A scalable gene network model of regulatory dynamics in single cells
FLeCS integrates gene networks into coupled ODEs, enabling scalable inference of single-cell transcriptional dynamics with improved interpretability.
Key Findings
Methodology
FLeCS embeds gene network structures into coupled nonlinear ODEs, using message passing algorithms for efficient computation of regulatory parameters. It employs the adjoint method for gradient calculation, facilitating large-scale parameter inference from (pseudo)time-series data. The model constructs gene expression dynamics by modeling production as a linear function of regulators' expression levels, activated through sigmoid functions. It allows network modifications to simulate perturbations like gene knockouts, and integrates cell trajectories via optimal transport matching. Training involves minimizing the discrepancy between predicted and observed gene expression profiles, enabling accurate dynamic reconstruction and mechanistic insights.
Key Results
- In myeloid differentiation datasets, FLeCS outperformed OT-CFM and scTour, achieving over 20% higher velocity confidence scores on held-out test cells, accurately capturing cell trajectories. The inferred regulatory parameters were sparse, aligning with biological expectations. Perturbation simulations correctly identified affected gene interactions, validated by posterior distribution analyses. Functional enrichment of identified gene sets showed strong overlap with known biological processes, surpassing traditional differential expression methods.
- The model successfully inferred gene regulatory mechanisms under Cebpa and Cebpe knockouts, revealing lineage-specific differentiation shifts consistent with experimental observations. Posterior distributions of interaction strengths indicated significant perturbation effects, with many relationships unaffected, demonstrating model specificity. Trajectory predictions under perturbations matched experimental lineage outcomes, confirming the model’s predictive power.
- FLeCS's ability to generate realistic single-cell trajectories and simulate perturbation effects at scale offers a new avenue for understanding cellular responses, disease mechanisms, and therapeutic targets, with potential for integration into multi-omics frameworks for comprehensive cellular modeling.
Significance
This work addresses the longstanding challenge of scalable, interpretable dynamic modeling of single-cell gene expression. By integrating gene networks into differential equations and leveraging message passing, FLeCS overcomes computational barriers faced by traditional methods. Its capacity to infer mechanistic regulatory relationships and simulate perturbations at large scale advances both fundamental biology and translational research, enabling precise dissection of cellular responses and intervention strategies. The approach bridges the gap between high-dimensional data and functional understanding, promising to accelerate discoveries in developmental biology, immunology, and disease modeling.
Technical Contribution
FLeCS introduces a novel framework combining gene network constraints with coupled nonlinear ODEs, solved efficiently via message passing algorithms. It employs the adjoint sensitivity method for gradient computation, allowing scalable training on high-dimensional gene expression data. Unlike black-box models, FLeCS provides explicit mechanistic parameters, supporting interpretability and targeted intervention simulations. Its flexible architecture accommodates network modifications, enabling direct modeling of perturbations, and its scalable inference pipeline makes it suitable for large datasets with tens of thousands of genes.
Novelty
This is the first method to explicitly incorporate gene regulatory network structures into large-scale differential equation models for single-cell data, avoiding low-dimensional embeddings. It combines network-guided modeling with efficient gradient-based training, enabling detailed mechanistic inference across thousands of genes. Unlike prior approaches limited to small networks or low-dimensional projections, FLeCS scales to real biological datasets, providing both trajectory inference and mechanistic insights simultaneously.
Limitations
- The assumption of time-invariant regulatory functions may oversimplify dynamic regulatory changes during processes like differentiation or stress responses.
- Dependence on the accuracy of the initial gene network constrains performance; incomplete or incorrect networks can bias results.
- High computational cost of solving large-scale coupled ODEs limits real-time application and may require substantial hardware resources.
Future Work
Future efforts will focus on integrating multi-omics data to refine network structures and capture dynamic regulatory changes. Enhancing computational efficiency through algorithmic innovations and parallelization will broaden applicability. Extending the framework to include stochastic effects and non-equilibrium dynamics could further improve biological realism, enabling broader adoption in systems biology and precision medicine.
AI Executive Summary
Understanding how genes regulate each other over time within single cells remains a fundamental challenge in biology. Traditional models often rely on low-dimensional embeddings or simplified assumptions, which limit their ability to reveal true regulatory mechanisms, especially when dealing with noisy, high-dimensional data. Addressing this gap, the present work introduces FLeCS, a scalable framework that embeds gene regulatory network structures directly into coupled nonlinear differential equations. By leveraging message passing algorithms, FLeCS efficiently computes regulatory parameters across thousands of genes, enabling detailed modeling of cellular transcriptional dynamics.
The core innovation lies in combining network-guided modeling with the adjoint method for gradient calculation, allowing the inference of time-invariant regulatory functions from large-scale single-cell trajectory data. The model constructs gene expression dynamics by modeling production as a linear function of regulators, activated through sigmoid functions, and incorporates perturbation simulations by modifying network structure. Extensive validation on myeloid differentiation and Perturb-seq datasets demonstrates that FLeCS outperforms existing methods like OT-CFM and scTour, achieving higher accuracy in trajectory prediction and mechanistic inference. It successfully identifies perturbed regulatory relationships, consistent with biological expectations, and reveals key gene modules involved in lineage specification.
Beyond trajectory inference, FLeCS offers the ability to simulate cellular responses under various perturbations, providing insights into gene function and interaction. Its capacity to handle large networks and noisy data marks a significant advance in single-cell systems biology. The approach opens new avenues for understanding cellular decision-making, disease mechanisms, and therapeutic interventions. Future developments aim to incorporate multi-omics data, improve computational efficiency, and model dynamic regulatory functions, further enhancing its utility in biomedical research.
Deep Dive
Abstract
Single-cell data provide high-dimensional measurements of the transcriptional states of cells, but extracting insights into the regulatory functions of genes, particularly identifying transcriptional mechanisms affected by biological perturbations, remains a challenge. Many perturbations induce compensatory cellular responses, making it difficult to distinguish direct from indirect effects on gene regulation. Modeling how gene regulatory functions shape the temporal dynamics of these responses is key to improving our understanding of biological perturbations. Dynamical models based on differential equations offer a principled way to capture transcriptional dynamics, but their application to single-cell data has been hindered by computational constraints, stochasticity, sparsity, and noise. Existing methods either rely on low-dimensional representations or make strong simplifying assumptions, limiting their ability to model transcriptional dynamics at scale. We introduce a Functional and Learnable model of Cell dynamicS, FLeCS, that incorporates gene network structure into coupled differential equations to model gene regulatory functions. Given (pseudo)time-series single-cell data, FLeCS accurately infers cell dynamics at scale, provides improved functional insights into transcriptional mechanisms perturbed by gene knockouts, both in myeloid differentiation and K562 Perturb-seq experiments, and simulates single-cell trajectories of A549 cells following small-molecule perturbations.