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Hi-C: Genome-wide Chromosome Conformation Capture

Indika Rajapakse

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Total Length of Genes = 50 Million Base Pairs

Human Genome

Full Length = 3 Billion Base Pairs

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INACTIVE Gene

ACTIVE Gene

DNA

Heterochromatin

DNA is CLOSED and inaccessible

Euchromatin

DNA is OPEN and accessible

Genome can be decomposed into Two Parts

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Chromosome Conformation Capture (Hi-C)

Lieberman-Aiden, Erez, et al. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." science 326.5950 (2009): 289-293.

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Chromosome Conformation

Hi-C: All-All

=

Contact Matrix

3C: One-One

4C: One-Many

5C: Many-Many

Intra-chromosomal contacts

Inter-chromosomal

contacts

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Genome-wide Chromosome Conformation Capture (Hi-C)

Intra-chromosome

The Cell Nucleus

Inter-chromosome

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Genome-wide Chromosome Conformation Capture (Hi-C)

The Cell Nucleus

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Hi-C

No locus-specific primers!

*

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Hi-C

A

50

0

reads/Mb²

Intensity =

# of Reads

Intra-chromosomal contacts

Chromosome 8

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Hi-C

A

B

A

50

0

reads/Mb²

Intensity =

# of Reads

Chromosome 8

Intra-chromosomal contacts

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Hi-C

A

C

B

A

50

0

reads/Mb²

Intensity =

# of Reads

Chromosome 8

Intra-chromosomal contacts

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Intra-chromosome

Inter-chromosome

Hi-C: Genome-wide

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(1880 x 1880)

Active

Inactive

Mixed

LOC100

TTC29

ZNF827

SLC10A7

PROM1

FGFBP2

FGFBP1

CD38

LSM6

POU4F2

CLOCK

SRD5A3

TMEM165

8

16

24

32

40

48

56

0

-1

-0.5

0.5

1

1.5

2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Time (h)

Function (RPKM)

Here only static information is shown

Gene expression over time

Our Work

Chen H, Chen J, Muir LA, Ronquist S, Meixner W, Ljungman M, Ried T, Smale S, Rajapakse I. "Functional Organization of the Human 4D Nucleome. " Proceedings of the National Academy of Sciences 112.26 (2015): 8002-8007.

Fig. 1. Topologically associating domain (TAD) and corresponding gene expression dynamics of Chr 4. (A) Mean RNA-seq counts (RPKM) of binned genes. (B) Fiedler vector computed from the normalized Hi-C matrix. Red bins are the genes associated with the positive Fiedler vector entries, and green bins are the genes associated with negative Fiedler vector entries. (C) Hi-C matrix of Chr 4 with activity of identified TADs annotated by colored boxes on the diagonal. Active (green), inactive (blue), or mixed (black) TADs contain genes that are all actively transcribed, repressed, or a mix of both, respectively. (D1) Left, fragment read contact map of an inactive TAD with genes annotated by color; Right, no detectable transcripts from any genes in this TAD over time, with individual genes colored corresponding to the left maps. (D2) Left, fragment read contact map of an active TAD; Right, active transcription of all genes in this TAD over time. (D3) Left, fragment read contact map of a mixed TAD; Right, expression patterns of its genes are both active and inactive over time. Dashed green lines on the maps indicate Hind-III cutting sites.

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Our Work

Chen J, Hero A, and Rajapakse I. "Spectral Identification of Topological Domains." Bioinformatics 32.14 (2016): 2151-2158.

Fig. 1. Topologically associating domain (TAD) and corresponding gene expression dynamics of Chr 4. (A) Mean RNA-seq counts (RPKM) of binned genes. (B) Fiedler vector computed from the normalized Hi-C matrix. Red bins are the genes associated with the positive Fiedler vector entries, and green bins are the genes associated with negative Fiedler vector entries. (C) Hi-C matrix of Chr 4 with activity of identified TADs annotated by colored boxes on the diagonal. Active (green), inactive (blue), or mixed (black) TADs contain genes that are all actively transcribed, repressed, or a mix of both, respectively. (D1) Left, fragment read contact map of an inactive TAD with genes annotated by color; Right, no detectable transcripts from any genes in this TAD over time, with individual genes colored corresponding to the left maps. (D2) Left, fragment read contact map of an active TAD; Right, active transcription of all genes in this TAD over time. (D3) Left, fragment read contact map of a mixed TAD; Right, expression patterns of its genes are both active and inactive over time. Dashed green lines on the maps indicate Hind-III cutting sites.

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Hypergraphs and Pore-C (Oxford Nanopore Technology)

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Pore-C: Long-range Interactions Between Genomic Loci

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Our Pore-C Paper

Dotson, Gabrielle A., Can Chen, Stephen Lindsly, Anthony Cicalo, Sam Dilworth, Charles Ryan, Sivakumar Jeyarajan et al. "Deciphering Multi-way Interactions in the Human Genome." Nature Communications 13, no. 1 (2022): 5498.

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Multi-way Interactions in the Human Genome

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Fibroblast

Local Organization of the Human Genome: Fibroblasts (Indika R)

Figure 2: Local organization of the genome. (A) Incidence matrix visualization of a region in Chromosome 22 from fibroblasts (V1-V4). The numbers in the left column represent genomic loci in 100 kb resolution, vertical lines represent multi-way contacts, where nodes indicate the corresponding locus’ participation in this contact. The blue and yellow regions represent two TADs, T1 and T2. The six contacts, denoted by the labels i-vi, are used as examples to show intra- and inter-TAD contacts in B, C, and D. (B) Hyperedge and read-level visualizations of the multi-way contacts i-vi from A. Blue and yellow rectangles (bottom) indicate which TAD each loci corresponds to. (C) A hypergraph is constructed from the hyperedges from B (multiway contacts i-vi from A). The hypergraph is decomposed into its pair-wise contacts in order to be represented as a graph. (D) Contact frequency matrices were constructed by separating all multi-way contacts within this region of Chromosome 22 into their pairwise combinations. TADs were computed from the pair-wise contacts using the methods from \cite{}. Example multi-way contacts i-vi are superimposed onto the contact frequency matrices. Multi-way contacts in this figure were determined in 100 kb resolution after noise reduction, originally derived from read-level multi-way contacts (Supplemental Materials \ref{}).

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B Lymphocyte

Fibroblast

Whole Genome

25 Mb Loci

Intra and inter

Intra only

Inter only

1

2

3

...

X

Chromosomes

1

2

3

...

X

Chromosomes

Genome-Wide Multi-Way Contacts

Degree

Genome-wide Patterning

Figure 4: Genome-wide patterning of multi-way contacts. Incidence matrix visualization of the top 10 most common multi-way contacts per chromosome. Matrices are constructed at 25 Mb resolution for both fibroblasts (V1-V4) and B lymphocytes. Specifically, 5 intra-chromosomal and 5 inter-chromosomal multi-way contacts were identified for each chromosome with no repeated contacts. If 5 unique intra-chromosomal multi-way contacts are not possible in a chromosome, they are supplemented with additional inter-chromosomal contacts. Vertical lines represent multi-way contacts, nodes indicate the corresponding locus’ participation in a multi-way contact, and color-coded rows delineate chromosomes. Highlighted boxes indicate example intra-chromosomal contacts (red), inter-chromosomal contacts (magenta), and combinations of intra- and inter-chromosomal contacts (blue). Multi-way contacts of specific regions are compared between cell types by connecting highlighted boxes with black dashed lines, emphasizing similarities and differences between fibroblasts and B lymphocytes. Normalized degree of loci participating in the top 10 most common multi-way contacts for each chromosome in fibroblast and B-lymphocytes are shown on the left. Red dashed lines indicate the mean degree for fibroblasts and B lymphocytes (top and bottom, respectively). Genomic loci that do not participate in the top 10 most common multi-way contacts for fibroblasts or B lymphocytes were removed from their respective incidence and degree plots. Multi-way contacts were determined in 25 Mb resolution after noise reduction (Supplementary Materials \ref{}).

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Data-driven Identification of Transcription Factories (clusters)

Figure 6: Data-driven identification of transcription factories. (A) A 5 kb region before and after each locus in a Pore-C read (between red dashed lines) is queried for chromatin accessibility and RNA Pol II binding (ATAC-seq and ChIP-seq, respectively) to identify “label”. Multi-way contacts between “label” are indicative of potential transcription clusters. Gene expression (RNA-seq, E₁ for gene 1 and E₂ for gene 2, respectively) and transcription factor binding sites (TF₁ and TF₂) are integrated to determine potential coexpression and coregulation within multi-way contacts with multiple genes. Transcription factor binding sites are queried +/- 5 kb from the gene’s transcription start site (Materials and Methods). (B) Pipeline for extracting transcription clusters (Supplementary Materials X). Genes are colored based on the overlapping Pore-C locus, and the extended line from each gene represents the 5 kb flanking region used to query transcription factor binding sites. (C) Schematic representation of a transcription cluster.

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Data-driven Identification of Transcription Factories (clusters)

Figure 6: Data-driven identification of transcription factories. (A) A 5 kb region before and after each locus in a Pore-C read (between red dashed lines) is queried for chromatin accessibility and RNA Pol II binding (ATAC-seq and ChIP-seq, respectively) to identify “label”. Multi-way contacts between “label” are indicative of potential transcription clusters. Gene expression (RNA-seq, E₁ for gene 1 and E₂ for gene 2, respectively) and transcription factor binding sites (TF₁ and TF₂) are integrated to determine potential coexpression and coregulation within multi-way contacts with multiple genes. Transcription factor binding sites are queried +/- 5 kb from the gene’s transcription start site (Materials and Methods). (B) Pipeline for extracting transcription clusters (Supplementary Materials X). Genes are colored based on the overlapping Pore-C locus, and the extended line from each gene represents the 5 kb flanking region used to query transcription factor binding sites. (C) Schematic representation of a transcription cluster.

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Classes of Transcription Clusters

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Hypergraph Analysis Toolbox (HAT)

Project Goal: Create an open source software for hypergraph analysis

Status: Our software is available on the Mathworks File exchange and in Python.

Pickard J, Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “HAT: Hypergraph Analysis Toolbox,” June 5, 2023

Availability:

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Hypergraphs

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Biology

Dotson G, Lindsly S, Chen C, Dilworth S, Jeyaraja S, Meixner W, Stansbury C, Cicalo A, Beckloff N, Ryan C, Surana A, Wicha M, Muir L, Rajapakse I. "Deciphering Multi-way Interactions in the Human Genome." Nature Communications (2022).

Mathematics

Rajapakse I, and Smale S. "Emergence of Function from Coordinated Cells in a Tissue." Proceedings of the National Academy of Sciences 114.7 (2017): 1462-1467.
Surana A, Chen C, Rajapakse I. "Hypergraph Similarity Measures." IEEE Transactions on Network Science and Engineering, 2022 October
Chen C, Surana A, Bloch A, Rajapakse I. "Controllability of Hypergraphs." IEEE Transactions on Network Science and Engineering, 2021 Mar 23(2021).
Chen C, Surana A, Bloch A, Rajapakse I. "Multilinear Control Systems Theory." SIAM Journal on Control and Optimization, 59.1 (2021): 749-776.
Chen C, Rajapakse I. "Tensor Entropy for Uniform Hypergraphs." IEEE Transactions on Network Science and Engineering 7.4 (2020): 2889-2900.
Pickard J, Surana A, Bloch A, Rajapakse I. Observability of Hypergraphs, arXiv:2304.04883, Accepted (2023 62nd IEEE Conference on Decision and Control (CDC)
Pickard J, Stansbury C, Chen C, Surana A, Bloch A, Rajapakse I. Kronecker product of tensors and hypergraphs, arXiv preprint arXiv:2305.03875

Toolbox

Pickard J, Can C, Salman R, Stansbury C, Kim S, Surana A, Rajapakse I. “HAT: Hypergraph Analysis Toolbox,” June 5, 2023

Patents

US20220406407A1: Deciphering Multi-Way Interactions In The Human Genome With Use Of Hypergraphs. Indika Rajapakse, Can Chen, Stephen Lindsly: Submitted November 2022.
115-008219-US-PS1 Network approach to navigating the human genome. Indika Rajapakse: Submitted November 2020.

Papers