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Applications of temporal graph learning for predicting the dynamics of biological systems

This work-in-progress paper proposes a temporal graph learning framework that models cellular dynamics as evolving gene regulatory networks, demonstrating its superiority over static foundation models like scGPT in forecasting gene expression and regulatory interactions across mouse developmental datasets.

Original authors: Manuel Dileo, Andrea Sottoriva

Published 2026-05-28

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CC BY 4.0

Original authors: Manuel Dileo, Andrea Sottoriva

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand how a single cell grows up to become a specialized part of the body, like a red blood cell or a pancreas cell.

The Problem: The "Snapshot" Limitation
Currently, scientists have powerful tools (called "foundation models") that are like super-smart encyclopedias. They have read millions of genetic "books" and can tell you what a cell looks like right now. However, these tools mostly take static snapshots. They can tell you, "This cell is a baby," or "This cell is a teenager," but they struggle to predict how the cell will change next.

Think of it like looking at a photo album. You can see a baby, a toddler, and a teenager, but if you only have the photos, it's hard to predict exactly what the teenager will look like when they become an adult. You miss the movement and the story of how they got there.

The New Idea: The "Movie" Approach
The authors of this paper propose a new way to look at biology. Instead of just taking photos, they want to make a movie.

They do this by:

Creating a Timeline: They take a pile of cells and arrange them in order, from "youngest" to "oldest," based on their genetic activity. They call this "pseudotime."
Drawing Maps: At each step of this timeline, they draw a map of how genes talk to each other. These are called Gene Regulatory Networks (GRNs). Imagine a map where genes are cities and the lines between them are roads showing who is giving orders to whom.
Watching the Movie: As the cell develops, these maps change. Roads open, roads close, and new cities become important. The authors treat this sequence of changing maps as a temporal graph (a graph that moves through time).

The Tool: The "Time-Traveling Architect"
To predict the future of these cells, they use a special type of AI called Temporal Graph Neural Networks.

Think of a standard AI as an architect who looks at one blueprint and guesses the next room. The new AI is like a time-traveling architect who watches the entire history of the building being constructed. It sees how the foundation was laid, how the walls went up, and how the plumbing was installed. Because it understands the process of construction, it can predict the next floor much better than someone who just looks at a single blueprint.

The Experiment: Testing the Movie
The team tested this on two real-life biological "movies":

Mouse Red Blood Cell Development: How a cell becomes a red blood cell.
Mouse Pancreas Development: How a cell becomes part of the insulin-making system.

They asked the AI three questions:

Gene Expression: "If the cell is doing X right now, what genes will it turn on next?"
Link Prediction: "Which genes will start talking to each other next?" (Like predicting who will become friends next).
Hub Prediction: "Which genes will become the most important bosses (hubs) in the next stage?"

The Results: The Movie Wins
The results were surprising and promising:

Beating the Encyclopedias: The "movie" approach (Temporal Graph Learning) performed better than the current "encyclopedia" champions (scGPT and scFoundation). This suggests that knowing the history of how genes interact is just as important as knowing what the genes are.
The Best Architect: A specific type of AI called GCRN-GRU (which uses a mix of graph math and memory) was the best at predicting the future. It was particularly good at spotting the "boss genes" that control the cell's development.
Real Biology: When the AI predicted which genes would become the "bosses," it turned out to be correct. It correctly identified genes known to be crucial for making blood cells, proving the model isn't just guessing; it's learning real biological rules.

The Bottom Line
This paper argues that to truly understand how life develops, we need to stop treating cells like static photos and start treating them like moving movies. By using AI that understands how relationships change over time, we can predict the future of biological systems more accurately than ever before.

Note: The authors state this is a "work-in-progress" paper, meaning they are still refining these ideas and plan to test them on more datasets in the future.

Technical Summary: Applications of Temporal Graph Learning for Predicting the Dynamics of Biological Systems

Problem Statement
Recent advances in biological foundation models (e.g., scGPT, scFoundation, Geneformer) have demonstrated strong performance in learning representations from single-cell transcriptomic data using transformer architectures. However, these approaches predominantly operate in static settings, failing to explicitly model the temporal evolution of developmental programs. This limitation is critical in developmental biology, where cellular states continuously emerge, differentiate, and reorganize. While technologies like pseudotime inference and RNA velocity allow for the reconstruction of ordered trajectories from asynchronous single-cell data, existing methods typically treat cellular states independently or model them as static snapshots, neglecting the evolving regulatory structure (Gene Regulatory Networks, or GRNs) that underpins developmental transitions. The core challenge is to formulate developmental biological systems as evolving graph processes suitable for temporal graph learning, thereby enabling the prediction of future biological states beyond static representation.

Methodology
The authors propose a pipeline that transforms single-cell transcriptomic data into discrete-time temporal graphs to apply Temporal Graph Neural Networks (TGNNs). The methodology proceeds as follows:

Trajectory Inference and Discretization: Starting from single-cell gene-expression matrices, developmental trajectories are inferred using Diffusion Pseudotime (DPT). Cells are then aggregated into temporal bins (snapshots) based on their pseudotime values. The bin size is optimized to balance temporal resolution with the statistical robustness required for GRN inference (typically targeting 300–500 cells per snapshot).
Temporal GRN Construction: For each pseudotime bin, a Gene Regulatory Network (GRN) is inferred using SCENIC. This framework combines gene co-expression analysis with transcription factor motif enrichment to identify biologically meaningful regulatory interactions. The result is a discrete-time temporal graph $G = \{G(1), \dots, G(T)\}$ $G = {G (1), \dots, G (T)}$ , where each snapshot $G(t)$ $G (t)$ contains:
- Nodes ( $V$ ): Genes with persistent identities across time.
- Edges ( $E(t)$ ): Regulatory interactions inferred at time $t$ .
- Node Features ( $X(t)$ ): Aggregated gene-expression statistics (mean, median, variance, etc.) within the bin.
- Edge Features: Confidence scores from the GRN inference.
Temporal Graph Learning: TGNNs are applied to this sequence of graphs to learn temporal node representations that capture both structural dependencies within snapshots and temporal dynamics across them.
Forecasting Tasks: The framework is evaluated on three complementary tasks:
- Future Gene-Expression Forecasting: Predicting the temporal variation in mean gene expression ( $\Delta x$ ) between consecutive snapshots.
- Future Link Prediction: Estimating the probability of regulatory interactions existing in the next snapshot $G(t+1)$ .
- Future Out-Degree Centrality Prediction: Forecasting the topological importance (out-degree) of genes in future snapshots to identify regulatory hubs.

Key Contributions and Results
The study evaluates the proposed framework on two publicly available mouse developmental datasets: erythroid gastrulation and pancreatic endocrinogenesis. The results highlight several key findings:

Superiority over Static Foundation Models: In gene-expression forecasting, graph-based temporal models consistently outperformed established biological foundation models (scGPT and scFoundation). This suggests that explicitly modeling the evolving regulatory structure provides predictive information that static, pre-trained representations alone cannot capture.
Effectiveness of Spectral Architectures: Spectral graph convolution architectures, specifically ChebNet and GCRN-GRU, emerged as the strongest performers across all tasks. The authors hypothesize that these architectures are particularly well-suited for the heterophilous and hub-centered topology of GRNs, where transcription factors act as central regulators connected to multiple targets. Spectral convolutions may effectively propagate information across multi-hop neighborhoods in these star-like topologies.
Temporal Dynamics in Link Prediction: For link prediction, temporal models (particularly GCRN-GRU) significantly outperformed static baselines (GCN, GAT) and simple memorization strategies (EdgeBank). This indicates that the datasets contain non-trivial temporal dynamics beyond simple edge persistence, which TGNNs successfully capture.
Biological Relevance of Hub Forecasting: The model successfully identified temporally important regulatory hubs. In the erythroid gastrulation dataset, the predicted centrality trajectories aligned with known biological programs: early stages were dominated by proliferative regulators (e.g., E2f8, Ran), while later stages showed increasing centrality for canonical erythroid regulators (e.g., Klf1, Spi1, Erg).

Significance and Claims
The paper positions temporal graph learning as a promising and complementary paradigm to current foundation-model approaches in single-cell biology. The authors claim that:

Explicit Modeling of Dynamics: Reformulating developmental systems as evolving graphs allows for the explicit modeling of regulatory structure changes, offering a distinct advantage over static representation learning.
Complementarity: Rather than replacing foundation models, temporal graph learning offers a necessary extension for tasks requiring the prediction of dynamic system evolution, such as developmental progression and disease trajectory.
Feasibility: Despite the destructive nature of single-cell RNA sequencing (which prevents direct tracking of individual cells), computational reconstruction of temporal graphs via pseudotime binning is a viable strategy for applying deep learning to dynamic biological systems.

The work is presented as a "work-in-progress," with the authors noting plans to extend the benchmark to additional datasets, newer foundation models, and more recent temporal attention-based architectures (e.g., DyGFormer) in future work.

Technical Summary: Applications of Temporal Graph Learning for Predicting the Dynamics of Biological Systems

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