Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations (2501.02409v2)

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.

• The paper introduces PerturbODE, a framework that integrates neural ODEs with regulatory constraints to jointly model cellular dynamics and infer gene regulatory networks.
• It employs implicit GRN encoding, dimensionality reduction, and explicit intervention inputs to capture non-linear interactions and cyclic gene regulation.
• Experimental results on simulated and TF Atlas data demonstrate improved scalability, precision, and generalization to unseen genetic perturbations.

Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations

The paper introduces PerturbODE, a novel framework designed to address the complexities inherent in gene regulatory network (GRN) discovery from high-throughput perturbational data. The methodology combines neural ordinary differential equations (neural ODEs) with novel regulatory constraints to model cellular dynamics and infer GRNs, offering a potential advancement over existing approaches that are often hindered by restrictive assumptions, such as linearity and acyclicity, and limited scalability.

Methodology Overview

PerturbODE integrates biologically informative neural ODEs to capture cell state trajectories under genetic perturbations, deriving causal GRNs from these dynamics. The framework is differentiated from other models by several key features:

1. Implicit GRN Encoding: The neural ODEs encode GRNs in their parameters, facilitating joint trajectory inference and GRN discovery.
2. Dimensionality Reduction: Cell states are mapped into a lower-dimensional "gene module" space, analogous to causal representation learning (CRL).
3. Explicit Intervention Input: The model allows explicit input of perturbed genes, enhancing its applicability in scenarios with diverse genetic perturbations.
4. Flexibility in Modeling: It supports modeling cycles and non-linear gene interactions, avoiding the acyclicity constraint that limits other methods.
5. Diffusion-Inspired Regularization: A novel regularization technique is incorporated to maintain the stability and consistency of predicted cell dynamics.

Experimental Results

The efficacy of PerturbODE is evaluated through simulated datasets using the SERGIO model and real experimental data from the TF Atlas. In simulated setups, PerturbODE shows competitive performance in terms of precision, recall, and AUPRC when compared to existing methods like DCDFG, DCDI, and NO-TEARS variants, while notably surpassing these models in scalability.

PerturbODE successfully demonstrates its ability to predict unseen interventions in the TF Atlas dataset, highlighting its potential for generalization across varied experimental conditions. With the TF Atlas data, it is shown to handle large-scale datasets involving thousands of genes, an area where many traditional methods falter due to computational complexity.

The model’s GRN predictions also revealed insightful biological modules that align with known regulatory interactions, underscoring PerturbODE’s potential in uncovering nuanced gene regulatory mechanisms, including cycles like negative autoregulation, which are often ignored by models constrained to DAG structures.

Implications and Future Directions

The development of PerturbODE represents a significant methodological step forward in the computational modeling of GRNs, providing a scalable and interpretable framework that can accommodate the vast complexity of genetic interactions at the cellular level. The ability to model non-linear dynamics and cycles offers researchers a more comprehensive tool for studying gene regulation, particularly in single-cell contexts where dynamic changes are paramount.

Practically, PerturbODE could enhance the understanding of cellular responses to genetic perturbations in fields such as developmental biology and cancer research. The framework's interpretability ensures that the inferred models remain accessible and usable by biologists, potentially guiding experimental design and validation efforts.

Future work might involve refining the theoretical underpinnings concerning the identifiability of neural ODEs in causal inference and expanding the framework's applicability to processing multi-modal data sources, integrating external datasets to further bolster prediction accuracy and biological relevance. Furthermore, exploring the integration of additional biological constraints into the model could further refine predictions and enhance the biological validity of inferred GRNs.