🧬 Loop Density Inference from Hi-C Data

Code and data accompanying the paper

“A universal polymer signature in Hi-C resolves cohesin loop density and supports monomeric extrusion”
K. Polovnikov & D. Starkov (2025). bioRxiv: 10.1101/2025.09.04.674214v2

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📘 Overview

This repository reproduces the main data–theory figures from the paper and provides a code to infer the cohesin loop density (inverse loop period $T^{-1}$) and the effective fragment length $v_0^{\text{eff}}$ from a precomputed Hi-C contact scaling curve $P(s)$.

At short genomic separations, the slope of the contact probability curve (P(s)) exhibits a conserved local minimum (“dip”) whose position scales with the geometric mean of loop period $T$ and $v_0^{\mathrm{eff}}$ and depth depends only on $v_0^{\mathrm{eff}}/T$:

$$ s_{\min} \sim \sqrt{T v_0^{\mathrm{eff}}}, \qquad y_{\min} = f\left(\frac{v_0^{\mathrm{eff}}}{T}\right) $$

This two-parameter reduction provides a universal fingerprint of cohesin loop density.

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📂 Repository Structure

├── data/
│ ├── full_logder_x_.pickle # Mids (genomic distances)
│ ├── full_logder_y_.pickle # Log-derivatives (smoothed slopes of log P(s))
│ ├── ... # Main datasets used in the paper & optimal parameters 
│ └── data_table_info.xlsx # The descriptive table of the datasets and the inferred parameters for each data
│
├── data/data_fig4
│ ├── full_logder_x_.pickle # Mids (genomic distances)
│ ├── full_logder_y_.pickle # Log-derivatives (smoothed slopes of log P(s))
│ └── ... # The datasets used for Fig. 4 and Fig. S4
│
├── notebooks/
│ ├── fig2A_logders_git.ipynb # Reproduces Fig. 2A (experimental log-derivatives)
│ ├── fig4A,S4A_RAD21_NIPBL_degron_git.ipynb # Reproduces Figs. 4A,S4A (partial RAD21 and NIPBL degradation)
│ ├── fig4B,S4B_protocol_variation_git.ipynb # Reproduces Figs. 4B,S4B (protocol effects for HFF & hESC cells)
│ ├── fig5A_fountain_git.ipynb # Reproduces Fig. 5A (fountain diagram)
│ ├── fig5A_fountain_aux_git.ipynb # Extra notebook with the parameter inference for data in Fig. 5A 
│ └── infer_params.ipynb # Example notebook: fit the model to a given Hi-C scaling or log-derivative
│
├── notebooks/src/
│ ├── utils.py # Helper fitting functions used in notebooks
| └── data_load.py # Helper functions to load the data
│
├── src/
│ ├── infer_density.py # Scripts to fit a user scaling from the CLI
│ ├── Cutoff_Full_Theory_shared.nb # a WM notebook with the full theory 
│
│
├── LICENSE
└── README.md

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⚙️ Data Description

All data used in the paper are stored in the data/ folder as Python pickle files.
Each dataset contains:

• full_logder_x_<dataset>.pickle → mids (genomic distances, kb)
• full_logder_y_<dataset>.pickle → log-derivative (smoothed derivative of log P(s))

These files correspond to the datasets analyzed in the manuscript (Abramo, Bonev, Rao, Zhang, Wutz, Schwarzer, etc.).

No preprocessing from raw .cool files is required — these intermediate products are already included for reproducibility.

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🧩 Reproducing Paper Figures

All figure notebooks are provided in the notebooks/ folder:

Notebook	Description
fig2A_logders_git.ipynb	Plots all experimental log-derivatives used in Fig. 2A.
fig4A,S4A_RAD21_NIPBL_degron_git.ipynb	Reproduces Figs. 4A,S4A — RAD21 & NIPBL degradation (loop density reduction).
fig4B,S4B_protocol_variation_git.ipynb	Reproduces Fig. 4B,S4B (protocol variation).
fig5A_fountain_git.ipynb	Reproduces Fig. 5A (fountain diagram).
fig5A_fountain_aux_git.ipynb	Extra notebook with the parameter inference for data in Fig. 5A
infer_params.ipynb	Demonstrates parameter inference from a given data.

Each notebook loads pickled genomic intervals and $P(s)$ log-derivatives from data/ to reproduce the paper's figures.

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🔍 Inferring Loop Density from Your Own Data

You can infer the loop period $T$, loop density $T^{-1}$, and effective fragment length $v_0^{\mathrm{eff}}$ for any custom scaling $P(s)$ using either:

• the interactive notebook notebooks/infer_params.ipynb, or
• the command-line tool src/infer_density.py.

Below is an example of using the command-line tool on two pickle files containing mids and slopes (log-derivatives) precomputed from a Hi-C .cool file:

python src/infer_density.py \
  --x data/full_logder_x_<dataset>.pickle \
  --y data/full_logder_y_<dataset>.pickle \

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⚙️ Installation

1. Clone the repository

git clone https://github.com/kipolovnikov/loop-density-hic.git
cd loop-density-hic

2. Create the conda environment

conda env create -f environment.yml
conda activate loop-density-hic

3. (Optional) Install manually via pip

pip install cooler numpy scipy matplotlib pandas jupyter

🤝 Acknowledgments

Developed by Kirill Polovnikov and Dmitry Starkov. We thank Job Dekker and Leonid Mirny for valuable feedback. Supported by the Russian Science Foundation (Grant No. 25-13-00277) and the Alexander von Humboldt Foundation.