Sachs: Radiation Biology Home Research Papers 97-98 clusters

### Modeling Large-Scale Clusters of Radiation-Induced Breaks Along Chromosomes

International Journal of Radiation Biology, 74, 185-206, 1998
RK Sachs*, David J. Brenner#, Philip J. Hahnfeldt%, and Lynn R. Hlatky%
*Department of Mathematics, University of California, Berkeley, CA 94720; #Center for Radiological Research, Columbia University, New York, NY 10032; %Joint Center for Radiation Therapy, Harvard Medical School, Boston, MA 02115.

Abstract.

Purpose: To study intrachromosomal clustering of DSBs (DNA double strand breaks) induced by ionizing radiation. Recent pulse field gel electrophoresis data for size distributions of DNA fragments after high doses of high LET radiation show DSBs are clustered non-randomly along chromosomes. We therefore extend the standard random-breakage model for DNA fragment-size distributions to a more general "clustered-breakage" formalism, which takes into account correlated DSB locations.

Methods: The new formalism is based on a single-track probability distribution, describing the DNA fragment-size pattern due to a single primary high-energy particle, a pattern determined by track structure and chromatin geometry. Multi-track fragment-size distributions are derived mathematically from the single-track distribution, so that dose-response relations are obtained.

Results: The clustered-breakage formalism is applicable to any chromosomal geometry and any radiation track structure. It allows systematic extrapolations of high-dose data to the much lower doses of interest for most applications. When applied to recently published data for irradiation of mammalian cells with ions of LET approximately 100 keV/micron it implies a pattern of megabase-scale DSB clusters, each containing a number of DSBs and corresponding to an extremely large multiply damaged chromatin site. Estimates of DSB yield are markedly increased by resolving such clusters into individual DSBs.

Conclusions: DSB clustering along chromosomes, which influences important radiobiological endpoints, is described systematically by the clustered-breakage formalism.

Key words: multiply damaged chromatin sites, non-random chromosome breakage, high LET radiation, DSB clusters, PFGE

Introduction

Double strand breaks (DSBs) are an important form of ionizing radiation damage (Ward 1994). DSBs cut a chromosome into smaller fragments. Recent pulse field gel electrophoresis (PFGE) data on DNA fragment-size distributions are informative about DSB clustering, dependent on chromatin geometry in mammalian cells during cell cycle interphase and on radiation track structure (Brenner 1990, Chatterjee and Holley 1991, Rydberg et al. 1994, Cedervall et al. 1995, Friedl et al. 1995, Holley and Chatterjee 1996, Lobrich et al. 1996, Rydberg 1996, Newman et al. 1997, Prise 1997, Kraxenberger 1996). Here and throughout we use "size" to mean DNA content, measured in base pairs, or kbp, or Mbp. In this context, "size" is synonymous with "molecular weight" (Newman et al. 1997) and with "molecular length" (Kraxenberger et al. 1995). Size is an indicator of the chromatin contour length along a chromosome, between two DSBs, or between a DSB and a telomere, or between two telomeres, or between two restriction enzyme cutting sites, etc.

It has long been clear that high LET ionizations are spatially clustered (Lea 1946), and that such clustering strongly influences the fate of irradiated cells (Goodhead 1985). The PFGE data are now starting to indicate how spatial clustering of ionizations is expressed in terms of DSB clustering along chromosomes.

DSB locations along chromosomes fully determine the DNA fragment-size distribution; but to elucidate the implications of the observed fragment-size distributions for the DSB locations requires modeling (Holley and Chatterjee 1996, Lobrich et al. 1996, Newman et al. 1997). In some cases, modeling has used detailed information on chromatin geometry (Chatterjee and Holley 1992, Friedland and Perzl 1995, Holley and Chatterjee 1996, Rydberg 1996, Friedland et al. 1997, Moiseenko et al. 1997, Andreev et al. 1997, Prise 1997, Brahme et al. 1997). Such models have been applied mainly to data on comparatively small sizes, analyzing locally multiply damaged sites on the 10 bp scale of the underlying double helix (Brenner and Ward 1992, Michalik 1993, Moiseenko et al. 1996), or "regionally multiply damaged sites" on scales of 10 bp to several kb, corresponding to nucleosomes and the 30 nm fiber (Holley and Chatterjee 1996, Rydberg 1996). However, the recent PFGE data include results on much larger sizes, up to more than 5 Mbp. Such sizes are so large the detailed chromatin geometry is not well characterized, the ability to view chromatin on a large scale during interphase being rather recent (Cremer et al. 1993, 1997). There is evidence of considerable randomness in chromatin structure at scales from 0.1 Mbp on up to the size of a chromosome (Sachs et al. 1995, Dernburg et al. 1997), but otherwise comparatively little is known about such scales. Thus models based on detailed chromatin geometry are problematical for the larger size fragments observed in the PFGE experiments.

Other analyses have used the standard random-breakage model, which assumes DSBs located at random within the genome. The random-breakage equations, based on the "broken stick" and exponential fragment-size distributions, do not require an explicit model of interphase chromatin geometry (reviews: Kraxenberger et al. 1994, Radivoyevitch and Cedervall 1996). However, the random-breakage model provides a poor fit for some high LET PFGE data (Lobrich et al. 1996, Newman et al. 1997, Kraxenberger 1996), so some recent analyses have generalized it. These generalizations treat the basic parameter of the random-breakage model, namely the average number of DSBs per unit size and dose, as a variable. Newman and coworkers (1997) use a different value for each measured fragment-size bin, a method which involves a large number of adjustable parameters.

The purpose of the present paper is to derive and illustrate a systematic, general extension of the random-breakage model, which we call the "clustered-breakage" formalism. The new formalism results from dropping one assumption of the random-breakage model, namely the assumption that locations of different DSBs in the genome are independent of each other. The formalism is based on a probability distribution for DNA fragment sizes under single-track action, involving the location along chromosomes of DSBs made by one event.\footnote{An event is one primary radiation track, with different events statistically independent; for the data considered here, an event constitutes all the energy depositions due either to one nitrogen ion (Lobrich et al. 1996) or to one primary alpha particle (Newman et al. 1997). We shall here use "single-track" as synonymous with "single-event".} The clustered-breakage appraoch is valid for any geometric configuration of the chromosomes, and for any radiation track structure. The chromatin geometry and radiation track structure in principle determine the single-event fragment-size distribution. Because events are statistically independent, predictions for multi-event effects can be derived mathematically in terms of the single-event distribution, determining dose-dependent DSB clustering patterns and giving dose-response relations for DNA fragment-size measurements.

The clustered-breakage formalism will be illustrated by applying it to two published data sets on DNA fragment-size distributions after irradiation of mammalian cells at high doses, using nitrogen ions or alpha particles, each having LET approximately 100keV/$\mu$m (Lobrich et al. 1996, Newman et al. 1997). The data suggest DSB yields of more than 0.01 DSB/Mbp-Gy, corresponding to approximately 80 DSBs per Gy per human genome, in contrast to markedly lower estimates obtained when DSB clusters smaller than a Mbp are not resolved into individual DSBs. Even for x-rays some increase in estimates of DSB yield is obtained when the small fragments are taken into account (Lobrich et al. 1996, Newman et al. 1997). However, the high LET RBE, which appears to be less than one when analyzing only larger fragments, is considerably more than one when the smaller fragments are taken into account. That is, high LET radiations make more small fragments relative to large fragments than do x-rays.

As discussed above, applying the clustered-breakage approach to the data involves specifying the distribution of DNA fragment sizes for single-event action. Since the formalism is valid for any single-event distribution, we here, to illustrate the approach concisely, use as the single-event distribution a two-parameter form which was chosen for mathematical convenience, rather than being derived by analyzing chromatin geometry and radiation track structure. For each of the two data sets, the two model parameters are determined by the fragment-size distribution at one dose. This results in predicted dose-response relations, which are compared to data at other doses; estimates are also obtained for the average size of a single-event DSB cluster on a chromosome and for the average number of DSBs such a cluster contains. Characterizing the single-event distribution using the high-dose PFGE data allows a mechanistically based extrapolation of the PFGE results down to the much smaller doses of interest in most applications.

Applying the model to the data shows that most DSBs are situated in extremely large-scale DSB clusters, corresponding to multiply damaged sites on the Mbp scale. This behavior would agree with the suggestion of Newman et al. (1997) that alpha irradiation may tend to produce an all-or-nothing outcome, with hits on a chromosome rare but each hit tending to produce a severe cluster. The particular two-parameter single-event fragment-size distribution used to illustrate the clustered-breakage formalism is phenomenological, so the detailed numerical results obtained are less well grounded than would be the case for a distribution based on radiation track structure and chromatin geometry. However, we will argue that the major conclusions concerning extremely large-scale clusters are robust.

The main results of the paper are presented in Subsection 2.7, which summarizes the clustered-breakage formalism. The other parts of the paper motivate, derive, elaborate, illustrate or apply the formalism, and discuss its implications.