**2.3. Analytical and Computer Simulations Theoretic Evaluation**

**2.2. Dynamics and Structure Revealed by FCS**

74 Chromatin and Epigenetics

To investigate the 3D genome architecture and dynamics also by an orthogonal genome wide and *in vivo* approach, a novel *in vivo* FCS technique exploring the structure and dynamics by measuring chromatin movement combined with a novel analytical approach was introduced [27]. It is based on the fact that a specific chromatin quasi-fibre and its higher-order architecture directly influences its intrinsic dynamics. Thus, the concept dissects intra-molecular polymer dynamics from fluorescence intensity fluctuations measured with FCS to investigate meso-scale chromatin dynamics in living cells and connects this to the underlying threedimensional organization. Besides, the classical analytical polymer models where extended to include dynamics, physical properties, and accessibility. As primary tracer protein for chromatin movement a linker histone H1.0-EGFP construct was chosen [18, 19, 22]. On the one hand, H1.0 decorates chromatin globally and reflects its density. On the other hand, it binds only transiently such that photobleached molecules are constantly replaced by fluorescent ones, and thus chromatin dynamics becomes amenable to FCS analysis (see also [20, 54]): Here, topologically and dynamically independent chromatin domains of 500 kbp to 1.5 Mbp in size were identified that are best described by a compacted chromatin fibre and a loopcluster polymer model under theta-solvent conditions. In more detail again the formation of stable loops and stable multi-loop aggregates/rosettes from a chromatin fibre with certain density and flexibility properties emerged as prominent structural feature of dynamically independent domains - and this throughout the cell nucleus in living cells! The detailed quantitative values for the involved parameters again lead in essence to the same values as found already in the T2C data: a quasi-fibre compaction of 5 ± 1 nucleosomes per 11 nm, with an average persistence length of ~80 to 120 nm, and loops and linkers of ~30 to 100 kbp [27]. Notably, it cannot be stressed enough that the loops and multi-loop aggregates/rosettes form *stable* entities on the time scales which were approachable by FCS (between 10 μs and 10 to 20 s) and do neither open, close, or in any other way reform (longer timescale up to hours are historically known). This not only moves many an assumption currently proposed (see Introduction) into the realm of fairy tales—conceptually and by hard experimental facts in agreement with the research of the last ~30 years (e.g. [18–20, 22, 54, 71]). Visualization of simulated structures illustrates this clearly (Movies 1, 2 [26]): structures described consistently throughout the literature would dissolve immediately - what has never been observed (though attempted to be measured) - and also in consistent agreement with the T2C results measured at the limit of resolution. Beyond, also characteristic variations were found between eu- and heterochromatin: Hydrodynamic relaxation times and gyration radii of independent chromatin domains are larger for open (161 ± 15 ms, 297 ± 9 nm) than for dense chromatin (88 ± 7 ms, 243 ± 6 nm) and increase globally upon chromatin hyperacetylation or ATP depletion. Thus, functional changes are a variation of a basic theme, e.g. more compact heterochromatic domains have a larger inaccessible volume fraction than more open euchromatic ones. Nevertheless, molecular diffusion is fast enough to roam a complete domain within few microseconds, during which the domain itself appears static. Relaxation of domains in the 100 ms range affects genome access in a protein concentration-dependent manner: highly abundant molecules at several 100 nM concentrations 'fill' the fluctuating domain so that a larger volume fraction than for a static TAD becomes adiabatically accessible. In contrast,

To better understand the 3D genome organisation suggested e.g. by the above results, to evaluate hypotheses, and to plan future experiments, we were the first who have - since 1996 - developed polymer models with pre-set conditions for *in silico* super-computer simulations (i.e. without attempting to fit data; [7, 21–23, 26, 49–52, 70]) and later also an analytical mathematics framework [27]. The simulations use a stretchable, bendable, and volume excluded polymer (hydrodynamic) approximation of the 30 nm chromatin fibre consisting of individual homogenous segments with a resolution of ~1.0 to 2.5 kbp while combining Monte Carlo and Brownian Dynamics approaches (**Figures 2**–**4**). The analytical polymer approach extends and applies for the first time Gaussian chain and Kratky-Porod model descriptions in combination with the Rouse and Zimm models for polymer dynamics to complex star and rosette topologies under real excluded volume conditions as well as dilute and semi-dilute solvent conditions [27]. Whereas the analytical model is exact, the simulations explore emerging effects not explicitly introduced into the analytical model.

Simulations (**Figure 2**) of the Random-Walk/Giant-Loop model in which large individual loops (0.5–5.0 Mbp) are connected by a linker resembling a flexible backbone, as well as the Multi-Loop Subcompartment (MLS) model with rosette-like aggregates (0.5–2 Mbp) with smaller loops (60–250 kbp) connected by linkers (60–250 kbp), have already predicted that only an MLS model, i.e. a compacted quasi-fibre forming stable loops and stable loop aggregates/rosettes connected by a linker, can properly explain the formation of chromosome arms and territories [22], the spatial distances measured both using fluorescence *in situ* hybridization (FISH) experiments [7, 21–23, 26, 49–52, 70], and beyond even the general morphology of nuclei *in vivo* using histone fluorescence fusion proteins [22, 51], nucleosome concentration distributions, as well as dynamic and functional properties such as the diffusion of macromolecules [18, 19, 22, 53, 54]. These models also contained already enough information/aspects to cover other architectures such as free random-walks, random or fractal globules as well as their stability and dynamics. Additionally, the visualization (**Figures 2**–**4**, Movies 1, 2 [26]) creates an immediate feeling for the behaviour of genomes in 3D - a fact which already by pure visual inspection rules out many of the introduction mentioned obscure suggestions immediately.

With the unprecedented quality of both the interaction mapping by T2C and the FCS dynamic measurements (see above) the introduction of simulation and analytical models complex enough to approximate the 3D genome organization adequately showed even more clearly that only a quasi-fibre, stable loop, stable loop aggregate/rosette-like architecture is compatible with the measurements: In essence the simulations and analytical models describe even the slightest details of the T2C and FCS measurements correctly including many at first sight

**Figure 3.** Determination of the 3D architecture in the IGF/H19 11p 15.5-15.4 region by T2C interaction mapping and computer simulations: Interaction matrices (logarithmic and colour coded scale; left & right) in HB2 and HEK293T TEV cells [26] show in unprecedented clarity the formation of a quasi-chromatin fibre, folding into stable loops (red lines; xL: number of loops), forming due to the grid-like pattern stable multi-loop aggregates/rosettes, i.e. subchromosomal domains separated by a linker (borders: pink lines, right; D1s, D1e: start and end of domains). A grid-like pattern is also visible in the interactions between the domains and corresponds to trans-domain loop interactions. The aggregation into a chromatin quasi-fibre is visible near the diagonal and loop internal structures are also detectable. Between different cell types or 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.

to a relatively low crosslink probability, radius, and frequency in experiments comparing the clearly visible fine-structure (such as the (anti-)parallel neighbouring of the chromatin quasifibre at loop bases [26]. Also both the simulation and analytical approach describe in detail every aspect of the experimentally found multi-scaling behaviour with a fine-structure not only of the architecture and dynamics, but also of the DNA sequence (see below) to a degree of detail even we are still astonished about. The stability of the architecture with respect to the intrinsic chromatin fibre dynamics can also be illustrated by e.g. the decondensation from a mitotic chromosome into interphase (Movie 1 [26]) or just in a normal interphase state (Movie 2 [26]). This also shows that any 3D architecture would dissolve within seconds if it would not be stabilised. Consequently, both theoretic approaches came with old and new data

**Figure 4.** Insight into the spatial and dynamic/diffusional properties and morphology of the 3D organization of entire nuclei: The detailed view from the outside into a simulation for an MLS model with 126 kbp loops and linkers [22] shows the structure and low overlap of chromosome territories, the rosette like subchromosomal domains, and that the mean spacing between quasi-fibres ranges at least from 50 to 100 nm. Hence, the obstruction of diffusing particles (see spherical legend) is proportional to their size. Thus, small molecules as nucleotides and most (subunits of) proteins or gene transcripts reach every location of the nucleus by moderately obstructed diffusion. Consequently, active transport of molecules should be restricted to few exceptions and a channel like network for transportation (proposed by the Inter Chromosomal Domain model) is not necessary. Nevertheless, obviously the rosette core is denser leading to a general diffusion limited access. Thus, the interplay between accessibility and obstruction while considering the fast Brownian

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300nm

200nm

dynamics of the quasi-fibre and the entire system is of functional relevance.

100nm 80nm 60nm 40nm 20nm 10nm 7.5nm 5.0nm 2.5nm 1.0nm

paradoxical results as e.g. i) that high numbers of especially small loops in a rosette result due the high density in steric exclusion and thus stretched loops eventually even "shielding" inner-rosette parts, ii) that inter-domain interactions are influenced by the connecting linker, loop size and numbers, and how non-equilibrium effects would appear, as well as iii) the isotropy breaking of consecutive subchromosomal domains as seen in the interactions at the border of domains and the domain-domain interactions. On a more general level the simulations support also the large and at first sight remarkable emptiness of interaction matrices and its link to the existence of a dedicated chromatin quasi-fibre. Additionally, the simulations hint A Consistent Systems Mechanics Model of the 3D Architecture and Dynamics of Genomes http://dx.doi.org/10.5772/intechopen.89836 77

**Figure 4.** Insight into the spatial and dynamic/diffusional properties and morphology of the 3D organization of entire nuclei: The detailed view from the outside into a simulation for an MLS model with 126 kbp loops and linkers [22] shows the structure and low overlap of chromosome territories, the rosette like subchromosomal domains, and that the mean spacing between quasi-fibres ranges at least from 50 to 100 nm. Hence, the obstruction of diffusing particles (see spherical legend) is proportional to their size. Thus, small molecules as nucleotides and most (subunits of) proteins or gene transcripts reach every location of the nucleus by moderately obstructed diffusion. Consequently, active transport of molecules should be restricted to few exceptions and a channel like network for transportation (proposed by the Inter Chromosomal Domain model) is not necessary. Nevertheless, obviously the rosette core is denser leading to a general diffusion limited access. Thus, the interplay between accessibility and obstruction while considering the fast Brownian dynamics of the quasi-fibre and the entire system is of functional relevance.

to a relatively low crosslink probability, radius, and frequency in experiments comparing the clearly visible fine-structure (such as the (anti-)parallel neighbouring of the chromatin quasifibre at loop bases [26]. Also both the simulation and analytical approach describe in detail every aspect of the experimentally found multi-scaling behaviour with a fine-structure not only of the architecture and dynamics, but also of the DNA sequence (see below) to a degree of detail even we are still astonished about. The stability of the architecture with respect to the intrinsic chromatin fibre dynamics can also be illustrated by e.g. the decondensation from a mitotic chromosome into interphase (Movie 1 [26]) or just in a normal interphase state (Movie 2 [26]). This also shows that any 3D architecture would dissolve within seconds if it would not be stabilised. Consequently, both theoretic approaches came with old and new data

paradoxical results as e.g. i) that high numbers of especially small loops in a rosette result due the high density in steric exclusion and thus stretched loops eventually even "shielding" inner-rosette parts, ii) that inter-domain interactions are influenced by the connecting linker, loop size and numbers, and how non-equilibrium effects would appear, as well as iii) the isotropy breaking of consecutive subchromosomal domains as seen in the interactions at the border of domains and the domain-domain interactions. On a more general level the simulations support also the large and at first sight remarkable emptiness of interaction matrices and its link to the existence of a dedicated chromatin quasi-fibre. Additionally, the simulations hint

log interaction frequency 10<sup>1</sup> 1 10<sup>2</sup> 10<sup>3</sup> 10<sup>4</sup> 10<sup>5</sup> 10<sup>6</sup>

**Figure 3.** Determination of the 3D architecture in the IGF/H19 11p 15.5-15.4 region by T2C interaction mapping and computer simulations: Interaction matrices (logarithmic and colour coded scale; left & right) in HB2 and HEK293T TEV cells [26] show in unprecedented clarity the formation of a quasi-chromatin fibre, folding into stable loops (red lines; xL: number of loops), forming due to the grid-like pattern stable multi-loop aggregates/rosettes, i.e. subchromosomal domains separated by a linker (borders: pink lines, right; D1s, D1e: start and end of domains). A grid-like pattern is also visible in the interactions between the domains and corresponds to trans-domain loop interactions. The aggregation into a chromatin quasi-fibre is visible near the diagonal and loop internal structures are also detectable. Between different cell types or 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

D2.e D3.s

D1.e D2.s

6 L 16 L 9 L 5 L

D3.e D4.s

HB2

total TEV

1.5 2.0 2.5 3.0

ASCL2

C11orf21 TSPAN32

CD81 TSSC4 KCNQ1

CDKN1C SLC22A18

PHLDA2

NAP1L4

SNORA54

CARS

OSBPL5

probes BglII Genes

TRPM5

MUC2

MUC5AC

MUC5AC

MUC5B

BRSK2

76 Chromatin and Epigenetics

C11orf81 DUSP8

consensus architecture.

KRTAP5−1 KRTAP5−2 KRTAP5−3 KRTAP5−4

KRTAP5−5

FAM99A

KRTAP5−6

CTSD

SYT8 TNNI2 LSP1

TNNT3

MRPL23

C11orf89

H19

MIRN675

IGF2 IGF2AS INSTH

HS 11 p15.4-5 position [Mbp]

MIRN483

TOLLIP

consistently to the same conclusion whatever orthogonal high-quality method is used and thus are a theoretical framework for the understanding, test, and engineering of genomes.

of previous notions in [22, 24]). Thus, in the future from the DNA sequence and other higherorder codes (e.g. the epigenetic code) most architectural genome features can be potentially determined, since most structural/architectural features left a footprint on the DNA sequence and other code levels and vice versa as one would expect from a stable scale bridging systems

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The above described holistic combination of several new orthogonal approaches [26, 27] including the heuristics of the field leads interestingly undoubtedly to a consistent picture of genome architecture, dynamics, and in general organization, by establishing that nucleosomes compact into a quasi-fibre folded into stable loops, forming stable multi-loop aggregates/rosettes connected by linkers creating chromosome arms and entire chromosomes. Nevertheless, the heuristics of the field immediately questions whether i) we really now have an evolutionary consistent picture of genome organization, ii) whether this is the unavoidable outcome of Darwinian natural selection and Lamarkian self-referenced manipulation (what we introduce here), and iii) finally whether we can understand now genome organization in its systems context within cells, organs, and the entire organism? This in essence already relates back to the fundamental question of how life emerged from the primordial soup [5, 6, 22]; see details in following sections) but in the context discussed here can be addressed by first reflecting on the existing major functions of genomes, thus setting the stage: i) genomes need to stably store genetic information, ii) the information needs to be differentially read out to give rise to and regulate the molecular machinery, and iii) genomes need to replicate and mutate to spread

**i.** Obviously the by far most important function is to stably store over long periods of time genetic information though with enough flexibility including mutations - or in short: without proper storage neither information retrieval, nor replication, nor evolutionary development exist. This involves obviously being resistant against physical/ chemical and/or in- or external mechanical destruction. Whereas, the first act mainly as from the bottom up involving one or a group of chemical bonds in proximity by direct interactions in the molecular soup, the latter depends on the large-scale structure of the basic molecular components and thus acts indirectly top-down on chemical bonds, i.e. that in- or external global stress is transferred and eventually accumulated via the global structure down to molecular levels while leading to mechanical failure. Both this physico-chemical and structural conformation-based destruction paradigms, influence genome architecture on all its levels under evolutionary pressure. They can be formulated such that a) mechanical failure rates are minimized regarding very long time spans, and b) in- or external mechanical failure rates reach an optimum due to the right balance between internal stability increasing with scale (for sensible ranges) and external stress decreasing the stability with increasing scale. From the well known average DNA breaking length of ~300–500 bp after already relatively severe sonication, this translates right away to the nucleosome and chromatin quasi-fibre level assuming that internal

**3. Systems Consistency of the 3D Genome Organization**

genomic entity.

and evolve:

#### **2.4. DNA-Sequence Fine-Structured Multi-Scaling**

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 [22–24, 55], and because evolutionary surviving mutations of all sorts will be biased by the genome architecture itself and vice versa, the correlation and thus scaling behaviour of the DNA sequence [22–24, 26, 55] and its connection to the 3D genome architecture scaling - either from T2C interaction mapping [26] or from simulations [21–23] - allows for comprehensive investigation of genome organization in a unified scale-bridging manner from a few to the mega base pair level. Using to this end, the perhaps simplest correlation analysis possible (to avoid information loss or biases), we calculated the mean square deviation of the base pair composition (purines/pyrimidines) within windows of different sizes and calculating the function *C(l)* and its local slope *δ(l)*, which measures the correlation degree, or in more practical lay-men terms, is similar to a spectral measure [22–24, 26]: in relation to mammalian genome organization for each of two different human and mouse strains i) long-range power-law correlations were found on almost the entire observable scale, ii) with the local correlation coefficients showing a species specific multi-scaling behaviour with close to random correlations on the scale of a few base pairs, a first maximum from 40 bp to 3.6 kbp, and a second maximum from 8 × 10<sup>4</sup> to 3 × 10<sup>5</sup> bp, and iii) an additional fine-structure is present in the first and second maxima. The correlation degree and behaviour within the species are nearly identical comparing different chromosomes (with larger differences for the X and Y chromosomes). The behaviour on all scales is equivalent concerning the different measures used to investigate the long-range multiscaling of the genome architecture with the transitions of behaviours even at similar scaling positions [26] and can be associated with a single base pair resolution 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 linkers. Additionally, the already previously proven association to nucleosomal binding on the fine-structural level [22–24] is not only found again, but also is in agreement with the fine-structure found in the interaction scaling. Since the correlation analysis is genome-wide (in contrast to the T2C analysed regions so far) and since individual chromosomes show a highly similar scaling this clearly shows the genome-wide validity of the 3D organization. Moreover, the existence and details of this behaviour show the stability and persistence of the architecture 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. This is again in agreement with our simulations of the dynamics or the genome wide *in vivo* FCS measurements [27]. Consequently, this shows not only by two analysis of completely independent "targets" (the T2C interaction experiments and the analysis of the DNA sequence) the compaction into a chromatin quasi-fibre and a stable multi-loop aggregate/rosette genome architecture again, but proved here also the long discussed notion that what is near in physical space is also near, i.e. more similar, in sequence space. Hence, the 3D architecture and DNA sequence organization are co-evolutionarily tightly entangled (review of previous notions in [22, 24]). Thus, in the future from the DNA sequence and other higherorder codes (e.g. the epigenetic code) most architectural genome features can be potentially determined, since most structural/architectural features left a footprint on the DNA sequence and other code levels and vice versa as one would expect from a stable scale bridging systems genomic entity.
