Nasonova E, Ritter S, Friedrich T, Alpha-Particle Exposure Induces Mainly Unstable Complex Chromosome Aberrations Which Do Not Contribute to Radiation-associated Cytogenetic Risk. Radiat Res 2021. [DOI] [PubMed] [Google Scholar]
- 9.Loucas BD, Durante M, Bailey SM, Cornforth MN, Chromosome Damage In Human Cells By Rays, Particles of Heavy Ions: Track Interactions in Basic Dose-Response Relationships. Radiat Res 2013; 179, 9–20. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.Cornforth M, Shuryak I, Loucas B, Lethal of Nonlethal Chromosome Aberrations By Gamma Rays of Heavy Ions: A Cytogenetic Perspective on Dose Fractionation in Hadron Radiotherapy. Translational Cancer Research 2017, S769–S78. [Google Scholar]
- 11.Gray LH, Radiation Biology of Cancer. In: University of Texas MDAHTI Editor. Cellular Radiation Biology. Place Baltimore, Williams & Wilkins: Baltimore, Williams & Wilkins; 1965. [Google Scholar]
- 12.Han A, Hill CK, Elkind MM, Repair of Cell Killing of Neoplastic Transformation at Reduced Dose Rates of 60Co Gamma-Rays. Cancer Res 1980; 40, 3328–32. [PubMed] [Google Scholar]
- 13.Fomina J, Darroudi F, Boei JJ, Natarajan AT, Discrimination Between Complete of Incomplete Chromosome Exchanges In X-Irradiated Human Lymphocytes Using FISH With Pan-Centromeric of Chromosome Specific DNA Probes In Combination With Telomeric PNA Probe. Int J Radiat Biol 2000; 76, 807–13. [DOI] [PubMed] [Google Scholar]
- 14.Oliveira M, Einbeck J, Higueras M, Ainsbury E, Puig P, Rothkamm K, Zero-Inflated Regression Models for Radiation-Induced Chromosome Aberration Data: A Comparative Study. Biom J 2016; 58, 259–79. [DOI] [PubMed] [Google Scholar]
- 15.Shuryak I, Loucas BD, Cornforth MN, Straightening Beta: Overdispersion of Lethal Chromosome Aberrations Following Radiotherapeutic Doses Leads To Terminal Linearity In The Alpha–Beta Model. Frontiers In Oncology 2017; 7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16.Virsik RP, Harder D, Statistical Interpretation of the Overdispersed Distribution of Radiation-Induced Dicentric Chromosome Aberrations At High LET. Radiat Res 1981; 85, 13–23. [PubMed] [Google Scholar]
- 17.Couzin D, Papworth DG, The Over-Dispersion Between Cells of Chromosomal Aberrations. J Theor Biol 1979; 80, 249–58. [DOI] [PubMed] [Google Scholar]
- 18.Edwards AA, Lloyd DC, Purrott RJ, Radiation Induced Chromosome Aberrations of the Poisson Distribution. Radiat Environ Biophys 1979; 16, 89–100. [DOI] [PubMed] [Google Scholar]
- 19.Revell SH, Relationship Between Chromosome Damage of Cell Death. In: Ishihara T, Sasaki MS Editors. Radiation-Induced Chromosome Damage In Man. Place Liss: Liss; 1983. [Google Scholar]
- 20.Cornforth MN, Bedford JS, A Quatitiative Comparison of Potentially Lethal Damage Repair of The Rejoining of Interphase Chromosome Breaks In Low Passage Normal Human Fibroblasts. Radiat Res 1987; 111, 385–405. [PubMed] [Google Scholar]
- 21.Cornforth MN, Durante M, Radiation Quality of Intra-Chromosomal Aberrations: Size Matters. Mutation Research/Genetic Toxicology of Environmental Mutagenesis 2018. [DOI] [PubMed] [Google Scholar]
- 22.Cornforth MN, Bedford JS, Bailey SM, Destabilizing Effects of Ionizing Radiation on Chromosomes: Sizing Up The Damage. Cytogenet Genome Res 2021, 1–24. [DOI] [PubMed] [Google Scholar]
- 23.Singleton BK, Griffin CS, Thacker J, Clustered DNA Damage Leads to Complex Genetic Changes In Irradiated Human Cells. Cancer Research 2002; 62, 6263–9. [PubMed] [Google Scholar]
- 24.Loucas B, Shuryak I, Kunkel S, Cornforth M, Dose-Dependent Transmissibility of Chromosome Aberrations at First Mitosis after Exposure to Gamma Rays. I. Modeling and Implications Related to Risk assessment. Radiat Res 2022; 197, 376–83. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25.Ray FA, Robinson E, Mckenna M, Hada M, George K, Cucinotta F, et al. Directional Genomic Hybridization: Inversions as a Potential Biodosimeter for Retrospective Radiation Exposure. Radiation & Environmental Biophysics 2014; 53, 255–63. [DOI] [PubMed] [Google Scholar]
- 26.oferson RM, Marsden SJ, Wright EG, Kadhim MA, Goodhead DT, Griffin CS, Complex Chromosome Aberrations in Peripheral Blood Lymphocytes as a Potential Biomarker of Exposure to High-LET Alpha-Particles. Int J Radiat Biol 2000; 76, 31–42. [DOI] [PubMed] [Google Scholar]
- 27.Ritter S, Durante M, Heavy-Ion Induced Chromosomal Aberrations: A Review. Mutation Research/Genetic Toxicology of Environmental Mutagenesis 2010; 701, 38–46. [DOI] [PubMed] [Google Scholar]
- 28.Cornforth MN, Analyzing Radiation-Induced Complex Chromosome Rearrangements By Combinatorial Painting. Radiat Res 2001; 155, 643–59. [DOI] [PubMed] [Google Scholar]
- 29.Savage JR, The Transmission of FISH-Painted Patterns Derived from Complex Chromosome Exchanges. Mutat Res 1995; 347, 87–95. [DOI] [PubMed] [Google Scholar]
- 30.Durante M, George K, Cucinotta F, Chromosomes Lacking Telomeres Are Present In The Progeny of Human Lymphocytes Exposed To Heavy Ions. Radiat Res 2006; 165, 51–8. [DOI] [PubMed] [Google Scholar]