The 2009 Hi-C study of Lieberman-Aiden and colleagues mapped proximity contacts across the human genome at 1-Mb resolution and established two descriptive folding principles — genome-wide spatial segregation of open and closed chromatin into two compartments, and a megabase-scale conformation consistent with a fractal (crumpled) globule — while leaving open the mechanisms that generate these structures, the definitive polymer organization, cell-to-cell variability, locus-level regulatory contacts, and the effects of cancer-associated rearrangements. Seventeen years of follow-up work resolved several of these strands: kilobase-resolution and promoter-capture contact maps now exist, single-cell Hi-C and super-resolution imaging have characterized cell-to-cell variability, and the effects of rearrangements on domain structure have been systematically studied in disease and cancer. The fractal globule hypothesis was superseded at the sub-megabase scale by the discovery of contact domains and the loop-extrusion model. The surviving open core is the mechanistic question: which molecular factors and biophysical dynamics generate and maintain the segregation of open and closed chromatin into A/B compartments — with histone-mark-dependent phase separation, cooperative bridging, and dimerization-driven condensation still competing as explanations — and what polymer organization and topological state megabase-scale chromatin actually adopts in vivo, as validated by a quantitative account of genome-wide contact statistics.

Background

Chromosome conformation capture (3C) methods detect physical proximity between genomic loci by chemically crosslinking cells, ligating DNA fragments that lie close together in the nucleus, and sequencing the ligation products. Hi-C, introduced by Lieberman-Aiden et al. in 2009, applies this idea without preselecting target loci, producing a genome-wide contact matrix whose entries count ligation products between pairs of genomic bins; because the experiment is done on a population of cells, the matrix is an ensemble average over millions of nuclei. Analyzing the human genome at 1-Mb bin size, that study confirmed chromosome territories (the tendency of each chromosome to occupy a restricted nuclear region) and revealed two additional levels of organization. First, the genome partitions into two spatial compartments, later called A and B: loci in compartment A are open, gene-rich, actively transcribed chromatin, while compartment B is closed, gene-poor chromatin, and loci of the same type preferentially lie in spatial proximity across chromosomes. Second, the intrachromosomal contact probability I(s)I(s) between loci separated by genomic distance ss decays approximately as s−1.08s^{-1.08} at the megabase scale, close to the prediction for a fractal globule (also called a crumpled globule): a compact polymer state that arises when topological constraints prevent one segment of the chain from passing across another, so the chain remains unknotted and densely yet accessibly packed, in contrast to the knotted equilibrium globule a free polymer would reach. The authors emphasized that their data were consistent with, but did not prove, this model. Subsequent work transformed this picture: Rao et al. (2014) used in situ Hi-C with ~4.9 billion read pairs to reach ~1-kb resolution, revealing ~10,000 chromatin loops that frequently connect enhancers (distal regulatory DNA elements) and promoters, and contact domains (median length ~185 kb, later called topologically associating domains, or TADs — intervals that contact themselves more than they contact flanking sequence). Sanborn et al. (2015) showed these contact domains are inconsistent with both an equilibrium globule and a fractal globule, and proposed instead that loops and domains form by loop extrusion: ring-shaped cohesin complexes progressively extrude a growing loop of chromatin until they stall at boundary elements bound by CTCF, a zinc-finger architectural protein whose binding motifs arrest extrusion when oriented convergently. The loop-extrusion model was formalized in simulations by Fudenberg et al. (2016) and confirmed decisively by Rao et al. (2017), who showed that acute degradation of cohesin eliminates all loop domains while compartment domains and histone marks remain intact. This dissociation splits the 2009 problem in two: loops and TADs have an accepted molecular mechanism, whereas compartments arise through a cohesin-independent, chromatin-state-dependent process whose physical basis is still contested. Candidate mechanisms include liquid-liquid phase separation (LLPS — demixing of the nucleoplasm into condensates driven by multivalent interactions among chromatin-associated proteins and chromatin bearing histone marks), cooperative binding of bridging proteins that cross-link segments of similar chromatin state, and dimerization-driven condensation of heterochromatin protein 1 (HP1) on methylated H3K9 marks; recent work pulls in different directions (a 2025 C. elegans study attributes H3K9me chromatin segregation to HP1 dimerization rather than LLPS). In parallel, single-cell Hi-C (Nagano et al. 2013; Stevens et al. 2017) and super-resolution chromatin tracing (Bintu et al. 2018) established that TAD-like domains and loops vary substantially from cell to cell while A/B compartments and lamina-associated domains (stretches of chromatin tethered to the nuclear lamina, the protein meshwork lining the inner nuclear membrane) are organized consistently genome-wide, and electron-microscopic tomography (chromEMT; Ou et al. 2017) showed chromatin in situ as a disordered 5–24-nm-diameter curvilinear chain without regular hierarchical folding. What remains missing is an accepted mechanistic and polymer-physical account of the compartment-level and megabase-scale organization that the original Hi-C map described: the responsible molecular factors, the biophysical dynamics that maintain segregation against diffusive mixing, and the actual in-vivo polymer organization and topology (e.g., whether the chain is effectively unknotted on these scales) — together with quantitative agreement with genome-wide contact statistics and with perturbation outcomes.

Problem Statement

The 2009 Hi-C study left the mechanistic basis of its two folding principles undetermined. With the resolution, single-cell-variability, and cancer-rearrangement strands since resolved and the pure fractal-globule hypothesis superseded at the sub-megabase scale, the surviving open problem, stated at the generality of the source, is: identify the molecular factors and the biophysical dynamics that generate and maintain (i) the spatial segregation of open and closed chromatin into the two genome-wide compartments and (ii) the megabase-scale organization of chromatin — including determination of the polymer organization and topological state (for example, whether the chain is effectively unknotted, as a crumpled-globule-like state requires) that chromatin actually adopts in living cells — and provide a quantitative account of genome-wide contact statistics (contact-probability decay, compartment strength and segregation) under physiological conditions. These components stand as independently refutable sub-questions, so resolving any one of them is a partial resolution of the task; the mechanistic component is resolved only when the competing explanations — histone-mark-dependent phase separation, cooperative bridging, and dimerization-driven condensation — are discriminated by a quantitative account that agrees both with the genome-wide contact statistics and with the outcomes of perturbations that remove or neutralize each candidate.

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