Dose-dependent Transmissibility of Chromosome Aberrations at First Mitosis after Exposure to Gamma Rays. I. Modeling and Implications Related to Risk Assessment

Abstract

The relationship between certain chromosomal aberration (CA) types and cell lethality is well established. On that basis we used multi-fluor in situ hybridization (mFISH) to tally the number of mitotic human lymphocytes exposed to graded doses of gamma rays that carried either lethal or nonlethal CA types. Despite the fact that a number of nonlethal complex exchanges were observed, the cells containing them were seldom deemed viable, due to coincident lethal chromosome damage. We considered two model variants for describing the dose responses. The first assumes independent linear-quadratic (LQ) dose response shapes for the yields of both lethal and nonlethal CAs. The second (simplified) variant assumes that the mean number of nonlethal CAs per cell is proportional to the mean number of lethal CAs per cell, meaning that the shapes and magnitudes of both aberration types differ only by a multiplicative proportionality constant. Using these models allowed us to assemble dose response curves for the frequency of aberration-bearing cells that would be expected to survive. This took the form of a joint probability distribution for cells containing ≥1 nonlethal CAs but having zero lethal CAs. The simplified second model variant turned out to be marginally better supported than the first, and the joint probability distribution based on this model yielded a crescent-shaped dose response reminiscent of those observed for mutagenesis and transformation for cells “at risk” (i.e. not corrected for survival). Among the implications of these findings is the suggestion that similarly shaped curves form the basis for deriving metrics associated with radiation risk models.

INTRODUCTION

The induction of large-scale structural variants in the genome is a hallmark property of ionizing radiation (IR) that frequently manifests itself as microscopically visible chromosomal aberrations (CAs) (1). By comparison to the vast array of known genotoxic agents, ionizing radiation is uniquely potent in producing CAs and eliciting reproductive cell death, and numerous studies have shown strong associative and causal links between these two biological endpoints. CAs are found in all cancers where they serve as important drivers of the carcinogenic process. They are exquisitely sensitive to induction by radiation and, unlike most other measures of radiation damage, provide information on an individual cell-by-cell basis. In addition, virtually all agents capable of causing CAs are both mutagenic and carcinogenic. In this context it is understandable that quantitative measurement of dose-dependent CA yields finds usefulness as a surrogate measure of radiation risk for carcinogenesis and for many other biological effects of ionizing radiation of concern to public health.

The thrust of this paper centers on the cytogenetic interrogation of cells at the first mitosis after irradiation for the purpose of identifying those individual cells carrying CAs, and then determining whether each was likely to have produced clonal progeny. In other words, we focused on the dose response specifically for nonlethal CAs that can be transmitted to the cell’s descendants, thereby potentially producing a malignant or pre-malignant cell lineage.

The rationale and criteria used in this process begin with a fundamental understanding of the various aberration types induced by radiation, the large majority of which are exchange-type rearrangements that result from pairwise misrejoinings of broken ends produced by two (or more) initial radiogenic breaks. Such misrejoinings can involve broken ends on different chromosomes (interchanges), or broken ends within the same chromosome (intrachanges). Both the interchange and intrachange classes of aberrations can present in two basic forms. Asymmetrical exchanges (e.g. dicentrics and rings) are always accompanied by acentric fragments, whereas symmetrical exchanges (e.g. reciprocal translocations and inversions) never produce acentric fragments (Fig. 1).

FIG. 1.

Simplified schematic of the types of exchange aberrations assessed for transmissibility. Top panels represent asymmetrical aberrations deemed lethal. Panel a: Interstitial deletion/acentric ring. Panel b: Simple dicentric. Panel c: Complex 3-way exchange. Bottom panels represent exchange configurations of the transmissible symmetrical type. Panel d: Inversion (not detectable by mFISH). Panel e: Simple reciprocal translocation. Panel f: Complex 3-way exchange. CAB values indicating the minimum number of chromo-somes/arms/breaks required for aberration formation are shown for each column.

Asymmetrical forms are largely lethal, since their acentric fragments lack the centromeres necessary to ensure the equitable assortment of genetic material they contain to daughter cells during ensuing mitoses, or because of mechanical problems they cause to the mitotic mechanism, such as anaphase bridging. Exceptions to lethality for these aberration types can be made for diminutive acentric ring products (e.g. tiny interstitial deletions). Cells with such lesions can sometimes survive, provided that the material loss does not involve vital genes. All microscopically identifiable asymmetrical forms are easily recognizable after common histological staining by reagents like Giemsa.

In addition to a potential growth advantage they may confer, any consideration of CAs in connection with cancer and mutation should focus on aberration types that do not clonogenically inactivate cells harboring them. For that reason, asymmetrical forms like dicentrics and larger rings would be expected to play a relatively minor role in the genesis of mutations and cancer, at least by comparison to the symmetrical interchanges (i.e. translocations) and intrachanges (i.e. inversions). Since neither of these latter symmetrical types produce acentric fragments, they would be considered largely transmissible by the criteria described above. For example, in an unrelated series of experiments, we have isolated from irradiated cell populations several dozen independent clones. Of the clones found to carry CAs, all contained translocations, whereas none contained asymmetrical exchanges (2). Exceptions can be imagined for the breakpoint junctions of translocations that (for example) cleave vital genes, but such events would be infrequent given the sparse density (≤ 2%) of coding sequences per unit genome length (3).

Here we consider these concepts as applied to chromo-some-type exchanges, which appear at mitosis from radiation damage inflicted in the earlier G1 or G0 phases of the cell cycle. In a general sense they would also apply to the chromatid-type exchanges (particularly interchanges) which, unlike the chromosome types, are the result of damage produced in S- or G2 phases of the cell cycle. These too can exist in either symmetrical or asymmetrical forms. Although the latter forms are not transmissible (e.g. U-type quadriradials), the symmetrical forms (i.e. X-type quadriradials) are partially transmissible, whereupon they are converted to chromosome-type exchanges (translocations) following subsequent mitoses. Thereafter, expectations related to cell survival would be the same as for the chromosome types.

Since translocations and inversions are not as readily detected as their asymmetrical counterparts (e.g. dicentrics and rings) by solid histological staining, they require more specialized cytogenetic approaches. In principle, techniques like G- or Q-banding would suffice for their detection, but suffer limitations related to pattern recognition that make them less than ideal for this purpose. Techniques in which a few select chromosomes can be “painted” with hybridization fluor cocktails greatly increases the ease and accuracy with which symmetrical interchanges can be measured. However, their detection is limited to exchanges involving those chromosomes one has chosen to paint. A related complication is that radiation-induced exchanges are frequently complex, meaning they involve multiple chromosomes and exchange breakpoints, a situation made worse by the fact that their frequency relative to simple exchanges increases rapidly with dose for radiations such as gamma rays.

These problems are largely circumvented through the use modern combinatorial fluorescent hybridization techniques like mFISH, which allows for the unambiguous identification of each individual chromosome type within the haploid set. For the current study this means the 24 different chromosome types making up the human genome. A detailed description of the criteria used to discern the viability of cells carrying complex exchanges is given in the following section. Basically, those cells whose rearrangement(s) have spawned one of more acentric elements are destined to undergo reproductive cell death; otherwise they will survive and transmit their rearrangements to future progeny. This is irrespective of the number of breakpoints junctions or how many chromosomes may be involved.

As mentioned above, there are important reasons for wanting to know the dose response for nonlethal CAs, the most obvious being that only surviving cells possess mutagenic/carcinogenic potential. To our knowledge only one previous study (4) has specifically addressed the issue of cell viability in connection with the dose response for nonlethal CAs. We feel the importance of this phenomenon to radiation-induced health effects makes the topic worthy of further investigation.

For in vitro studies of mutagenesis it is common to express the yields of radiation-induced mutants per surviving cell. In such cases mutation yields are typically found to increase monotonically with dose, sometimes linearly, but often with some degree of upward curvature. While expressing the data in this way can be informative, it belies the well-known fact that the incidence of mutations per cell exposed (i.e. all cells “at risk”) takes on an altogether different shape. Namely, a dose-dependent increase to some peak value, followed later by a sharp decline at higher doses. For technical reasons, doseresponse relationships for gene mutations are far less precise than those for CAs (5). Nevertheless, the data are sufficiently robust to demonstrate that this decline in mutant yields is due to cell killing. This conclusion is supported by the fact that the shape of the dose response for mutation frequency (per cell at risk) mirrors that of clonogenic survival at high doses. The same can be said for in vitro models of cell transformation by radiation and, by inference, carcinogenesis (6–8). Somewhat similar dose response relationships have long been reported for radiation-induced carcinogenesis in mouse model systems (9, 10) where the initial response to tumor induction begins to flatten with increasing dose, often followed by a downturn at still higher doses, a result often explained on the basis of concomitant killing of cells carrying cancerous lesions.

Early radiobiological studies tended to treat concepts like ‘‘lethal lesions’’ and ‘‘carcinogenic lesions’’ in the abstract, without ascribing to them any specific subcellular identities. Here we consider transmissible CA’s (or a subset of them) as a cause for these effects. Since only surviving cells are capable of transmitting potentially mutagenic/carcinogenic lesions to future cell progeny, we constructed a dose response for the frequency of gamma-irradiated cells carrying only nonlethal aberrations. The data were subsequently fitted to a joint probability model which explains the shape of the resulting dose response curve as a competition between two dose-dependent processes: one for the induction of nonlethal CAs; the other for the induction of lethal CAs. We argue this approach is appropriate when considering CA data as a surrogate measure of radiation risk.

MATERIALS AND METHODS

Cell Culture Conditions and Irradiations

Venous blood was obtained from a consented healthy volunteer after procedures approved by the Institutional Review Board of the University of Texas Medical Branch. Blood was collected in heparinized BD Vacutainer tubes (Beckton-Dickinson, Franklin Lakes, NJ) and cultured in 5 ml of RMPI-1640 medium in T25 tissue culture flasks. Cultures were irradiated with graded doses of ¹³⁷Cs γ rays using a JL Shepheard Mark I-68A Irradiator at a dose rate of 85.6 cGy/min. Immediately after irradiation, cells were stimulated with phytohemagglutinin (Remel, Lenexa, KS) and mitotic cells were collected, fixed, and spread onto slides 48 h later.

mFISH Preparation and Analysis

Hybridization and karyotyping were conducted as described previously (11). Briefly, fixed cells spread onto glass microscope slides were treated with acetone, RNase A and proteinase K before fixation in 3.7% formaldehyde. Slides were dehydrated through an ethanol series (70, 85 and 100%) and air dried before incubation in 72°C formamide (70%) in 2x SSC (0.3 M NaCl, 0.03 M sodium citrate) for 2 min to denature the chromosomal DNA. After dehydration through another ethanol series, 10 µl of denatured (10 min at 72°C) 24XCyte Human Multicolor FISH Probe (MetaSystems USA, Boston, MA) was applied to each slide. Slides were covered with a 22 × 22 mm glass coverslip sealed into position with rubber cement. Samples were allowed to hybridize for 48 h in a 37°C incubator. After hybridization, coverslips were removed, and the slides washed for 2 min in 0.4x SSC containing IGEPAL (0.3%) nonionic detergent at 72°. This was followed by a 30 s wash in 2x SSC (0.1% IGEPAL) at room temperature. Finally, 15 DAPI (MetaSystems) was applied to each slide and covered with a 24 × 40 mm coverslip.

Images of chromosome spreads were captured using a Zeiss Axio Imager.M1 epifluorescence microscope equipped with a CoolCube 1 digital high-resolution CCD camera (MetaSystems). Karyotypes were constructed from about 100 chromosome spreads using ISIS FISH Imagining System software (MetaSystems). Metaphase cells were analyzed by following procedures previously established (11). First, mPAINT descriptors were assigned to chromosomes involved in aberrations (12). Next, each rearrangement was brought to ‘‘pattern closure’’ by grouping elements in the most conservative way possible; minimizing the number of exchange breakpoints required. Reciprocal pairwise rejoinings between one (as in the case of ring formation) or two chromosomes were scored as simple exchanges. Exchanges involving three or more breakpoints were regarded as complex. This classification was also applied to incomplete exchanges where one or more elements failed to rejoin, as well as to so called ‘‘one-way’’ exchanges where one or more translocated segments of chromosome appeared to be missing, presumably because they were too small to be resolved by mFISH (13).

Aberration Scoring Criteria

The specific criteria for judging a cell’s ability to survive while containing 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. In principle, 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, 14). 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. Cell-by-cell classifications regarding survivability were tabulated as follows.

• Cells: The total number of cells scored for a given dose.

• Unaffected: Cells for which no chromosome aberrations were found.

• Affected: Cells which contained any sort of chromosome aberration; no distinction made between lethal and nonlethal aberrations.

• Dead affected: Cells that we predict should fail to form colonies on the basis of them containing one or more lethal aberration.

• Live affected: Cells that contain only nonlethal aberrations and should not be lethal (i.e. cells deemed transmissible).

• Total aberrations: Sum of all types of aberrations for the given dose.

• Lethal aberrations: Sum of only lethal types of aberrations.

• Lethal breakpoints: The total number of initial breaks in chromosomes necessary to have produced the lethal aberration.

• Nonlethal aberrations: Sum of only nonlethal types of aberrations.

• Nonlethal breakpoints: Sum of initial breaks in chromosomes necessary to have produced the nonlethal aberration.

Analysis of Probability Distributions of Lethal and Nonlethal Aberrations

A core principle driving our analysis was proposed many years ago by Gray (6) and later employed by Elkind and coworkers (7). Translated for use in the present context, it considers, as competing processes, the dose response for cells containing nonlethal aberrations (F_D,N) and the dose response for cells having sustained lethal chromosome damage (F_D,L) at dose D. 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.

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 (0, 0.25, 0.5, 1, 2, 4 and 6 Gy). Summary statistics (mean, median, 1st and 3rd quartiles, minimum and maximum) and histograms were calculated for each distribution (lethal or nonlethal CAs at each 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 4.0.3 software. Fitting was performed by maximum likelihood techniques, and relative fit quality of the Poisson and NB distributions was 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 preferred to the NB distribution based on AIC for each aberration class and radiation dose. Therefore, the former was assumed as we proceeded to model the radiation dose responses of lethal and nonlethal CAs.

We considered two model variants (labeled A and B for convenience) for describing the dose responses. Variant (A) assumes independent (unique) linear-quadratic (LQ) dose-response shapes for lethal and nonlethal CAs. It is described by the following equations, where D is the radiation dose, µ_lA is the mean number of lethal CAs per cell, c_lA is the mean number of lethal CAs per cell in unirradiated cells, α_lA and β_lA are the linear and quadratic dose response parameters for lethal CAs, and c_nA, α_nA and β_nA are analogous parameters for nonlethal CAs:

$${\mu }_{lA}=c_{lA}+{\alpha }_{lA}D+{\beta }_{lA}{D}^2,{\mu }_{nA}=c_{nA}+{\alpha }_{nA}D+{\beta }_{nA}{D}^2$$ (1)

A (simplified) model variant (B) assumes that the mean number of nonlethal CAs per cell is proportional to the mean number of lethal CAs per cell. In other words, it assumes that 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 modified model is described by the following equations:

$${\mu }_{lB}=c_{lB}+{\alpha }_{lB}D+{\beta }_{lB}{D}^2,{\mu }_{nB}=P{\mu }_{lB}=P\left(c_{lB}+{\alpha }_{lB}D+{\beta }_{lB}{D}^2\right)$$ (2)

Variant (A) contains 6 adjustable parameters (c_lA, α_lA, β_lA, c_nA, α_nA and β_nA ), whereas the modified variant (B) contains only 4 (c_lB, α_lB , β_lB ,and P), and thereby benefits statistically by the reduction of two degrees of freedom.

Since transmissible CAs are (by definition) mutations, we imagine that some of the cells carrying them have the potential to become the ancestors of malignant clones. Consequently, for each model, we were interested in estimating the joint probability distribution for cells containing ≥1 nonlethal CAs, but zero lethal CAs. The fractions of cells (F) with ≥1 nonlethal CAs and zero lethal CAs were estimated for each model variant (F_A and F_B, respectively) using the following equations based on the Poisson distribution, where the terms µ_lA, µ_nA, µ_nA, and µ_nA were taken from Eq. (1), and the terms µ_lB, µ_nB, µ_nB, and µ_nB were taken from Eq. (2):

$$F_A=e^{-{\mu }_{lA}}\left(1-e^{-{\mu }_{nA}}\right),F_B=e^{-{\mu }_{lB}}\left(1-e^{-{\mu }_{nB}}\right)$$ (3)

Model Fitting and Parameter Estimation

Both model variants [Eqs. (1) and (2)] were fitted to the data by Poisson regression based on maximizing the log likelihood, implemented in Maple 2020 software. The relative fit quality of these variants was compared by AIC. Profile likelihood was used to estimate the 95% confidence intervals (CI) for each model parameter.

Transmissibility of Complex Exchanges

Consider the formation of a complex exchange derived from a minimum number of initial radiogenic breakpoints (n), distributed among an equal number of chromosomes and chromosome arms (CAB_initial n/n/n). As can be deduced from the equations of Levy et al. (15), if one disregards restitution, the fraction F_n of all possible complex rejoining configurations that do not produce asymmetrical elements, and are therefore transmissible, is given by:

$$F_n=\frac{1}{2^{\left(n-1\right)}}$$ (4)

RESULTS

Analysis of the distributions for lethal and nonlethal CAs per cell suggested that the Poisson distribution provided a better fit (based on AIC) for each aberration class and at all radiation doses, compared with the more complex NB distribution. Consequently, our modeling approaches for the radiation dose responses for lethal and nonlethal CAs [Eqs.( 1–3)] relied on the Poisson distribution. The average fraction of nonlethal/total aberrations per cell was 24.6%. Naturally, this number was dominated by data at higher doses (1–6 Gy), where most of the aberration counts occurred. The range at these doses was 23.6 to 33.3%. Predictably, more variation was found at lower doses, with range of 9.5 to 23.5%, where the aberration counts were low.

The simplified model variant B [Eq. (2)] turned out to be marginally better supported by AIC (by 0.5 units), compared with the variant A [Eq. (1)]. Thus, assuming a simple proportionality constant (P) between the dose responses for lethal and nonlethal CAs appeared to provide a reasonable fit to the data set analyzed here. The result of best-fit dose response predictions for this preferred model variant B [Eq. (2) are shown in Fig. 2. Its parameter values were: c_lB = 0.046 (95% CI: 0.015, 0.092), α_lB = 0.230 (0.139, 0.315) Gy^–1, β_lB =0.056 (0.039, 0.074) Gy^–2, and P = 0.326 (0.284, 0.373). The more complex and somewhat worse-performing model variant A [Eq. (1)] had the following best-fit parameters: c_lA = 0.064 (95% CI: 0.023, 0.124), α_lA = 0.193 (0.081, 0.291) Gy^–1, β_lA = 0.062 (0.043, 0.084) Gy^–2, c_nA = 0 (95% CI: 0, 0.002), α_nA = 0.111 (0.061, 0.159) Gy^–1, β_nA = 0.012 (0.001, 0.022) Gy^–2.

FIG. 2.

Best-fit model predictions based on the preferred model variant B, Eqs. (2) and (3) for the mean number of lethal and nonlethal aberrations per cell (panel A) and for the fractions of cells with ≥1 lethal or ≥1 nonlethal aberrations (panel B). Error bars on the data points represent 95% CIs. Panel A shows the CIs were estimated for the Poisson distribution based on the normal distribution approximation with variance equal to the mean. Panel B shows the CIs were estimated for the Binomial distribution using the score confidence interval approach (20).

Predictions for the joint probability distribution for cells that have ≥1 nonlethal CAs and zero lethal CAs were estimated by substituting best-fit parameter values for each model variant (A) or (B) into Eq. (3). Such predictions for the best-supported simplified model variant (B) are shown in Fig. 3. The maximum predicted fraction of cells with ≥1 nonlethal CAs and zero lethal CAs was 10.3%, which occurred at a radiation dose of 2.29 Gy. The somewhat worse-fitting model variant (A) resulted in a similar predicted maximum of 11.7% at 2.19 Gy.

FIG. 3.

Best-fit model predictions based on the preferred model variant B, Eqs. (2) and (3) for the fraction of cells with ≥1 nonlethal aberrations and zero lethal aberrations. Error bars on the data points represent 95% CIs, estimated for the binomial distribution using the score confidence interval approach (20).

DISCUSSION

An unanticipated result of our findings and mathematical modeling was that the fraction of nonlethal/lethal aberrations per cell was consistent with it being constant over the dose range examined. In other words, differences between the two measures of damage were merely dose-modifying; their dose responses had the same shape and could be made to match each other simply by scaling the dose. The reason for this phenomenon is not understood. Nevertheless, this finding on the data analyzed here justifies the construction of joint probability functions with a reduced number of parameters. Aside from this statistical advantage, the finding that nonlethal aberrations comprise a potentially constant fraction of all aberrations allows the frequency of cells containing only nonlethal CAs to be estimated, based solely on lethal aberration data as input. The fact that cytogenetic data of this type can be had using conventional histological stains begs the question of whether more advanced (and expensive) methods like mFISH are required to produce the type of dose response shown in Fig. 3.

This work involved samples from a single volunteer, and we are mindful of the fact that variations in radiation sensitivity exist among individuals. For this and other reasons, we do not dismiss the possibility that this relationship represents a serendipitous occurrence that applies only to our specific data set. On the other hand, it seems plausible that a common dose-modifying factor may be the norm for cytogenetic data of this type. In that case, the answers to certain questions become pertinent. For example, how would such a constant of proportionality [P of Eq. (2)] change for radiations with dramatically different ionization densities (LET) and track structures, for example, HZE particles encountered in deep space environments, or heavy-charged particles used in radiotherapy. Conceivably, radiations with different qualities might tend to express their own reproducibly unique values of P, although it goes without saying that further studies would be needed to justify such an assumption.

Apart from any conjecture regarding P, the basic shape of the dose response shown in Fig. 3 prompts speculation on several fronts. The first relates to the peak response which, for gamma rays, occurred at about 2 Gy. Similar values for the peak response were obtained by the recent study of Hartel et al. (4), who also estimated the yield of human lymphocytes carrying transmissible aberrations. It is noteworthy that the dose corresponding to this peak response is similar to the fraction sizes used in conventional photon-based radiotherapy regimens. Thus, while such fractionation serves the intended purpose of limiting damage to late-responding normal tissues that surround the tumor, it also corresponds to the maximum proportion of cells that carry nonlethal CAs. The premise that such CAs are surrogate measures of mutagenesis and carcinogenesis would appear to suggest that the benefit of sparing normal tissues during conventional fractionated radiotherapy can unwittingly go hand-in-hand with an increased risk of producing secondary radiogenic cancers. In cases where this becomes an overriding concern, one would hope that avoiding doses near the peak response for aberration transmissibility would not materially compromise the ultimate objectives of tumor control and normal tissue sparing.

It should be abundantly clear from Eq. (3) that virtually any type of ionizing radiation will demonstrate a crescent-shaped dose response curve reminiscent of that shown in Fig. 3 due to competition between processes of nonlethal and lethal CA induction. We plan to address this topic in a future paper but, for the time being, we imagine that the dose response for radiations of higher ionization densities will alter the shape of this curve in predictable ways, as suggested for α particles in the recent study of Hartel et al. (4). For example, similar analysis of CAs produced by heavy charged particles would be expected to produce peak values shifted towards lower doses. We surmise that a comparison of high- vs. low-LET curves of this type would form the basis for estimating dose-dependent relationships of relative biological effectiveness (RBE).

Prior knowledge about the shape of this dose response would benefit the experimentalist who, for one reason or another, may wish to isolate, from an irradiated population, clonal derivatives of single progenitor cells exposed to radiation (2, 16). Because such isolations are both tedious and laborious, it benefits the investigator to judiciously consider the level of dose applied. In situations where the number of cells in the initial irradiated population is severely limited in number, high doses can result in few or no surviving colonies. In this case, it may be prudent to use a dose that produces the highest ratio of aberration-bearing clones to the total number of irradiated cells (i.e. the peak response of Fig. 3). If instead the purpose of clonal isolation is merely to ensure that a maximum number of surviving clones will contain an unspecified level of chromosome damage, and the number of cells in the exposed population is large enough as to be inconsequential, then doses well beyond the peak dose response may suffice. This would result in fewer surviving clones as a fraction of total cells irradiated but will help maximize the chances that the surviving cells within those clones will contain transmissible aberrations.

However, such doses often extend well beyond those capable of producing biological effects in the low-dose region. Since this is a paramount consideration in many instances, one would logically select doses no higher than that corresponding to the peak of the dose response, the lower, the better within the limits of feasibility. As is evident from the data shown in Fig. 3, doses to the left of the peak will yield progressively fewer aberration-bearing clones. Simultaneously, this will result in a growing fraction of clones containing no discernable chromosome damage, i.e. null clones. Since nulls would be uninformative for most subsequent analyses, their isolation and characterization may represent an unwanted expenditure of valuable resources (time and money). Application of Eq. (3) would put the investigator in a position to make informed decisions regarding the range of doses they consider relevant and/or practicable. As it relates the shape of the dose response shown in Fig. 3, the same arguments would apply to endpoints other than CAs.

In the past we have argued that the number of exchange breakpoint junctions, and not the exchange events comprised of them, is a more appropriate measure of genotoxic damage (11). This stems from the fact that simple exchanges (e.g. dicentrics and reciprocal translocations) involve only two breakpoint junctions, whereas complex exchanges involve (at a bare minimum) three such junctions. An appeal to common sense results in placing more mutagenic/carcinogenic potential on the latter class of aberrations. For that reason we carefully tallied the number of breakpoint junctions associated with each exchange event (Materials and Methods). This was done with the expectation that such breakpoint data would be analyzed and function-fitted in a manner similar to that used to produce Figs. 2 and 3.

As expected, complex exchanges were commonly observed among the cells of the irradiated cell populations, particularly at higher doses. Astonishingly to us, despite the fact that a sizable proportion of these complex CAs were classified as being transmissible, they were conspicuously absent among cells that were deemed destined to survive. Out of the 645 irradiated cells we examined in this study, only one complex exchange was found in a cell judged viable by our criteria (See Supplementary Table S1; https://doi.org/10.1667/RADE-21-00180.1.S1). This, even though the predicted transmissibility of some the most common complex exchanges is reasonably high. These include complex exchanges involving three initial radiogenic breaks on three different chromosomes such as a CAB 3/3/3 (17) which, based on random rejoining of three initial radiogenic breaks, and ignoring restitution, would be expected to transmit 25% of the time [Eq. (4)]. By that criterion, complex exchanges involving three breaks on two different chromosomes (e.g. CAB 2/2/3) would have an even higher predicted level (50%) of transmissibility.

This seeming conflict between theory and observation was resolved upon further examination of the raw data, which showed that virtually all cells containing otherwise-transmissible complex exchanges were deemed not capable of surviving because of additional coincident chromosome damage. In other words, while many of the complex exchanges were themselves transmissible, they almost always occurred in cells that contained other lethal chromosome damage. In hindsight, this seems likely due to the fact that the relative frequency of complex exchanges compared to simples is strongly dose-dependent (11, 18). Consequently, doses high enough to produce significant levels of complex exchanges are also likely to produce additional exchanges within the same cell: simple exchanges (many are lethal) as well as additional complex exchanges (most are lethal) (Supplementary Table S1; https://doi.org/10.1667/RADE-21-00180.1.S1). In any case, this forces the conclusion that essentially all the exchange aberrations found among cells predicted to survive are simple two-breakpoint exchanges, in agreement with previous reports (4). For that reason, it became pointless to model separately our exchange breakpoint data.

mFISH is quite robust in its capacity to detect large-scale structural rearrangements occurring between different chromosomes (interchanges) such as translocations and dicentrics. It is also capable of discerning asymmetrical exchanges that occur within the same chromosome (intra-changes). This includes all products belonging to the ring family, inclusive of interstitial deletions. However, it lacks the ability to detect symmetrical intrachanges (inversions), which is unfortunate because radiation-induced inversions are likely produced in yields equaling (or surpassing) those of translocations (19), and because, like translocations, they are highly transmissible. Until a detailed data set can be built to include inversions, we can only speculate as to the influence these aberration types would have on our conclusions. Of course, there are also categories of genomic damage smaller in scale than those observable by microscopy to consider. These would include submicro-scopic interstitial deletions and the like which are certainly capable of causing mutations. Thus, while it is likely that the quantitative aspects of this study may be applied to future cytogenetic studies, we hesitate to attach undue significance to the absolute numerical values they represent in the broader context of radiation risk. Rather, it is the concept implied by the basic shape of the curve shown Fig. 3 that we wish to impress upon the reader and, going forward, its broader implications related to the biophysical modeling of radiation damage.

TABLE 1.

Summary of CA Quantification and Classification Results

Dose (Gy)	No. cells	Lethal aberrations			Nonlethal aberrations			Cells with ≥1 nonlethal and 0 lethal aberrations
		Count	Per cell	95% CI* error bar	Count	Per cell	95% CI	Count	Per cell	Lower 95% CI**	Upper 95% CI**
0	49	3	0.061	0.069	0	0.000	0.000	0	0.000	0.000	0.073
0.25	99	13	0.131	0.071	4	0.040	0.040	3	0.030	0.010	0.085
0.5	100	19	0.190	0.085	2	0.020	0.028	2	0.020	0.006	0.070
1	103	24	0.233	0.093	12	0.117	0.066	8	0.078	0.040	0.146
2	100	70	0.700	0.164	28	0.280	0.104	15	0.150	0.093	0.233
4	100	202	2.020	0.279	70	0.700	0.164	6	0.060	0.028	0.125
6	143	482	3.371	0.301	149	1.042	0.167	1	0.007	0.001	0.039

Notes.

^*95% CIs estimated for the Poisson distribution based on the normal distribution approximation with variance equal to the mean.

^**95% CIs estimated for the Binomial distribution using the score confidence interval approach (20).