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Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations

Zaikang Lin, Sei Chang, Aaron Zweig, Minseo Kang, Elham Azizi, David A. Knowles

TL;DR

PerturbODE introduces a scalable, dynamics-aware approach to GRN discovery from perturbation-rich scRNA-seq data by modeling cell trajectories with a neural ODE whose parameters encode the GRN via a latent gene-module representation. The framework combines shift and perfect interventions, an OT-based loss with diffusion regularization, and a post-hoc mapping of module interactions to the full gene network $\mathbf{G} = A \ \mathrm{diag}(\alpha) \ B$, enabling both trajectory prediction and causal discovery. Across SERGIO, BoolODE, TF Atlas, and ChIP-Atlas benchmarks, PerturbODE achieves competitive or superior performance to scalable baselines and reveals interpretable regulatory modules aligned with known developmental programs. The results demonstrate strong generalization to held-out perturbations and offer a path toward integrating additional omics data to further refine GRN inference, with implications for developmental biology and therapeutic target discovery.

Abstract

Modern high-throughput biological datasets with thousands of perturbations provide the opportunity for large-scale discovery of causal graphs that represent the regulatory interactions between genes. Differentiable causal graphical models have been proposed to infer a gene regulatory network (GRN) from large scale interventional datasets, capturing the causal gene regulatory relationships from genetic perturbations. However, existing models are limited in their expressivity and scalability while failing to address the dynamic nature of biological processes such as cellular differentiation. We propose PerturbODE, a novel framework that incorporates biologically informative neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the causal GRN from the neural ODE's parameters. We demonstrate PerturbODE's efficacy in trajectory prediction and GRN inference across simulated and real over-expression datasets.

Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations

TL;DR

PerturbODE introduces a scalable, dynamics-aware approach to GRN discovery from perturbation-rich scRNA-seq data by modeling cell trajectories with a neural ODE whose parameters encode the GRN via a latent gene-module representation. The framework combines shift and perfect interventions, an OT-based loss with diffusion regularization, and a post-hoc mapping of module interactions to the full gene network , enabling both trajectory prediction and causal discovery. Across SERGIO, BoolODE, TF Atlas, and ChIP-Atlas benchmarks, PerturbODE achieves competitive or superior performance to scalable baselines and reveals interpretable regulatory modules aligned with known developmental programs. The results demonstrate strong generalization to held-out perturbations and offer a path toward integrating additional omics data to further refine GRN inference, with implications for developmental biology and therapeutic target discovery.

Abstract

Modern high-throughput biological datasets with thousands of perturbations provide the opportunity for large-scale discovery of causal graphs that represent the regulatory interactions between genes. Differentiable causal graphical models have been proposed to infer a gene regulatory network (GRN) from large scale interventional datasets, capturing the causal gene regulatory relationships from genetic perturbations. However, existing models are limited in their expressivity and scalability while failing to address the dynamic nature of biological processes such as cellular differentiation. We propose PerturbODE, a novel framework that incorporates biologically informative neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the causal GRN from the neural ODE's parameters. We demonstrate PerturbODE's efficacy in trajectory prediction and GRN inference across simulated and real over-expression datasets.
Paper Structure (44 sections, 18 equations, 28 figures, 6 tables)

This paper contains 44 sections, 18 equations, 28 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Neural ODE formulation for over-expression with shift intervention
  5. Neural ODE formulation with perfect intervention
  6. Mapping dynamics to targets using optimal transport
  7. Diffusion-based regularization of neural dynamics
  8. Results
  9. GRN inference on simulated datasets
  10. GRN inference on the TF Atlas
  11. PerturbODE achieves the highest recall and statistical significance on the TF Atlas human reference GRNs.
  12. PerturbODE achieves the highest AUPRC on reference GRNs from ChIP-Atlas.
  13. PerturbODE uncovers biologically meaningful gene network structure from its latent GRN modules.
  14. Predicting the effects of held-out interventions on gene expression
  15. Discussion
  16. ...and 29 more sections

Figures (28)

  • Figure 1: PerturbODE models the effect of a TF perturbation on stem cell differentiation by integrating the learned neural ODE function $f$ from the initial cell states $Y^{(0)}$ under intervention $I_r$. The predicted final cell states $\widehat{Y}^{(r)}$ are then compared to the observed differentiated gene expression values using the Wasserstein distance. From the parameters of $f$, we extract an underlying GRN.
  • Figure 2: Performance metrics on data simulated from a synthetic GRN ($10$ genes) using BoolODE assuming perfect over‑expression (CRISPR‑a). $5$ runs are conducted for the synthetic GRN.
  • Figure 3: Performance metrics on SERGIO‑simulated data assuming perfect over‑expression (CRISPR‑a). $5$ runs are conducted for the yeast GRN.
  • Figure 4: GRN inference performance on the TF Atlas dataset ($812$ genes), evaluated against three experimentally validated human GRNs.
  • Figure 5: GRN inference on TF Atlas dataset ($812$ genes), validated with ChIP-Atlas.
  • ...and 23 more figures