One Chromatin, Many Structures: From Ensemble Contact Maps to Single-Cell 3D Organization

Area of Science:

• * *Chromatin organization and genome architecture.
• * *Computational biology and biophysics.

Background:

• * *Experimental assays for chromatin folding capture low-dimensional projections of heterogeneous polymer structures.
• * *Understanding three-dimensional chromatin folding and its relationship to experimental observables remains a challenge.

Purpose of the Study:

• * *To present an ensemble-based interpretive framework, the Self-Returning Excluded Volume (SR-EV) model, for generating and analyzing chromatin conformations.
• * *To interpret experimental signatures like Hi-C loops and topologically associating domains (TADs) as ensemble-level statistical enrichments.

Main Methods:

• * *Development of the SR-EV model, a minimal generator of nucleosome-resolution chromatin conformations using stochastic return rules and excluded-volume geometry.
• * *Generation of large ensembles of three-dimensional chromatin configurations.
• * *Projection of 3D conformations onto 2D contact maps and 1D genomic profiles; calculation of coordination number and probe-based accessibility.

Main Results:

• * *The SR-EV model reproduces key experimental signatures across scales, including nanoscale packing domains, sparse single-configuration contact patterns, and ensemble-level contact enrichment consistent with TADs.
• * *Hi-C loops and TADs are interpreted as statistical enrichments within heterogeneous ensembles, not invariant single-cell features.
• * *A unified link is established between 3D packing, 2D contact maps, and 1D genomic profiles via coordination number and accessibility.

Conclusions:

• * *Chromatin domains and TADs can emerge from minimal geometric rules and ensemble-level bias, rather than requiring explicit molecular interactions or deterministic folding.
• * *The SR-EV framework highlights the probabilistic nature of genome architecture, emphasizing that chromatin organization is realized in individual cells but best analyzed through ensembles.
• * *Provides a tractable reference for interpreting multimodal genomic and imaging data by distinguishing single-configuration heterogeneity from ensemble statistical organization.