MODELLING CHROMOSOMAL ABERRATION INDUCTION BY
IONISING RADIATION: THE INFLUENCE OF INTERPHASE
CHROMOSOME ARCHITECTURE
A. Ottolenghi, F. Ballarini, and M. Biaggi
Dipartimento di Fisica - Università di Milano and INFN - Sezione di Milano, via Celoria 16, 20133
Milano (Italy)
ABSTRACT
Several advances have been achieved in the knowledge of nuclear architecture and functions during the
last decade, thus allowing the identification of interphase chromosome territories and sub-chromosomal
domains (e.g. arm and band domains). This is an important step in the study of radiation-induced
chromosome aberrations; indeed, the coupling between track-structure simulations and reliable
descriptions of the geometrical properties of the target is one of the main tasks in modelling aberration
induction by radiation, since it allows one to clarify the role of the initial positioning of two DNA lesions
in determining their interaction probability. In the present paper, the main recent findings on nuclear and
chromosomal architecture are summarised. A few examples of models based on different descriptions of
interphase chromosome organisation (random-walk models, domain models and static models) are
presented, focussing on how the approach adopted in modelling the target nuclei and chromosomes can
influence the simulation of chromosomal aberration yields. Each model is discussed by taking into
account available experimental data on chromosome aberration induction and/or interphase chromatin
organisation. Preliminary results from a mechanistic model based on a coupling between radiation trackstructure features and explicitly-modelled, non-overlapping chromosome territories are presented.
INTRODUCTION
The induction of chromosome aberrations is a biological endpoint of particular interest, since there is
evidence that certain aberration types are correlated with cell reproductive death (Cornforth and Bedford,
1987) and with specific tumours (Forman and Rowley, 1982). For instance, a characteristic reciprocal
translocation between chromosomes 15 and 17 is observed in most human Acute Promyelocytic
Leukemia cells (APL cells), in which an oncoprotein is produced after fusion of the genes PML and
RAR (de The et al., 1991). Furthermore, in case of accidental radiation exposure, where physical dose
measurements are not available, or exposure to mixed fields, where physical dosimetry is not sufficient
for tracing back to the radiation quality and performing reliable estimates of health risk, aberrations can
be regarded as biological dosemeters. For instance, in the particular case of astronauts exposure to space
radiation, comparisons between aberration yields observed in post-flight samples of Peripheral Blood
Lymphocytes (PBL) and calibration curves (i.e. dose-response curves for specific aberrations induced by
in vitro irradiation with a reference radiation, usually X-rays or -rays), allow direct estimation of the
equivalent dose; this is the approach adopted by NASA for biodosimetry in astronauts (Yang et al., 1997).
1
Indeed, predicting the effects of exposures to the complex space environment is extremely difficult,
mainly due to the presence of different types of charged particles, including high-energy heavy ions (HZE
particles), whose radiobiological features are still not known in detail. Extensive descriptions of the
nature and intensity of space radiation can be found elsewhere (NCRP report no. 98, 1989); in this
context, it is sufficient to remind that the charged particles constituting space radiation are generated by
Van Allen belts, Galactic Cosmic Rays (GCR) and Solar Particle Events (SPE). Van Allen belts, which
play an important role in Low Earth Orbit (LEO) missions, mainly consist of electrons and protons
trapped in the Earth's geomagnetic field; protons of Van Allen belts can reach energies of 100 MeV.
GCR, consisting of 87% protons, 12% helium and about 1% HZE particles, provide chronic low-dose
exposures (1 mSv/day) to different ions. Although HZE particles provide a little contribution to the
GCR flux, they can account for up to the 50% of the absorbed dose. SPE are rare events consisting of
injections of light and heavy ions coming from the sun in association with a solar flare; their prediction is
extremely difficult, even though it is known that solar flares are correlated with the number of sunspots.
One can have an idea of the great threat represented by such events, which can provide acute high-dose
exposures, by considering that the large solar flare that occurred in August 1972, four months after the
Apollo 16 lunar mission, would be lethal for an unprotected crew on the surface of the moon. It is worthy
pointing out that when dealing with the effects of space radiation, it has also to be taken into account that
the external field is modulated by the interactions with the spacecraft walls and shielding structures,
where nuclear interactions can occur; this scenario is further complicated by microgravity, since it is still
not clear to what extent weightlessness conditions can influence the time evolution of radiation-induced
biological damage.
An extensive review on biological dosimetry in astronauts can be found in Durante (1996); the main
aspects will be summarised herein. A significant increase of the background level of chromosome
aberrations is usually observed in cell samples of astronauts who participated in long-term missions; the
negligible increase reported for the crew members of the 59 days Skylab-3 mission of 1973 (Bailey et al.,
1977) can be ascribed to the very unusual nomenclature adopted in aberration scoring. One can have a
quantitative idea by considering that at least a twofold increase of dicentric exchanges was observed in
the members of the different crews who spent time on the MIR space station (Testard et al., 1996; Yang et
al., 1997). PBL samples were taken from Russian cosmonauts and German, French and American
astronauts who participated in MIR missions of different duration; in particular, 5 Russian cosmonauts
spent 6 months on MIR during the French missions ANTARES (1992) and ALTAIR (1993). Cytogenetic
analysis of their blood samples performed by dicentric scoring in uniformly-stained metaphases (Testard
et al., 1996), revealed a large variability in individual response. The maximum increase was observed for
crew member B, for which the mean number of dicentrics per cell raised from 0.005 (pre-flight analysis)
to 0.02 (post-flight); a similar increase was found for member C. On this subject, it is worthy reporting
that both members B and C were on their third 6-month mission on MIR, and that not only the dicentric
yield was higher for them, but heavily-damaged cells were observed in their PBL, with up to 19 breaks
and several rearrangements, including a tricentric chromosome for member B.
The extreme complexity of the space environment is not the only reason that makes it difficult to
predict chromosome aberration induction (and thus health risk) after exposure to space radiation. Indeed,
the process itself, from the initial energy depositions in living cells to the production of observable
aberrations, is still not known in detail. In a previous work (Ottolenghi et al., 1999) the main open
questions on aberration induction by radiation were outlined: 1) is a single radiation-induced DNA lesion
able to produce a chromosomal exchange ("one-hit hypothesis"), as hypothesised by Goodhead and coworkers (Wilkinson et al., 1985)? 2) what is the molecular nature of the DNA lesions leading to
aberrations? double-helix "discontinuities", as assumed by Revell (1974), or double-strand breaks, as
hypothesised by Lea (1946), or more complex lesions (e.g. clustered dsb), as suggested during the last
decade by different authors (e.g. Sachs and Brenner, 1993; Chen et al., 1997; Ballarini et al., 1999)? 3) is
the aberration formation probability dependent on the initial distance between such lesions, and, if so,
what are the features of such distance-dependence law? 4) do incomplete exchanges really occur? 5) how
does the structural organisation of interphase nuclei modulate the process of aberration production? In
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Ottolenghi et al. (1999), we emphasised how mechanistic models and Monte Carlo simulations, possibly
based on track-structure codes, can be of great help in better understanding the intermediate steps of
aberration induction. Different modelling approaches available in the literature were presented and
discussed, focussing attention on the assumptions adopted for the critical points summarised above. This
study clearly indicated that, while track structure codes allow very detailed and reliable descriptions of
the features of the projectile (e.g. the spatial distribution and entity of energy depositions), the target
geometry (i.e. nuclear and chromosomal architecture) is usually modelled with rough approximation. This
kind of approach is well represented by a model developed by Edwards et al. (1996), who described the
radiation with event-by-event simulations at the nanometre level, whereas he assumed that chromatin was
uniformly distributed throughout the whole cell nucleus. Models able to couple track-structure
simulations with interphase chromosome descriptions attaining a comparable level of detail are therefore
highly desirable.
The present paper will focus on chromosomal architecture modelling (see open question no. 5 above).
A brief overview will be given on the present status of the knowledge on nuclear and chromosomal
architecture, which is becoming more and more satisfactory due to the continuous advances in techniques
such as Fluorescence In Situ Hybridisation (FISH), immuno-FISH (i.e. simultaneous detection of proteins
and genes with specific fluorescent antibodies), and computer 3-D reconstruction of images from
confocal microscopes. A few models of chromosome aberration induction will be presented and
discussed, focussing the attention on the approaches adopted in modelling interphase chromosome
organisation, and their possible coupling with track structure descriptions.
NUCLEUS AND CHROMOSOME ARCHITECTURE DURING INTERPHASE
The first description of the cell nucleus was provided by Brown in 1831; however, the nuclear
structure and function is still a subject of debate. At one extreme, the nucleus is thought to have its own
nucleoskeleton and organelles, whereas at the other, it is regarded as a disordered "bag" containing
nucleic acids, proteins and other molecules, in which transient structures are constructed and disrupted
depending on the particular activities (replication, transcription, etc.) that take place in the various
regions.
Many important results on nuclear architecture and its relationship with nuclear functions were
achieved during the last decade. Indeed, chromosomes were visualised in the 1860s, and a localisation of
interphase chromosomes in sub-nuclear territories had already been proposed by Carl Rabl (Rabl, 1885)
and Theodor Boveri (Boveri, 1909); however, this hypothesis was first neglected and then abandoned in
the late 1960s and early 1970s, due to the failure of electron microscopy techniques in detecting such
territories. Fluorescence In Situ Hybridisation (FISH) clearly demonstrated that individual interphase
chromosomes are localised whithin intranuclear territories (see T. Cremer et al., 1993 for a review); the
first visualisations of entire human chromosome territories with in situ hybridisation are due to
Manuelidis (1985) and Schardin et al. (1985). Furthermore, there is now strong evidence that no
significant overlapping occurs between distinct chromosome-territories/arm-domains at the resolution of
the light microscope (Dietzel et al., 1998; Visser and Aten, 1999). Indeed in 1993 it was hypothesised the
existence of an "Inter Chromosomal Domain compartment" (ICD compartment) in which activities such
as DNA replication and repair, and RNA transcription, splicing, maturation and transport would take
place (Zirbel et al., 1993). This hypothesis has recently been supported by experimental observations: by
introducing in human cells a filamentous protein called vimentin, a system of interconnecting intranuclear
channels can be observed, localised almost exclusively outside of chromosome territories (Bridger et al.,
1998); moreover, this study indicated that there is no accessible space between chromosomes and the
nuclear periphery, possibly due to an association of specific chromatin regions with the nuclear envelope.
However, the authors themselves pointed out that this experiment does not demonstrate the existence of a
well defined and structured intranuclear compartment; the ICD compartment remains therefore an
assumption.
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It was also shown that within individual chromosomal territories, R-bands and G-bands (early- and
late-replicating DNA, respectively) occupy distinct domains (Zink et al., 1999); moreover, active and
inactive genes are preferentially located at the periphery, whereas non-coding DNA sequences tend to
occupy the interior of the territory (Kurz et al., 1996). Furthermore, while GC-rich DNA sequences,
which are rich in genes, were found to be localised in all subvolumes of chromosome territories at similar
frequencies, AT-rich regions, which are gene-poor, were observed more to the interior of the territories
(Tajbakhsh et al., 2000). Similarly, chromatid damage in Chinese-hamster fibroblasts irradiated with Xrays were found to involve more frequently euchromatin (i.e. early-replicating chromatin, with relatively
low condensation degree) than eterochromatin (late-replicating, higher condensation degree) (Slijepcevic
and Natarajan, 1994a). It is also worthy reporting that at least some chromosomes show preferential
relative positioning in quiescent (i.e. non-cycling) human fibroblasts (Nagele et al., 1999).
To what extent this organisation remains unaltered during the various phases of the cell cycle, is still
an open question. Centromere movements over distances of about a micrometer were observed in vivo,
albeit infrequently (Lamond and Earnshaw, 1998), and chromosome arms move during interphase
depending on the cell-cycle stage (Li et al., 1998). Some of these movements may be linked to DNA
replication, consistent with the hypothesis that replication occurs at intranuclear fixed sites called
"replication factories" (Lamond and Earnshaw, 1998).
EXAMPLES OF APPROACHES IN MODELLING CHROMOSOME ABERRATIONS:
IMPLICATIONS OF INTERPHASE CHROMOSOME DESCRIPTION
In this section a few approaches adopted in modelling radiation-induced chromosome aberrations will be
presented, focussing the attention on the description of interphase chromosome organisation and its
consequences on the final outcomes of the calculations. The models described below will be grouped in
three categories: those based on polymer physics approaches ("Random-Walk Models"), those in which
interphase chromosomes are described by means of subnuclear regions regardless of the detailed
chromatin structure within such regions ("Subnuclear-Domain Models"), and those in which track
structure is combined with static models of the genome ("Static Models").
Random-Walk Models
Biphasic Random Walk
In a model developed by Wu et al. (1997), the DNA double helix during interphase was treated as a
flexible polymer, for which it is known that the probability of the physical distance, l, between two points
follows a 3-D Gaussian distribution (Doi and Edwards, 1988), i.e.:
P(l)dl = 4/ 3 exp(-2l2 ) l2 dl
< l > = 3/2
2
(1)
2
For a simple random walk,  = (3/2na2)1/2, where n is the distance in base-pairs between the two points
and a2 is a scale factor; thus the mean square (physical) distance between the two points is directly
proportional to their genomic separation, i.e. < l2 > = a2n (Doi and Edwards, 1988). However, to take into
account that during interphase each chromosome is spatially localised, Wu and co-workers expressed the
3-D mean square distance between two points of the same chromosome as follows ("biphasic" random
walk):
< l2 > = a2n
n<m
< l2 > = (a2-b2)m + b2n
nm
4
(2)
This means that < l2 > increases linearly with n following two different slopes, a2 for genomic distances
smaller than m and b2 for larger genomic distances, with a2 > b2. Here m represents the genomic size
separating the two slopes a2 and b2; the numerical values of the three parameters (m = 1.3 Mbp, a2 = 3
m2/Mbp and b2 = 0.14 m2/Mbp) were derived from Yokota et al. (1995), who studied the correlation
between the physical distance and the genomic distance between pairs of points of specific interphase
chromosomes by using a set of DNA markers. The probability distribution for the distance between two
points of a certain chromosome was approximated by Eq. (1), with  given by (3/2na2)1/2 for n<m and
(3/2[(a2-b2)m+b2n])1/2 for nm. This corresponds to a loose random walk at small scales and a tighter one
at large scales. In this context, it is worthy reminding that the size of the smallest fragment detectable
with the Giemsa and FISH staining techniques is no smaller than a few Mbp.
The main purpose of the authors was to quantify the role of proximity effects in the induction of extra
acentric fragments, consisting of acentric rings and acentric linear fragments not associated with a centric
ring or a dicentric chromosome. Since the frequency of acentric rings cannot be obtained directly from
experimental data, the authors estimated it by finding an expression for the ratio between acentric rings
and centric rings; the yields of centric rings were taken from published data. The model was applied to the
case of low-LET radiation, where distinct dsb can be assumed to be independent. Isolated dsb were
assumed to restitute (legitimate repair), whereas chromosome exchanges were assumed to originate from
pairwise interactions of (non isolated) dsb. By assuming that the interaction probability between two dsb
was proportional to their collision rate (i.e. to < l2 >-3/2), and considering all possible locations for two dsb
on the two arms of the same chromosome, the authors expressed the ratio of acentric rings to centric rings
by means of a2, b2, m and the size of the smallest detectable fragment of condensed chromatin, which was
fixed to 6 Mbp. The ratio calculated by Wu and co-workers with this model was more than twice the ratio
obtained by the same authors with ad hoc calculations neglecting the effects of chromosome localisation,
thus indicating that interphase chromosome localisation play an important role. The fact that the
calculated frequency of acentric rings was not sufficient to account for all the observed acentric fragments
was explained by assuming that the remaining excess acentric fragments are due to incomplete
exchanges.
Since the crucial point of this model was to calculate a ratio, the authors were not interested in
expressing the absolute yields of specific aberration types. Therefore, no assumption was needed on the
nature of the DNA lesions able to produce aberrations; such lesions were termed "double-strand breaks"
in a general sense, i.e. a break in the double helix.
Random-Walk/Giant-Loop
Two years before with respect to the biphasic random-walk model described above, a "RandomWalk/Giant-Loop" (RW/GL) model was proposed by Sachs et al. (1995), who suggested that the largescale (above 1 Mbp) geometry of chromatin during the G0/G1 phase of the cell cycle consists of flexible
"giant loops" with a random-walk backbone. In other words, a chromosome was described as a sequence
of large chromatin loops of equal size (3 Mbp) attached to a randomly-folded backbone structure; each
loop consists of a sequence of 30 "beads". Since the probability density for a certain bead configuration
can be regarded as a Boltzmann distribution (Doi and Edwards, 1988), it was expressed as proportional to
exp (-U/kB T), where T is the temperature of the system of beads, U is the potential energy and kB is
Boltzmann's constant. By starting from the joint probability density for two Cartesian intervals, the
authors found an expression for the distance probability density between pairs of beads. In the case of
intermediate genomic distances, between 0.1 and 1.5 Mbp, this lead to a mean square geometrical
distance, < r2 >, directly proportional to the genomic distance, n, whereas for larger genomic distances the
following expression was found: < r2 > = Rn + S [ni (n0-ni ) + nj (n0-nj)]. Here ni and nj are the (genomic)
distances from the closest bead for the two points (identified with the letters i and j), whereas the
parameters R, S and n0 (n0 is the size of the loops) were adjusted to 0.08 m2/Mbp, 0.83 m2/Mbp and 3
Mpb, respectively, after comparison with the data of Yokota et al. (1995), who measured geometrical
distances between pairs of FISH signals on a given interphase chromosome.
5
This model accounts well for the data of Yokota and co-workers. However, it has to be pointed out
that this kind of models (see also Hahnfeldt et al., 1993) imply a highly-random geometry of chromosome
territories, and thus they are not consistent with the observed systematic compartmentalisation of subterritorial domains such as arm domains and band domains. Indeed, the model of Sachs and co-workers
fits the 3-D measurements of distances between chromosomal subregions (e.g. centromeric regions) of
human chromosomes performed by Dietzel et al. (1995) reasonably well only for some chromosome
territories/subterritories, whereas it yields significant differences for others; in particular, the observed
strong differences in 3-D distance distributions between the active and inactive X-chromosomes, cannot
be reproduced with the model of Sachs. A detailed discussion on this topic can be found in C. Cremer et
al. (1996). Furthermore, following the RW/GL model, the various sections of a chromosome territory
would have a similar probability to be exposed at the territory surface, due to possible changes of the loop
positioning; thus, chromosomal interchanges should occur with similar frequencies in R-bands and Gbands. This is not consistent with the observation that at least in certain cell types, aberrations
preferentially involve G-light (gene-rich) bands (Slijepcevic and Natarajan, 1994b).
Subnuclear-Domain Models
Interaction Sites
A model based on the idea that the cell nucleus is divided into a certain number of "interaction sites"
was developed by Chen et al. (1997). The authors assumed that only the chromosome breaks induced
within the same site can interact to produce exchange-type chromosomal aberrations. The model was
applied with a Monte Carlo simulation in which the number of sites, S, was taken as an adjustable
parameter; its typical values were found to be in the range 5-25. For each cell, each of the 46
chromosomes was randomly assigned to a certain site, and chromosome aberrations were assumed to
originate from interactions of "reactive" dsb in the same site. Reactive dsb (rdsb) were assumed to
increase linearly with dose, and the yield of reactive dsb per Gy per cell was taken as an adjustable
parameter. In the case of low-LET radiation, rdsb were randomly distributed on chromosomes, and the
probability for a rdsb to be inflicted on a particular chromosome arm was taken as proportional to the arm
genomic length. Simulation of random interactions between rdsb within the same site allowed calculation
of the yields of apparently simple and visibly complex exchanges. Comparisons with experimental data
obtained by Simpson and Savage (1995) with X-rays, lead to 13 interaction sites, with a corresponding
mean number of rdsb/Gy/cell of 2.4. In the case of high-LET, flattened human fibroblast nuclei were
represented as right cylinders, having an ellipsoidal projected cross-section A and height parallel to the
radiation beam. The nucleus was modelled as a single layer of S sites, each of them having a crosssectional area of A/S; this value, together with the particle LET, determined the mean number of tracks
per site per Gy. For a given dose value and a given LET value, for each site an actual number of tracks
traversing that site was extracted from a Poisson distribution. The distribution for the total specific energy
imparted to a site was calculated on the basis of the probability of having 0,1,2, …tracks intersecting the
site; the probability that a given chromosome arm in a given site experienced exactly n reactive dsb was
then calculated by a superposition of Poisson distributions whose mean value was determined by the yield
of rdsb/Gy/cell. The best overall fit to the fibroblast data of Griffin et al. (1995) was obtained with 25
interaction sites per nucleus and 9.5 reactive dsb/Gy/cell.
This model was discussed in detail elsewhere (Ottolenghi et al., 1999). In this context, it is worthy
outlining that the parameter representing the mean number of sites per cell has not a clear biophysical
meaning, since its value changes significantly with LET, thus reflecting the features of the radiation track
structure rather than the target geometry.
Inter Chromosomal Domain (ICD) compartment
The "Inter Chromosomal Domain (ICD)" compartment model, developed by T. Cremer and coworkers (Zirbel et al., 1993; T. Cremer et al., 1993; T. Cremer et al., 1995), was extensively described
and discussed by C. Cremer et al. (1996); the main features will be summarised below. The authors
6
hypothesised the existence of a 3-D network of intra-nuclear channels containing the proteins needed for
cellular activities such as DNA- replication and repair and RNA- transcription and splicing. Such
channels were supposed to start at the nuclear pores and to expand between the surfaces of chromosomal
territories; from the territorial surface, other channels would lead into the territory interior and would
expand between sub-chromosomal domains (e.g. arm domains and band domains). In particular, for DNA
replication and repair, this model requires a dynamic organisation of chromosomal territories and subchromosomal domains, to allow the access of double-helix strands to the ICD channels; similarly, for
transcriptional activities, this model implies that genes are located at the surfaces of territories and
domains. The authors explained the formation and topology of this channel network by assuming that
chromosomal territories and sub-chromosomal domains are negatively-charged under physiological
conditions, thus leading to repulsive electric forces between opposite surfaces. The negative charges at
the surfaces may originate from non-neutralised, negatively-charged phosphate groups and non-histone
proteins. The channel width, which was predicted to be of the order of a few nm, was assumed to be
modulated by the morphology of territories/domains, by local differences in repulsive forces, and by
Brownian movements of domain surfaces. Transport of proteins and RNA molecules within the channel
network would take place either by diffusion, and/or via matrix filaments. As a consequence, channels in
regions with ongoing DNA-replication/repair or RNA transcription may strongly be enlarged; this is
consistent with the experimentally-observed macromolecular domains detectable as "speckles" or "foci"
(Zirbel et al., 1993).
According to the model described above, double-strand breaks located within a common boundary
zone of distinct chromosomal territories can lead to interchanges by illegitimate rejoining of two
chromosome ends in the ICD region, whereas illegitimate rejoining of dsb in channels located within the
same chromosomal territory leads to intrachanges. This implies that the frequency of chromosomal
aberrations depends both on the surface areas of adjacent territories/domains and on the accessibility of
repair complexes at these surfaces. It is worthy pointing out that repair (legitimate or illegitimate) of dsbs
induced at a certain distance from the ICD channels requires the motion of these dsbs to the
territory/domain surfaces. C. Cremer et al. (1996), on the basis of the ICD-compartment model and of 3D measurements of the surface areas of individual interphase chromosomes, derived quantitative
estimates of chromosome aberration frequencies, aimed to interpret the translocation rates observed by
Tanaka et al. (1983) and Muhlmann-Diaz and Bedford (1994) for the X-chromosome. Taking into
account that the surface area of the of the inactive chromosome-X (Xi) territory was found to be much
smaller with respect to the active X-chromosome (Xa), C. Cremer et al. (1996) assumed equal
translocation rates for the X chromosome of male cells and the Xa chromosome of female cells; this
translocation rate, according to the ICD-compartment model, was assumed to be proportional to the
surface area adjacent to other chromosome territories, and an expression was found linking the
translocation rate of Xi to the translocation rate of Xa. A re-examination of the data of Tanaka and coworkers suggested that the lower number of breaks observed for X chromosomes can be explained by
assuming that the surface fraction of Xi participating in translocations is significantly smaller than the
surface fraction of Xa, and by adopting a value of 1.4 for the ratio between the measured surface area of
Xa and that of Xi. Also the data obtained by Muhlmann-Diaz and Bedford were found to be compatible
with the application of the ICD-compartment model performed by C. Cremer et al. (1996).
An example of coupling between interphase chromosome geometry and track structure
In a previous work on modelling chromosomal aberrations induced by protons and alpha particles
(Ballarini et al., 1999), human lymphocyte nuclei were taken as spheres of 7 m diameter, and interphase
chromosomes were implicitly described as spherical territories with volumes proportional to the genomic
content. More specifically, the tracks traversing the nucleus were represented as linear segments and the
traversal lengths were extracted from a triangular distribution; for each nuclear traversal, a set of
intersected chromosomes was selected as follows. The first chromosome intersected by that track was
randomly extracted, and the chromosomal traversal length (i.e. the fraction of the nuclear traversal
contained in the spherical territory representing that chromosome) was also extracted from a triangular
7
DICENTRICS/CELL
distribution. A second, third,… chromosome were added along the particle track, under the condition that
the sum of the chromosome traversal lengths would not exceed the nucleus traversal length, within a 10%
tolerance interval. The process of selection of intersected chromosomes was then repeated for each track,
being the mean number of tracks determined by the nucleus radius and the radiation LET and dose.
It was also assumed that only severe DNA damage, operationally defined as 2 or more ssb on each
strand within 30 bp and called "Complex Lesions", can lead to aberrations; these lesions were distributed
along the radiation tracks, and the yield of CL per m was derived from the yield of CL/Gy/dalton
calculated in a previous work on DNA damage modelling (Ottolenghi et al., 1995). It was therefore
possible to obtain the number of CL in each traversed chromosome; within a given damaged
chromosome, each CL was then assigned to one of the two arms on the basis of their DNA content. Doseresponse curves for different Giemsa- and FISH-stained aberrations were calculated, and good agreement
was found with experimental data.
In the work described above, interphase chromosome territories were modelled only implicitly,
meaning that they were not defined in terms of 3-D coordinates within the nuclear volume. However this
approach, by making it possible to couple the geometrical features of track structure with those of the
target nuclei, allowed reproduction of the experimentally-observed ratio of interchanges (typically
dicentrics) to intrachanges (typically centric rings), which is strongly influenced by what is usually called
"proximity effect". Indeed, in a previous version of the model (Ballarini, 1997), in which neither
interphase chromosome localisation nor the geometrical features of light-ion tracks were taken into
account, a higher yield of dicentrics (factor 2) and a lower yield of centric rings was obtained (same
factor), thus confirming that both the target structure and the lesion spatial distribution play a relevant role
in the induction of chromosomal aberrations.
DOSE (Gy)
Fig. 1. Giemsa-stained dicentrics induced by gamma rays. The solid and dashed lines are simulation
results for two different values of the cut-off distance d. Experimental data are from Lloyd et al., 1975
(+); Bauchinger et al., 1983 (x); Fabry et al., 1985 ( , ■ ); Schmid et al., 1995 (*).
8
A future development of the work will consist in simulating interphase chromosomal territories and
subchromosomal domains in an explicit manner. As a first approach, a grid of small cubic elements
("boxes") was superimposed to a spherical cell nucleus, and non-overlapping chromosome territories
were constructed with step-by-step occupation of the closest neighbouring boxes, starting from 46
randomly-selected boxes. To simulate aberration induction by sparsely ionising radiation, DNA lesions
were randomly distributed in the nuclear volume, and they were allowed to interact according to a step
function of their initial distance. In Figure 1, the results of a preliminary test on dicentric dose-response
curves are reported for two different values of the cut-off distance, i.e. the maximum distance allowing
interaction of two chromosome free-ends (each DNA lesion produces two free-ends). A comparison
between the two cases can provide a quantitative estimate of the influence of the distance-dependence law
on the final outcome of the simulations: an increase in the cut-off distance from 1 to 1.2 m produces
almost a twofold increase in the dicentric yields.
Static Models
In this section two examples of "static" models of the genome will be reported, in which the biological
target was described by a function representing the expected fraction of "sensitive matrix" (i.e. the region
of interest for radiation-induced damage) contained in spherical shells randomly located within the cell
nucleus; the radiation itself was described by the expected amount of energy deposited in these shells.
Both models are based on a generalised formulation of the Theory of the Dual Radiation Action (TDRA)
due to Kellerer and Rossi (1978), who assumed that biological "lesions" (e.g. chromosome aberrations)
are due to distance-dependent interactions of pairs of "sublesions" (e.g. chromosome breaks). The interest
in this kind of approaches, which are much earlier than those presented in the previous sections, mainly
relies on the fact that they provided interesting suggestions on how the probability of interaction between
two sublesions depends on their initial distance, that is still an important open question.
The "floccule" approach
The "floccule" approach was developed by Kellerer and co-workers two years after the generalised
TDRA (Kellerer et al. 1980). For a randomly centred spherical shell of radius x and thickness dx, t(x)dx
("energy proximity function") was defined as the expected energy imparted to the shell, whereas s(x)dx
("geometry proximity function") was defined as the expected mass of the sensitive matrix contained in the
shell. A function g(x) was also introduced, representing the interaction probability between two
sublesions with initial distance x. Following the generalised TDRA, the probability that two energy
transfers produce a lesion is proportional to s(x)g(x)/(4x2). Although experimental data do not provide
information on s(x) and g(x) separately, they can give information on their product. Therefore the authors
introduced a function (x) = [s(x)g(x)/(4x2)] / ∫ s(x)g(x)dx with x ranging from 0 to ∞; finding an
expression for (x) consistent with experimental data was the main goal of this work.
Experiments on V-79 cell survival following irradiation with pairs of correlated deuteron ions having a
LET of 33 keV/ μm were carried out, and the data were used to derive expressions for (x). More
specifically, the usual expression for the surviving fraction S = exp [-k(ξD+D2)] was fitted to the data
obtained at different doses D, thus allowing to derive the corresponding value of ξ. As a second step, (x),
which was required to be a smooth and monotonically decreasing function of the distance, was obtained
by unfolding the expression ξ = ∫ (x)t(x)dx, where t(x) was determined by the radiation LET and the
distribution of the distances between two correlated ions at a depth midway in the cell nucleus.
The main finding of this work is that only (x) extending to several micrometers are consistent with
experimental data, and that (x) must decline sharply below distances of the order of 0.1 μm.
Furthermore, interactions between two sublesions produced by the same primary track (intra-track
combinations), were found to occur predominantly below 0.1 μm, whereas inter-track combination was
predominant at the micrometer range. Importantly, the authors observed that the resulting (x) functions
were similar to those that would result if DNA were the target and if it were randomly distributed over a
9
region of several μm diameter in "floccules" having linear dimensions up to 0.1 μm. The derivation of
(x) for the specific case of spherical floccules of diameter δ randomly distributed in a spherical site of
diameter d lead to acceptable agreement with data for δ=0.1 μm and d=4μm, although the precise form of
the functions (x) could not be given with certainty. On the basis of the recent findings on nuclear
structure (see the section "Nucleus and chromosome architecture during interphase" ), this interpretation
of the results is of extreme interest, since the floccules of Kellerer and co-workers might be identified
with some kind of domains at the sub-chromosome level.
The Drosophila approach
Also starting from the generalised TDRA (Kellerer and Rossi 1978), D. Brenner (1988) proposed an
ab initio model of chromosome aberration induction by different radiation types, with the main aim of
quantifying the role of the target geometry and of the distance between sublesions. Chinese hamster
chromosomes were modelled by using information on Drosophila chromosomes, whose structure was
taken from an experimental study describing the spatial organisation of Drosophila chromosomes with
Cartesian coordinates (Hochstrasser et al. 1986). More specifically, the total chromosomal content of a
Chinese hamster cell was modelled by random superposition of four Drosophila nuclei. A large number
of spheres were then located along each chromosome, so that the union of these spheres had about the
same volume as that of the nucleotides in the nucleus; each sphere represented a nucleotide pair. The
distribution of the distances, s(x), between pairs of points randomly extracted within the sensitive matrix
(i.e. the union of the spheres) was then calculated by splitting it into two components, referring to pairs of
points in the same chromosomes and in two distinct chromosomes, respectively.
Following the TDRA, chromosome aberrations were assumed to be produced by a two-step
mechanisms, the first step consisting in the induction of sublesions (e.g. chromosome breaks) in the
sensitive matrix, and the second step consisting in pairwise interactions of sublesions to form lesions. The
aberration yield was found to increase with dose in a linear-quadratic fashion, since the aberration yield at
a certain dose was assumed to be proportional to the lesion yield, which following the TDRA is a linearquadratic function of dose. On the basis of TDRA, the ratio of the linear to the quadratic coefficient was
expressed by means of the functions t(x) and (x), where t(x)dx represents the expected value of the
energy deposited in a spherical shell of radius x and thickness dx centered at a randomly-extracted
deposition point, and (x) is the probability that two energy depositions at distance x will interact and
form a lesion. The function (x) was considered to comprise two components, s(x) and g(x), where the
latter represents the probability that two sublesions having initial distance x will interact to produce a
lesion. (x) was calculated by unfolding the expression for the ratio between the linear and the quadratic
coefficient of chromosome aberration dose-response curves; this expression was found by fitting the
linear-quadratic relationship to experimental data sets obtained after irradiation of hamster cells with
different radiation types (Skarsgard et al. 1967).
The probability for two sublesions to interact and form a lesion was found to be very similar to a step
function with a cut-off distance of 1 m. The author therefore concluded that the enhancement shown by
(x) at nanometre level is due to the contribution of s(x) rather than g(x), suggesting that the target
structure rather than the cell response is one of the main responsible factors for proximity effects in
aberration induction. Although the numerical results should be considered carefully, this model provides
very interesting indications, since the dependence of the interaction probability of two chromosome
breaks on their initial separation is considered to be a relevant open question.
DISCUSSION AND CONCLUSIONS
Recent advances in techniques such as 3D reconstruction of confocal microscope images of FISHstained chromosomes, provided a reliable picture of nuclear architecture during interphase. A large
number of experimental studies have clearly indicated that the cell nucleus is a highly organised structure,
in which individual interphase chromosomes occupy distinct territories; similarly, each chromosome
territory contains non-overlapping sub-chromosomal domains, typically arm domains and band domains.
10
Although the "Inter Chromosomal Domain compartment" proposed by Cremer and co-workers is still an
hypothesis, it has been demonstrated that proteins, and possible other molecules such as RNAs, can
penetrate between the various territories and domains, whereas there is no available space between
chromosome territories and the nuclear envelope.
These findings have relevant implications in understanding the mechanisms underlying chromosome
aberration induction. Indeed, the structural - and possibly functional - organisation of the cell nucleus
summarised above, implies that only DNA breaks at the periphery of neighbouring chromosome
territories/sub-chromosomal domains should contribute to chromosome exchanges, since the enzyme
complexes necessary for repair should be preferentially located between distinct territories/domains rather
than in their interior. As a consequence, the interaction probability between two breaks at the periphery of
different territories/domains is essentially governed by their adjacent surface area. Therefore, broken
chromosomes having similar volumes (and thus similar DNA content) but different surface areas adjacent
to neighbouring territories, in principle have different probabilities to be involved in a chromosome
exchange. This can provide an explanation for experiments in which the observed yield of exchanges was
not proportional to the genomic content of the chromosomes involved, as is the case of Muhlmann-Diaz
and Bedford (1994), who observed a strong deviation from the linear expectation for aberrations
involving X-chromosomes in human cell lines. It is also worthy pointing out that the fraction of the
territory surface attached to the nuclear envelope would not participate in exchanges; therefore, also
chromosomes with similar surfaces can have different probability to be involved in the production of
exchange-type aberrations.
However, the scenario is much more complicated than it may appear, since the organisation of the
nucleus is highly dynamic, being modulated by the different cellular activities ongoing in the various
regions (see De Boni, 1994 for a review on the dynamic aspects of interphase nuclear structure).
Although interphase chromosomes in non-cycling cells have shown preferential relative positioning, it is
still not clear to what extent chromosome territories can move throughout the nucleus. Furthermore, even
though the movement of entire territories as a whole were not significant, there is substantial evidence
that sub-chromosomal domains are subject to continuous movements within the chromosome territory
during the various cell-cycle phases, that should affect the exchange frequency. For instance, a break
initially induced in the interior of the territory could subsequently move towards the periphery, thus
increasing its probability to be involved in exchanges.
These considerations indicate that models coupling track-structure simulations with static
representations of interphase nuclei, although necessary to delineate the initial conditions (DNA damage
induction), may not be sufficient to reproduce the production of aberrations (damage evolution); indeed,
simulations taking into account chromatin movements after irradiation, to be tested against PCC data,
may be necessary.
ACKNOWLEDGMENTS
This work was partially supported by the EC contract no. FIGH-CT1999-00005 ("Low dose risk
models") and the ASI (Italian Space Agency) contract no. I/R/090/00. We are also grateful to Dr. Mario
Faretta of the European Institute of Oncology (Milan) for useful discussions.
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