A polymer model for the structural organization of chromatin loops and minibands in interphase chromosomes

Robustness of carbon-ion radiotherapy against DNA damage repair associated radiosensitivity variation based on a biophysical model

BACKGROUND

Interpatient variation of tumor radiosensitivity is rarely considered during the treatment planning process despite its known significance for the therapeutic outcome.

PURPOSE

To apply our mechanistic biophysical model to investigate the biological robustness of carbon ion radiotherapy (CIRT) against DNA damage repair interference (DDRi) associated patient-to-patient variability in radiosensitivity and its potential clinical advantages against conventional radiotherapy approaches.

METHODS AND MATERIALS

The "UNIfied and VERSatile bio response Engine" (UNIVERSE) was extended by carbon ions and its predictions were compared to a panel of in vitro and in vivo data including various endpoints and DDRi settings within clinically relevant dose and linear energy transfer (LET) ranges. The implications of UNIVERSE predictions were then assessed in a clinical patient scenario considering DDRi variance.

RESULTS

UNIVERSE tests well against the applied benchmarks. While in vitro survival curves were predicted with an R2 > 0.92, deviations from in vivo RBE data were less than 5.6% The conducted paradigmatic patient plan study implies a markedly reduced significance of DDRi based radiosensitivity variability in CIRT (13% change ofD 50 ${{D}_{50}}$ in target) compared to conventional radiotherapy (62%) and that boosting the LET within the target further amplifies this robustness of CIRT (8%). In the case of heightened tumor radiosensitivity, a dose de-escalation strategy for photons allows a reduction of the maximum effective dose within the normal tissue (NT) from aD 2 ${{D}_2}$ of 2.65 to 1.64 Gy, which lies below the level found for CIRT (D 2 ${{D}_2}$  = 2.41 Gy) for the analyzed plan and parameters. However, even after de-escalation, the integral effective dose in the NT is found to be substantially higher for conventional radiotherapy in comparison to CIRT (D m e a n ${{D}_{mean}}$ of 0.75, 0.46, and 0.24 Gy for the conventional plan, its de-escalation and CIRT, respectively).

CONCLUSIONS

The framework offers adequate predictions of in vitro and in vivo radiation effects of CIRT while allowing the consideration of DRRi based solely on parameters derived from photon data. The results of the patient planning study underline the potential of CIRT to minimize important sources of interpatient divergence in therapy outcome, especially when combined with techniques that allow to maximize the LET within the tumor. Despite the potential of de-escalation strategies for conventional radiotherapy to reduce the maximum effective dose in the NT, CIRT appears to remain a more favorable option due to its ability to reduce the integral effective dose within the NT.

Modeling of ionizing radiation-induced chromosome aberration and tumor prevalence based on two classes of DNA double-strand breaks clustering in chromatin domains

There has been some controversy over the use of radiobiological models when modeling the dose-response curves of ionizing radiation (IR)-induced chromosome aberration and tumor prevalence, as those curves usually show obvious non-targeted effects (NTEs) at low doses of high linear energy transfer (LET) radiation. The lack of understanding the contribution of NTEs to IR-induced carcinogenesis can lead to distinct deviations of relative biological effectiveness (RBE) estimations of carcinogenic potential, which are widely used in radiation risk assessment and radiation protection. In this work, based on the initial pattern of two classes of IR-induced DNA double-strand breaks (DSBs) clustering in chromatin domains and the subsequent incorrect repair processes, we proposed a novel radiobiological model to describe the dose-response curves of two carcinogenic-related endpoints within the same theoretical framework. The representative experimental data was used to verify the consistency and validity of the present model. The fitting results indicated that, compared with targeted effect (TE) and NTE models, the current model has better fitting ability when dealing with the experimental data of chromosome aberration and tumor prevalence induced by multiple types of IR with different LETs. Notably, the present model without introducing an NTE term was adequate to describe the dose-response curves of IR-induced chromosome aberration and tumor prevalence with NTEs in low-dose regions. Based on the fitting parameters, the LET-dependent RBE values were calculated for three given low doses. Our results showed that the RBE values predicted by the current model gradually decrease with the increase of doses for the endpoints of chromosome aberration and tumor prevalence. In addition, the calculated RBE was also compared with those evaluated from other models. These analyses show that the proposed model can be used as an alternative tool to well describe dose-response curves of multiple carcinogenic-related endpoints and effectively estimate RBE in low-dose regions.

Impact of DNA Repair Kinetics and Dose Rate on RBE Predictions in the UNIVERSE

Accurate knowledge of the relative biological effectiveness (RBE) and its dependencies is crucial to support modern ion beam therapy and its further development. However, the influence of different dose rates of the reference radiation and ion beam are rarely considered. The ion beam RBE-model within our "UNIfied and VERSatile bio response Engine" (UNIVERSE) is extended by including DNA damage repair kinetics to investigate the impact of dose-rate effects on the predicted RBE. It was found that dose-rate effects increase with dose and biological effects saturate at high dose-rates, which is consistent with data- and model-based studies in the literature. In a comparison with RBE measurements from a high dose in-vivo study, the predictions of the presented modification were found to be improved in comparison to the previous version of UNIVERSE and existing clinical approaches that disregard dose-rate effects. Consequently, DNA repair kinetics and the different dose rates applied by the reference and ion beams might need to be considered in biophysical models to accurately predict the RBE. Additionally, this study marks an important step in the further development of UNIVERSE, extending its capabilities in giving theoretical guidance to support progress in ion beam therapy.

The Impact of Sub-Millisecond Damage Fixation Kinetics on the In Vitro Sparing Effect at Ultra-High Dose Rate in UNIVERSE

The impact of the exact temporal pulse structure on the potential cell and tissue sparing of ultra-high dose-rate irradiation applied in FLASH studies has gained increasing attention. A previous version of our biophysical mechanistic model (UNIVERSE: UNIfied and VERSatile bio response Engine), based on the oxygen depletion hypothesis, has been extended in this work by considering oxygen-dependent damage fixation dynamics on the sub-milliseconds scale and introducing an explicit implementation of the temporal pulse structure. The model successfully reproduces in vitro experimental data on the fast kinetics of the oxygen effect in irradiated mammalian cells. The implemented changes result in a reduction in the assumed amount of oxygen depletion. Furthermore, its increase towards conventional dose-rates is parameterized based on experimental data from the literature. A recalculation of previous benchmarks shows that the model retains its predictive power, while the assumed amount of depleted oxygen approaches measured values. The updated UNIVERSE could be used to investigate the impact of different combinations of pulse structure parameters (e.g., dose per pulse, pulse frequency, number of pulses, etc.), thereby aiding the optimization of potential clinical application and the development of suitable accelerators.

How Genomes Emerge, Function, and Evolve: Living Systems Emergence-Genotype-Phenotype-Multilism-Genome/Systems Ecology

What holds together the world in its innermost, what life is, how it emerges, functions, and evolves, has not only been an epic matter of endless romantic sunset poetry and philosophy, but also manifests explicitly in its perhaps most central organization unit-genomes. Their 3D architecture and dynamics, including the interaction networks of regulatory elements, obviously co-evolved as inseparable systems allowing the physical storage, expression, and replication of genetic information. Since we were able to fill finally the much-debated centennial gaps in their 3D architecture and dynamics, now entire new perspectives open beyond epigenetics reaching as far as a general understanding of living systems: besides the previously known DNA double helix and nucleosome structure, the latter compact into a chromatin quasi-fibre folded into stable loops forming stable multi-loop aggregates/rosettes connected by linkers, creating hence the again already known chromosome arms and entire chromosomes forming the cell nucleus. Instantly and for the first time this leads now to a consistent and cross-proven systems statistical mechanics genomics framework elucidating genome intrinsic function and regulation including various components. It balances stability/flexibility ensuring genome integrity, enabling expression/regulation of genetic information, as well as genome replication/spread. Furthermore, genotype and phenotype are multiplisticly entangled being evolutionarily the outcome of both Darwinian natural selection and Lamarckian self-referenced manipulation-all embedded in even broader genome ecology (autopoietic) i(!)n- and environmental scopes. This allows formulating new meta-level functional semantics of genomics, i.e. notions as communication of genes, genomes, and information networks, architectural and dynamic spaces for creativity and innovation, or genomes as central geno-/phenotype entanglements. Beyond and most fundamentally, the paradoxical-seeming local equilibrium substance stability in its entity though far from a universal heat-death-like equilibrium is solved, and system irreversibility, time directionality, and thus the emergence of existence are clarified. Consequently, real deep understandings of genomes, life, and complex systems in general appear in evolutionary perspectives as well as from systems analyses, via system damage/disease (its repair/cure and manipulation) as far as the understanding of extraterrestrial life, the de novo creation and thus artificial life, and even the raison d'etre.

Combined DNA Damage Repair Interference and Ion Beam Therapy: Development, Benchmark, and Clinical Implications of a Mechanistic Biological Model

PURPOSE

Our purpose was to develop a mechanistic model that describes and predicts radiation response after combined DNA damage repair interference (DDRi) and particle radiation therapy.

METHODS AND MATERIALS

The heterogeneous dose distributions of protons and ⁴He ions were implemented into the "UNIfied and VERSatile bio-response Engine" (UNIVERSE). Predictions for monoenergetic and mixed fields over clinically relevant dose and linear energy transfer range were compared with experimental in vitro survival data measured in this work as well as data available in the literature, including different cell lines and DDR interferences. Ultimately, UNIVERSE predictions were investigated in a patient plan.

RESULTS

UNIVERSE accurately predicts survival of cell lines with and without DDRi in clinical settings of ion beam therapy based only on 3 parameters derived from photon data. With increasing dose or linear energy transfer, the radiosensitizing effect of DDRi decreases, resulting in diminished relative biological effect of ion beam radiation for cells subjected to DDRi in comparison to cells that are not. Similar trends were observed in patient plan recalculations; however, this analysis also suggests that DDRi + particle radiation therapy may better preserve the therapeutic window in comparison to DDRi + photon radiation therapy.

CONCLUSIONS

The presented framework represents the first mechanistic model of combined DDRi and particle radiation therapy comprehensively benchmarked in clinically relevant scenarios and a step toward more personalized treatment. It reveals potential differences between DDRi + photon radiation therapy versus DDRi + particle radiation therapy, which have not been described so far. UNIVERSE could aid in appraising the clinical viability of combined administration of radiosensitizing drugs and charged particle therapy, as well as the identification of patients with known DDR deficiencies in the tumor who might benefit from therapy with light ions, freeing limited space at heavy ion therapy centers.

Prediction of Cell Survival after Exposure to Mixed Radiation Fields with the Local Effect Model

Mixed radiation fields comprise the most common form of radiation exposure. Given their relevance in radiation protection, cancer radiotherapy and space research, accurate predictions of the corresponding radiation effects are essential. The local effect model (LEM) allows the prediction of cell survival after ion irradiation based on the knowledge of the cells' response to photon radiation. The assumption is made that the same spatial DNA double-strand break (DSB) distributions in the cell nucleus lead to the same effects, independent of the radiation quality that produced the DSBs. This makes the LEM an ideal tool for predictions of cell survival after exposure to any mixed radiation field. In this work, the LEM is applied to calculate cell survival for extreme mixed irradiation scenarios, i.e., high-linear energy transfer (LET) ion radiation combined with low-LET photon radiation, which can be understood as a consistency test for the high-LET model. Available experimental data covering several ion species and energies in combination with photon exposure are predicted with the LEM. Furthermore, the results are compared to the microdosimetric model by Zaider and Rossi and the lesion additivity model by Lam, which allow the prediction of cell survival after exposure to mixed radiation fields based on the knowledge of the survival curves of the two radiation components. Although the LEM uses only photon dose-response data as input, it is able to compete with the empirical radiobiological models that additionally require ion dose-response curves as input. Certain experimental scenarios are presented in which the specific consideration of spatial DSB distributions could be essential for an accurate prediction of the effect of mixed radiation fields.

A comparison of mechanism-inspired models for particle relative biological effectiveness (RBE)

BACKGROUND AND SIGNIFICANCE

The application of heavy ion beams in cancer therapy must account for the increasing relative biological effectiveness (RBE) with increasing penetration depth when determining dose prescriptions and organ at risk (OAR) constraints in treatment planning. Because RBE depends in a complex manner on factors such as the ion type, energy, cell and tissue radiosensitivity, physical dose, biological endpoint, and position within and outside treatment fields, biophysical models reflecting these dependencies are required for the personalization and optimization of treatment plans.

AIM

To review and compare three mechanism-inspired models which predict the complexities of particle RBE for various ion types, energies, linear energy transfer (LET) values and tissue radiation sensitivities.

METHODS

The review of models and mechanisms focuses on the Local Effect Model (LEM), the Microdosimetric-Kinetic (MK) model, and the Repair-Misrepair-Fixation (RMF) model in combination with the Monte Carlo Damage Simulation (MCDS). These models relate the induction of potentially lethal double strand breaks (DSBs) to the subsequent interactions and biological processing of DSB into more lethal forms of damage. A key element to explain the increased biological effectiveness of high LET ions compared to MV x rays is the characterization of the number and local complexity (clustering) of the initial DSB produced within a cell. For high LET ions, the spatial density of DSB induction along an ion's trajectory is much greater than along the path of a low LET electron, such as the secondary electrons produced by the megavoltage (MV) x rays used in conventional radiation therapy. The main aspects of the three models are introduced and the conceptual similarities and differences are critiqued and highlighted. Model predictions are compared in terms of the RBE for DSB induction and for reproductive cell survival.

RESULTS AND CONCLUSIONS

Comparisons of the RBE for DSB induction and for cell survival are presented for proton (¹ H), helium (⁴ He), and carbon (¹² C) ions for the therapeutically most relevant range of ion beam energies. The reviewed models embody mechanisms of action acting over the spatial scales underlying the biological processing of potentially lethal DSB into more lethal forms of damage. Differences among the number and types of input parameters, relevant biological targets, and the computational approaches among the LEM, MK and RMF models are summarized and critiqued. Potential experiments to test some of the seemingly contradictory aspects of the models are discussed.

Novel Biological Approaches for Testing the Contributions of Single DSBs and DSB Clusters to the Biological Effects of High LET Radiation

The adverse biological effects of ionizing radiation (IR) are commonly attributed to the generation of DNA double-strand breaks (DSBs). IR-induced DSBs are generated by clusters of ionizations, bear damaged terminal nucleotides, and frequently comprise base damages and single-strand breaks in the vicinity generating a unique DNA damage-clustering effect that increases DSB "complexity." The number of ionizations in clusters of different radiation modalities increases with increasing linear energy transfer (LET), and is thought to determine the long-known LET-dependence of the relative biological effectiveness (RBE). Multiple ionizations may also lead to the formation of DSB clusters, comprising two or more DSBs that destabilize chromatin further and compromise overall processing. DSB complexity and DSB-cluster formation are increasingly considered in the development of mathematical models of radiation action, which are then "tested" by fitting available experimental data. Despite a plethora of such mathematical models the ultimate goal, i.e., the "a priori" prediction of the radiation effect, has not yet been achieved. The difficulty partly arises from unsurmountable difficulties in testing the fundamental assumptions of such mathematical models in defined biological model systems capable of providing conclusive answers. Recently, revolutionary advances in methods allowing the generation of enzymatic DSBs at random or in well-defined locations in the genome, generate unique testing opportunities for several key assumptions frequently fed into mathematical modeling - including the role of DSB clusters in the overall effect. Here, we review the problematic of DSB-cluster formation in radiation action and present novel biological technologies that promise to revolutionize the way we address the biological consequences of such lesions. We describe new ways of exploiting the I-SceI endonuclease to generate DSB-clusters at random locations in the genome and describe the possible utility of Zn-finger nucleases and of TALENs in generating DSBs at defined genomic locations. Finally, we describe ways to harness the revolution of CRISPR/Cas9 technology to advance our understanding of the biological effects of DSBs. Collectively, these approaches promise to improve the focus of mathematical modeling of radiation action by providing testing opportunities for key assumptions on the underlying biology. They are also likely to further strengthen interactions between experimental radiation biologists and mathematical modelers.

Anomalous diffusion in fractal globules

The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.

A statistical model of intra-chromosome contact maps

A statistical model describing a fine structure of the intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) is proposed. The model combines hierarchical chain folding with a quenched heteropolymer structure of primary chromatin sequences. It is conjectured that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding. It is shown that the existence of a quenched primary structure coupled with hierarchical folding induces a full range of features observed in experimental Hi-C maps: hierarchical elements, chess-board intermittency and large-scale compartmentalization.

The link between cell-cycle dependent radiosensitivity and repair pathways: a model based on the local, sister-chromatid conformation dependent switch between NHEJ and HR

The different DNA damage repair pathways like homologous recombination (HR) and non-homologous end joining (NHEJ) have been linked to the variation of radiosensitivity throughout the cell cycle. However, no attempts have been made to test the various hypotheses derived from these studies in a quantitative way e.g. by using modeling approaches. Here we present the first modeling approach that allows predicting the cell cycle dependent radiosensitivity of repair proficient as well as of repair deficient cell lines after photon irradiation based on a small set of parameters and assumptions. A key element of the model is the classification of DNA damage according to its complexity on the level of chromatin loops of about 2Mbp size. Isolated DSB (iDSB), characterized by a single DSB within a chromatin loop, are distinguished from clustered DSB (cDSB), characterized by two or more DSB within a chromatin loop. The class of iDSB is further subdivided into two sub-classes, characterized by the replication status of the corresponding chromatin loop. For iDSB in replicated loops that are in close contact, error-free homologous recombination is assumed to be effective; in unreplicated loops or in replicated loops that have already been separated, iDSB are assumed to be repaired by error-prone non-homologous end joining. cDSB are assumed not to be repairable effectively by neither HR nor NHEJ. Assigning empirically derived lethalities to these three damage classes and pathways, we demonstrate that the model is able to accurately reproduce cell cycle dependent survival probabilities. Notably, the relevant parameters are derived solely from two survival curves for normal, repair proficient cells in G1 and late-S phase. Based on a comparison of model predictions with a large data set reported in the literature, we show that the lethality values for wild type cells are simultaneously predictive for the cell cycle dependent variation of sensitivity observed for HR-deficient and NHEJ-deficient cells.

Radiation oncology in vitro: trends to improve radiotherapy through molecular targets

Much has been investigated to improve the beneficial effects of radiotherapy especially in that case where radioresistant behavior is observed. Beyond simple identification of resistant phenotype the discovery and development of specific molecular targets have demonstrated therapeutic potential in cancer treatment including radiotherapy. Alterations on transduction signaling pathway related with MAPK cascade are the main axis in cancer cellular proliferation even as cell migration and invasiveness in irradiated tumor cell lines; then, for that reason, more studies are in course focusing on, among others, DNA damage enhancement, apoptosis stimulation, and growth factors receptor blockages, showing promising in vitro results highlighting molecular targets associated with ionizing radiation as a new radiotherapy strategy to improve clinical outcome. In this review we discuss some of the main molecular targets related with tumor cell proliferation and migration as well as their potential contributions to radiation oncology improvements.

A model of photon cell killing based on the spatio-temporal clustering of DNA damage in higher order chromatin structures

We present a new approach to model dose rate effects on cell killing after photon radiation based on the spatio-temporal clustering of DNA double strand breaks (DSBs) within higher order chromatin structures of approximately 1–2 Mbp size, so called giant loops. The main concept of this approach consists of a distinction of two classes of lesions, isolated and clustered DSBs, characterized by the number of double strand breaks induced in a giant loop. We assume a low lethality and fast component of repair for isolated DSBs and a high lethality and slow component of repair for clustered DSBs. With appropriate rates, the temporal transition between the different lesion classes is expressed in terms of five differential equations. These allow formulating the dynamics involved in the competition of damage induction and repair for arbitrary dose rates and fractionation schemes. Final cell survival probabilities are computable with a cell line specific set of three parameters: The lethality for isolated DSBs, the lethality for clustered DSBs and the half-life time of isolated DSBs.

By comparison with larger sets of published experimental data it is demonstrated that the model describes the cell line dependent response to treatments using either continuous irradiation at a constant dose rate or to split dose irradiation well. Furthermore, an analytic investigation of the formulation concerning single fraction treatments with constant dose rates in the limiting cases of extremely high or low dose rates is presented. The approach is consistent with the Linear-Quadratic model extended by the Lea-Catcheside factor up to the second moment in dose. Finally, it is shown that the model correctly predicts empirical findings about the dose rate dependence of incidence probabilities for deterministic radiation effects like pneumonitis and the bone marrow syndrome. These findings further support the general concepts on which the approach is based.

From a melt of rings to chromosome territories: the role of topological constraints in genome folding

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

Modelling of cell killing due to sparsely ionizing radiation in normoxic and hypoxic conditions and an extension to high LET radiation

PURPOSE

An approach for describing cell killing with sparsely ionizing radiation in normoxic and hypoxic conditions based on the initial number of randomly distributed DNA double-strand breaks (DSB) is proposed. An extension of the model to high linear energy transfer (LET) radiation is also presented.

MATERIALS AND METHODS

The model is based on the probabilities that a given DNA giant loop has one DSB or at least two DSB. A linear combination of these two classes of damage gives the mean number of lethal lesions. When coupled with a proper modelling of the spatial distribution of DSB from ion tracks, the formalism can be used to predict cell response to high LET radiation in aerobic conditions.

RESULTS

Survival data for sparsely ionizing radiation of cell lines in normoxic/hypoxic conditions were satisfactorily fitted with the proposed parametrization. It is shown that for dose ranges up to about 10 Gy, the model describes tested experimental survival data as good as the linear-quadratic model does. The high LET extension yields a reasonable agreement with data in aerobic conditions.

CONCLUSIONS

A new survival model has been introduced that is able to describe the most relevant features of cellular dose-response postulating two damage classes.

Calculation of the biological effects of ion beams based on the microscopic spatial damage distribution pattern

PURPOSE

To present details of the recent version of the 'Local Effect Model' (LEM), that has been developed and implemented in treatment planning for the ion beam therapy pilot project performed at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany.

MATERIALS AND METHODS

The new version of the model is based on a detailed consideration of the spatial distribution of the initial damages, i.e., double-strand breaks (DSB). This spatial distribution of DSB is obtained from the radial dose profile of the ion track using Monte Carlo methods. These distributions are then analyzed with regard to the proximity of DSB. This version of the model also facilitates the calculation of full dose response curves up to arbitrary high doses, thus allowing to thoroughly check the approximations previously used to estimate the quadratic term (β-term) for the linear-quadratic description of dose response curves.

RESULTS

The accuracy of the model predictions is demonstrated by good agreement of the relative biological effectiveness (RBE) as a function of the linear energy transfer (LET) with experimental data obtained for V79 cells after carbon irradiation. The β-values predicted by the full simulation tend to be larger as compared to the approximation in the intermediate LET range.

CONCLUSION

The new version of the model allows a more mechanistic description of the biological effects of ion radiation. The full simulation is a prerequisite for tests of the validity of the approach at high doses, which are of particular interest for application in hypofractionation studies.

Structural analysis of interphase X-chromatin based on statistical shape theory

The 3D folding structure formed by different genomic regions of a chromosome is still poorly understood. So far, only relatively simple geometric features, like distances and angles between different genomic regions, have been evaluated. This work is concerned with more complex geometric properties, i.e., the complete shape formed by genomic regions. Our work is based on statistical shape theory and we use different approaches to analyze the considered structures, e.g., shape uniformity test, 3D point-based registration, Fisher distribution, and 3D non-rigid image registration for shape normalization. We have applied these approaches to analyze 3D microscopy images of the X-chromosome where four consecutive genomic regions (BACs) have been simultaneously labeled by multicolor FISH. We have acquired two sets of four consecutive genomic regions with an overlap of three regions. From the experimental results, it turned out that for all data sets the complete structure is non-random. In addition, we found that the shapes of active and inactive X-chromosomal genomic regions are statistically independent. Moreover, we reconstructed the average 3D structure of chromatin in a small genomic region (below 4 Mb) based on five BACs resulting from two overlapping four BAC regions. We found that geometric normalization with respect to the nucleus shape based on non-rigid image registration has a significant influence on the location of the genomic regions.

Packing of the polynucleosome chain in interphase chromosomes: evidence for a contribution of crowding and entropic forces

In the crowded intranuclear environment, entropic depletion forces between macromolecules are expected to be strong. A review of simulations of linear polymers leads to several predictions about probable conformations of a polynucleosome chain in these conditions. These include a globular conformation, variable compaction due to different local rigidity or curvature of the mosaic of isochores, satellite sequences, and nucleosomes containing different histone variants, and the possibility that chromosomes represent separate phases like those seen in heterogeneous particle mixtures by experiment and simulation. Experimental results which show that macromolecular crowding alone, in the absence of exogenous cations, can stabilise interphase chromosomes and cause self-association of polynucleosome chains are presented. Together, these considerations suggest that macromolecular crowding and entropic forces are major factors in packing polynucleosome chains in vivo.

DNA Fragmentation Induced in Human Fibroblasts by Accelerated56Fe Ions of Differing Energies

DNA fragmentation was studied in the fragment size range 0.023-5.7 Mbp after irradiation of human fibroblasts with iron-ion beams of four different energies, i.e., 200 MeV/nucleon, 500 MeV/nucleon, 1 GeV/nucleon and 5 GeV/nucleon, with gamma rays used as the reference radiation. The double-strand break (DSB) yield (and thus the RBE for DNA DSB induction) of the four iron-ion beams, which have LETs ranging from 135 to 442 keV/mum, does not vary greatly as a function of LET. As a consequence, the variation of the cross section for DSB induction mainly reflects the variation in LET. However, when the fragmentation spectra were analyzed with a simple theoretical tool that we recently introduced, the results showed that spatially correlated DSBs, which are absent after gamma irradiation, increased markedly with LET for the iron-ion beams. This occurred because iron ions produce DNA fragments smaller than 0.75 Mbp with a higher probability than gamma rays (a probability that increases with LET). These sizes include those expected from fragmentation of the chromatin loops with Mbp dimensions. This result does not exclude a correlation at distances smaller than the lower size analyzed here, i.e. 23 kbp. Moreover, the DSB correlation is dependent on dose, decreasing when dose increases; this can be explained with the argument that at increasing dose there is an increasing fraction of fragments produced by DSBs caused by separate, uncorrelated tracks.

Dynamic simulation of active/inactive chromatin domains

In the present study a model for the compactification of the 30 nm chromatin fibre into higher order structures is suggested. The idea is that basically every condensing agent (HMG/SAR, HP1, cohesin, condensin, DNA-DNA interaction …) can be modeled as an effective attractive potential of specific chain segments. This way the formation of individual 1 Mbp sized rosettes from a linear chain could be observed. We analyse how the size of these rosettes depends on the number of attractive segments and on the segment length. It turns out that 8-20 attractive segments per 1 Mbp domain produces rosettes of 300-800 nm in diameter. Furthermore, our results show that the size of the rosettes is relatively insensitive to the segment length.

Low frequency rhythms in human DNA sequences: a key to the organization of gene location and orientation?

We explore large-scale nucleotide compositional fluctuations of the human genome using multiresolution techniques. Analysis of the GC content and of the AT and GC skews reveals the existence of rhythms with two main periods of 110+/-20 kb and 400+/-50 kb that enlighten a remarkable cooperative gene organization. We show that the observed nonlinear oscillations are likely to display all the characteristic features of chaotic strange attractors which suggests a very attractive deterministic picture: gene orientation and location, in relation with the structure and dynamics of chromatin, might be governed by a low-dimensional nonlinear dynamical system.

A polymer model for large-scale chromatin organization in lower eukaryotes

A quantitative model of large-scale chromatin organization was applied to nuclei of fission yeast Schizosaccharomyces pombe (meiotic prophase and G2 phase), budding yeast Saccharomyces cerevisiae (young and senescent cells), Drosophila (embryonic cycles 10 and 14, and polytene tissues) and Caenorhabditis elegans (G1 phase). The model is based on the coil-like behavior of chromosomal fibers and the tight packing of discrete chromatin domains in a nucleus. Intrachromosomal domains are formed by chromatin anchoring to nuclear structures (e.g., the nuclear envelope). The observed sizes for confinement of chromatin diffusional motion are similar to the estimated sizes of corresponding domains. The model correctly predicts chromosome configurations (linear, Rabl, loop) and chromosome associations (homologous pairing, centromere and telomere clusters) on the basis of the geometrical constraints imposed by nuclear size and shape. Agreement between the model predictions and literature observations supports the notion that the average linear density of the 30-nm chromatin fiber is approximately 4 nucleosomes per 10 nm contour length.

Rejoining of radiation-induced DNA double-strand breaks: pulsed-field electrophoresis analysis of fragment size distributions after incubation for repair

The repair of radiation-induced DNA double-strand breaks (DSBs) is frequently investigated by measuring the time-dependent decrease in the fraction of fragmented DNA that is able to enter electrophoresis gels. When transformed into equivalent doses without repair, such measurements are thought to reflect the removal of DSBs, and they typically exhibit a fast initial component and a decreasing rate at longer repair intervals. This formalism, however, assumes that the spatial distribution of unrejoined breakage resembles the pattern of induction of DSBs. While the size distributions for initial fragmentation, such as that resolved by conventional pulsed-field gel electrophoresis (PFGE) (between about 10(5) and 10(7) bp), are well known to agree with the prediction of random breakage, no data are available from studies explicitly testing this relationship for residual breakage. Therefore, Chinese hamster V79 cells and MeWo (human melanoma) cells were irradiated with different doses (10-100 Gy) or were incubated for repair for up to 4 h after a single dose of 100 Gy (V79) or 90 Gy (MeWo) before being subjected to PFGE. Fragment size distributions were calculated by convolution of the PFGE profiles with an appropriately generated size calibration function. The results clearly demonstrate an over-representation of smaller fragments (below about 2-3 Mbp) compared to the prediction of randomness for residual breakage. In consequence, the time-dependent decrease of dose-equivalent values calculated from data on the fraction released may not directly reflect DSB rejoining rates. The present findings are compatible with an earlier suggestion of slow rejoining of breaks which have been induced as multiple breaks (two or more) in large chromosomal loops, thus also predicting an increase of the slowly rejoining DSB fraction with increasing dose.

Chromosomal G-dark bands determine the spatial organization of centromeric heterochromatin in the nucleus

Gene expression can be silenced by proximity to heterochromatin blocks containing centromeric alpha-satellite DNA. This has been shown experimentally through cis-acting chromosome rearrangements resulting in linear genomic proximity, or through trans-acting changes resulting in intranuclear spatial proximity. Although it has long been been established that centromeres are nonrandomly distributed during interphase, little is known of what determines the three-dimensional organization of these silencing domains in the nucleus. Here, we propose a model that predicts the intranuclear positioning of centromeric heterochromatin for each individual chromosome. With the use of fluorescence in situ hybridization and confocal microscopy, we show that the distribution of centromeric alpha-satellite DNA in human lymphoid cells synchronized at G(0)/G(1) is unique for most individual chromosomes. Regression analysis reveals a tight correlation between nuclear distribution of centromeric alpha-satellite DNA and the presence of G-dark bands in the corresponding chromosome. Centromeres surrounded by G-dark bands are preferentially located at the nuclear periphery, whereas centromeres of chromosomes with a lower content of G-dark bands tend to be localized at the nucleolus. Consistent with the model, a t(11; 14) translocation that removes G-dark bands from chromosome 11 causes a repositioning of the centromere, which becomes less frequently localized at the nuclear periphery and more frequently associated with the nucleolus. The data suggest that "chromosomal environment" plays a key role in the intranuclear organization of centromeric heterochromatin. Our model further predicts that facultative heterochromatinization of distinct genomic regions may contribute to cell-type specific patterns of centromere localization.

Higher-order structure of chromatin and chromosomes

The linear array of nucleosomes that comprises the primary structure of chromatin is folded and condensed to varying degrees in nuclei and chromosomes forming 'higher order structures'. We discuss the recent findings from novel experimental approaches that have yielded significant new information on the different hierarchical levels of chromatin folding and their functional significance.

Chromosome territories, nuclear architecture and gene regulation in mammalian cells

The expression of genes is regulated at many levels. Perhaps the area in which least is known is how nuclear organization influences gene expression. Studies of higher-order chromatin arrangements and their dynamic interactions with other nuclear components have been boosted by recent technical advances. The emerging view is that chromosomes are compartmentalized into discrete territories. The location of a gene within a chromosome territory seems to influence its access to the machinery responsible for specific nuclear functions, such as transcription and splicing. This view is consistent with a topological model for gene regulation.

Assessment of compositional heterogeneity within and between eukaryotic genomes

Using large amounts of long genomic sequences, we studied the compositional patterns of eukaryotic genomes. We developed a simple measure, the compositional heterogeneity (or variability) index, to compare the differences in compositional heterogeneity between long genomic sequences. The index measures the average difference in GC content between two adjacent windows normalized by the standard error expected under the assumption of random distribution of nucleotides in a window. We report the following findings: (1) The extent of the compositional heterogeneity in a genomic sequence strongly correlates with its GC content in all multicellular eukaryotes studied regardless of genome size. (2) The human genome appears to be highly compositionally heterogeneous both within and between individual chromosomes; the heterogeneity goes much beyond the predictions of the isochore model. (3) All genomes of multicellular eukaryotes examined in this study are compositionally heterogeneous, although they also contain compositionally uniform segments, or isochores. (4) The true uniqueness of the human (or mammalian) genome is the presence of very high GC regions, which exhibit unusually high compositional heterogeneity and contain few long homogeneous segments (isochores). In general, GC-poor isochores tend to be longer than GC-rich ones. These findings indicate that the genomes of multicellular organisms are much more heterogeneous in nucleotide composition than depicted by the isochore model and so lead to a looser definition of isochores.

Assessment of Compositional Heterogeneity Within and Between Eukaryotic Genomes

Using large amounts of long genomic sequences, we studied the compositional patterns of eukaryotic genomes. We developed a simple measure, the compositional heterogeneity (or variability) index, to compare the differences in compositional heterogeneity between long genomic sequences. The index measures the average difference in GC content between two adjacent windows normalized by the standard error expected under the assumption of random distribution of nucleotides in a window. We report the following findings: (1) The extent of the compositional heterogeneity in a genomic sequence strongly correlates with its GC content in all multicellular eukaryotes studied regardless of genome size. (2) The human genome appears to be highly compositionally heterogeneous both within and between individual chromosomes; the heterogeneity goes much beyond the predictions of the isochore model. (3) All genomes of multicellular eukaryotes examined in this study are compositionally heterogeneous, although they also contain compositionally uniform segments, or isochores. (4) The true uniqueness of the human (or mammalian) genome is the presence of very high GC regions, which exhibit unusually high compositional heterogeneity and contain few long homogeneous segments (isochores). In general, GC-poor isochores tend to be longer than GC-rich ones. These findings indicate that the genomes of multicellular organisms are much more heterogeneous in nucleotide composition than depicted by the isochore model and so lead to a looser definition of isochores.

Targeting the chromatin-remodeling MSL complex of Drosophila to its sites of action on the X chromosome requires both acetyl transferase and ATPase activities

Dosage compensation in Drosophila is mediated by a multiprotein, RNA-containing complex that associates with the X chromosome at multiple sites. We have investigated the role that the enzymatic activities of two complex components, the histone acetyltransferase activity of MOF and the ATPase activity of MLE, may have in the targeting and association of the complex with the X chromosome. Here we report that MLE and MOF activities are necessary for complexes to access the various X chromosome sites. The role that histone H4 acetylation plays in this process is supported by our observations that MOF overexpression leads to the ectopic association of the complex with autosomal sites.

Radiation-produced chromosome aberrations: colourful clues

Ionizing radiation produces many chromosome aberrations. A rich variety of aberration types can now be seen with the technique of chromosome painting. Apart from being important in medicine and public health, radiation-produced aberrations act as colorful molecular clues to damage-processing mechanisms and, because juxtaposition of different parts of the genome is involved, to interphase nuclear organization. Recent studies using chromosome painting have helped to identify DNA double-strand-break repair and misrepair pathways, to determine the extent of chromosome territories and motions, and to characterize different aberration patterns left behind by different kinds of radiation.

Higher-order structure of mammalian chromatin deduced from viscoelastometry data

The results of viscoelastometry (VE) for mammalian DNA have been puzzling because they have two orders of magnitude smaller measured viscoelastic relaxation times for mammalian chromosomes than that expected for DNA linear coils of chromosomal size. In an attempt to resolve this discrepancy, we have applied a recent model of G1 chromosome structure (J.Y. Ostashevsky, Mol Biol. Cell 9, 3031-3040, 1998) in which the 30 nm chromatin fiber of each chromosome forms a string of loop clusters (micelles). This model has two parameters: the number of loops per micelle (f) and the average loop size (Mf), which can be estimated independently from VE data. Using our VE data for plateau phase V79 Chinese hamster cells (unirradiated and X-irradiated with doses up to 40 Gy) we show that f approximately 13 , which is close to other estimates made using the model (f ranges from 10-20), and Mf approximately 2 Mbp, which is similar to estimates made from our nucleoid data (1.3 Mbp) and to estimates made in the literature using a variety of techniques (1-3 Mbp).