PHi-C: Deciphering Hi-C Data Into Polymer Dynamics - PubMed

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Abstract

Genomes are spatiotemporally organized within the cell nucleus. Genome-wide chromosome conformation capture (Hi-C) technologies have uncovered the 3D genome organization. Furthermore, live-cell imaging experiments have revealed that genomes are functional in 4D. Although computational modeling methods can convert 2D Hi-C data into population-averaged static 3D genome models, exploring 4D genome nature based on 2D Hi-C data remains lacking. Here, we describe a 4D simulation method, PHi-C (polymer dynamics deciphered from Hi-C data), that depicts 4D genome features from 2D Hi-C data by polymer modeling. PHi-C allows users to interpret 2D Hi-C data as physical interaction parameters within single chromosomes. The physical interaction parameters can then be used in the simulations and analyses to demonstrate dynamic characteristics of genomic loci and chromosomes as observed in live-cell imaging experiments. PHi-C is available at https://github.com/soyashinkai/PHi-C.

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Figures

Figure 1.

Figure 1.

Overview of PHi-C pipeline. Hi-C…

Figure 1.

Overview of PHi-C pipeline. Hi-C contact matrix data generated from a hic file…

Figure 1. Overview of PHi-C pipeline. Hi-C contact matrix data generated from a hic file through JUICER are deciphered by the PHi-C optimization algorithm based on the polymer network model. Then, 4D polymer dynamics simulations of the polymer network model with the optimized interaction parameters are carried out.
Figure 2.

Figure 2.

(Upper) In the bead–spring model,…

Figure 2.

(Upper) In the bead–spring model, the probability density of the distance r ij …

Figure 2. (Upper) In the bead–spring model, the probability density of the distance rij between the ith and jth beads (or monomers) is characterized by only the standard deviation Σij. (Lower) The contact Gaussian kernel function can capture contacts with the contact distance σ.
Figure 3.

Figure 3.

The polymer network model is…

Figure 3.

The polymer network model is characterized by connectivity between all pairs of monomers,…

Figure 3. The polymer network model is characterized by connectivity between all pairs of monomers, expressed by the interaction matrix kij. The matrix kij is reversibly converted into the contact matrix Cij through matrix transformations formula image. Each matrix has dimensionless values with a normalization factor.
Figure 4.

Figure 4.

( A ) Theoretical curves…

Figure 4.

( A ) Theoretical curves of the contact probability P ( s )…

Figure 4. (A) Theoretical curves of the contact probability P(s) in Equation (4). P(s) is normalized by the value at s/c = |i − j| = 1, where i and j are monomer indices of the fractal polymer and c represents the genomic size corresponding to every monomer. (Left) P(s) for fixed df = 2.0 and σ/b = 0.2, 0.5, 1.0, 2.0 and 5.0. (Right) P(s) for fixed σ/b = 1.0 and df = 1.5, 2.0, 3.0 and 4.0. Theoretical scaling relations, as in Equation (5), are shown. (B) Contact probability (blue) for yeast cells with 160-bp nucleosome resolution (31) as a function of genomic distance averaged across the genome, and the theoretically fitted curve (orange) at a small genomic distance.
Figure 5.

Figure 5.

Painting contact patterns for intra-…

Figure 5.

Painting contact patterns for intra- and interdomain interactions ( A ), loop interactions…

Figure 5. Painting contact patterns for intra- and interdomain interactions (A), loop interactions (B) and heterogeneous connectivity along the polymer backbone (C). (Upper) Designed interactions in the polymer network model. (Lower) Converted contact matrix, with a snapshot of polymer conformations in the polymer dynamics simulation (Supplementary Videos S1–S3). (C) TAD-like domains are highlighted by dashed lines. (Right) Removal of a domain-boundary part (yellow) results in domain fusion.
Figure 6.

Figure 6.

Demonstrations of PHi-C for Hi-C…

Figure 6.

Demonstrations of PHi-C for Hi-C data of mESCs. ( A ) PHi-C analysis…

Figure 6. Demonstrations of PHi-C for Hi-C data of mESCs. (A) PHi-C analysis for chromosomes 6 (left) and 17 (right) of mESCs. (Upper) Contact matrices of the Hi-C experiment (binned at 500 kb), and contact probabilities as a function of genomic distance. (Middle) 4C-like profiles of Nanog (left) and Oct4 (right) loci. High-interaction regions are highlighted (pink). (Lower) Optimized contact matrices by PHi-C, and correlation plots between formula image and formula image. (B) Theoretical MSD curves of Nanog and Oct4 loci. (C) Probability densities of the gyration radius of 105 conformations for the 50.5-Mb genomic regions around Nanog and Oct4 loci in mESCs. (D) Polymer models derived from PHi-C analysis for Nanog and Oct4 loci on chromosomes 6 and 17, respectively. Pink highlighted regions on the polymer models correspond to the regions in the 4C-like profile of (A).
Figure 7.

Figure 7.

Demonstrations of PHi-C for Hi-C…

Figure 7.

Demonstrations of PHi-C for Hi-C data of DT-40 cells. ( A ) PHi-C…

Figure 7. Demonstrations of PHi-C for Hi-C data of DT-40 cells. (A) PHi-C analysis for chromosome 7 of DT-40 cells at G2 (0 min), 5, 15, 30 and 60 min. Contact matrices of the Hi-C experiment with 100-kb bins (upper) and optimized contact matrices with the correlation value (lower). (B) Snapshots of polymer conformations in a 4D polymer dynamics simulation. (C) Time series of the shape lengths of the major (yellow) and minor (purple) axes for polymer conformations in 100 polymer dynamics simulations starting from the same initial conformation. Thick curves represent the averages. (D) Curves of optimized interaction parameters, formula image, averaged at each genomic distance (separation, |i − j| × 100 kb). A triangle indicates a position of a local peak inducing compaction within 2 Mb. Arrows indicate positions of a local peak generating periodicity of attractive interactions around 4, 6 and 10 Mb at 15, 30 and 60 min, respectively.
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