Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin

Abstract

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally-defined domains observed by single cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as Rad21 degradation.

Figure 1.. Schematic representation of the conversion process from SRRW to SR-EV.

The SRRW configurational motif hides the overlap of several beads in a molecule that has the structure of a branching polymer. By the introduction of excluded volume in SR-EV, the overlapping beads separate to form a cluster and a linear molecule.

Figure 2.. Example SRRW and SR-EV configurations.

The top row are for the SRRW case, and bottom row corresponds to the associated SR-EV configuration. (A) and (E) represent the bonds of the full configurations and show that while SR-EV looks denser than the SRRW case the overall structure is preserved upon removal of the original overlaps. (B) and (F) correspond to the same small portion of the conformation and shows SR-EV having many more beads than SRRW due to the excluded volume between beads. The red circles explicitly highlight a structural motif that in SRRW is a central bead with 7 bonds branching out (a sequence of seven consecutive jump and returns steps) that transform to 15 linearly connecting beads forming a cluster. (C) and (G) display the chromatin conformations wrapped by a tight mesh suggesting the separation between a chromatin rich and a chromatin depleted regions, the latter being the space that free crowders could easily occupy. (D) and (H) show the bare interface between the two regions that resembles the interface dividing two bi-continuous phases and also clearly expose the difference between SRRW and SR-EV.

Figure 3.. Packing domains and nucleosome accessibility.

Same SR-EV configuration displayed on Figure 2, but colored by the coordination number of each nucleosome. A) Full configuration reveals the spacial dispersity of packing domains in red, consistent with heterochromatic region, intercalated with low coordinated, accesible regions. B) 50 nm slab cut at the center of the configuration displaying details of the system heterogeneity and transition from packing domains to the intermediate, low coordinated, region. Note the white nucleosomes (CN ∼ 6) at the periphery of the packing domains.

Figure 4.. Slab images:

A) representation of a 100 nm slab cut at the center of a SR-VE conformation obtained with $\varphi =0.16$ and $\alpha =1.10$. B) 2D chromatin density corresponding to coordinates of panel A). C) ChromSTEM 2D chromatin density obtained from a 100 nm slab of a A549 cell. The 2D density color scale is the same for B) and C), and the density is normalized to its highest value in each image.

Figure 5.. Theoretical and experimental polymeric properties of chromatin:

SR-EV ensemble average of (A) end-to-end distance and (B) contact probability a as a function of the genomic distance for all simulated conditions. The crossover between short distance intra-domain and long distance inter-domain regimes is explicitly indicated, as well as the confinement effect at longer distances. Notice that on these two panels there are four lines per $\alpha$ value, while $\alpha \in \{1.10,1.15,1.20\}$. (C) Experimental (Hi-C) contact probability for chromosome 1 of HCT-116 cells showing quantitative agreement with the theoretical results.

Figure 6.

Chromatin Volume Concentration for A) $\varphi =0.08$, B) $\varphi =0.12$, C) $\varphi =0.16$ and A) $\varphi =0.20$ and $\alpha \in \{1.10,1.15,1.20\}$. The results for $\varphi =0.20$, $\alpha =1.15$ are the closest to the experimental findings of Ref (Ou et al., 2017). $\varphi =0.08$ produce CVC distributions with a much larger contribution of low density regions, and $\varphi =0.20$, $\alpha =1.10$ over enhance the high density regions.

Figure 7.. Chromatin packing domains:

(A) Distributions of domain radii $R_{d,i}$ for all combinations of SR-EV parameters $\alpha$ and $\varphi$, as labeled in the figure. (B) Mean value $\langle R_d\rangle$ of the domain radii distributions. (C) In green, experimental distribution of domain radii obtained with ChromSTEM on A549 cell line, and the closest approximation from SR-EV that corresponds to $\alpha =1.15$ and $\varphi =0.16$.

Figure 8.. Packing coefficient D:

(A) Ensemble average cumulative pair correlation function $\langle G(r)\rangle$ for $\varphi =0.16$ and the three studied values of $\alpha$. The vertical black lines mark the boundaries used to perform a power law regression to calculate $D$. (B) Packing coefficient $\langle D\rangle$ as a function of $\varphi$ and $\alpha$. (C) Distribution of packing coefficient $D_i$ for all the individual configurations for the twelve simulated conditions and, for comparison, we inserted the experimental PWS $D$ results for U2OS cells that agrees very well with the SR-EV results for $\varphi =0.12$ and $\alpha =1.15$.

Figure 9.. Local correlation between packing parameter and chromatin volume concentration:

Relation between the calculated $D_i$ with the average local volume fraction $\langle {\varphi }_i\rangle$. Both quantities are calculated for the same configuration and in the same spherical region of 240 nm in radius. The figure includes one point for each one of the 12,000 configurations of the twelve simulated ensembles.

Figure 10.. Effect of degrading Rad21 on the relation between packing parameter and chromatin volume concentration:

The small open symbols are the SR-EV results for $\varphi =0.12$, $\alpha =1.10$ and 1.15. The filled symbols represent the experimental values obtained with ChromSTEM (Li et al., 2024) for the control sample (blue) and the Rad21 degrade sample (red)