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