On Genome Topology 2: The Fractal Globule

As a follow-up to my last post on the use of Hi-C to discover highly self-interacting genomic ‘topological domains’, I wanted to discuss a very interesting aspect of the original paper describing Hi-C. As well as finding a division of the genome into two chromatin compartments, Lieberman-Aiden et al. used their Hi-C data to compare and contrast two models of the topology of chromatin folding within the nucleus.

In this first description of Hi-C, Leberman-Aiden divided their genome-wide contact matrix into 1Mb regions (ie.10 times less definition than the Dixon et al study). They found that, at this level of resolution, the genome can be partitioned into two varieties of spatial compartment, termed A and B. Greater interaction occurs within each compartment than across compartments. Compartment A displays a more open form of chromatin, with a high gene density and high levels of gene expression. Compartment B shows a more densely packed, closed chromatin state. Although the authors do not equate these compartments to euchromatin and heterochromatin, they sound distinctly similar to this old cytogenetic division.

In the later section of the paper, Lieberman-Aiden et al. discuss how their Hi-C data can be used to test models of the three dimensional folding of chromatin. The ‘Equilibrium globule’ model has been used to describe polymers in a poor solvent at equilibrium. In it chromatin is pictured as being in a densely knotted configuration. The ‘Fractal Globule’ model describes polymers self-organising into long-lived, non-equilibrium conformations:

“This highly compact state is formed by an unentangled polymer when it crumples into a series of small globules in a “beads-on-a-string” configuration. These beads serve as monomers in subsequent rounds of spontaneous crumpling until only a single globule-of-globules-of-globules remains. The resulting structure resembles a Peano curve, a continuous fractal trajectory that densely fills 3D space without crossing itself”

(C) Top: An unfolded polymer chain, 4000 monomers (4.8 Mb) long. Coloration corresponds to distance from one endpoint, ranging from blue to cyan, green, yellow, orange, and red. Middle: An equilibrium globule. The structure is highly entangled; loci that are nearby along the contour (similar color) need not be nearby in 3D. Bottom: A fractal globule. Nearby loci along the contour tend to be nearby in 3D, leading to monochromatic blocks both on the surface and in cross-section. The structure lacks knots. (D) Genome architecture at three scales. Top: Two compartments, corresponding to open and closed chromatin, spatially partition the genome. Chromosomes (blue, cyan, green) occupy distinct territories. Middle: Individual chromosomes weave back-and-forth between the open and closed chromatin compartments. Bottom: At the scale of single megabases, the chromosome consists of a series of fractal globules.

When the intrachromasomal contact probability is plotted against genomic distance a power law scaling is observed between ~500kb and ~7Mb. This scaling figure (s1.08) is much closer to that predicted for the fractal globule model (s-1) than that for the equilibrium globule (s-3/2). Likewise, data on the 3D distance between pairs of loci from 3D-FISH is in agreement with a fractal globule topology.

It therefore seems that, at the scale of several megabases, chromatin is organised in these knot-free conformations of globules within globules, allowing unfolding and refolding, whilst also enabling maximally dense packing. I must admit that I don’t have too much insight into the meaning of this; but frankly fractals are cool, and I love the idea of crumpling into globules of globules!

Lieberman-Aiden, E., van Berkum, N., Williams, L., Imakaev, M., Ragoczy, T., Telling, A., Amit, I., Lajoie, B., Sabo, P., Dorschner, M., Sandstrom, R., Bernstein, B., Bender, M., Groudine, M., Gnirke, A., Stamatoyannopoulos, J., Mirny, L., Lander, E., & Dekker, J. (2009). Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome Science, 326 (5950), 289-293 DOI: 10.1126/science.1181369


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