The detailed 3D multi-loop aggregate/rosette chromatin architecture and functional dynamic organization of the human and mouse genomes.

BACKGROUND: The dynamic three-dimensional chromatin architecture of genomes and its co-evolutionary connection to its function-the storage, expression, and replication of genetic information-is still one of the central issues in biology. Here, we describe the much debated 3D architecture of the human and mouse genomes from the nucleosomal to the megabase pair level by a novel approach combining selective high-throughput high-resolution chromosomal interaction capture (T2C), polymer simulations, and scaling analysis of the 3D architecture and the DNA sequence.
RESULTS: The genome is compacted into a chromatin quasi-fibre with ~5 ± 1 nucleosomes/11 nm, folded into stable ~30-100 kbp loops forming stable loop aggregates/rosettes connected by similar sized linkers. Minor but significant variations in the architecture are seen between cell types and functional states. The architecture and the DNA sequence show very similar fine-structured multi-scaling behaviour confirming their co-evolution and the above.
CONCLUSIONS: This architecture, its dynamics, and accessibility, balance stability and flexibility ensuring genome integrity and variation enabling gene expression/regulation by self-organization of (in)active units already in proximity. Our results agree with the heuristics of the field and allow "architectural sequencing" at a genome mechanics level to understand the inseparable systems genomic properties.

Background

The structure and function of genomes obviously co-evolved as an inseparable system allowing the physical storage, replication, and expression of genetic information [1-4]. However, the dynamic three-dimensional higher-order architecture of genomes, their spatial and temporal modifications and/or relation to functional multi-dimensional interaction and regulatory networks have yet to be determined in detail (e.g. [4-11]). The DNA double helix and the nucleosome [12-14] have been determined in general structurally at the very highest level of detail including genome sequences and histone modifications. Additionally, it became apparent that genome organization and function indeed form a systems genomic entity ([4, 6, 9, 10, 15–17]; see also references within all these) responsible for gene expression (e.g. [18, 19]) and form the basis for individual differences and disease.

However, the immense size and structural complexity of genomes spanning many orders of magnitude impose huge experimental challenges and hence the higher-order architecture is still widely discussed. How nucleosomes are positioned, spaced, remodelled, and whether and how nucleosome chains fold into fibres at physiological salt concentrations have been matters of continuing debate (e.g. [20]): Finch and Klug [21] proposed a relatively regular solenoid and in vivo neutron scattering experiments revealed a compacted fibre with a diameter of 30 ± 5 nm as a dominant nuclear feature [22-25]. In contrast other and especially more recent suggestions range from basically no compaction at all (rev. [26-28]), to highly polymorphic compacted [29, 30] nucleosome position [31] and function-dependent structures [32, 33]. The latter are essential to explain nucleosome concentration distributions [34-37], or chromatin dynamics [38] and functional properties such as the nuclear diffusion of macromolecules [5, 39]. Notably, the fine-structured multi-scaling long-range correlation behaviour of the DNA sequence also predicts a compacted chromatin fibre [5, 16, 40].

The higher-order chromatin architecture has been a matter of even greater debate: Pioneering light microscopy studies by Rabl (1885, [41]) and Boveri (1909, [42]) suggested a hierarchical self-similar, territory like organization. Electron microscopy suggested a more random interphase organization as in the models of Comings (1968, [43, 44]) and Vogel and Schroeder (1974, [45]). In the radial loop scaffold model of Paulson and Laemmli (1980, [46]), ~60 kbp-sized chromatin loops attached to a nuclear matrix/scaffold should explain the condensation degree of metaphase chromosomes. According to Pienta and Coffey (1977, [47]), these loops persisted in interphase and formed stacked rosettes in metaphase. Micro-irradiation studies by Cremer and Cremer (1974, [48, 49]) and fluorescence in situ hybridization (FISH) (1988, [4, 50]) and studies thereafter finally confirmed a territorial organization of chromosomes, their arms, and stable subchromosomal domains during interphase, including their structural persistence during metaphase (de-)condensation (see [6, 17, 51]). The assumption since then has been that the ~850 G, Q, R, and C ideogram bands (Additional file 1: Refs. [S1, S2]) split into ~2500 subchromosomal interphase domains. Chromatin rosettes explaining the (sub)territorial folding were visualized by electron microscopy (1989, [52-54]) but remained unappreciated, whereas Belmont and Bruce proposed the EM-based helical hierarchy chromonema fibre (CF) model (1994, [55]). Spatial distance measurements between small FISH-labelled genetic regions led to the Random-Walk/Giant-Loop (RW/GL) model with the first analytical looped polymer description (1995, [56-58]). Here, 1 to 5 Mbp loops are attached to a non-protein backbone, following the line of Pienta and Coffey [47]. Later, a combination of distance measurements by more structure preserving FISH, high-resolution microscopy, and massive parallel polymer simulations of chromosomes and entire cell nuclei, was only compatible with the rosette-like Multi-Loop-Subcompartment (MLS) model. In this model 60 to 120 kbp loops form rosettes connected by a similar sized linker [3, 5, 7, 8, 15, 16, 59]. The MLS model is also in agreement with studies of transcription (e.g. [52, 60]) and replication ([52], and thereafter [61]). In vivo FCS measurements of nucleosome concentration distributions and the dynamic and functional properties such as the architectural stability and dynamics of chromosomes [5, 31, 36, 62] or the diffusion of macromolecules [5, 36, 63] are essentially also in agreement with a small loop aggregate/rosette like chromatin folding [5, 35–37, 59, 64]. Fine-structured multi-scaling long-range correlations of the DNA sequence again predict this [5, 16, 40].

However, to further investigate various aspects and to distinguish better between the different architecture proposals crosslinking techniques (used since the last century) were developed into a family of interaction capture techniques (Additional file 2: Table S1) such as 3C [65, 66], 3C-qPCR [67], 4C [68], 3C-seq/4C-seq [69], 5C [70], and Hi-C [71]. They once more confirmed the existence of looping and subchromosomal domains [72], now referred to as topologically associating domains (TADs) with a higher localization accuracy when compared to FISH. These led to a number of suggestions, such as the fractal globule model [71], the loop array architecture in mitotic chromosomes [73], and the highly dynamic loop formation based on single cell ([74]; compatible with a switch and binder model [75]), or cell population experiments [76]. However, these suggestions are based on experimental (raw) data that are open to other interpretations (this publication [5, 11, 37, 62, 64], Imam et al., in prep.) and are in contrast to previous observations (see above). Nevertheless, whatever the suggested architectural model, these methods clearly showed, that physical interactions between functional elements proposed earlier ([77-79]; see review [19]), are at the heart of genome function by regulating gene transcription. These often take place over huge genomic separations by direct contact via a preformed architecture and its modification [7, 8] or the formation of complexes such as in transcription factories [19, 80–82]. Additionally, more structural factors such as CTCF and/or cohesin play a role here ([83] and references therein), which seems obvious also from co-evolutionary considerations.

Here we use T2C, a novel selective high-throughput high-resolution chromosomal interaction capture developed by us [84, 85], which detects all probable physical genomic interactions (selective everything with everything) for a specific genomic region. Thus, it provides the means for efficient and cost effective “architectural genome sequencing” and allows to approach the major open questions discussed above with high quality: (i) Whether a chromatin fibre exists and how it is compacted, (ii) how it is folded, (iii) whether there is a general scaling behaviour of this architecture in agreement with the fine-structured multi-scaling long-range correlations of the DNA sequence organization, (iv) whether this satisfies also the functional requirements with respect to the genomic life-cycle as well as dynamic in vivo properties, and (v) whether all this is consistent with earlier experiments from a few to the megabase pair level. First we briefly describe the T2C design used here to investigate the human chromosome 11p 15.5–15.4 IGF/H19 locus, the mouse chromosome 7qE3–F1 β-globin region, as well as 15 regions under different differentiation and functional aspects basically from the base pair to the entire chromosome level. Next we show that T2C reaches the fundamental resolution limits where “genomic” statistical mechanics and uncertainty principles apply which is of fundamental importance for architectural T2C result interpretation. Thereafter, we show the high interaction frequency range, the reproducible detection of rare interaction events, and the high signal-to-noise ratio >105–106—all at the statistical limit. Next we further analyse these loci in terms of the 3D architecture which suggests that a chromatin quasi-fibre with ~5 ± 1 nucleosomes/11 nm forms stable ~30–100 kbp loops clustered into stable aggregate/rosette like subchromosomal domains connected by a similar sized linker, with only minor but significant variations in the architecture in terms of cell types/functional states. In depth combination with super-computer polymer simulations as well as scaling analysis of the 3D architecture and the DNA sequence itself (where this architecture is represented by sequence specific “footprints”) results in the same conclusion and confirms the tight co-evolutionary entanglement between genome architecture and sequence. This is in excellent agreement with recent in vivo FCS measurements of the dynamics of the chromatin quasi-fibre and a developed analytical polymer model [11]. Consequently, T2C, polymer simulations, DNA sequence organization, in vivo dynamic FCS measurements, and an analytical model are all in agreement. Since this is also consistent with the heuristics of the field, we finally conclude this architecture, its dynamics, and accessibility balance stability and flexibility ensuring genome integrity and variation enabling gene expression/regulation by self-organization of (in)active units already in proximity.

Results

T2C a novel selective high-resolution high-throughput chromosome interaction capture

T2C is a selective high-resolution high-throughput chromosome interaction capture approach [84, 85] which we developed to design interaction capture studies with respect to their purpose—here efficient, high resolution/quality, and cost effective “architectural genome sequencing”. Briefly, T2C in this setup involves (Fig. 1a, details in Additional file 1: Supplemental Methods): (i) Starting with ~107 cultured/prepared cells, (ii) the cells are formaldehyde-fixed (i.e. all kinds of combinations of nucleic and protein crosslinks are formed), (iii) permeabilized to allow intra-nuclear cutting with a 1st restriction enzyme, (iv) extensively diluted to promote mono-molecular re-ligation reactions, before (v) de-crosslinking, purification, and final shortening of the DNA chimeric fragments to sizes <500 bp by a 2nd high-frequency restricting enzyme or by sonication. Then, (vi) a region-specific DNA library of interacting fragments is produced using hybridization to region specific arrays of DNA oligonucleotides, representing the end of each restriction fragment produced by the 1st restriction enzyme. With ~109 molecules of each hybridization-optimized oligonucleotide the capture is always in the linear range well below saturation relative to e.g. ~107 input cells. (vii) After elution, the hybridized fragments are paired-end sequenced, and (viii) each sequence pair is trimmed up to the 1st restriction enzyme and mapped to the whole reference genome. Only uniquely mapped sequences are used (eventually only between the two restriction enzymes). No other correction or cleaning resulting in information loss is performed due to the very nature of this method (see below).

Fig. 1

T2C description, interaction mapping, and direct determination of the chromatin quasi-fibre and the aggregated loop/rosette 3D architecture of the human and mouse genomes: a Cell nuclei in a population of cells (transmission light and fluorescence microscopy, [89]) have an underlying chromatin architecture (simulated cell nucleus containing 1.2 million polymer segments; resolution 5.2 kbp, i.e. ~50 nucleosomes; Multi-Loop-Subcompartment (MLS) rosette model with 126 kbp loops and linkers; [5]). After crosslinking the DNA is restricted within the nucleus by a 1st restriction enzyme, before the crosslinked fragments are extracted and diluted such that intra-fragment re-ligation is favoured. After de-crosslinking, the re-ligated material is shortened by a 2nd restriction enzyme or sonication and purified by a capture array with oligos designed next to the 1st restriction enzyme, before paired-end-sequencing over the ligation position. After alignment to the reference genome, this results in interactions frequency matrices (b–d) and scaling curves (Fig. 2). b, c Interaction matrices (logarithmic and colour-coded scale; left and right) of the human IGF/H19 11p 15.5-15.4 region (b) in HB2, HEK293T TEV (intact cohesin) and HEK293T HRV (cleaved cohesin) as well as the mouse β-globin 7qE3-F1 region (c) for fetal brain (inactive β-globin) and liver cells (active β-globin) show the formation of subchromosomal domains separated by a linker (borders: pink lines, right; D1s, D1e: start and end of domains), which consist of loops (red lines; 8L: number of loops), representing due to the grid-like pattern loop aggregates/rosettes. A grid-like pattern is also visible in the interactions between the domains and corresponds to the interactions of loops and loop bases of interacting domains. Near the diagonal the aggregation into a chromatin quasi-fibre and loop internal structures are visible (zooming in and out the images can make this clearer). Between different cell types and functional states only some local differences are visible resulting in a consensus architecture and allowing simulation of the 3D architecture (middle; resolution <~1 kbp). Note that the simulation is driven by the dominant consensus architecture. d The interaction matrix of a 380 kbp subchromosomal domain in the mouse 12qF1–F2 region at high resolution clearly shows the regular rosette-like picture with a detailed structure of the loop base with in- and outgoing loop fibre stretches as seen in simulations (e, f). e Simulated Multi-Loop-Subcompartment (MLS) model with an averaged spatial distance map for exact spatial distances 〈R 〉 (left) and on the diagonal normalized interaction maps for interaction radii 〈d 〉 of 50 nm, 70 nm, and 150 nm (right), for an MLS model with 126 kbp loops and linkers [16 Mbp upper and 1.2 Mbp zoom-in (z) lower row), showing clearly the formation of domains connected by a linker, their interaction, and the underlying loop aggregates/rosette architecture, with (anti-)parallel fibre stretches at the loop base. The dependence on the interaction radii corresponding to different crosslink probabilities is also clearly visible. f Sketch of the different structures visible on different scales in the experimental and simulated interaction matrices (spatial distance matrix: left; simulated interaction matrix: upper) (from e): On the smallest scale, near the diagonal the compaction of nucleosomes into the quasi-fibre (yellow line) and the fibre regime (dark blue line) can be found. On the largest scale the domains are clearly bordered (pink lines) and connected by a linker. On medium scales the loop aggregate/rosette like structure is characterized by the loop bases (red circles: within domains, blue circles: between domains) as well as the loop interactions (green triangles). The fine structure of the loops representing the (anti-)parallel loop stretches at the base (red crosses) and within loops (green stretches near diagonal)

Fig. 2

Scaling analysis of experiments, simulations, and the DNA sequence showing the formation of a chromatin quasi-fibre and the loop aggregate/rosette genome architecture: a The fine-structured multi-scaling resulting from the T2C interaction frequency as a function of the genomic separation for the human IGF/H19 11p 15.5–15.4 region and the mouse β-globin locus 7qE3–F1 (3 bp average (1–200 bp) and thereafter a grouping with a 1 % resolution per order of magnitude which for clarity is smoothed by a running window average for >103 bp; see also Additional file 27: Figure S14; the values <10 bp are due to the algorithm used and for transparency not discarded since they nevertheless show the extrapolation from values >10 bp), shows: (i) The structure of the nucleosome, (ii) the formation of a plateau from 195 to ~1000 bp, indicating the formation of a chromatin quasi-fibre with a density of 5 ± 1 nucleosomes per 11 nm, (iii) the chromatin quasi-fibre regime, (iv) a mixed chromatin fibre/loop regime with a slightly higher interaction decrease, (v) the plateau indicating the loop aggregate/rosette state, and (vi) in principle the linker regime (not visible in a but in d). c, d The fine-structured multi-scaling is even clearer for the average of 15 loci covering in total ~99 Mbp in mouse MEL cells with subnucleosomal fragment resolution: After an initial increase a plateau is reached from ~50 to ~100 bp, followed by a sharp peak from ~110 to 195 bp (width at plateau level ~85 bp), followed by a second ~10 % decreasing plateau up to 1.0–1.2 kbp, which after a sharp decent until ~104 bp transits to the known multi-scaling behaviour (d, compare with a). With this resolution the fine structure visible (Additional file 28: Figure S15), can be associated with the binding of the DNA double helix to the nucleosome, since up to ~195 bp many of the small peaks (the most prominent at 145 bp) can be associated with the fine structure in the fine-structured multi-scaling behaviour of DNA sequence correlations (e; Additional file 28: Figure S15, Additional file 29: Figure S16). Whereas the structure of the nucleosome vanishes using “secured” interactions (c, pink and light blue), above 195 bp the plateau and multi-scaling behaviour remain. Again the values <10 bp are due to the algorithm used and for transparency not discarded since they nevertheless show the extrapolation from values >10 bp. b The interaction scaling of a simulated Multi-Loop-Subcompartment model with 126 kbp loops and linkers as well as a Random-Walk/Giant-Loop model with 1 Mbp loops and 126 kbp linkers consistently shows for different interaction radii a multi-scaling behaviour. The MLS model shows the characteristic rosette plateau, followed by the random scaling regime of the linker conducting a random-walk. The peaked fine structure originates from the loops forming the rosettes. In contrast, the RWGL model is characterized by random-walk regime and only one major fine structure attributable to the single loops. At greater scales the limit of the entire chromosome is seen in the cut-off. The MLS model agrees in detail with experiments (a, c–d) and the DNA sequence organization (e). e The fine-structured multi-scaling long-range correlation behaviour of each of two human and mouse strains shows clearly again the architectural features: a general increase until a plateaued maximum (including the 145 bp peak), a first plateau area until ~1200 bp, transition to a sharper decrease at ~3.6 kbp (the sweet point used in the calculation of the persistence length) until a minimum ~10–20 kbp and a second statistically significant maximum at ~100 kbp, followed by a random regime and a final cut-off. The first maximum and plateau are characteristic for the nucleosome and formation of the quasi-fibre (c; Additional file 28: Figure S15, Additional file 29: Figure S16) which then transits to chromatin loops and their clustering into loop aggregates/rosettes which are connected by a random-walk behaving linker. Thus, due to the higher statistics here, the architectural features and their tight representation within the DNA sequence organization are even clearer

Thus, T2C has clearly several advantages with respect to studying genome architecture in depth: (i) It provides a choice between costs, resolution, interaction frequency range, size of the captured region, and multiplexing of samples in a study-specific manner. E.g. a ~500 bp average fragment resolution, in a 2 Mbp region, with six orders of magnitude interaction frequency range, and multiplexing of ten samples can be easily achieved sequencing 5 lanes. (ii) The design of the oligonucleotide position ensures optimized data cleanness and high signal-to-noise ratio, allowing maximum interaction information with a minimum amount of sequencing (Fig. 1b–d; Additional file 2: Table S1, Additional file 3: Table S2, Additional file 4: Table S3; Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3). (iii) Additionally, the process has been optimized for structure, and thus architectural preservation [5, 59], minimal DNA loss during the procedure, and no use of signal amplification until sequencing when a limited number of PCR cycles could be performed (Additional file 1: Supplemental Methods, Additional file 2: Table S1).

To investigate the chromatin fibre conformation and the 3D genome architecture at the required resolution we chose the human chromosome 11p 15.5–15.4 IGF/H19 locus and the mouse chromosome 7qE3–F1 β-globin region (Additional file 3: Table S2). Both ~2.1 Mbp regions have been well studied by FISH and other capture techniques. Bgl II or Hind III as 1st and Nla III as 2nd restriction enzyme yields average fragment sizes of 3–6 kbp with many fragments, however, near the principle limit of the technique of a few base pairs (Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3, Additional file 8: Figure S4, Additional file 9: Figure S5, Additional file 10: Figure S6; average nucleosomal repeat length ~195 bp; 3–6 kbp correspond to ~15–30 nucleosomes). To determine the general chromatin fibre conformation at still higher resolution and to gain further insights into small scale architectural features, we also investigated 15 other regions (Additional file 3: Table S2) covering in total 99.5 Mbp distributed over 10 different mouse chromosomes using Apo I as 1st restriction and sonication instead of a 2nd restriction leading to average fragment length of 549 bp (with many much smaller). This is even more at the technical limit and at nucleosomal/molecular resolution (Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3, Additional file 8: Figure S4). To investigate architectural and functional differences between species, cell lines, functional, and architectural differences, the human breast endothelial 1–7HB2 cell line (HB2), the HEK293T TEV/HRV RAD21-eGFP cell lines allowing cleavage of cohesin [83], and mouse fetal brain and fetal liver [β-globin (in)active] cells were used. To investigate the chromatin fibre conformation at high resolution undifferentiated murine erythroleukemia (MEL) cells were used.

T2C reaches the fundamental resolution limits where “genomic” statistical mechanics and uncertainty principles apply

Since for “architectural sequencing” resolution is key, designing T2C using short fragment lengths down to even a few base pairs applying frequently cleaving restriction enzymes (Additional file 3: Table S2; Fig. 1b–d; Additional file 4: Table S3, Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3, Additional file 8: Figure S4) not only molecular resolution (mind e.g. also the persistence length of free DNA ~50 nm, i.e. ~140 bp; typical protein/nucleosome binding regions are ~100–500 bp) is reached and thus the fundamental limits of crosslinking techniques, but also the mechanism of observation is now, however, on the same scale as the observables (in analogy to classic and quantum mechanics). Actually due to the stochastics following the bias of the system behaviour, the observables, the observation, and thus the measured values are constrained by what we call “genomic” statistical mechanics with corresponding uncertainty principles. This originates from the individual complexity of each highly resolved interaction with a unique but coupled individual probabilistic fragment setting in each cell at a given time, e.g.: (i) The cell population has a distribution of cell states and functional differences, (ii) each fragment has a more or less dynamic individual DNA, RNA, protein, restriction association and length, and hence (iii) a different crosslinking, restriction, re-ligation, oligonucleotide capture, sequencing, and mapping efficiency. The actual conditions and components can be determined only partially with high accuracy while with low accuracy otherwise and are eventually even entirely destroyed by the measurement. In essence, the entire T2C measurement process is highly quantitative but the local origin of this (including biases e.g. due to the oligonucleotide sequence or position), and thus its comparability, remains elusive due to its local individuality and our present incapability to determine all parameters linked in a complex network in detail and simultaneously as well as the attached biased system noise. Thus, the central limit theorem applies with an overlap of system inherent and real noise stochastics, and hence in the end only probabilistic analyses and statements can be drawn as hitherto is well known from classic mechanics, and more so from quantum (mesoscopic) systems. Consequently, population based or multiple single-cell experiments have to be interpreted and understood in a “genome” statistical mechanics manner with uncertainty principles due to the inseparability of factors/parameters also seen there. Thus, in practical terms, valid results are obtained when the statistical limit is reached, i.e. when scaling up the experiment does not narrow down the distribution any further and does not lead to fundamental (overall) changes anymore in observables. Due to the complexity involved, this has the immediate consequence that there are currently no means for adequate corrections. Even if certain biases might be known, the effect of a correction in terms of the many T2C steps remains illusive. This is the case for any interaction capture technique, although the effects of the individual complexity are partly averaged out by the lower resolutions mostly used in previous studies. This is no longer the case at the fundamental resolution limits. Nevertheless, if the statistical limit is reached and if the quality parameters like resolution, frequency range, and signal-to-noise ratio are sound, conclusions could be drawn as in the many cases of classic mechanics, and more so of quantum (mesoscopic) systems within the discussed boundaries.

T2C reproducibly detects rare genomic interactions at the statistical limit with unprecedented signal-to-noise ratio

For the above mentioned experimental systems, with ~107 input cells, the corresponding samples (e.g. two different states) were multiplexed on the capture array to guarantee identical conditions (Additional file 4: Table S3). Only sequences unique in the entire genome with a reasonably small mismatch rate (accounting for sequencing differences to and errors in the reference genome; see Additional file 1: Supplemental Methods) and cleaned for sequences only mapping between the 1st and 2nd restriction sites were analysed. Approximately ~60–380 million paired-end sequencing reads were produced of which ~10–65 % could be mapped uniquely (Additional file 4: Table S3). The regional interactions (after normalization for the total counts within the region) sorted and plotted in an upright squared interaction matrix/map with a logarithmic and rainbow colour-coded frequency range [86], including the diagonal (non- or self-ligation), show directly the quality of the experiments and the unprecedented frequency range spanning 5–6 orders of magnitude (Fig. 1b–d; Additional file 5: Figure S1). Thus, also rare interactions with a frequency of 10−4–10−6 can be found and visualized under these conditions of region size, fragment resolution, and sequencing depth. We estimate an overall/cumulative (i.e. from cells to interaction matrix) efficiency of T2C of ~0.1–1.0 % from the ratio of cumulated counts per fragment to the number of input cells of ~107. The interaction patterns show, that the level of the stable statistical mechanical limit is reached, since data from different sequencing lanes or experiments (whether multiplexed or not) only show visually minor statistical deviations (Fig. 1b–c; Additional file 5: Figure S1). Quantitatively, the statistical measures we used (e.g. frequency distributions) also hardly show a change upon e.g. a twofold increase of input cells or sequencing. At the statistical level reached, such a change leads only to an increase in novel interactions <0.1 %, mostly in the lowest interaction frequency regime. In contrast, a tenfold sequencing decrease results in a massive interaction loss of >25 %. Most importantly, all the interaction matrices of different experiments are reproducibly mostly empty. Only ~5–15 and 1.0–1.5 % of the possible interactions show a signal for the IGF/H19 and for the β-globin, respectively (Additional file 4: Table S3). Thus, there is no obvious uniform noise/background, despite the high number of sequence reads and the high number of diagonal elements showing entries of non- or self-ligated fragments. The “emptiness” is also not arbitrary, but structured, and appears virtually the same in replicates, different cell types or functional states (Fig. 1b–d; Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3). Moreover, interactions neither suddenly appear statistically nor cluster statistically somewhere near other or more prominent interactions. The signal-to-noise ratio is >105–106, even though noise could in principle appear at any step of the procedure, and even when assuming a highly unlikely biased distortion of a normal distributed noise signal towards e.g. interactions. A shot-noise (e.g. Poisson-like) analysis confirms this, in agreement with the change being <0.1 % during experimental scale-up (see above). Consequently, these values show that an analysis of these data with respect to genome architecture can be conducted within the limits of the above mentioned genome mechanical statistics constraints.

The chromatin quasi-fibre forms stable loops clustered into aggregate/rosette like subchromosomal domains connected by a linker

The interaction patterns (Fig. 1b–d; Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3) can also be recognized clearly on all scales (within and between domains), including their re-emergence as attenuated repetition on other scales since genomes are scale-bridging systems [5, 15]. This behaviour shows once more the sensitivity of T2C allowing 3D architecture investigations despite the numerous and nonlinear parameters involved, since the probability that such repetitive patterns arise stochastically and even reproducibly is negligibly small relative to the number of those potentially formed combinatorially by hundreds of fragments. Additionally, T2C reveals agreement with other interaction techniques, e.g. 4C-seq, but with much cleaner and sharper interaction patterns for the same fragment setting (Additional file 6: Figure S2, Additional file 7: Figure S3). The interaction patterns are next interpreted on the scales associated with the chromatin fibre, subchromosomal domains, and within the subchromosomal domains.

On the smallest genomic scale (Fig. 1b, c; Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3), a dense and high interaction frequency pattern is observed in the region from 3 to 10 kbp (i.e. <~5–15, and ~50 nucleosomes, respectively; for quantification, see scaling analysis below) along each point of the diagonal. This pattern varies independently of the local fragment size with distinct interactions and non-interacting “gaps” in-between. This is different from a homogenous random-walk or Rayleigh-like interaction “smear” decreasing uniformly and monotonously with increasing genomic separation. Additionally, the extension of the band of interactions is also smaller than that a random-walk of nucleosomes would predict. A structurally uniform fibre like that seen in the (solenoid-like) helical chromatin fibre model [21] would result in a highly regular and defined pattern, which is also not observed. Thus, the pattern suggests, that there are defined stable interactions at the scale of DNA/nucleosomes forming an irregular yet locally defined and compacted structure. Hence, nucleosomes must form an irregular fibre, which we refer to as a “quasi-fibre” due to its inherent variation with average properties (e.g. an average linear mass density). While reading along the diagonal local interactions, compaction of nucleosomes, as well as other local properties of the chromatin quasi-fibre can be determined. In contrast to a basically uncompacted sea of nucleosome like organization [26-28], the formation of such a quasi-fibre is in agreement with previous experimental results [21, 22], as well as simulations [32, 33]. This is also consistent with a variety of compacted structures described throughout the literature (see e.g. [29, 30, 32, 33]), the absolute nucleosome concentration distributions [35, 36], the dynamic and functional properties such as the architectural stability and movement of chromosomes [3, 5, 39, 62, 64], chromatin dynamics [38], as well as the diffusion of molecules inside nuclei (e.g. [5, 39, 64]). Moreover, recent genome-wide in vivo FCS measurements of the chromatin quasi-fibre dynamics [11] also suggest such a chromatin quasi-fibre with variable, function-dependent properties. (See below for a quantification of T2C for the quasi-fibre properties.)

On the largest scale, stable square-like domains (TADs; [72]) are visible in the range of several hundred kbp to ~1–1.5 Mbp with clear borders and interactions with other domains (Fig. 1b–d; Additional file 5: Figure S1). They are more prominent e.g. in the IGF/H19 region, which shows two complete and two incomplete domains (Fig. 1b), when compared to the β-globin region with its single full domain and only two partially visible domains at the borders of the captured region (Fig. 1c). The domains feature several general properties: Firstly, the interaction frequency within domains has in general a higher average uniform height compared to interactions between domains, with a sharp drop at the edge of domains. The exact position of the border can be deducted from the folding within the domain and can therefore be respectively assigned exactly (see below). Thus, there is a cascade-like (average) behaviour of interactions with increasing genomic separation as predicted before [3, 5, 15, 59], in contrast to the often expected general monotonous interaction decrease with growing genomic separation. Moreover, the interactions to other domains are clearly defined also in detail. Secondly, between the borders of the domains there is a clear transition or linker region, which again can be determined with respect to the folding of the chromatin quasi-fibre within the domain (see below). In and around these linker regions especially strong and complicated interactions are present depending on the specific domains. Such interactions originate from a combination of the chromatin quasi-fibre possibly not being shielded as is the case within the domains as well as the folding of the chromatin quasi-fibre itself (see below). A closer inspection of the interactions in the vicinity of the linker actually allows several interpretations in terms of the underlying domain architecture folding giving rise to these patterns. We favour that the genetic regions of the domains next to the linker interact more frequently compared to other domain parts due to the breaking of spatial isotropy. Two other possibilities that this is due to allelic differences (i.e. the patterns arise from two different allelic domain architectures), or that the linker being a very small linker domain consisting e.g. of a single or a few loops, are much less likely (see below). A closer inspection of interactions near the linker in combination with the dynamic behaviour of subchromosomal domains (see dynamics below and Additional file 11: Movie S1, Additional file 12: Movie S2, Additional file 13: Movie S3, Additional file 14: Movie S4) points also to a directionality along the “back-bone” (the combination of several linkers of several subchromosomal domains), which is breaking the spatial isotropy of single unconnected subchromosomal domains. Consequently, these results confirm the existence of structurally stable subchromosomal domains which by (de-)condensation or (de-)looping explain the (de-)condensation of chromosomes through the cell cycle [4, 5, 17, 47, 51–54, 59–62]. The interaction pattern between subchromosomal domains and at their borders points already to a loop aggregate/rosette like architecture, since neither a free random-walk, an encaged random-walk, a random or a fractal globule like folding, nor a Random-Walk/Giant-Loop architecture would lead to sharp and defined borders. Instead, they would lead to gradual/soft transitions instead. Constantly changing and thus very dynamic architectures with an average topology of these models or even that of a highly dynamic loop aggregate/rosette like architecture would also not result in the observed patterns. This is in agreement with previous predictions on subchromosomal domains [4, 5, 7, 8, 16, 17, 51–54, 59, 62]. Moreover, these patterns are also in agreement with in vivo FCS measurements of the nucleosome concentration distribution [35, 36], the dynamic and functional properties such as the architectural stability and movement of chromosomes [5, 39, 62], chromatin dynamics [39], as well as the diffusion of molecules inside nuclei (e.g. [5, 39, 64]). Moreover, recent genome-wide in vivo FCS measurements of the dynamics of the chromatin quasi-fibre come to the same conclusion with characteristic functional differences [11]. The intrinsic chromatin fibre dynamics with movements on the millisecond scale (Additional file 11: Movie S1, Additional file 12: Movie S2, Additional file 13: Movie S3, Additional file 14: Movie S4) also points to the fact that the subchromosomal domains must have a stable architecture since otherwise they would dissolve immediately (see simulations below [11]). The break of the spatial isotropy of sequentially adjacent subchromosomal domains visible in the linker region is also linked to this stability.

At intermediate scales within the subchromosomal domains, the interaction pattern is characterized by clearly distinct gaps and a crossed linear (grid-like) arrangement of interactions (Fig. 1b–d; Additional file 5: Figure S1, Additional file 6: Figure S2, Additional file 7: Figure S3). Interestingly, the linear pattern continues outside the subchromosomal domain and “crosses” with the linear pattern originating from the sequentially subsequent domain. Furthermore, the pattern outside is much simpler/clearer since it lacks the extra interactions originating inside the domain from e.g. the chromatin quasi-fibre, or its higher-order structure like e.g. intra-loop or loop-loop interactions (for illustration see Fig. 1e, f). This grid of interactions can also be quantified by projecting the interactions vertically and horizontally over the entire matrix, resulting in a peak-like pattern along the chromosome sequence (Additional file 15: Figure S7; see also [11], for details). These peaks coincide with the grid-like pattern (Additional file 15: Figure S7). Projections within or outside the domains lead in essence to the same patterns with nevertheless subtle characteristic differences (see also [11]). Since interactions on scales of tens of kilo base pairs can only be due to chromatin looping, the conclusion must be that several consecutive loops have a coinciding loop base and hence form a loop aggregate/rosette like architecture. Hence, the interactions between subchromosomal domains result from the interactions of (i) loops from domains next to each other, (ii) loop bases of subsequent loop aggregates/rosettes when there is a relatively low density of loops, and (iii) mitotic chromosomes present in the cell population. The borders of the domains seen on the medium scale (see above) are determined by the loops, and thus also the linker between subchromosomal domains is given by the end and start of loops of two subsequent subchromosomal domains. The border behaviour of domains near the linker was already discussed (see above). Determination of the loop positions and sizes (Additional file 16: Table S4, Additional file 17: Table S5) visually as well as by projections (Additional file 15: Figure S7; for further details see also [11]) with an error on the level of corresponding local fragment resolution and with respect to the loop base structure of ~3 kbp, reveals a consensus architecture independent of cell type or functional state with loop sizes of 48.6 ± 14.5 ± 2.4 kbp (average, StDev, StErr) and linker sizes of 46.7 ± 15.1 ± 8.7 kbp in the mouse β-globin region. In the human IGF/H19 locus the values are 57.8 ± 16.2 ± 2.9 kbp and 69.2 ± 19.2 ± 13.6, respectively. The subchromosomal domain sizes can now be calculated in detail for those subchromosomal domains which are completely covered by the T2C array: excluding the linker, the size is 1343.6 ± 3 kbp for the single complete subchromosomal domain in the β-globin region, as well as 728.5 ± 3 and 403.4 ± 3 kbp for the two complete subchromosomal domains of the IGF/H19 locus.

Although the Apo I T2C experiment was designed to elucidate the details of the chromatin fibre conformation only, one finds e.g. a 380 kbp subchromosomal domain region showing this pattern in greater detail (Fig. 1d). In addition to showing the same stable loop aggregate/rosette like architecture with 37.0 ± 9.9 ± 3.3 kbp loops (Additional file 18: Table S6), and a subchromosomal domain size of 333.3 ± 3 kbp, part of the detailed loop base fine structure with in- and outgoing loop fibres spanning a region of ~6 kbp can be seen (see simulations below; Fig. 1f; Additional file 19: Figure S8, Additional file 20: Figure S9).

The observation that the linear grid-like pattern outside of the domains is also not a homogeneous smear, shows that the loops and their arrangements into loop aggregates/rosettes are stable and not very variable. Once more the gaps between interactions as well as the grid-like pattern inside and outside the domains show that a free random-walk, an encaged random-walk, a fractal globule like folding, nor a Random-Walk/Giant-Loop architecture would lead to the patterns we find. Constantly changing and thus very dynamic architectures with an average topology of these or even that of a highly dynamic loop aggregate/rosette like architecture would also not result in these patterns. Finally, a non-compacted chromatin quasi-fibre, which a sea of nucleosome like organization predicts [26-28], would result in hugely homogeneous and very dynamic interaction possibilities, and thus patterns we do not find. Of course, the relatively simple notion of a quasi-fibre forming loop aggregates/rosettes connected by a linker becomes more complex due to the variation along the quasi-fibre, the variation of loop size and structure (e.g. super-helical topologies), and their arrangement either at the loop base or core of the loop aggregates/rosettes. Consequently, also on this architecture level the aggregate/rosette architecture also links interphase with metaphase very nicely and shows the architectural persistence during (de-)condensation within the replication process in agreement with experimental data (see [51] and thereafter). Moreover, this agrees with previous predictions on the internal structure of subchromosomal domains [4, 5, 7, 8, 16, 17, 51–54, 59, 61] and again is also in agreement with in vivo FCS measurements of the nucleosome concentration distribution [35, 36] and the dynamic and functional properties such as the architectural stability and movement of chromosomes [5, 39, 62], chromatin dynamics [39], as well as the diffusion of molecules inside nuclei (e.g. [5, 39, 64]). Most importantly, the analysis of recent in vivo FCS measurements [11] shows similar loop sizes and loop numbers per subchromosomal domain. Thus, both T2C and the FCS in vivo measurements are in excellent agreement even though we investigate a number of specific regions with T2C, opposed to averaging over several regions in the FCS in vivo measurements, which suggests that this architecture occurs genome wide. We would like to stress again that the intrinsic chromatin fibre dynamics (on the millisecond scale) point to stable subchromosomal domains since the structure would otherwise dissolve immediately (see also simulations below; Additional file 11: Movie S1, Additional file 12: Movie S2, Additional file 13: Movie S3, Additional file 14: Movie S4; and [11]).

Comparison with the consensus 3D genome architecture shows small differences between species, cell type, or functional state

To investigate how the genome architecture depends on species, cell type, functional or structural differences due to regulation or deliberate system distortion, we investigated the human IGF/H19 11p 15.5–15.4 region in human HB2, HEK293T TEV (intact cohesin), and HEK293T HRV (proteolytically cleaved cohesin) cells [83], and the mouse β-Globin 7qE3-F1 locus in mouse fetal brain (FB; inactive β-globin) and fetal liver (FL; active β-globin) cells: As has been seen before (see introduction for any a 3C-type assay) the subchromosomal domains are clearly very similar under different conditions (Fig. 1b, c; Additional file 5: Figure S1). The denser interaction pattern found in the HB2 cells when compared to the HEK293T cells may be due to differences in the level of crosslinkability. Comparing mouse FB to FL cells only shows subtle differences often belonging to single or a small group of interactions resulting from activation of the β-globin locus (Fig. 1c; Additional file 5: Figure S1, Additional file 7: Figure S3). Cleaving cohesin, which is thought to play a major constitutive role in genome architecture, does not lead to dramatic changes on all scales despite some clear interaction losses and gains. Visual or quantitative determination of the loop positions also shows only minor differences (Additional file 15: Figure S7), which nevertheless might be functionally important. This might suggest that once formed, cohesin may not be required anymore to maintain the overall subchromosomal domain architecture. Thus, the detailed role of cohesin (as well as other factors like CTCF) in interphase chromatin remains unclear and needs to be clarified.

Consequently, these and other experiments from various laboratories as already mentioned show that organisms rely on a consensus architecture (overview in [4, 17]). This architecture has small functional variations on all scales from the chromatin quasi-fibre to the subchromosomal domains within the genomic regions. Between the subchromosomal domains, the architecture obviously varies more than within domains in agreement with the FCS in vivo measurements [11], where differences were found for different genomic regions or functional states such as eu- and hetero chromatin, or during massive changes by (de-)compacting the chromatin quasi-fibre by Trichostatin A or Azide treatment. The dynamics of the chromatin quasi-fibre on the millisecond scale in comparison with the size of the differences stresses again how stable this architecture is (see also simulations below; Additional file 11: Movie S1, Additional file 12: Movie S2, Additional file 13: Movie S3 and Additional file 14: Movie S4; and [11]). Hence, this illustrates the notion of the variation of a theme and points to the evolutionary balance between flexibility and stability of genome architecture in agreement with other findings/predictions [4–10, 15–17, 51–54, 59–61]. The biological implications of this are discussed below.

Simulated polymer models in silico predict and confirm the genome organization in detail found by T2C

To better understand the above results we developed polymer models with preset conditions (i.e. without attempting to fit data; [3, 5, 7, 8, 15, 59, 87, 88])—briefly (see Additional file 21: Supplemental Results; Additional file 22: Table S7): We simulated the Random-Walk/Giant-Loop and the Multi-Loop Subcompartment (Additional file 23: Figure S10) including their dynamics and stability with sufficient information/aspects of free random-walks, random, or fractal globules. The two-dimensional spatial distance and interaction maps (Fig. 1e, f; Additional file 19: Figure S8, Additional file 20: Figure S9) calculated from this not only reflect the underlying models even in subtle details (such as the (anti-)parallel neighbouring of the chromatin quasi-fibre at loop bases; Fig. 1d–f) but also show that only an MLS and thus loop aggregate/rosette like genome architecture could explain all the above observations and thus confirm previous predictions (see introduction; [4, 5, 7–10, 15, 17, 47, 51–54, 59, 61, 87, 88]). The simulations also show large emptiness of interaction matrices and its link to the existence of a dedicated chromatin quasi-fibre as well as the appearance of non-equilibrium effects hinting on the behaviour of domain borders near the linker (see above). The stability of the architecture can also be illustrated by e.g. the decondensation from a mitotic chromosome into interphase (Additional file 11: Movie S1): Any 3D architecture would dissolve within seconds if it would not be stable which agrees with the analytical polymer models developed recently to describe both structure and dynamics of the chromatin quasi-fibre [11]. Moreover, using this simulation approach we also visualized the 3D organization and its dynamics using the experimental interaction matrices as input. Since in vivo chromosomes are adiabatic systems (they never fold from scratch), we used here the consensus loop and domain positions (Additional file 16: Table S4, Additional file 17: Table S5, Additional file 18: Table S6) as input starting conditions, rather than dropping a free linear polymer chain into the interaction landscape expecting it to fold in a defined knot-free 3D architecture. The outcome (Fig. 1b–d, middle) confirms that the chromatin quasi-fibre forms rosette-like subchromosomal domains with a high degree of agreement with the experiments and the analytical model mentioned above [11].

Simulations and experimental T2C show a fine-structured multi-scaling behaviour revealing general aspects and the detailed aggregate/rosette 3D genome organization/architecture

To comprehensively investigate and quantify the general behaviour of interactions as a function of genomic separation in a unified scale-bridging manner, we already used scaling analysis to understand genome organization and showed its capabilities (see Additional file 1: Supplemental Methods; Additional file 24: Figure S11; [5, 16, 59]). Again the scaling of the interaction frequency for the different simulated models (see Additional file 1: Supplemental Methods, Additional file 21: Supplemental Results; Fig. 2b; Additional file 25: Figure S12, Additional file 26: Figure S13) represents all model parameters in detail (which holds for other scaling measures, Additional file 24: Figure S11) and predicts again that chromosomes show clear long-range power-law scaling, with a multi-scaling behaviour and a fine structure on top in excellent agreement with the alternative analytical model [11]. Determination of the experimental scaling behaviour (see Additional file 1: Supplemental Methods, Additional file 21: Supplemental Results) of the IGF/H19 locus, the β-globin region (Fig. 2a; Additional file 27: Figure S14), and that of the average of 15 regions in MEL cells (Fig. 2c, d; Additional file 28: Figure S15), which has a higher (nucleosomal) resolution, for scales >104 bp, all interactions clearly show fine-structured multi-scaling long-range power-law behaviour (Fig. 2a; Additional file 27: Figure S14), the details of which are only in agreement with the multi-loop aggregate/rosette like architecture (Fig. 2b; Additional file 25: Figure S12, Additional file 26: Figure S13) as predicted by us [5, 16, 59]. In agreement with the simulations this represents (i) the general interaction decrease of the chromatin quasi-fibre up to ~3 × 104–105 bp, (ii) the stable loop and aggregated loop/rosette like structure in the subchromosomal domains from ~3 × 104 up to 105–106 bp, (iii) the subchromosomal domain like structure from ~105 to 106 bp, and (iv) the random-walk behaviour of the subchromosomal domain linkers above ~0.8 × 106 bp (i.e. the “backbone” behaviour of the entire chromosome). As before the differences between species, cell type, or functional states are again small, and the behaviour again shows the stability and functional variability of the system. We also found this scaling behaviour for Hi–C experiments of others (e.g. [71, 73, 74, 76]), suggesting the same 3D architecture (Imam et al., in prep.).

High-resolution T2C scaling analysis reveals the detailed nucleosome structure and proves the formation of a chromatin quasi-fibre

Interestingly, we also get a dedicated fine-structured multi-scaling behaviour on scales from the base pair level up to 104 bp [5, 15, 16]. This is especially true for the combined scaling curves of the 15 Apo I restricted regions due to the high resolution of a few base pairs and the high statistical validity (Fig. 2c, d; Additional file 27: Figure S14, Additional file 28: Figure S15). The dedicated fine structure (Additional file 28: Figure S15) suggests clearly that this general multi-scaling behaviour up to ~195 bp (Additional file 28: Figure S15C) is associated with the nucleosome (Additional file 21: Supplemental Results; [14]) and with the polymer behaviour of the nucleosomal chain thereafter—all features we found earlier by DNA sequence pattern analysis (see below; [5, 15, 16]). We also find multiples of the 145.5 bp and the 195 bp nucleosomal repeat length, e.g. at 290 bp as well as at 385 bp the peaks are exactly where di-nucleosomal features are expected (Fig. 2c; Additional file 28: Figure S15B). From a detailed analysis (Additional file 21: Supplemental Results) we conclude that nucleosomes N4–N6 see the first nucleosome N1 with nearly the exact same probability, but the interaction decreases dramatically for N7 and thereafter. Thus, each individual nucleosome has on average 4–6 clearly distinct nearest neighbour nucleosomes, suggesting the formation of a chromatin quasi-fibre with an average (!) density of 5 ± 1 nucleosomes per 11 nm (see Additional file 21: Supplemental Results for the detailed calculation). Moreover, the genome-wide in vivo FCS measurements of the dynamics of the chromatin quasi-fibre [11] show similar average quasi-fibre densities.

Apparent and average persistence length Lp of the chromatin quasi-fibre

To gain insight into the average mechanical properties of the chromatin quasi-fibre, we calculated the average apparent persistence length L p from the interaction scaling behaviour between 103 and 104 bp—briefly (for details Additional file 21: Supplemental Results): At the so called sweet point at ~3.6 kbp (Fig. 2e; see below) where the nucleosome composition transitions to an average fibre for 4–6 nucleosomes per 11 nm, L p ranges from ~80 to 120 nm, respectively. This is in agreement with earlier values (see introduction; [32, 33]), with values derivable from spatial distance measurements between genetic markers [5, 7, 8, 87], and again with values for L p extractable from genome-wide in vivo FCS measurements [11]. Importantly, this average stiffness predicts that the average loop sizes will have to be on the scale seen above to ensure e.g. their stability, strongly supporting the experimental findings.

The DNA sequence organization shows fine-structured multi-scaling long-range correlations tightly entangled with the 3D architecture

Since what is near in physical space should also be near (i.e. in terms of similarity) in DNA sequence space and this presumably genome wide [5, 15, 16, 40], and because evolutionary surviving mutations of all sorts will be biased by the genome architecture itself and vice versa, we also investigated the correlation behaviour of the DNA sequence (see Additional file 1: Supplemental Methods; [5, 16, 40]; and references therein) for two different human and mouse strains (Fig. 1e; Additional file 29: Figure S16, Additional file 30: Figure S17, Additional file 31: Figure S18, Additional file 32: Figure S19, Additional file 33: Figure S20, Additional file 34: Figure S21)—briefly (see Additional file 21: Supplemental Results): Again we found species-specific multi-scaling behaviour long-range power-law correlations with a fine structure representing the (i) the nucleosome, (ii) the compaction into a quasi-fibre, (iii) the chromatin fibre regime, (iv) the formation of loops, (v) subchromosomal domains, and (vi) their connection by a linker. On all scales this is equivalent for the different scaling measures used (Fig. 2b; Additional file 21: Supplemental Results, Additional file 24: Figure S11, Additional file 25: Figure S12, Additional file 26: Figure S13). Moreover, the transition from the basic nucleosomal compaction into the quasi-fibre regime (“sweet” point) can be easily seen at ~3.6 kbp. Additionally, on the fine-structural level, the already previously proven association to nucleosomal binding [5, 16, 40] is not only found again (Additional file 29: Figure S16), but also is in agreement with the fine structure found in the interaction scaling (Additional file 28: Figure S15). Also the loop aggregated/rosette structure is present, predicting loop sizes from ~30 to 100 kbp and subchromosomal domain sizes from ~300 kbp to ~1.3 Mbp (see also [5, 16, 40]). All this does not only hint that, in contrast to the regional T2C data, the genome folding is a genome-wide phenomenon, but additionally that this architecture is stable and persistent, since sequence reshuffling or other destructive measures would result in a loss of this pattern. This would also be the case for an unstable architecture, which would not leave a defined footprint within the sequence. Once more this agrees with our simulations of the dynamics as well as the genome-wide in vivo FCS measurements [11]. Moreover, thus the 3D architecture and DNA sequence organization are indeed co-evolutionary tightly entangled (review of previous notions in [5, 16]). Consequently, in the future from the DNA sequence and other higher-order codes (e.g. the epigenetic code) most architectural genome features can be determined, since also most structural/architectural features and vice versa left a footprint on the DNA sequence and other code levels as one would expect from a stable scale-bridging systems genomic entity.

Discussion and conclusions

Here we present the much debated 3D genome architecture and its entanglement with the DNA sequence from a few to the megabase pair level of the eukaryotic human and mouse genomes based on combining a novel selective high-throughput high-resolution chromosomal interaction capture (T2C), with a scaling analysis of the architecture as well as the DNA sequence organization, and polymer simulations. T2C has many a significant advantage, ranging from cost effectiveness, via a huge signal-to-noise ratio, to reaching the level of the “genomic” statistical mechanics with uncertainty principles. The latter is of major importance since here fundamental limits are reached with consequences for the setup and interpretation of experiments involving the architecture and dynamics of genomes. Actually, we face a situation very similar to the revolution in quantum mechanics brought about at the beginning of the twentieth century. Thus, an entirely new way of thinking will be needed to further determine and understand the organization and function of genomes.

With this background, we show here (i) the association of the DNA to the structure of the nucleosome core in detail and the existence of a chromatin quasi-fibre with an average of 5 ± 1 nucleosomes per 11 nm with an average persistence length L p from ~80 to 120 nm, (ii) the existence of stable chromatin loop aggregates/rosettes connected by a linker with loops and linkers ranging from ~30 to 100 kbp (with details of the fibre folding at loop bases), (iii) the existence of a consensus architecture with only small differences between species, cell type, or functional states likely to persist through the cell cycle, (iv) the existence of fine-structured multi-scaling behaviour of the architecture, and last but not least that (v) the genome architecture is closely linked to the fine-structured multi-scaling long-range behaviour of the DNA sequence. This is a consistent scale-bridging systems picture of the 3D architecture, its dynamics, and functional variation of two mammalian genomes from the single base pair to the megabase pair level. All this is in agreement with many observations about the architecture, its dynamics, the diffusion of molecules, as well as the replication, storage, and expression of genetic information which have been made in the field (see “Background”). Most interestingly, this is in agreement with novel genome wide in vivo FCS measurements of the chromatin quasi-fibre dynamics [11]. Inevitably, there are still many an open question, such as the identification of all the molecule complexes (proteins, RNA, etc.) involved in looping, their dynamics, the inherent variability in the system, but our results provide now a framework for “architectural and dynamic sequencing” and the detailed analysis after all major architectural components in the human and mouse genome have been determined.

The implications of the architecture presented here are many-fold, of which we would like to mention a few: (i) The balance between stability and flexibility of the whole system ensures that the overall genome integrity is maintained when local disturbance/damage takes place due to its modular build, while at the same time it allows fine adjustment of the architecture to enable the development of different gene expression programs/cell types. (ii) The signals due to functional interactions do not stand out above those due to proximity, which is an intrinsic property of the loop aggregate/rosette like folding of the genome. This suggests that the interaction of functional elements (both with respect to transcription as well as to replication) is achieved between fragments that are already in close proximity before their function is required. This proximity and being “tethered” in a subchromosomal domain increase the probability of interaction. (iii) This architecture is open enough to allow the rapid diffusion of molecules such as transcription factors and also allows the movement of sequences to self-organize and form active and inactive units of the genome. These (and other) aspects together form an inseparable system giving rise to a functional genome.