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

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.

Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization

“…c . This explains the intrachromosomal contact frequency P (s) ∼ s −1.5 for yeast genome, pointing to an equilibrium globule [8,[37][38][39].…”

“…For illustrative purposes, we adopt the nucleus volume V human nucls ≈ 60 − 110 µm 3 from the average size of mammalian cell nucleus 2 × R ≈ 5 − 6 µm [8,40]. Since the volume taken by the entire 46 chromosomes, as a diploid with 2×N ≈ 2×3×10 9 bp, is V human gen = 6 × 10 9 bp/200 bp × V nuc ≈ 3 × 10 10 nm 3 , the volume fraction of human genome is φ human = V human gen /V human nucls ≈ 0.3 − 0.5 φ ∞ c .…”

Confined disordered strictly jammed binary sphere packings

“…Besides the packings of binary hard spheres confined between two parallel hard planes we have studied in this work, there are many other interesting packing problems in confined space that remain to be investigated [75][76][77]. For example, while bulk MRJ packings of nonspherical particles that span a wide range of shapes, including ellipsoids [78][79][80], superballs [81,82], and polyhedra [24,25,72,83] have been studied in detail, nothing is known about confined MRJ packings of nonspherical particles.…”

“…Understanding how confined MRJ packings of nonspherical particles differ from their bulk counterparts and confined MRJ sphere packings are outstanding questions. Extensions of this work to DNA packaging is an interesting avenue for future research [77].…”

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

“…This is very different from the scaling expected for 'equilibrium' globules, as it is the case of collapsed chains. In that case R 2 (s) 1/2 should obey Gaussian statistics as chains in a melt (∼ s 1/2 ), reaching a plateau at s ≈ (3N/4π) 2/3 ≈ 20 where the radius of the confining sphere is reached and the Gaussian paths are bounced back [31,32]. Likewise, a dense equilibrium globule would lead to Porod scattering [22] w(q) ∼ q −4 in the form factor, i.e, an effective exponent ν = 0.25 much lower than those observed for k = 8 (Fig.…”