Radiat Environ Biophys (2015) 54:305–316 DOI 10.1007/s00411-015-0601-x

ORIGINAL PAPER

Modeling radiation-induced cell death: role of different levels of DNA damage clustering M. P. Carante1,2 • S. Altieri1,2 • S. Bortolussi2 • I. Postuma1,2 • N. Protti2 F. Ballarini1,2

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Received: 24 February 2015 / Accepted: 28 April 2015 / Published online: 9 May 2015  Springer-Verlag Berlin Heidelberg 2015

Abstract Some open questions on the mechanisms underlying radiation-induced cell death were addressed by a biophysical model, focusing on DNA damage clustering and its consequences. DNA ‘‘cluster lesions’’ (CLs) were assumed to produce independent chromosome fragments that, if created within a micrometer-scale threshold distance (d), can lead to chromosome aberrations following mis-rejoining; in turn, certain aberrations (dicentrics, rings and large deletions) were assumed to lead to clonogenic cell death. The CL yield and d were the only adjustable parameters. The model, implemented as a Monte Carlo code called BIophysical ANalysis of Cell death and chromosome Aberrations (BIANCA), provided simulated survival curves that were directly compared with experimental data on human and hamster cells exposed to photons, protons, a-particles and heavier ions including carbon and iron. d = 5 lm, independent of radiation quality, and CL yields in the range *2–20 CLs Gy-1 cell-1, depending on particle type and energy, led to good agreement between simulations and data. This supports the hypothesis of a pivotal role of DNA cluster damage at sub-micrometric scale, modulated by chromosome fragment mis-rejoining at micrometric scale. To investigate the features of such critical damage, the CL yields were compared with experimental or theoretical yields of DNA fragments of different sizes, focusing on the base-pair scale (related to the so-called local clustering), the kbp scale (‘‘regional clustering’’) and the Mbp scale, corresponding to & F. Ballarini [email protected] 1

Physics Department, University of Pavia, Via Bassi 6, 27100 Pavia, Italy

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INFN, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy

chromatin loops. Interestingly, the CL yields showed better agreement with kbp fragments rather than bp fragments or Mbp fragments; this suggests that also regional clustering, in addition to other clustering levels, may play an important role, possibly due to its relationship with nucleosome organization in the chromatin fiber Keywords Ionizing radiation  Cell death  DNA cluster damage  Chromosome aberrations  Chromatin fragmentation  Biophysical models

Introduction Since more than three decades, DNA cluster damage is widely recognized to play an important role with respect to the harmful effects of ionizing radiation (Ward 1985, 1994; Jenner et al. 1993; Goodhead 1994; Prise et al. 2001; Sutherland et al. 2002; Rothkamm and Lobrich 2003). Recently, O’Neill and co-workers showed in real time that not only complex double-strand breaks (DSBs) are repaired more slowly than simple ones, but also DSB complexity strongly influences the repair by non-homologous endjoining (NHEJ), involving specific factors such as DNAPKcs (Reynolds et al. 2012). In this framework, Schipler and Iliakis (2013) classified DSBs according to six levels of increasing complexity, from ‘‘clean’’ DSBs, like those generated by restriction endonucleases, to DSB clusters, that is several DSBs ‘‘in close proximity.’’ According to these authors, while all repair pathways can in principle remove lesion clustering at the DSB site, such pathways are more likely to fail when they encounter DSB clusters. These clusters undermine local chromatin stability generating small DNA fragments, the loss of which is likely to impair the function of all DSB repair pathways and to

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cause cell death and other endpoints including chromosome aberrations (Terzoudi et al. 2011). However, the meaning of ‘‘close proximity’’ still needs to be elucidated, and it is still not clear how small these critical DNA fragments should be. Starting from the eighties, fragments with size of a few tens base pairs have been object of many theoretical studies based on radiation track-structure simulations, in which the attention was focused on the so-called DSB?? (generally defined as at least two DSBs within 30 base pairs) and other types of local DNA cluster damage (Goodhead and Nikjoo 1989; Charlton et al. 1989; Chatterjee and Holley 1992; Ottolenghi et al. 1995; Nikjoo et al. 2001; Friedland et al. 2011). Experimentally, DNA fragments smaller than 70 bp were suggested to be implicated in the enhanced cell killing observed after high LET irradiation by Wang et al. (2010), who attributed the enhanced toxicity of these fragments to their inability to accommodate bidirectional binding of the Ku-protein; even shorter fragments (14–20 bp) were found to inhibit the activity of DNA-PK (Pang et al. 2011). In the nineties, a role for larger fragments was suggested by Rydberg and co-workers basing on both experiments and simulations (Holley and Chatterjee 1996; Rydberg 1996; Rydberg et al. 1998, 2002). More specifically, exposing human fibroblasts to X-rays or accelerated ions, they observed a prominent fragmentation peak at 78 bp, corresponding to one turn of DNA around the nucleosome, and broader peaks at about 185, 290, 370 and 450 bp, which should reflect the arrangement of the nucleosomes relative to each other; simulations based on a zigzag chromatin model showed good agreement with the experimental data (Rydberg et al. 1998). The authors concluded that, in addition to local clustering, also a clustering at the chromatin fiber level, which they called ‘‘regional clustering,’’ may be important. Furthermore, these authors stated that ‘‘if these clusters are important for cell killing, a possible hypothesis could involve chromatin fiber breakage at sites of clusters and a high probability of forming chromosomal aberrations’’ (Rydberg 1996). In the same period, Bryant and colleagues (Johnston and Bryant 1994; Johnston et al. 1997) proposed that the spatial distribution of DSBs in looped chromatin domains at the Mbp level plays a crucial role in DSB repair and that mis-repair involves DNA fragment loss at such DSB clusters. An important role of DSB clusters within these loops was also hypothesized in some modeling studies on cell death and chromosome aberrations (Ponomarev and Cucinotta 2006; Friedrich et al. 2012). Albeit necessary, a characterization of the relevant initial DNA damage is not sufficient to fully explain subsequent endpoints like chromosome aberrations and cell death, which are also influenced by repair. Even before the discovery of the double helix, Lea (1946) suggested that only

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chromosome free-ends that are close enough can undergo (mis-)rejoining and the consensus on this issue is wide. However, the relationship linking the initial distance between two free-ends and their probability of being rejoined is still an open question. Some modeling studies proposed a rejoining probability P that decreases very rapidly with increasing distance d: for instance, Edwards et al. (1994, 1996) assumed an inverse power law of the form PðdÞ ¼ k=dn where k and n are adjustable parameters. While good agreement was found with experimental data on dicentric chromosomes in human lymphocytes exposed to gamma rays, the model overestimated dicentric induction by alpha particles. A very similar relationship was adopted by Kreth et al. (2007) applying their spherical chromatin domain model to chromosome aberration induction in gamma-irradiated human lymphocytes, which led to good agreement with dicentric data but overestimated the yield of centric rings. On the contrary, other authors assumed that the rejoining of DNA free-ends involves larger distances, at the micrometer scale. According to Brenner (1988), who modeled chromosome aberration induction in Chinese hamster cells exposed to different radiation types, the probability that two chromosome free-ends at distance x apart will (mis-)rejoin does not vary significantly up to a threshold distance of the order of the micrometer and then decreases very rapidly. This suggests that the distance dependence of the rejoining probability between two chromosome free-ends may be described by a step function, with a cutoff distance probably depending on the specific target cell features. Based on the observed complex exchanges in irradiated primary human fibroblasts, also Savage (1996) estimated values around *1 lm for the average rejoining distance. Furthermore, he suggested that one place for chromosome break meeting would be the inter-arm domain channels, where active chromatin is extruded, many functional activities take place and where ‘‘wandering’’ threads must run to reach other regions of the nucleus. He also hypothesized the existence, on the nuclear matrix, of specific repair complexes (‘‘like garages’’) to which breaks migrate and accumulate for repair. These ideas were formalized in a chromosome aberration model applied to human fibroblasts exposed to X-rays and alpha particles (Chen et al. 1997). In that study, the nucleus was assumed to be divided into a certain number, S, of ‘‘interaction sites,’’ meaning that only the chromosome breaks inflicted at the same site can undergo rejoining and produce exchange-type aberrations. S was an adjustable parameter, the value of which was estimated as 13 after low LET and 25 after high LET radiation, consistent with rejoining distances at the micrometer scale. Many years later, Neumaier et al. (2012) found experimental evidence for DNA

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repair centers in mammalian cells. These authors, applying live cell imaging to X-irradiated MCF10A human cells, found that the radiation-induced foci (RIF) of the DNA damage-sensing protein 53BP1 are not proportional to radiation dose (*15 RIF/Gy after 2 Gy, versus *64 RIF/Gy after 0.1 Gy). Since DSBs should be well separated at the considered doses, the authors concluded that there must exist discrete locations in the cell nucleus to which DSBs 1–2 lm apart can migrate for repair. The ‘‘repair centers’’ hypothesis received further support exposing the cells to energetic heavy ions, after which uniformly spaced RIFs along the particle track were observed, rather than randomly spaced RIFs. The mis-rejoining of chromosome fragments leads to various types of chromosome aberrations, some of which are known to be correlated with cell death (Carrano 1973; Bedford et al. 1978; Nagasawa and Little 1981), although such correlations are not always so clear-cut. One of the most elegant works has been carried out by Cornforth and Bedford (1987), who investigated chromosome aberrations and clonogenic inactivation in AG1522 human fibroblasts exposed to X-rays. The authors found a one-to-one relationship between –lnS and the average number of ‘‘lethal aberrations’’ per cell, where S is the fraction of surviving cells and ‘‘lethal aberrations’’ refer to Giemsa-stained dicentrics, rings and deletions. Moreover, an excellent correlation was observed between the fraction of surviving cells and the fraction of cells without visible aberrations. Importantly, these findings refer to a cell line where in general apoptosis is not observed. These data support the hypothesis that the so-called asymmetrical aberrations represent the principal mechanism for radiation-induced mitotic death in mammalian cells (Hall 2000). Subsequent studies with fluorescence in situ hybridization (FISH) revealed that also complex exchanges are involved in cell killing. A very important contribution was provided by Savage (1995), who analyzed more than 200 patterns deriving from complex exchanges on the basis of their transmissibility, assuming that any exchange that produces an acentric fragment will be ultimately eliminated in a continuously dividing cell population. In this framework, we developed a biophysical model of radiation-induced cell death based on the idea that complex DSBs (called ‘‘cluster lesions,’’ or CLs) play a fundamental role in the formation of chromosome aberrations and that in turn some aberration types lead to cell death. The model, implemented as a Monte Carlo simulation code called BIophysical ANalysis of Cell death and chromosome Aberrations (BIANCA), was applied to human and hamster normal fibroblasts exposed to X-rays or c-rays, protons, alpha particles and heavier ions, with focus on carbon, which is now used for cancer therapy (Durante and Loeffler 2010; Durante 2013), and iron, which is of interest for

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space radiation research (Schimmerling et al. 2003). Different energies, and thus different LET values, were considered for each particle type. Simulated survival curves were compared with experimental data taken from the literature; these comparisons provided indications on the aforementioned open questions, that is the role of complex DSBs and their spatial distribution with respect to repair, and the role of chromosome aberrations with respect to cell death. Attempting to provide a characterization for such critical DNA damage, the yields of ‘‘cluster lesions’’ were then compared with experimental or theoretical yields of DNA fragments of different sizes taken from the literature, focusing on the *bp scale (local clustering, related to the double helix), the *kbp scale (regional clustering, related to the chromatin fiber) and the *Mbp scale (related to chromatin fiber loops).

Materials and methods A detailed description of the model and the simulation code is beyond the scope of this paper and can be found in previous works (Ballarini 2010; Ferrari et al. 2011; Ballarini et al. 2011, 2013, 2014, 2015). The main issues will be summarized and discussed herein with focus on the basic model assumptions: (1) radiation induces DNA cluster lesions (CLs), each of these CLs giving rise to two independent chromosome free-ends; (2) only pairs of chromosome free-ends with initial distance below a threshold d can undergo end-joining, leading to chromosome aberrations in case of mis-rejoining; (3) dicentrics, rings and large deletions (see below for the deletion size) lead to clonogenic cell death. Since a characterization of the critical DNA cluster damage is still an open question, we chose not to define a priori the cluster lesions introduced in the model, leaving the average number of CLs per Gy and per cell as an adjustable parameter. Assumption (2) takes into account the distance dependence of chromosome fragment rejoining, implicitly considering the existence of DNA repair centers where DSBs—no matter whether complex or not— migrate for repair. The threshold distance d is the second, and last, adjustable parameter, which is expected to have values at the micrometer scale (e.g., Neumaier et al. 2012). Like in previous works, free-ends with initial distance smaller than d will undergo end-joining with 100 % probability, where ‘‘end-joining’’ includes both correct joining and mis-rejoining. Assumption (3) derives from the relationship between chromosome aberrations and cell death observed by Cornforth and Bedford, as reported in the Introduction. Like in previous works (e.g., Ballarini et al. 2013, 2014), V79 cell nuclei were modeled as cylinders with circular

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base (height and radius: 6 lm), whereas AG1522 nuclei were modeled as cylinders with elliptical base (height 4 lm; major axis 20 lm; minor axis 10 lm). Also smaller values are reported in the literature for the thickness of these cell nuclei, but such values in general refer to electron microscopy measurements; more recent measurements based on confocal microscopy, especially in living cells, provide larger values. For instance, both Belli et al. (1998) and Bettega et al. (1998) report about 6 lm for the average thickness of V79 cell monolayers, which implies a nucleus thickness of about 5 lm if one considers a cytoplasm thickness of about 1 lm (Carpenter et al. 1989), whereas according to Hill et al. (1998), the thickness of V79 nuclei is about 7 microns; this led us to choose 6 lm as an intermediate value. Concerning human fibroblasts, Bolzer et al. (2005) represent the nuclei of these cells by an ellipsoidal shape with average axes of 20 lm (major axis), 10 lm (minor axis) and 5 lm (height) determined from light-optical stacks; to have a similar nucleus volume by a cylindrical shape rather than an ellipsoidal shape, the cylinder height must be smaller, which is the reason why we chose 4 lm instead of 5 lm. Each interphase chromosome territory was represented as the union of adjacent cubic voxels of 0.2 lm side, to obtain chromosome territories with volume proportional to the corresponding DNA content. Within the cell nucleus, the various CLs were distributed randomly for X-rays and gamma rays, and along segments parallel to the cylinder axis for (low-energy) protons and alpha particles. For heavier ions, each CL was assumed to have a 0.5 probability to be induced along the trajectory of the primary particle, and a 0.5 probability to be shifted radially, to take into account the effects of energetic secondary electrons. Although an equal division of the deposited energy between core and penumbra leads to some incongruities at the core/penumbra interface (Chatterjee and Schaefer 1976), this is not a problem for these cluster lesions, for which the relevant information is whether a given CL falls in a certain chromosome territory or in another one, which is a micrometer-scale question. For those CLs that were shifted, the probability to be induced at distance r from the primary particle was taken as proportional to 1/r; the maximum radial distance was set equal to the maximum range of secondary electrons, which was calculated basing on the maximum energy of secondary electrons according to Paretzke (1987) below 20 keV, or Katz and Penfold (1952) above 20 keV. The subsequent simulation steps consisted of: identification of the chromosome and the chromosome arm hit by each CL; rejoining of chromosome free-ends within the threshold distance; scoring of lethal aberrations (dicentrics, rings and deletions visible in Giemsa); and calculation of the corresponding surviving fraction. Chromosome

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fragments smaller than 3 Mbp were assumed as not visible in metaphase, as reported by Cornforth and Bedford (1987). Other studies report larger values for the size of the smallest fragment visible in Giemsa: for instance, Wu et al. (1997) used 6 Mbp. We chose 3 Mbp because this is the value estimated by Cornforth and Bedford (1987) in the work where they observed the relationship between chromosome aberrations and cell death that we applied in the present work. In any case, increasing this value up to 10 Mbp did not lead to significant changes in the results for X-rays and, more generally, low LET radiation. The maximum difference was found for high LET alpha particles, for which using 10 Mbp instead of 3 Mbp led to a 15 % increase in cell survival. The repetition for different doses provided simulated survival curves directly comparable with experimental data. For each experimental data set considered for comparison, where each set consisted of a photon survival curve and one or more charged particle curves, the first step consisted of reproducing the photon curve adjusting separately d and CL. Subsequently, for each particle type and energy belonging to that data set, the value of d was maintained unvaried with respect to the value adjusted for the photon curve, whereas a specific CL yield for that particle type and energy was adjusted comparing the simulated and measured surviving fraction at intermediate dose (e.g., 2 Gy). That CL yield was then used as a code input also for other doses, to obtain a simulated survival curve for that particle type and energy.

Results and discussion Cell survival Simulated survival curves for different radiation types (photons, protons, helium ions and heavier ions) were compared with experimental survival data taken from the literature, focusing on AG1522 and V79 cells. The former, which are normal human fibroblasts, were chosen because they are the system in which Cornforth and Bedford observed the relationship between (lethal) chromosome aberrations and cell death applied in our model; the latter, which are normal Chinese hamster fibroblasts and are rather radio-resistant, were chosen because they are widely used in radiobiology studies, including the characterization of many hadron therapy beams. More specifically, the following data sets were considered for comparison in the present work: V79 cells exposed to X-rays and protons (Folkard et al. 1996), V79 cells exposed to c-rays and alpha particles (Cox et al. 1977, Thacker et al. 1979, Phoenix et al. 2009), AG01522 cells exposed to X-rays and protons (Chaudhary et al. 2014), AG01522 cells exposed to carbon

Radiat Environ Biophys (2015) 54:305–316 V79 γ sim. V79 γ data V79 X sim. V79 X data AG γ sim. AG γ data AG X sim. AG X data

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ions (Kavanagh et al. 2013), and AG1522 cells exposed to c-rays and iron ions (Tsuboi et al. 1992). To make the comparison more informative, a few results published in previous works (Ballarini et al. 2013, 2014 and references therein) were also included. Concerning V79 cells, it is worth mentioning that, due to the short doubling time, it is likely that the most fast growing cell variants will dominate during long-term culturing. Furthermore, the studies from which experimental data were taken have used different V79 strains, which in principle may be significantly different in the response to radiation: Folkard et al. (1996) used V79-379A, Thacker et al. (1979) and Phoenix et al. (2009) used V79-4 and Belli et al. (1998, considered for comparison in Ballarini et al. 2013), used V79-753B. However, these three particular strains did not show large differences in the response to radiation. More specifically, Folkard et al. (1996) and Belli et al. (1998), who used X-rays as a reference radiation, report very similar fit parameters to a linear-quadratic survival curve (0.13 Gy-1 versus 0.129 Gy-1 for the alpha parameter; 0.048 Gy-2 versus 0.046 Gy-2 for the beta parameter, respectively), and this explains why their photon data could be reproduced using the same yield of CLs (see below). Although Thacker et al. (1979) and Phoenix et al. (2009) used the same cell strain (V79-4) and the same reference radiation (60Co c-rays), the photon survival curve reported by Thacker et al. (who declare 0.143 Gy-1 and 0.026 Gy-2 for the alpha and beta parameters, respectively) was (slightly) higher and more shouldered with respect to the curve reported by Phoenix et al. (who declare 0.237 Gy-1 and 0.0170 Gy-2). To reproduce this difference, we used a slightly higher CL yield for the data taken from Phoenix et al. than for those taken from Thacker et al. (see below). From top to bottom, Fig. 1 shows survival curves for V79 cells exposed to c-rays, V79 cells exposed to X-rays, AG1522 cells exposed to c-rays and AG01522 cells exposed to X-rays. The lines are simulation results, whereas the points are experimental data taken from the literature: Thacker et al. (1979), Belli et al. (2008) and Phoenix et al. (2009) for V79 cells exposed to c-rays; Folkard et al. (1996) for V79 cells exposed to X-rays; Neti et al. (2004) for AG1522 cells exposed to c-rays; and Chaudhary et al. (2014) for AG01522 cells exposed to X-rays. The curves reported in Fig. 1 were obtained with d = 5 lm for both cell lines; in general, smaller d values (coupled with higher CL yields to look for the agreement with the experimental data) tended to underestimate the effectiveness of low doses and to overestimate the effectiveness of high doses. The CL yields used to obtain the curves reported in Fig. 1 were in the range *2–4 CL Gy-1 cell-1, with lower values for hamster cells and higher values for human cells. These numbers need to be taken with caution; however, it is interesting to note that they are rather similar to the

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Dose [Gy] Fig. 1 Survival of V79 (two upper curves) and AG1522 (two lower curves) cells exposed to X- or c-rays. The lines are simulation outcomes, the points (with the corresponding error bars) are experimental data taken from the literature (Thacker et al. 1979; Belli et al. 2008; Phoenix et al. 2009 and Folkard et al. 1996 for hamster cells; Neti et al. 2004 and Chaudhary et al. 2014 for human cells)

yields of ‘‘reactive DSBs’’ obtained by Chen et al. (1997) in their chromosome aberration model, which led to 2.4 reactive DSBs per Gy and per cell for normal fibroblasts exposed to X-rays. Analogous to the cluster lesions introduced in our model, ‘‘reactive’’ DSBs were defined as those DSBs that, being severe and thus difficult to repair, can lead to chromosome aberrations following mis-rejoining of chromosome fragments. Cell survival after proton irradiation is reported in Fig. 2, which shows survival curves for V79 cells exposed to monoenergetic proton beams of 10.1, 17.8 and 27.6 keV/ lm, and for AG01522 cells exposed to monoenergetic protons of 1.1, 11.9 and 22.6 keV/lm. The lines are simulation results, whereas the points are experimental data taken from the literature, more specifically from Folkard et al. (1996) and Belli et al. (1998) for V79 cells, and from Chaudhary et al. (2014) for AG01522 cells. Analogous results were found for AG01522 cells exposed to monoenergetic protons of 4.0, 7.0 and 17.98 keV/lm; the corresponding survival curves, which were not reported here to avoid making the figure too ‘‘crowded,’’ were in good agreement with experimental data taken from Chaudhary et al. (2014). The value of d, which should depend on the target cell features rather than the radiation quality, was left unvaried with respect to the photon simulations. On the contrary, the yield of cluster lesions, which should strongly depend on radiation quality—that is particle type and energy and thus LET—was adjusted separately for each curve. For the curves of Fig. 2, CL yields in the range *2–12 CL Gy-1 cell-1 were used; these values will be reported and discussed in the next section.

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V79 10.1 sim. V79 10.1 data V79 17.8 sim. V79 17.8 data V79 27.6 sim. V79 27.6 data AG 1.1 sim. AG 1.1 data AG 11.9 sim. AG 11.9 data AG 22.6 sim. AG 22.6 data

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Fig. 2 Survival of V79 and AG01522 cells exposed to different monoenergetic proton beams. From top to bottom, V79 cells exposed to protons of 10.1, 17.8 and 27.6 keV/lm; AG01522 cells exposed to protons of 1.1, 11.9 and 22.6 keV/lm. The lines are simulation outcomes, the points (with the corresponding error bars) are experimental data taken from the literature (Folkard et al. 1996 for V79 cells; Chaudhary et al. 2014 for AG01522 cells)

Fig. 3 Survival of V79 and AG1522 cells exposed to He ions of different LET. From top to bottom, V79 cells exposed to He ions of 20, 28, 50, 90 and 120 keV/lm; AG1522 cells exposed to 132 keV/ lm alpha particles. The lines are simulation outcomes, the points (with the corresponding error bars) are experimental data taken from the literature (Cox et al. 1977; Thacker et al. 1979 and Phoenix et al. 2009 for V79 cells; Neti et al. 2004 for AG1522 cells)

Despite the general agreement between simulated and experimental survival curves reported in Fig. 2, some of the simulated curves (for instance, those at 27.6 and 22.6 keV/lm) tend to show a slope decrease at the highest considered doses; this behavior is also visible for the two upper curves in Fig. 1. Most likely, this reflects the model assumption that cell inactivation derives from simple aberrations (dicentrics, rings and deletions), which at high doses, especially at low and intermediate LET, tend to show a linear–sublinear (rather than quadratic) behavior due to the competition with complex aberrations. This suggests that, if one wants to apply the model at high doses, the current version of the model should be refined to take into account the role played by complex-type chromosome aberrations. As mentioned in the Introduction, also some types of complex exchanges can lead to cell killing (e.g., Savage 1995). Since complex exchanges start becoming important at high doses (because by definition they involve at least three chromosome breaks and at least two chromosomes), if their role in cell killing is implemented in the model, the survival at high doses is expected to decrease, whereas at low doses the changes in survival should be not significant. Overall, this is expected to lead to a better agreement with the experimental survival at high doses. It is also likely that the dose above which this phenomenon becomes important depends on radiation quality: in general, the expected slope change should occur at higher doses for low LET radiation with respect to high LET. In this context, it is worth mentioning that, especially for intermediate-to-low LET radiation, cell repair via enzyme catalysis or repair ‘‘pool’’ molecules from the cell

environment can also play an important role, and models taking into account these mechanisms can predict a linear dose dependence of survival curves at both low and high doses, with a shoulder situated in between these two extremes. Recently, an interesting work in this direction has been performed by Belkic (2014), who provided an exact solution for the equation for lethal lesions in the framework of the ‘‘Pool Repair Lambert’’ (PRL) model. The investigation was then extended to alpha particles. The results are shown in Fig. 3, which reports survival curves for V79 cells exposed to alpha particles of 20, 28, 50, 90 and 120 keV/lm (compared with experimental data taken from: Cox et al. 1977 for 20 and 50 keV/lm; Thacker et al. 1979 for 28 and 90 keV/lm; Phoenix et al. 2009 for 120 keV/lm) and for AG1522 cells exposed to 132 keV/lm alpha particles (compared with data from Neti et al. 2004). Analogous results, which were not reported in the figure for the sake of clarity, were found for V79 cells exposed to 70 keV/lm alpha particles. Like for protons, d was maintained unvaried at 5 lm, whereas the yield of cluster lesions was adjusted separately for each curve. The curves reported in Fig. 3 were obtained with CL yields in the range *3–18 CL Gy-1 cell-1 (see next section). Figure 4 reports survival curves for V79 cells exposed to carbon ions of 13 and 75 keV/lm (experimental data for comparison taken from Belli et al. 2008), AG01522 cells exposed to carbon ions of 48.8 and 147.6 keV/lm (data from Kavanagh et al. 2013), and AG1522 cells exposed to Fe ions of 300 keV/lm (data from Tsuboi et al. 1992). In previous works, analogous agreement between simulations and experimental data was obtained for V79 cells exposed

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311 V79 C 13 sim. V79 C 13 data V79 C 75 sim. V79 C 75 data AG C 48.8 sim. AG C 48.8 data AG Fe 300 sim. AG Fe 300 data AG C 147.6 sim. AG C 147.6 data

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Dose [Gy] Fig. 4 Survival of V79 and AG1522 cells exposed to different heavyion beams. From top to bottom, V79 cells exposed to C ions of 13 and 75 keV/lm; AG01522 cells exposed to C ions of 48.8 keV/lm, Fe ions of 300 keV/lm, and C ions of 147.6 keV/lm. The lines are simulation outcomes, the points (with the corresponding error bars, with the exception of Fe ion data for which the errors were not available in the experimental work) are experimental data taken from the literature (Belli et al. 2008 for hamster cells; Kavanagh et al. 2013 and Tsuboi et al. 1992 for human cells)

agreement was obtained for many different radiation qualities adjusting only one free parameter (that is the yield of cluster lesions), whereas the second parameter, that is the maximum initial distance for chromosome fragment endjoining, d, was left unvaried at 5 lm. Although smaller values are reported in the literature concerning the threshold distance for chromosome fragment rejoining, this value is not inconsistent with the findings by Neumaier et al. (2012), according to whom a DSB end in MCF10A human mammary epithelial cells can migrate 1–2 lm apart for repair. Of course the precise value of d needs to be taken with caution, also because it is expected to be strongly dependent on the specific target cell features (cell line, cell shape and dimensions, number of chromosomes, interphase chromatin organization…). In general, for a given number of chromosomes, it is reasonable to expect smaller values for smaller cells, as it occurred in our previous works on human lymphocytes (e.g., Ottolenghi et al. 2001; Ballarini and Ottolenghi 2004, 2005; Ballarini et al. 2008).

DNA cluster lesions to carbon ions of 24, 40 and 50 keV/lm (Ballarini et al. 2013), for AG1522 cells exposed to carbon ions of 76.3 and 108 keV/lm (Ballarini et al. 2014), and for AG1522 cells exposed to Fe ions of 200 and 500 keV/lm (unpublished). Again, d was maintained at 5 lm, whereas the yields of cluster lesions, which were in the range *2–12 CL Gy-1 cell-1, were adjusted separately for each curve. In addition to the aforementioned slope decrease at high doses, some of the curves reported above tend to show an overestimation of cell survival at low doses (typically around 1 Gy or less). Very preliminary investigations seem to suggest that this might be related to the so-called incomplete exchanges, that is those chromosome aberrations for which not all the involved chromosome fragments find a partner for rejoining, giving rise to additional acentric fragments. In the current version of the model, all exchanges are assumed to be complete; however, the introduction of incomplete exchanges is expected to lead to higher yields of acentric fragments and thus lower levels of cell survival. This should be particularly relevant at low doses, where small numbers of CLs are induced in the cell. Despite the discrepancies discussed above, the simulated survival curves were in good general agreement with the considered experimental data. This supports the main hypothesis of the model, according to which clonogenic cell death can be explained by DNA cluster damage mediated by lethal chromosome aberrations including dicentrics, rings and large deletions. It is worth mentioning that such

The yields (average number per Gy and per cell) of cluster lesions used to obtain the various survival curves are shown in Fig. 5a as a function of the particle type and LET. In addition to the CL yields related to the present work, Fig. 5a also reports a few CL yields taken from previous works (Ballarini et al. 2013, 2014). With the exception of very high LET values, the CL yield for a given particle type was found to increase with LET for both cell lines; furthermore, lighter particles were more effective than heavier particles of the same LET. Both these features are consistent with the hypothesized clustering nature of such lesions, since DNA cluster damage is known to show this kind of dependence on radiation quality (e.g., Ottolenghi et al. 1995; Belli et al. 1998). The particle and LET dependence shown by CLs reflect the dependence shown by cell survival, which is characterized by a peak of effectiveness around 100–200 keV/lm. Concerning higher LET values, where the effectiveness in cell killing is known to decrease, the effectiveness in DNA (cluster) damage is still an open question. In general, one might expect that the effectiveness at inducing DNA cluster damage continues to increase also at very high LET, as it has been shown, for instance, for the aforementioned DSB??. However, different behaviors have been found for DSB? (generally defined as one DSB associated with one or more additional SSBs), which culminated at about 300 keV/lm (Friedland et al. 2011), for DNA fragments in the size range 0.1–2 kbp, which showed a peak at about 400 keV/lm (Holley and Chatterjee 1996), and for a

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(b) p (AG) p (V79) He (AG) He (V79) C (AG) C (V79) Fe (AG)

16 14 12 10 8 6 4 2 1

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Fig. 5 a Yields of cluster lesions (average number of CLs per Gy and per cell) used in the simulations to obtain the various survival curves. The lines are simply guides for the eye, whereas the points represent CL yields induced by protons (circles), He ions (triangles), C ions (squares) and Fe ions (asterisks). Empty symbols refer to V79 cells, full symbols and asterisks refer to AG1522 cells. b Comparison between the CL yields reported in a for AG1522 cells (solid line for protons, dashed line for He ions, dashed-dotted line for C ions and dotted line for Fe ions) and calculated yields of DSB?? taken from the literature (Alloni et al. 2010; Friedland et al. 2011) induced by protons (circles), He ions (squares), Fe ions (triangles) and other heavy ions (asterisks), that is: B of 37 and 180 keV/lm; N of 75 and 320 keV/lm; Ne of 210 and 680 keV/lm; O of 430 keV/lm; C of 100, 201, 240 and 442 keV/lm. c Comparison between the CL yields reported in a for AG1522 cells (solid line for protons, dashed line for He ions, dashed-dotted line for C ions and dotted line for Fe ions) and

experimental or theoretical yields of kbp size DNA fragments taken from the literature (Tabocchini et al., personal communication, and Rydberg et al. 2002 for the experimental yields; Alloni et al. 2010 for the theoretical yields) induced by c-rays or protons (circles), He ions (squares), C ions (asterisks) and Fe ions (triangles). A LET value of 0.3 keV/lm was assigned to c-rays (ICRU 1970). d Comparison between the CL yields reported in a for AG1522 cells (solid line for protons, dashed line for He ions, dashed-dotted line for C ions and dotted line for Fe ions) and theoretical yields of DNA fragments with size in the range 0.023–1 Mbp induced by He ions (full square), C ions (asterisks) or Fe ions (triangles) taken from Alloni et al. (2010), as well as experimental yields of DNA fragments with size in the range 0.005–1 Mbp induced by c-rays (circle), 40 keV/lm He ions (empty square) and N ions of 80, 125, 175 and 225 keV/lm (crosses) taken from Hoglund et al. (2000)

‘‘mixture’’ of different types of complex DSBs (defined as a weighted sum of DSB, DSB? and DSB?? in a 18-kbp chromatin fiber stick), the trend of which was in good agreement with cell survival RBE (Friedland et al. 2006). Similarly, the CLs used in this work showed a decrease after 300–400 keV/lm.

Concerning the differences between the two cell lines for a given particle type and LET, the lower CL yields for hamster fibroblasts reflect the lower radiosensitivity of these cells with respect to human fibroblasts. This is related to the fact that, in the current version of the model, not only the CL yield depends on radiation quality, but it is also

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modulated by the target cell response. Like the ‘‘reactive DSBs’’ introduced by Chen et al. (1997), cluster lesions represent those DNA lesions which are severe and thus difficult to be repaired: while severity depends on radiation quality, the difficulty in repair depends on the specific cell repair machinery. In a future development, this parameter might be ‘‘split’’ into two parameters, to separate the dependence on the projectile from that on the target. For instance, what is now called ‘‘CL’’ might be expressed as the product of two parameters, CL0 and f, where CL0 would reflect the dependence on the projectile, and f would represent the dependence on the target. A possible strategy would consist of assigning f = 1 to a well-known reference cell line (e.g., V79 cells), and adjusting f by comparison with experimental data for other cell lines. With the aim of finding a characterization for these lesions, the CL yields above were compared with yields of DNA fragments taken from experimental or theoretical works available in the literature. The comparison was focused on three fragment size scales: (1) the base-pair (bp) scale, which is the scale of the so-called DSB?? investigated in many modeling studies; (2) the kbp scale, which is thought to be related to nucleosome packing in the chromatin fiber; and (3) the Mbp scale, which is related to interphase chromatin organization in loops. In Fig. 5b, the CL yields reported in Fig. 5a for the case of AG1522 cells are compared with yields of DSB?? (at least two DSBs within 30 base pairs) calculated by PARTRAC Monte Carlo simulations (Alloni et al. 2010; Friedland et al. 2011). With respect to DSB??, CLs increased with LET much less rapidly, showing in general higher values at low LET and lower values at high LET. Furthermore, while DSB?? continued to increase also at very high LET, CLs showed a (slight) decrease after 300–400 keV/lm. In Fig. 5c, the CL yields for AG cells are compared with experimental or theoretical yields of DNA fragments with size at the kbp scale induced in normal human fibroblasts (always AG1522 cells, with the exception of the data from Rydberg et al. 2002 that are for GM98 cells). More specifically, the following fragment data were considered: experimentally detected fragments with size in the range 1–9 kbp induced by gamma rays and 28.5 keV/lm protons (Tabocchini et al., personal communication of data based on the Constant Field Gel Electrophoresis technique described in Antonelli et al. 2004), experimentally detected fragments with size in the range 0.1–9 kbp induced by alpha particles of increasing LET in the range 67–120 keV/ lm (Rydberg et al. 2002) and calculated fragments with size in the range 1–9 kbp induced by the following radiation types: 100 keV/lm alpha particles, C ions of 13.8, 201, 240 and 442 keV/lm and Fe ions of 201, 260 and 442 keV/lm (Alloni et al. 2010). This particular size range was chosen because 0.1 kbp corresponds to about one turn

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of DNA around the nucleosome, whereas a few kbp are related to the packing of nucleosomes in the chromatin fiber. The particle and LET dependence shown by cluster lesions are rather similar to the dependence shown by these kbp fragments, suggesting that these fragments may play an important role in the induction of cell death and possibly other endpoints such as chromosome aberrations. This would be in line with Rydberg’s hypothesis (see the Introduction), as well as with the idea that endpoints like chromosome aberrations and cell death require the disruption of the chromatin fiber continuity, which is very likely following DSB clusters, but much less likely following less complex DSBs (Schipler and Iliakis 2013; Terzoudi et al. 2011). Interestingly, an analogous conclusion has been drawn by means of Monte Carlo simulations by Friedland et al. (2006), who found that regional DNA damage clusters (within a 18-kbp chromatin fiber stick) were in closer correlation to cell inactivation experimental data with respect to local clusters. Figure 5d reports a comparison between the CL yields reported in Fig. 5a for AG1522 cells and theoretical yields of DNA fragments with size in the range 0.023–1 Mbp calculated by Monte Carlo simulations with the PARTRAC code (Alloni et al. 2010), as well as experimental yields of DNA fragments with size in the range 0.005–1.1 Mbp taken from Hoglund et al. (2000). The latter were obtained applying pulsed-field gel electrophoresis and fragment analysis to normal human skin fibroblasts (GM 5758) exposed to 60Co c-rays, 40 keV/lm He ions and N ions of 80, 125, 175 and 225 keV/lm. Quantitatively, the yields taken from the experimental work (empty symbols and crosses) are higher than those deriving from PARTRAC simulations (full symbols and asterisks); this may depend on the fact that the experimental data were obtained at much higher doses (in the range 30–200 Gy) with respect to the simulations, which were performed at 5 Gy. However, both data sets suggest that the radiation effectiveness at inducing these fragments does not increase substantially in the region of intermediate-to-high LET; this trend is very different with respect to cluster lesions, which showed a steep increase. A similar behavior (lack of steep increase up to about 100 keV/lm) was suggested also by Lobrich et al. (1996), who measured the size distribution of DNA fragments in GM38 normal human fibroblasts exposed to X-rays, 97 keV/lm N ions and 150 keV/lm Fe ions, covering a total range between 0.1 kbp and 10 Mbp. It is worth noting that, among the three DNA fragment sizes considered above, CLs showed a better agreement with kbp size fragments rather than DSB?? or Mbp size fragments. This is particularly interesting due to the relationship between kbp fragments and the chromatin fiber, especially in light of the idea that endpoints like cell death and chromosome aberrations require the disruption of the

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chromatin fiber continuity. However, two or more classes of DNA cluster damage may play a role, although probably with different ‘‘weights’’: An interesting attempt in this sense has been made by Friedland et al. (2006), who found good agreement between experimental RBE for cell inactivation and calculated RBE for a weighted sum of three different DSB classes (DSB, DSB? and DSB??), especially for the case of regional clustering within a 18-kbp chromatin fiber stick. Further studies, both theoretical and experimental, are therefore desirable in this direction.

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tumor cell line. In the framework of tumor therapy, this model may also be applied to simulate the induction of non-lethal, transmissible chromosome aberrations in the normal cells surrounding the tumor region, because some of these aberration types (typically, reciprocal translocations involving specific genes) are known to be related to the induction of (second) tumors. Acknowledgments The authors are grateful for data sharing and useful discussions to M.A. Tabocchini and co-workers concerning DNA fragmentation and to K. Prise and G. Schettino concerning cell survival. This work was partially supported by Istituto Nazionale di Fisica Nucleare (INFN), project ‘‘ETHICS.’’

Conclusions A biophysical, mechanism-based model of cell killing was applied to normal human and hamster fibroblasts exposed to photons, light ions and heavy ions, finding general agreement with experimental survival data taken from the literature. This supported the hypothesized pivotal role of DNA cluster damage at the sub-micrometric scale, modulated by micrometer-scale end-joining of chromosome fragments leading to cell death via lethal chromosome aberrations. Furthermore, comparisons between yields of DNA ‘‘cluster lesions’’ adopted in the present work and yields of DNA fragments of different sizes (at the *bp, *kbp and *Mbp scale) taken from the literature showed that the particle and LET dependence of such cluster lesions were more similar to the behavior of kbp size fragments with respect to bp or Mbp size fragments. This is in line with the hypothesis, already introduced by others (e.g., Rydberg 1996; Friedland et al. 2006), that also the so-called regional clustering, in addition to other levels of clustering, may play an important role for cell death and other endpoints including chromosome aberrations, possibly due to its relationship with nucleosome packing in the chromatin fiber. Possible future refinements of the model will include the implementation of additional mechanisms (e.g., taking into account the role of complex-type chromosome aberrations in clonogenic cell killing and the role of other forms of cell death including apoptosis) and explicit modeling of the target cell radiosensitivity (which in the current version is implicitly ‘‘included’’ in the CL yield), as well as an investigation of the overestimate of cell survival shown by some simulated curves at low and/or high doses. Furthermore, it is in our plans to extend this approach to other cell lines including tumor cells, also in view of possible applications in the field of cancer therapy including hadron therapy. This extension will need particular caution, also considering that tumor cells are often affected by tetraploidy or other changes in the karyotype; this will require the implementation of an ad hoc cell nucleus model with an appropriate number of chromosomes for a given

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