The fractal globule as a model of chromatin architecture in the cell - PubMed (original) (raw)

The fractal globule as a model of chromatin architecture in the cell

Leonid A Mirny. Chromosome Res. 2011 Jan.

Abstract

The fractal globule is a compact polymer state that emerges during polymer condensation as a result of topological constraints which prevent one region of the chain from passing across another one. This long-lived intermediate state was introduced in 1988 (Grosberg et al. 1988) and has not been observed in experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent characterization of human chromatin using a novel chromosome conformational capture technique brought the fractal globule into the spotlight as a structural model of human chromosome on the scale of up to 10 Mb (Lieberman-Aiden et al. 2009). Here, we present the concept of the fractal globule, comparing it to other states of a polymer and focusing on its properties relevant for the biophysics of chromatin. We then discuss properties of the fractal globule that make it an attractive model for chromatin organization inside a cell. Next, we connect the fractal globule to recent studies that emphasize topological constraints as a primary factor driving formation of chromosomal territories. We discuss how theoretical predictions, made on the basis of the fractal globule model, can be tested experimentally. Finally, we discuss whether fractal globule architecture can be relevant for chromatin packing in other organisms such as yeast and bacteria.

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Figures

Fig. 1

Fig. 1

a Root-mean squared end-to-end distance R(s) as a function of the genomic distance s between the ends of a subchain (in the units of formula image) for globules of N = 32,000 monomers. Blue, equilibrium globule; green, fractal globule. At small s, both globules show scaling characteristic of the self-avoiding random walk (3/5), followed by 1/2 of the ideal coil. Notice there is a plateau for the equilibrium globule. b The probability of a contact as a function of genomic distance s for the equilibrium globule (blue) and the fractal globule (green). Notice the robust scaling of −1 which spans two orders of magnitude for the fractal globule

Fig. 2

Fig. 2

Conformations of the fractal (a) and equilibrium (b) globules. The chain is colored from red to blue in rainbow colors as shown on the top. The fractal globule has a striking territorial organization, which strongly contrasts with the mixing observed in the equilibrium globule. Territorial organization of the fractal globule (c) is evident when two chains of 1,000 monomers each are outlined. The equilibrium globule (d), in contrast, has two chains mixed together in space

Fig. 3

Fig. 3

The fractal globule (a) consist of dense globules formed on all scales. Subchains of 100, 300, 1,000, and 3,000 monomers (left to right) are shown by a red tube in a globule of N = 32,000 monomers. For comparison, same regions of the equilibrium globule (b) are diffuse inside the globule

Fig. 4

Fig. 4

Opening of a loop that is a part of the fractal globule (a), and the equilibrium globule (b). Globules of 32,000 monomers were folded by pairwise attractive interactions. The fractal globule was formed by Molecular Dynamics which keeps track of topological constrains, while the equilibrium globule was equilibrated folded by Monte Carlo simulations (Reith and Virnau 2010) that violate topological constrains leading to significant entanglement. On the next step of molecular dynamics simulation, attractive interactions for a region of 3,000 monomers were removed allowing the region to open up due to the chain entropy. In the fractal globule, the region opened up forming a large loop (a). The same region failed to open from the equilibrium globule (b) due chain entanglements in this state

Fig. 5

Fig. 5

Despite having an organized territorial architecture, spatially neighboring regions of the fractal globule (shown in red and blue) have a large number of interactions between them, deeply penetrating into each other's volumes. The number of interactions of crumples has scales linear with its volumes (see Eq. 12). Thus a fixed fraction of crumples volume (rather than its surface) is involved in interactions.

Fig. 6

Fig. 6

Equilibration of the fractal globule. A series of snapshots obtained at four logarithmically spaced timepoints of long equilibration simulations. Notice gradual loss of the territorial organization, characteristic of the fractal globule, and increasing mixing, leading to formation of the equilibrium globule. Since the ends of the globule remain attached to the surface while being able to slide on it, the structure remains unentangled. This equilibration is very slow. The details of these simulations will be published elsewhere

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