Spatial Graph Neural Network

The foundational step where tissue is abstracted into a Spatial Neighborhood Graph. Nodes represent cells or capture spots, and edges are defined by spatial proximity.

• Delaunay Triangulation: Connects nodes without crossing edges, ideal for single-cell data.
• k-Nearest Neighbors (kNN): Connects each node to its k closest neighbors, controlling graph sparsity.
• Radius Graphs: Connects all nodes within a fixed distance r, preserving a physical distance threshold.

The choice of graph construction directly impacts the receptive field and the scale of biological patterns the GNN can detect.

The core learning mechanism where nodes iteratively aggregate feature information from their neighbors. This process embeds spatial context directly into gene expression profiles.

• GraphSAGE: Learns an aggregation function (mean, LSTM, pooling) to combine neighbor features.
• Graph Attention Networks (GAT): Uses multi-head attention to learn the importance of each neighboring node, allowing the model to focus on biologically relevant interactions.
• ChebNet: Defines convolutional filters in the spectral domain of the graph Laplacian, enabling efficient localized filtering.

After L message-passing layers, a node's representation captures information from its L-hop neighborhood.

An unsupervised learning task where a GNN clusters nodes into functional tissue compartments without prior anatomical labels. This is often achieved by optimizing a modularity or graph cut objective.

• Spatially Informed Clustering: Methods like SpaGCN combine gene expression, spatial location, and histology images in a joint latent space before clustering.
• Contrastive Learning: Models like STAGATE use a graph attention autoencoder with a contrastive loss to learn boundary-aware representations.
• Hidden Markov Random Fields: A probabilistic framework that models spatial dependencies between domain labels to ensure smooth, contiguous regions.

GNNs are uniquely suited to model intercellular communication by predicting interactions between spatially proximal cell types. This moves beyond simple co-expression to a spatially constrained interaction model.

• Heterogeneous Graphs: Nodes are typed as different cell phenotypes, and edges represent potential ligand-receptor (L-R) pairs.
• Link Prediction: The GNN is trained to predict the likelihood of an L-R interaction between two nodes based on their local neighborhood context.
• Directional Communication: Attention weights in a GAT can be interpreted as the direction and strength of a signaling gradient from a ligand-expressing cell to a receptor-expressing cell.

GNNs can computationally enhance the resolution of spatial transcriptomics data by predicting gene expression at unmeasured locations or for unmeasured genes.

• Denoising Autoencoders: A GNN-based autoencoder reconstructs a clean expression matrix from a corrupted input, correcting for spatial dropout and technical noise.
• Super-Resolution: Models like XFuse use a generative GNN framework to predict sub-spot expression patterns by integrating histological image features with low-resolution spatial data.
• Cross-Modality Prediction: A GNN trained on spatial transcriptomics can predict the spatial distribution of proteins or epigenetic marks, performing spatial multi-omics integration in silico.

GNNs can reconstruct dynamic biological processes, such as cellular differentiation, by ordering cells based on their spatial context and gene expression.

• Graph Autoencoders: Learn a low-dimensional latent space where cells are ordered along a pseudotime trajectory, constrained by the spatial graph structure.
• Optimal Transport: A GNN learns to map cells from one spatial distribution to another, inferring the most probable developmental paths through tissue space.
• RNA Velocity on Graphs: A GNN smooths and propagates RNA velocity vectors across the spatial neighborhood graph, predicting the future transcriptional state of cells in situ.