Modelling Cytogenet Genome Res 104:157–161 (2004) DOI: 10.1159/000077481 Virtual radiation biophysics: implications of nuclear structure G. Kreth,a J. Finsterle,a and C. Cremera a Kirchhoff Institute for Physics, INF 227 Heidelberg (Germany) Abstract. The non-random positioning of chromosome territories (CTs) in lymphocyte cell nuclei has raised the question whether systematic chromosome-chromosome associations exist which have significant influence on interchange rates. In such a case the spatial proximity of certain CTs or even of clusters of CTs is expected to increase the respective exchange yields significantly, in comparison to a random association of CTs. In the present study we applied computer simulated arrangements of CTs to calculate interchange frequencies between all heterologous CT pairs, assuming a uniform action of the molecular repair machinery. For the positioning of CTs in the virtual nuclear volume we assumed a) a statistical, and b) a gene density-correlated arrangement. The gene density-correlated arrangement regards the more experimentally observed interior localization of gene-rich and the more peripheral positioning of gene-poor CTs. Regarding one-chromosome yields, remarkable differences for single CTs were observed taking into account the gene density-correlated distribution of CTs. The formation of interchanges between different chromosome territories (CTs) requires spatial proximity of two or more broken genomic loci which have to be localized mainly at or near CT surfaces (Cremer et al., 1996; Sachs et al., 1997; Cornforth et al., 2002). In this context a non-random positioning of CTs in the nuclear volume and possibly a systematic chromosome-chromosome association will favor the probability by which two CTs undergo an interchange event. To study the influence of such proximity effects on interchange frequencies, Cornforth et al. (2002) determined frequencies between all possible heterologous pairs of CTs with 24-color whole-chromosome painting after damage to interphase lymphocytes by sparsely ionizing radiation in vitro. For lymphocyte cells, recently a close relationship between radial positioning of CTs in the nuclear volume and its gene densities was observed. That means that CTs with higher gene densities, e.g. #17, 19 are located more in the interior of the nuclear volume while CTs with lower gene densities, e.g. #18, come closer to the periphery (Boyle et al., 2001; Cremer et al., 2001). In the study of Cornforth et al. (2002), however, only a group of five chromosomes (#1, 16, 17, 19, 22), previously observed to be preferentially located near to the center of the nucleus (suggested by Boyle et al., 2001), showed a statistically significant deviation of a random CT–CT association. These findings suggest a predominantly random location of CTs with respect to each other in interphase lymphocyte cells. In the present contribution we applied the “Spherical 1 Mbp Chromatin Domain (SCD)” computer model to calculate interchange frequencies between CTs, assuming a statistical, or a gene density correlated distribution of CTs in a given spherical nuclear volume. Such an approach allows theoretical predictions of the effects of different radial CT arrangements on exchange yields. The present study was supported financially by the Deutsche Forschungsgemeinschaft (Grant CR 60/19-1). Received 10 September 2003; manuscript accepted 18 December 2003. Request reprints from Gregor Kreth, Kirchhoff Institute for Physics, INF 227 69120 Heidelberg (Germany); telephone: +49-6221-549275 fax +49-6221-549839; e-mail: gkreth@kip.uni-heidelberg.de ABC Fax + 41 61 306 12 34 E-mail karger@karger.ch www.karger.com © 2004 S. Karger AG, Basel 0301–0171/04/1044–0157$21.00/0 Copyright © 2003 S. Karger AG, Basel Materials and methods Computer-simulated nuclear structures The recent experimental findings about the large-scale interphase chromosome structure (compare Cremer and Cremer, 2001) revealed a compartmentalization of a chromosome territory into 300- to 800-nm sized (diameter) subchromosomal foci (with a mean DNA content of about F 1 Mbp). According to the “Spherical 1 Mbp Chromatin Domain (SCD)” model (Kreth et al., 2001; Kreth et al., submitted) each chromosome is built up by a linear chain of 500-nm sized spherical domains with a mean DNA content of F 1 Mbp which are linked together by entropic spring potentials. Different domains interact with each other also by a weakly increasing repulsive potential. These domains represent the experimentally observed foci, and the number is given by the respective DNA content of the chromosome. Besides a statistical distribution of the simulated chromosome chains in a spherical Accessible online at: www.karger.com/cgr nuclear volume (we choose here a diameter of 10 Ìm, according to the experimental investigations of Cremer et al. (2001); other diameters, e.g. for small lymphocytes, for the calculation of interchange yields have to be considered in further simulations), we extended the SCD model to take into account the specific positioning of gene rich and gene poor CTs in the nuclear volume. For this purpose the CTs were inserted in the nuclear volume according to the order of their gene densities: #19, 17, 22, 16, 20, 11, 1, 12, 15, 7, 14, 6, 9, 2, 10, 8, 5, 3, 21, X, 18, 4, 13, Y1; additionally the distance of CTs to the nuclear center was weighted with a radial probability density function which considers the respective gene density of a CT. In this way the gene-rich CTs are placed closer to the middle of the nucleus and those that are gene poor closer to the periphery (Kreth et al., submitted). The large variation in the position of the CTs is maintained by this procedure. Beginning from a mitotic-like strongly condensed start configuration of the CTs, where the 1-Mbp domains are placed side by side, we used the Importance Sampling Monte Carlo method to create relaxed equilibrium configurations with respect to the potential energy. Virtual irradiation algorithm On the assumption of a random distribution of double strand breaks (DSBs) within the DNA, the probability of a break occurring within a certain 1-Mbp domain can be modeled using Poisson distribution mathematics. This assumes that, although an ionizing radiation track may produce multiple DSBs, these are distributed randomly throughout the genome. Under the assumption that the number of DSBs induced within a nucleus increases linearly with dose and is proportional to the DNA content of the cell, the probability pn of an individual modeled 1-Mbp domain containing n DSBs is calculated from an adaptation of the equation of Poisson distribution (Johnston et al., 1997): pn = nn e–b n! (1) Here n is the number of DSBs within an individual domain; b is the mean number of breaks per domain for the whole nucleus and is given by: b=DWyWq (2) where D is the dose of radiation (Gy), q is the size of the domain in bp (here 1 W 106 bp) and y is the yield of DSBs which was adapted to y = 8.07 W 10–9 Gy–1 bp–1 to ensure a mean number of 50 DSBs per Gy per nucleus according to experimental observations (referred in Cornforth et al., 2002). The DSBs within the 1-Mbp domains were placed randomly. To determine an exchange (inter-/intra-change) between two DSBs, only those 1-Mbp domains containing DSBs were regarded which were directly neighbored. According to Kreth et al. (1998), for an exchange event in dependence of the distance d of the two DSBs, the normalized probability function pd was assumed: pd = 冉冊 r d 1.4 (3) Corresponding to the Monte Carlo process, an exchange event for such a domain pair was counted when a random number of the unit distribution [0;1] ^ pd. Here, r denotes the radius of a 1-Mbp domain which determines the maximal distance by which an exchange takes place in every case. When for a certain DSB an exchange was not counted, other directly neighbored domains containing DSBs were tested. When this procedure failed, the DSB will be considered as repaired. Exchanges between domains of the same chromosome were counted as intrachanges and were separated from interchanges. Experimental comparison For an experimental comparison of the calculated interchange yields the study of Cornforth et al. (2002) was applied. In this study peripheral blood lymphocytes were exposed during the G0/G1 part of the cell cycle to radiation doses of 2 or 4 Gy, after which the mFISH technique was used to score aberrations at the first subsequent metaphase. A total of nine data sets with 1,587 cells were taken. 1 Human human/ 158 Genome Resources: http://www.ncbi.nlm.nik.gov/genome/guide/ Cytogenet Genome Res 104:157–161 (2004) Results In the simulated case for each of both assumptions about the distribution of CTs in the nuclear volume (statistical or gene density correlated), 50 nuclei were simulated. To get comparable statistics with the experimental data of Cornforth et al. (2002) each simulated nucleus was “irradiated” with 3 Gy (we used a median value between 2 and 4 Gy, because the experimental number of cells irradiated with 2 or 4 Gy was not known) virtually 32 times. That means that in a model nucleus with a given distribution of CTs, a dose of 3 Gy (F 150 randomly distributed DSBs) was assumed; the resulting exchanges were determined. Then the same model nucleus was used again, with a new set of randomly distributed DSBs, and the resulting exchanges were calculated. For each simulated nuclear structure, this procedure was repeated 32 times. In the end, an equivalent ensemble of 1,600 cells was obtained, corresponding to the number of cells evaluated experimentally by Cornforth et al. (2002). The absolute interchange yields in percent for each heterologous autosome pair for the two simulated cases and for the experimental case are given in Fig. 1. While the absolute values of the simulated and the experimental interchange yields were in the same order, in the case of a simulated gene density correlated distribution of CTs, one heterologous pair showed a difference 61.5 % to the experimental case (marked in black), and 25 heterologous pairs showed a difference 60.8 % (marked in gray). In the case of a statistical distribution of CTs, three heterologous pairs revealed a difference 61.5 % and 22 pairs 60.8 %. On the basis of these absolute interchange yields, an unequivocal conclusion about a better agreement of one of the two simulated yields with the experimental yield cannot be made. In the case of the gene density-correlated distribution however the more interior localization of gene rich CTs like 16, 17 and 19 resulted directly in higher exchange rates between these CTs, which was confirmed partially also in the experimental case. According to Cornforth et al. (2002), in Fig. 2 we therefore plotted the one-chromosome yields which are derived from Fig. 1 by summing over all interchange yields involving each given chromosome. To visualize differences between the experimental and the simulated gene density-correlated yields to the simulated statistical yields (which describe a random chromosome-chromosome association), all rates were normalized to 1,000 (error bars were determined by Poisson statistics). The one chromosome-yields for CTs #10–22 for the experimental and the simulated gene density-correlated data are in quite good agreement. An exception is the yield for CT #19 which is underrepresented in the experimental case. A possible explanation would be the experimental observation that many cells with a CT #19 (the gene-richest chromosome of the human genome) translocation die. These events are not regarded in the evaluation process (personal communication Karin GreulichBode). The largest difference between the experimental and the simulated gene density-correlated yield resulted from chromosome #1: in the case of the simulated gene density-correlated distribution the yield was considerably higher than the experimentally observed yield for this chromosome. It may be noted Absolute interchange yields in % Experiment (Cornforth et al. 2002, 1587 cells) A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1.26 1.07 1.51 1.01 0.82 1.01 0.69 0.88 1.01 0.63 0.38 0.13 0.44 0.69 0.57 0.82 0.32 0.5 0.57 0.5 0.95 1.5 1 1.3 1.1 0.4 0.8 0.7 0.6 1.1 1.1 0.6 0.3 1.1 0.4 0.6 0.2 0.3 0.4 0.4 0.7 0.7 1 1.2 0.8 0.8 0.9 0.6 0.7 0.8 0.8 0.6 0.3 0.6 0.5 0.4 0.6 0.4 0.5 0.4 0.7 0.6 0.8 0.6 0.9 0.8 0.4 0.7 0.8 0.8 0.5 0.8 0.7 0.3 0.3 0.5 0.4 0.2 0.63 0.88 0.63 0.63 0.76 1.01 0.88 0.88 0.5 0.82 0.32 0.63 0.25 0.25 0.38 0.32 0.13 0.38 0.76 1.01 0.82 0.38 1.01 0.57 0.69 0.57 0.44 0.13 0.38 0.44 0.25 0.19 0.32 0.5 0.5 0.44 0.82 0.82 0.25 0.63 0.25 0.5 0.57 0.44 0.25 0.57 0.25 0.06 0.4 0.4 0.7 0.3 0.8 0.6 0.5 0.3 0.4 0.4 0.1 0.4 0.1 0.2 0.6 1 0.3 0.8 0.9 0.6 0.6 0.6 0.7 0.2 0.2 0.2 0.2 0.4 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.4 0.3 0.1 0.8 0.1 0.4 0.6 0.5 0.6 0.3 0.4 0.4 0.2 0.4 0.38 0.5 0.25 0.32 0.38 0.13 0.44 0.38 0.13 0.25 0.7 0.3 0.3 0.3 0.5 0.2 0.3 0.2 0.4 0.63 0.32 0.25 0.57 0.06 0.19 0.5 0.38 0.69 0.5 0.13 0.25 0.32 0.32 0.13 0.6 0.5 0.6 0.7 0.4 0.4 0.3 0.1 0.1 0.3 0.4 0.3 0.2 0.4 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3.69 2.56 1.69 2.13 1.31 1 2.19 1.44 2.06 1.31 0.19 1.19 0.56 1.19 1.38 1.75 1.69 1 0.75 0.56 0.38 1.6 1.6 0.9 1.3 1.3 1.6 1.2 0.5 1.3 1.9 1.3 1.3 1.1 1.3 1.3 0.5 0.6 0.8 0.6 0.6 0.9 0.8 1.2 1.5 0.5 1.8 0.5 1.4 1 0.5 1.1 0.7 0.8 0.3 0.3 0.9 0.7 0.4 0.4 1 1.6 1.5 1.1 0.6 0.9 1.4 1.7 0.3 1.1 1.4 0.4 0.5 0.8 0.3 0.6 0.4 0.3 1.13 0.94 0.94 1.19 1.06 1.06 1.06 0.63 1 0.94 1 0.69 0.69 0.63 0.69 0.13 0.19 1.06 2 0.63 0.44 1 1.5 0.75 0.5 0.94 1.19 0.63 0.13 0.31 0.94 0.88 0.38 0.75 0.88 1.25 0.63 0.88 1 0.69 0.38 0.81 0.94 1 0.44 1 0.31 0.63 0.5 0.9 0.9 0.7 0.4 1.2 1.1 0.6 0.6 0.4 0.3 0.6 0.4 0.5 0.8 0.9 1.6 1.2 0.8 0.9 0.5 0.3 0.6 0.3 0.3 0.6 0.9 1.6 0.9 0.8 0.7 0.7 0.8 0.4 0.6 0.4 0.3 0.4 0.4 0.4 0.8 0.9 0.6 0.6 1.2 0.5 1 0.6 0.5 0.8 1.19 0.56 0.25 0.44 0.63 0.5 0.31 0.44 0.31 0.63 1.1 0.6 0.3 0.2 0.8 0.1 0.3 0.4 0.3 0.38 0.44 0.56 0.56 0.13 0.31 0.31 0.19 0.56 0.19 0.31 0.31 0.44 0.19 0.31 0.8 0.3 1.6 0.6 0 0.6 0.1 1.3 0.8 0.2 0.6 0.3 0.2 0.2 0.1 0.4 0 0.3 0.6 0.4 0.3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2.25 2.63 1.19 1.56 1.88 1.75 1.25 1.25 0.88 1.38 1.38 1.63 1.5 1.38 0.88 0.56 0.56 0.63 0.88 1.06 0.88 1.4 1.3 2.2 1.1 1.8 1.2 1.2 1.3 1 1.6 1.1 1.9 1.3 0.8 0.8 1.3 0.4 0.4 0.3 0.9 1.5 1.1 1.3 1.1 1.8 1.3 1.2 1.1 1.3 0.9 1.4 0.4 1.1 0.4 0.9 0.7 0.8 0.4 0.3 1.5 1.8 0.6 0.6 0.5 1.8 2.2 0.8 0.7 1.1 0.9 0.7 0.8 0.6 0.3 0.6 0.3 1.3 0.94 1.31 0.88 0.81 1.44 0.44 1.25 0.88 0.63 0.75 0.38 0.56 1.06 0.5 0.63 0.56 0.63 1.13 1.13 1.06 1.38 1.06 0.56 0.69 0.5 1 0.69 0.69 0.5 0.94 0.5 0.56 0.5 0.81 1.56 0.94 0.94 0.81 1 0.63 0.75 1 0.44 0.19 0.75 0.63 0.63 0.63 0.8 1.1 0.6 0.5 0.6 0.6 0.6 0.3 0.3 0.4 0.3 0.8 0.6 0.5 1.1 0.9 1.2 0.6 0.7 1.2 0.4 0.9 0.6 0.6 0.6 0.3 0.2 1.1 0.6 0.8 0.3 0.8 1.1 0.9 0.6 0.6 0.6 0.9 0.3 1 1.1 0.6 1.1 0.4 0.6 0.7 0.5 0.2 0.1 0.3 0.44 0.81 0.19 0.63 0.44 0.44 0.38 0.19 0.38 0.25 0.5 0.8 0.4 0.4 0.4 0.1 0.6 0.2 0.2 0.56 0.38 0.31 0.5 0.63 0.44 0.56 0.06 0.31 0.63 0.19 0.19 0.44 0.31 0.44 0.6 0.4 0.3 0.3 0.5 0.1 0.5 0.3 0.3 0.2 0.2 0.6 0.1 0.4 0.1 0.1 0.4 0.4 0.3 0 0.1 0.2 0 0.2 0.2 0.1 0.1 Simulation (gene density correlated, 1600 cells) B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 20 21 Simulation (statistical, 1600 cells) C Fig. 1. Absolute interchange yields in percent for each heterologous autosome pair for the both simulated (statistical (C) and gene density correlated distribution (B) of CTs according to the SCD model) and the experimental case (A) (irradiated peripheral blood lymphocytes; adapted from Cornforth et al., 2002). For the two simulated cases (B, C) an absolute difference of 1.5 % or more to the experimental case (A) was marked in black and a difference of 0.8 % or more in gray. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Cytogenet Genome Res 104:157–161 (2004) 20 21 159 individual autosome yields Fig. 2. Relative (the plotted yields were normalized to 1,000) one-chromosome yields for the two simulated and the experimental case. The simulated statistical case can be considered as a representation for a random chromosome-chromosome association. Error bars were taken from Poisson statistics. rel. one-chromosome yield 100 simul. statistical distribution (1600 cells) 90 simul. gene density correlated distributon (1600 cells) 80 exp. Cornforth et al. (1587 cells) 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 B 0.1 rel. one-chromosome yield 9 Chromosome number irradiation of simulated nuclei (3 Gy) (statistical distribution of CTs) A 8 irradiation of simulated nuclei (3 Gy) (gene density correlated distribution of CTs) 0.1 0.09 0.09 statistical (50000 cells) 0.08 gene density correlated (50000 cells) 0.08 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.7826 y = 0.001x 2 R = 0.9971 0.02 0.01 0.6651 y = 0.0017x 2 R = 0.9154 0.02 0.01 0 0 0 50 100 150 200 250 300 DNA content 0 50 100 150 200 250 300 DNA content Fig. 3. Relative one-chromosome yields for both simulated cases were plotted versus the DNA content (in this graph a simulated ensemble of 50,000 cells was applied for each case). Potential fitting curves revealed the expected dependency of: yield F (DNA content)2/3. that both (experimental and simulated gene density-correlated) yields revealed differences for single chromosomes in comparison to random chromosome-chromosome associations (represented by the simulated statistical distribution). To assure that this behavior is not an effect of insufficient statistics, in Fig. 3 the relative one-chromosome yields were calculated for both simulated CT distribution cases for 50,000 cells (each of the 50 simulated nuclei was irradiated virtually 1,000 times). According to previous studies (Cremer et al., 1996; Kreth et al., 1998), the dependency of one-chromosome yield and DNA content follows the relation: yield F (DNA content)2/3. While in the case of the simulated statistical distribution of CTs all data points were close to the potential fitting curve, for the gene density correlated distribution remarkable differences for single CTs were obtained. 160 Cytogenet Genome Res 104:157–161 (2004) Discussion In the present contribution we tested the effect of a nonrandom (gene density-correlated) simulated CT distribution in the nuclear volume on interchange yields. The comparison with an experimentally obtained interchange yield revealed that these one-chromosome yields showed for single CTs remarkable differences to a random chromosome-chromosome association (given by a simulated statistical distribution of CTs in the nuclear volume). For CTs #10–22 the agreement between experimental and simulated gene density-correlated yields was quite good; an exception is CT#19 which is underrepresented in the experimental case. We can conclude that the simulations confirm the influence of proximity effects on interchange yields. To enhance such comparisons a) the ensemble of simulated nuclei has to be increased to be sure that the observed deviations are not the result of the multiple virtual radiation of single simulated nuclei; this can have a significant influence on the calculated yields. b) The experimental observations were made in the subsequent metaphase. That means that aberrations, e.g. translocations with chromosome #19, or most complex aberrations may lead to cell death and will cause an underestimation of certain CT yields. A direct analysis in interphase nuclei with mFISH techniques after irradiation might be useful in further experimental investigations. Acknowledgment For stimulating discussions we thank T. Cremer (Munich) and K. Greulich-Bode (Heidelberg). References Boyle S, Gilchrist S, Bridger JM, Mahy NL, Ellis JA, Bickmore WA: The spatial organization of human chromosomes within the nuclei of normal and emerin-mutant cells. Hum molec Genet 10:211– 219 (2001). Cornforth MN, Greulich-Bode KM, Bradford DL, Arsuaga J, Vazquez M, Sachs RK, Brückner M, Molls M, Hahnfeldt P, Hlatky L, Brenner DJ: Chromosomes are predominantly located randomly with respect to each other in interphase human cells. J Cell Biol 159:237–244 (2002). Cremer C, Muenkel C, Granzow M, Jauch A, Dietzel S, Eils R, Guan XY, Meltzer PS, Trent JM, Langowski J, Cremer T: Nuclear architecture and the induction of chromosomal aberrations. Mutat Res 366:97–116 (1996). Cremer M, von Hase J, Volm T, Brero A, Kreth G, Walter J, Fischer C, Solovei I, Cremer C, Cremer T: Non-random radial higher-order chromatin arrangements in nuclei of diploid human cells. Chrom Res 9:541–567 (2001). Cremer T, Cremer C: Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nature Rev 2:292–301 (2001). Johnston PJ, Olive PL, Bryant PE: Higher-order chromatin structure-dependent repair of DNA doublestrand breaks: modeling the elution of DNA from nucleoids. Radiat Res 148:561–567 (1997). Kreth G, Muenkel C, Langowski J, Cremer T, Cremer C: Chromatin structure and chromosome aberrations: modeling of damage induced by isotropic and localized irradiation. Mutat Res 404:77–88 (1998). Kreth G, Edelmann P, Cremer C: Towards a dynamical approach for the simulation of large scale cancer correlated chromatin structures. It J Anat Embryol 106:21–30 (2001). Sachs RK, Chen AM, Brenner DJ: Proximity effects in the production of chromosome aberrations by ionizing radiation. Int J Radiat Biol 71:1–19 (1997). Cytogenet Genome Res 104:157–161 (2004) View publication stats 161