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.
clusters