[Paper Review] From Effective Interactions Extracted Using Hi-C Data to Chromosome Structures in Conventional and Inverted Nuclei

Sucheol Shin, Guang Shi+1 more|arXiv (Cornell University)|Apr 5, 2023

Genomics and Chromatin Dynamics76 references4 citations

TL;DR

This study introduces a parameter-free method to extract effective interaction energies between chromosomal loci directly from Hi-C data using statistical potentials (SP), revealing that heterochromatin attraction drives A/B compartment formation. Polymer simulations using these SP-derived energies quantitatively reproduce chromosomal organization, including TADs and phase separation, and predict an inverted nuclear architecture consistent with rod photoreceptors—validating the SP approach as a physically grounded, predictive framework for chromosome structure.

ABSTRACT

Contact probabilities between loci, separated by arbitrary genomic distance, for a number of cell types have been reported using genome-wide chromosome conformation capture (Hi-C) experiments. How to extract the effective interaction energies between active euchromatin (A) and inactive heterochromatin (B) directly from the experimental data, without an underlying polymer model, is unsolved. Here, we first calculate the pairwise effective interaction energies (A-A, B-B, or A-B) for interphase chromosomes based on Hi-C data by using the concept of Statistical Potential (SP), which assumes that the interaction energy between two loci is proportional to the logarithm of the frequency with which they interact. Polymer simulations, using the extracted interaction energy values $ extit{without any parameter}$, reproduce the segregation between A and B type loci (compartments), and the emergence of topologically associating domains (TADs), features that are prominent in the Hi-C data for interphase chromosomes. Remarkably, the values of the SP automatically satisfy the Flory-Huggins phase separation criterion for all the chromosomes, which explains the mechanism of compartment formation in interphase chromosomes. Strikingly, simulations using the SP that accounts for pericentromeric constitutive heterochromatin (C-type), show hierarchical structuring with the high density of C-type loci in the nuclear center, followed by localization of the B type loci, with euchromatin being confined to the nuclear periphery, which differs from the expected nuclear organization of interphase chromosomes, but is in accord with the imaging data of the inverted nuclei found in photoreceptor rods in nocturnal mammals. The proposed parameter free method and applications show that compartment formation in conventional and inverted nuclei is best explained by the inequality between the effective interaction energies.

Motivation & Objective

• To develop a parameter-free method for extracting effective interaction energies between chromosomal loci directly from Hi-C contact maps.
• To determine whether statistical potentials (SPs) derived from Hi-C data can reproduce key chromosomal features like compartments and TADs without fitting polymer model parameters.
• To test if the Flory-Huggins phase separation criterion is satisfied by the extracted SPs, explaining A/B compartment formation.
• To investigate whether the same SP-derived interactions can predict non-conventional nuclear architectures, such as inverted nuclei in nocturnal mammalian rods.
• To validate the robustness of SPs across different Hi-C data normalization methods.

Proposed method

• Apply the statistical potential (SP) formalism to Hi-C contact frequency data, defining interaction energy as ΔG ∝ -kB T ln(P(r_ij)/Q(r_ij)), where P is observed contact probability and Q is reference distribution.
• Use the Redner-des Cloizeaux distribution as the reference Q(r_ij), based on Rouse or self-avoiding chain models, with parameters derived from normalization and first-moment constraints.
• Calculate mean SP values for A-A, B-B, and A-B interactions from raw, unbalanced Hi-C contact matrices to avoid bias from matrix normalization.
• Use the extracted SP values as input for polymer simulations based on the Chromosome Copolymer Model (CCM), with no additional fitting.
• Compute the Flory-Huggins interaction parameter χ_FH from SP values to assess phase separation propensity.
• Compare simulated 3D chromosome structures with experimental Hi-C data and imaging data (e.g., FISH) to validate predictions.

Experimental results

Research questions

• RQ1 Can effective interaction energies between chromosomal loci be extracted directly from Hi-C data without fitting polymer model parameters?
• RQ2 Do the extracted SP values satisfy the Flory-Huggins criterion for phase separation, explaining A/B compartment formation?
• RQ3 Can SP-derived interactions in polymer simulations reproduce experimentally observed features such as TADs and compartmentalization?
• RQ4 Do the SP-derived interactions predict the inverted nuclear architecture seen in nocturnal mammalian rod photoreceptors?
• RQ5 How robust are the SP values to different Hi-C data normalization procedures?

Key findings

• The extracted SP values for A-B interactions are significantly more negative than A-A or B-B, indicating stronger heterochromatin attraction, which drives compartment formation.
• The Flory-Huggins parameter χ_FH calculated from SPs is greater than zero (χ_FH = 0.44 ± 0.13), confirming phase separation between A and B chromatin types.
• Polymer simulations using SP-derived interactions successfully reproduce TADs and A/B compartmentalization observed in Hi-C data.
• Simulations predict a hierarchical nuclear organization with C-type heterochromatin at the center, B-type in the middle, and A-type at the periphery—matching the inverted nucleus of nocturnal mammalian rods.
• SP values remain consistent across raw and normalized Hi-C matrices, with only minor differences in ε_BB and ε_AA, confirming robustness to data processing.
• The SP-based method successfully predicts the inverted nuclear architecture, validating its physical consistency with imaging data.