Local chromatin density: The fibre density around frequently transcribed loci (green) is smaller than in lowly expressed regions (red).

<p>Thus, on average, they do occupy a larger volume, indicating an increased decompactification of the highly transcribed parts. The bars (gray) represent the expression profiles and the green and red areas mark highly and lowly active regions, respectively <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037525#pone.0037525-Goetze1" target="_blank">[3]</a>.</p

Comparison between Dynamic Loop Model and self-avoiding walk.

<p><b>A.</b> The upper conformation is a Dynamic Loop Model chromatid with , cutoff size and mean loop concentration . For comparison, a conformation without loops with the same chain length is shown below. <b>B.</b> For both, self-avoiding walk and Dynamic Loop Model the coarse-graining method is applied and the directional correlation is calculated. The same degree of coarse-graining is used for both models. The figure shows an exponential decay of the directional correlation function of the Dynamic Loop Model, while the the self-avoiding walk does not show this behaviour. Most importantly, the Dynamic Loop Model chromatid is much stiffer than the self-avoiding walk. This shows that the entropic repulsion of the chromatin loops that are generated by the cross-linking mechanism leads to a considerable stiffening up. Error bars represent the standard error of the sampled conformations.</p

Comparison for bending stiffness from direct measurement and calculation using elastic response.

<p>Comparison for bending stiffness from direct measurement and calculation using elastic response.</p

Mean radial monomer density functions of different configurations.

<p><b>A.</b> Larger cutoff sizes give thicker model chromatids but smaller densities and lengthwise compaction ratios. <b>B.</b> The number of loops has only small influence on the chromatid thickness. However, chromatids with more loops show tighter compactions and hence higher monomer densities.</p

Averages of structural parameters for chromosomes 1 and 11 for human female primary fibroblast (04–147) and K562 lymphoblastoid.

<p>Averages of structural parameters for chromosomes 1 and 11 for human female primary fibroblast (04–147) and K562 lymphoblastoid.</p

The mean square distance of genomic loci to the center-of-mass of the chromosome territory (top, blue line) depends on the corresponding expression level [<b>3</b>] (gray): The lowly transcribed regions are closer to the center than more active parts of the fibre.

<p>The mean square distance to the surface of the chromosome territory (bottom, blue line) confirms that the highly expressed loci preferentially reside closer to the surface of each territory than lowly expressed regions.</p

Influence of the parameter settings on the spatial dimensions.

<p><b>A.</b> A linear relationship between the average distance of monomers from the backbone and the cutoff length is found. Together with the observed drop off of the monomer density at the central axis we conclude that the fibre coils around the backbone in a helical-like folding manner. However this gives just a general tendency and the exact structure is much more complicated. <b>B.</b> Interestingly we can see that at constant values for the lengthwise compaction ratio still increases linearly with the chain length . In this example and the mean loop concentration is . When extrapolating the linear curve to a compaction ratio of -fold, a polymer with statistical segments and cutoff length would be needed.</p

Examples for model chromatids with different parameter sets.

<p>The grey tube represents the chromatin fibre. The orange sticks visualize the cross-links between distant fibre segments. Each chain embodies a single chromatid. The chromatin fibre in both examples consisted of segments. The cutoff length for the loop sizes is . It means that fibre segments which are separated by a genomic distance greater than 50 monomers cannot form an additional bond. <b>A.</b> In this example, the mean loop concentration is . At these low loop concentrations the conformations are non-homogeneous. Rather, a2 formation of blobs can be observed in regions with many cross-links. These regions are connected by fibre section with no or only few loops. <b>B.</b> When the loop concentration is high enough, a condensation of the chromatin fibre into thick, homogeneous rods can be observed. In this configuration the loop concentration is . Cross-links are distributed homogeneously along the chain.</p

Mean square spatial distance (MSD) in chromosome 11 for human female primary fibroblast (04–147): The obtained average MSD for the total fibre (inset, blue line) is in good agreement with experimental data [<b>4</b>] (inset, black circles).

<p>The loci-specific MSD calculated from the simulated conformations (blue triangles) shows the same fluctuations between highly and lowly active loci as the experiment does (black circles). The MSD calculated for a fibre with homogeneous affinity (dashed blue line), meaning without expression dependence, is between the MSD for highly and lowly active regions. The MSD calculated specifically for highly transcribed regions (green area) exhibits a larger MSD than regions with less expressed loci (red area) because they are less compact. The corresponding regions taken for the analysis are highlighted in green and red, respectively, in Fig. 2 and were taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037525#pone.0037525-Goetze1" target="_blank">[3]</a>.</p

Directional correlation functions for model chromatids with varying parameters.

<p>The chain length for all configurations is . Error bars represent the standard error. <b>A.</b> For fixed mean loop concentration we can see that the stiffness increases with the cutoff length . Larger cutoff lengths result in thicker chromosomes and in turn less flexibility. <b>B.</b> Shown are results for and different mean loop concentrations. An increased number of cross-links is associated with a more densly packed chromosome. Thus, the distance between loops is decreased and the repulsive forces between them are stronger. Consequently higher bending rigidities are obtained.</p