PreprintCited by 6Genomics and Chromatin DynamicsProtein Structure and DynamicsGene Regulatory Network Analysis

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Chromatin Structures from Integrated AI and Polymer Physics Model

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Schultz, Eric R, Kyhl, Soren, Willett, Rebecca, de Pablo, Juan J·2024·PLoS Computational Biology

Preprint — published as 10.1371/journal.pcbi.1012912 · Paper page

Abstract

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. Three-dimensional characterization of genome structure is critical to understanding these biological processes. Direct experimental measurements of genome structure are challenging; computational models of chromatin structure are therefore necessary. We develop an approach that combines a particle-based chromatin polymer model, molecular simulation, and machine learning to efficiently and accurately estimate chromatin structure from indirect measures of genome structure. More specifically, we introduce a new approach where the interaction parameters of the polymer model are extracted from experimental Hi-C data using a graph neural network (GNN). We train the GNN on simulated data from the underlying polymer model, avoiding the need for large quantities of experimental data. The resulting approach accurately estimates chromatin structures across all chromosomes and across several experimental cell lines despite being trained almost exclusively on simulated data. The proposed approach can be viewed as a general framework for combining physical modeling with machine learning, and it could be extended to integrate additional biological data modalities. Ultimately, we achieve accurate and high-throughput estimations of chromatin structure from Hi-C data, which will be necessary as experimental methodologies, such as single-cell Hi-C, improve.

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Fig 1 Overview of key elements. (A) Schematic overview of the experimental data pipeline. Given an experimental contact map, we construct a probability distribution over chromatin structures corresponding to our chromatin polymer model. The graph neural network (GNN) uses the contact map as an input and predicts interaction parameters, U^, of our chromatin physics model. Given these parameters, the polymer model samples chromatin structures at random. Structures are colored by A/B compartmentalization as determined by the sign of the first principal component of the experimental genomic-distance normalized contact map. (B) Schematic overview of GNN training procedure. We train the GNN on simulated contact maps generated by the chromatin physics model where we know the ground truth interaction parameters. (C) Schematic illustration of chromatin polymer model. Particles are colored according to their position along the polymer to aid visualization. Particles in the same grid cell are defined as in contact. Grid size is not to scale.
Fig 1 Overview of key elements. (A) Schematic overview of the experimental data pipeline. Given an experimental contact map, we construct a probability distribution over chromatin structures corresponding to our chromatin polymer model. The graph neural network (GNN) uses the contact map as an input and predicts interaction parameters, U^, of our chromatin physics model. Given these parameters, the polymer model samples chromatin structures at random. Structures are colored by A/B compartmentalization as determined by the sign of the first principal component of the experimental genomic-distance normalized contact map. (B) Schematic overview of GNN training procedure. We train the GNN on simulated contact maps generated by the chromatin physics model where we know the ground truth interaction parameters. (C) Schematic illustration of chromatin polymer model. Particles are colored according to their position along the polymer to aid visualization. Particles in the same grid cell are defined as in contact. Grid size is not to scale.CC BY · PubMed Central
Fig 2 Chromatin simulation using GNN approach accurately reproduces experimental contact map. (A) Contact maps of IMR90 Chr2:56.3-81.9 Mb. The lower triangle shows the experimental contact map. The color bar is the same for both subfigures. Left: The upper triangle shows the GNN simulated contact map. Right: The upper triangle shows the maximum entropy simulated contact map. (B–C) Comparison of the experiment (black), maximum entropy simulation (blue), and GNN simulation (red). (B) Comparison of contact probability scaling as a function of genomic separation on a log-log scale. (C) Comparison of first principal component of genomic-distance normalized contact maps. (D) A representative structure from GNN simulation. Colored by A/B compartmentalization. (E) Comparison of total run time in minutes for all contact maps in the experimental test set ( n = 40 ) . Boxes represent the 25th and 75th quantiles, and the solid line indicates the median. Whiskers extend from the box by 1.5 times the interquartile range.
Fig 2 Chromatin simulation using GNN approach accurately reproduces experimental contact map. (A) Contact maps of IMR90 Chr2:56.3-81.9 Mb. The lower triangle shows the experimental contact map. The color bar is the same for both subfigures. Left: The upper triangle shows the GNN simulated contact map. Right: The upper triangle shows the maximum entropy simulated contact map. (B–C) Comparison of the experiment (black), maximum entropy simulation (blue), and GNN simulation (red). (B) Comparison of contact probability scaling as a function of genomic separation on a log-log scale. (C) Comparison of first principal component of genomic-distance normalized contact maps. (D) A representative structure from GNN simulation. Colored by A/B compartmentalization. (E) Comparison of total run time in minutes for all contact maps in the experimental test set ( n = 40 ) . Boxes represent the 25th and 75th quantiles, and the solid line indicates the median. Whiskers extend from the box by 1.5 times the interquartile range.CC BY · PubMed Central
Fig 3 GNN generalizes to unseen cell types. Left: GM12878 human lymphoblastoid cell line Chr2:5.1-30.7 Mb. Middle: HUVEC murine umbilical vein endothelial cell line Chr2:5.1-30.7 Mb. Right: CH12.LX mouse lymphoma cell line. (A) Comparison of experimental and GNN simulated contact maps. The lower triangle shows the experiment, and the upper triangle shows the GNN simulation. The color bar is the same for all subfigures. SCCs between simulated and experimental contact maps are 0.67, 0.70, and 0.76, respectively. (B–C) Comparison of the experiment (black), maximum entropy (blue), and GNN (red). (B) Comparison of the first principal component of genomic-distance normalized contact maps. (C) Comparison of contact probability scaling.
Fig 3 GNN generalizes to unseen cell types. Left: GM12878 human lymphoblastoid cell line Chr2:5.1-30.7 Mb. Middle: HUVEC murine umbilical vein endothelial cell line Chr2:5.1-30.7 Mb. Right: CH12.LX mouse lymphoma cell line. (A) Comparison of experimental and GNN simulated contact maps. The lower triangle shows the experiment, and the upper triangle shows the GNN simulation. The color bar is the same for all subfigures. SCCs between simulated and experimental contact maps are 0.67, 0.70, and 0.76, respectively. (B–C) Comparison of the experiment (black), maximum entropy (blue), and GNN (red). (B) Comparison of the first principal component of genomic-distance normalized contact maps. (C) Comparison of contact probability scaling.CC BY · PubMed Central
Fig 4 GNN reproduces patterns in spatial distances from super-resolution chromatin tracing experiments. We obtain experimental structures at 50 kb resolution Su et al. [3,4]. Top row: IMR90 Chr2:10-25.6 Mb. Bottom row: IMR90 Chr21:14-39.6 Mb. (A–B) Mean spatial distance scaling as a function of genomic separation for experiment (black), GNN simulation (red), and maximum entropy simulation (blue). (B) The additional dotted black line corresponds to an experimental structure of IMR90 Chr21:28Mb-29.2 Mb at 30 kb resolution from Bintu et al. [3]. (C–D) Mean spatial distance matrices. The lower triangle shows the experimental distance matrix. Left: The upper triangle shows the GNN simulated distance matrix. Right: The upper triangle shows the maximum entropy simulated distance matrix.
Fig 4 GNN reproduces patterns in spatial distances from super-resolution chromatin tracing experiments. We obtain experimental structures at 50 kb resolution Su et al. [3,4]. Top row: IMR90 Chr2:10-25.6 Mb. Bottom row: IMR90 Chr21:14-39.6 Mb. (A–B) Mean spatial distance scaling as a function of genomic separation for experiment (black), GNN simulation (red), and maximum entropy simulation (blue). (B) The additional dotted black line corresponds to an experimental structure of IMR90 Chr21:28Mb-29.2 Mb at 30 kb resolution from Bintu et al. [3]. (C–D) Mean spatial distance matrices. The lower triangle shows the experimental distance matrix. Left: The upper triangle shows the GNN simulated distance matrix. Right: The upper triangle shows the maximum entropy simulated distance matrix.CC BY · PubMed Central

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Metadata

Authors
Schultz, E. R., Kyhl, S., Willett, R., & de Pablo, J. J.
Affiliations
University of Chicago (US)
Venue
PLoS Computational Biology
Publisher
openRxiv
Published
2024-11-29
Volume
21
Issue
4
Pages
e1012912-e1012912
ISSN
1553-734X (ISSN-L)
OpenAlex
W4409311852
Cited by
6
References
2
Citations by year
2026: 4 · 2025: 2
FWCI
1.80
Type
journal article
Language
en
Open access
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Knowledge@UChicago (University of Chicago) (submittedVersion)
  • University of Chicago (cc-by)
Funders
  • National Science Foundation (2023109)
  • Simons Foundation (MP-TMPS- 00005320)
  • Division of Physics (PHY2317138)
  • Division of Mathematical Sciences (DMS-AWD00000326, DMS-2023109)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Chromatin Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
Keywords
chromatin structure, 3D genome organization, Hi-C data, graph neural networks, single-cell Hi-C
MeSH terms
Machine Learning, Chromatin, Computer Simulation, Humans, Models, Molecular, Polymers, Neural Networks, Computer, Computational Biology

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