🧬 biology

CellBRIDGE: Learning Cellular Trajectories via Interaction-Aware Alignment

CellBRIDGE is a novel framework that enhances trajectory inference in single-cell RNA sequencing by integrating ligand-receptor mediated cell-cell communication costs into Optimal Transport, thereby improving the accuracy of cellular dynamics reconstruction and enabling mechanistically interpretable in silico perturbations.

Original authors: Silas Ruhrberg Estévez, Nicolas Huynh, Tennison Liu, Roderik M. Kortlever, Gerard I. Evan, David L. Bentley, Mihaela van der Schaar

Published 2026-06-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Silas Ruhrberg Estévez, Nicolas Huynh, Tennison Liu, Roderik M. Kortlever, Gerard I. Evan, David L. Bentley, Mihaela van der Schaar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are trying to figure out the life story of a crowd of people, but you only have a few blurry snapshots taken at different times. You can't watch any single person move from one photo to the next because, in this experiment, taking a photo destroys the person (this is how single-cell RNA sequencing works: you have to kill the cell to read its genes).

Your goal is to connect the dots: "Who was that person in the first photo? Where did they go in the second? And what path did they take?"

This is the challenge of CellBRIDGE. Here is how the paper explains it, using simple analogies.

The Problem: The "Least Action" Mistake

Traditionally, scientists tried to solve this by assuming that people (cells) take the shortest, smoothest path between photos. If a person looks a bit like someone in the next photo, they probably moved there. This is like assuming everyone in a crowd walks in a straight line to their destination.

The Flaw: This ignores how people actually interact. In a real crowd, people don't just walk randomly; they talk to each other, push each other, or follow leaders. In biology, cells talk to each other using chemical "handshakes" called ligand-receptor pairs. A cell might send a signal (a ligand) that tells another cell (with a matching receptor) to change its behavior.

If you ignore these conversations, you might connect the wrong people. You might think Cell A moved to Spot B just because they look similar, when in reality, Cell A was actually pushed there by a signal from Cell C.

The Solution: CellBRIDGE (The "Conversation Map")

The authors created a new tool called CellBRIDGE. Instead of just looking at how similar two cells look (their "face"), it also looks at who they are talking to.

Think of it like trying to match up dancers in two different photos of a ballroom dance:

Old Method (Feature-Only): You match the dancers based on their outfits. "That guy in the red suit in Photo 1 must be the guy in the red suit in Photo 2."
CellBRIDGE: You match them based on their outfits AND who they are holding hands with. "That guy in the red suit in Photo 1 was holding hands with the girl in the blue dress. In Photo 2, the guy in the red suit is still holding hands with the girl in the blue dress. Therefore, they are definitely the same pair."

CellBRIDGE builds a "conversation map" for every snapshot. It figures out which cells are sending signals to which other cells. Then, when it tries to match cells from one time to the next, it ensures that the pattern of conversations stays consistent. If Cell A was talking to Cell B in the first photo, the tool looks for a match in the second photo where the new Cell A is still talking to the new Cell B.

How It Works (The "Bridge")

The paper uses a mathematical concept called Optimal Transport (which is basically finding the most efficient way to move a pile of sand from one spot to another).

The "Sand": The cells.
The "Cost": How much effort it takes to move a cell from one state to another.
The "Bridge": CellBRIDGE adds a new rule to the cost. It says, "Moving a cell is cheap if it looks similar, BUT it becomes very expensive (a bad match) if you break their conversation network."

By balancing these two rules (looking similar + keeping conversations intact), the tool builds a much more accurate "bridge" connecting the snapshots.

What They Found

The researchers tested this on both fake data (where they knew the answer) and real biological data (like lung cancer and immune cells).

Better Maps: When they used CellBRIDGE, the connections between cells were much more accurate than when they just looked at appearance.
Predicting the Future (In Silico): Because the tool understands the mechanism of communication (who talks to whom), they could run a "what-if" simulation.
- The Experiment: They told the computer, "Pretend Cell A stops sending its signal to Cell B."
- The Result: The computer predicted that the cells would change their path.
- The Validation: When they looked at real lung cancer data, silencing specific signals (like EGFR or ALK pathways) in the simulation caused the cells to change direction in a way that matched real-world medical knowledge about how drugs that block these pathways work.

The Bottom Line

CellBRIDGE is a new way to reconstruct the life stories of cells. It realizes that cells don't just evolve in isolation; they evolve by talking to each other. By listening to those conversations, we can build a much clearer picture of how diseases like cancer develop and how cells might react to treatments.

Important Note: The paper specifically mentions that this method works best when the "conversation patterns" stay somewhat stable over the time period being studied. If the cells are changing so fast that their entire social network collapses and rebuilds instantly (like in very rapid embryonic development over long gaps), the tool might get confused, just as a map would be useless if the roads kept disappearing and reappearing every second.

Technical Summary: CellBRIDGE

Problem Statement

Inferring cellular dynamics from population snapshots is a fundamental challenge in single-cell RNA sequencing (scRNA-seq). Because scRNA-seq measurements are destructive, individual cells cannot be tracked across time, rendering trajectory inference an underdetermined problem. While Optimal Transport (OT) provides a principled framework for aligning distributions across timepoints, standard approaches rely solely on gene-expression distances. These methods implicitly treat cells as independent particles, neglecting structured cell–cell communication (CCIs) mediated by ligand–receptor (LR) signaling, which is known to drive development and disease. Consequently, the choice of cost function in OT remains a bottleneck for generating biologically meaningful couplings.

Methodology: CellBRIDGE

The authors introduce CellBRIDGE (Cell-Based Regularized Interaction-Driven Gene Expression), a framework that augments feature-based OT with a directed, typed interaction cost derived from LR activity.

1. Interaction-Aware Cost Construction

Instead of relying on spatial coordinates (which are unavailable in dissociated scRNA-seq), CellBRIDGE constructs proxy communication networks within each snapshot:

Preprocessing: Gene expression counts are normalized and mapped to $[0, 1]$ using a Hill saturation function to capture receptor occupancy effects.
Scoring: For a set of $P$ ligand-receptor pairs, a directed, non-negative CCI tensor $G \in \mathbb{R}^{n \times n \times P}_{\geq 0}$ is constructed. The interaction score between a sender cell $i$ and receiver cell $j$ for pair $p$ is calculated as the product of ligand expression in $i$ and receptor expression in $j$ .
Structure: This results in a multi-channel, directed representation of cell–cell communication.

2. Fused Gromov–Wasserstein (FGW) Formulation

CellBRIDGE frames the alignment problem as a Fused Gromov–Wasserstein (FGW) optimization. It seeks a coupling $\Gamma$ that minimizes a weighted sum of two terms:

Feature Cost ( $F$ ): The standard transport cost in gene-expression space (e.g., squared Euclidean distance), enforcing smooth evolution of transcriptional states.
Structure Cost ( $S$ ): A distortion term measuring the mismatch between the directed, multi-channel interaction profiles of source and target cell pairs.

The objective function is:
$\min_{\Gamma \in \Pi(a,b)} (1-\alpha) \langle \Gamma, C \rangle_F + \alpha \sum_{i,k,j,l} \phi(g^{(0)}_{i \to k}, g^{(1)}_{j \to l}) \Gamma_{ij} \Gamma_{kl}$
where $\alpha \in [0, 1]$ balances feature similarity and interaction structure preservation, and $\phi$ is a similarity metric (default: squared Euclidean distance) between LR-channel vectors.

3. Modularity and Downstream Integration

A key design principle is that the interaction prior is injected only at the coupling level. The resulting coupling $\Gamma^*$ serves as a plug-and-play input for various continuous-time trajectory models, including:

Conditional Flow Matching (CFM): Learning deterministic velocity fields.
Metric Flow Matching (MFM): Learning flows on a data-dependent Riemannian manifold.
Stochastic Schrödinger Bridges (SF2M): Modeling stochastic dynamics.
Unbalanced OT: Accounting for population mass changes (proliferation/apoptosis).

The framework solves the non-convex FGW problem using a customized conditional-gradient (Frank-Wolfe) routine and employs a normalization scheme to ensure the feature and structure terms are on comparable scales.

Key Contributions

Cost-Function View: The paper identifies OT cost design as a critical lever for snapshot alignment, proposing the smoothness of directed, typed cell–cell communication as a biologically grounded prior orthogonal to the principle of least action in gene expression.
Typed, Directed FGW: The authors generalize FGW to handle multi-relation (vector-valued) directed interaction structures derived from LR signaling, yielding interaction-aware couplings.
Broad Applicability: The method demonstrates that interaction-aware couplings improve trajectory inference across diverse frameworks (CFM, MFM, SF2M, UOT), establishing CCI structure as a general-purpose prior.
Mechanistic Interpretability: By operating on the LR catalog, CellBRIDGE enables in silico perturbations. Silencing specific LR pairs in the catalog induces trajectory shifts that recapitulate expected biological effects of pathway inhibition.

Experimental Results

The authors evaluated CellBRIDGE on synthetic data and six real-world scRNA-seq datasets (including lung tumor, V1 cortex, dendritic cell stimulation, and mouse embryo development).

Coupling Quality: On synthetic data with known ground-truth transport maps, incorporating interaction structure ( $\alpha > 0$ ) significantly recovered the true transport map, whereas feature-only OT ( $\alpha=0$ ) failed due to misalignment of clusters with similar expression but different signaling roles.
Trajectory Inference: Across real datasets, CellBRIDGE consistently reduced interpolation errors (Wasserstein-1 and Wasserstein-2 distances) compared to state-of-the-art baselines (e.g., TrajectoryNet, DSB, Moscot, OT-CFM). The best performance was typically achieved with a balanced setting ( $\alpha \approx 0.5$ ), though some datasets (e.g., Dendritic Stimulus) favored structure-only ( $\alpha=1$ ).
Biological Grounding: Ablation studies confirmed that gains were driven by coherent LR structure. Randomizing the LR catalog or shuffling CCI tensor entries degraded performance.
In Silico Perturbations: On lung cancer data, silencing specific LR pairs (EGFR, ALK, MET) induced trajectory shifts consistent with known therapeutic pathway inhibition, while edits to unrelated cardio-renal pathways had negligible effects.
Limitations: The method relies on the assumption that interaction geometry is approximately persistent across snapshots. In rapidly remodeling systems with large temporal gaps (e.g., mouse embryo development over 6 days), the interaction prior became uninformative, and performance did not improve over feature-only OT.

Significance and Claims

The paper claims that CellBRIDGE addresses the underdetermined nature of trajectory inference by injecting a biological inductive bias: the smooth evolution of ligand-receptor communication. By decoupling the structural prior from the dynamics model, CellBRIDGE offers a modular, interpretable approach that improves alignment fidelity and enables mechanism-specific counterfactual analysis. The authors emphasize that their method does not require spatial data, making it applicable to standard dissociated scRNA-seq, and that it complements existing advances in generative modeling by refining the endpoint correspondence problem without altering downstream architectures.