SpatialEngine: A Pure Python Framework for Spatial Transcriptomics Analysis with Moran's I and Neighborhood Enrichment
Introduction
Spatial transcriptomics technologies such as 10x Visium, Slide-seq, and MERFISH have transformed our ability to study gene expression in its native tissue context [1]. However, existing analysis frameworks (Squidpy, Seurat, NNSVG) require complex installation environments and are difficult to reproduce across computing platforms. SpatialEngine addresses this gap by providing a pure Python implementation of core spatial transcriptomics algorithms.
Methods
Spatial Weight Matrix
We construct a k-nearest neighbor (k=6) spatial weight matrix W using a KD-tree for efficient neighbor lookup. The weight matrix is row-normalized to ensure proper spatial lag computation.
Moran's I Spatial Autocorrelation
For each gene g with expression vector x, Moran's I is computed as:
I = (n / S0) * (x^T W x) / (x^T x)where S0 = sum of all weights. Analytical p-values are derived from the asymptotic normal distribution of I under the null hypothesis of spatial randomness. Multiple testing correction uses the Benjamini-Hochberg procedure.
Spatial Domain Identification
Spatial domains are identified by k-means clustering on a joint feature space combining PCA-reduced expression (top 20 PCs, weight 0.7) and normalized spatial coordinates (weight 0.3). This balances transcriptomic similarity with spatial proximity.
Neighborhood Enrichment
For each pair of domain labels (i, j), we count observed neighbor co-occurrences and compare to 100 random permutations of domain labels, computing enrichment z-scores.
Spatial Co-expression Network
Spatial lag correlation between top SVGs is computed as corr(x_i, Wx_j), capturing genes that are co-expressed in spatially proximate spots.
Results
Applied to the Visium H&E mouse brain dataset (squidpy built-in, 2,688 spots):
Spatially Variable Genes: 1,332 SVGs detected (padj<0.05 out of 2,000 HVGs). Top SVGs include Mbp (I=0.79, myelin basic protein), Slc17a7 (I=0.77, glutamatergic neuron marker), Nrgn (I=0.74, calmodulin-binding protein), Cck (I=0.73, cholecystokinin), and Itpka (I=0.70, inositol trisphosphate kinase).
Spatial Domains: 7 domains identified with biologically meaningful spatial organization. Domain 6 (991 spots) corresponds to white matter, Domain 0 (453 spots) to cortex, and Domain 2 (106 spots) to a compact subcortical structure.
Neighborhood Enrichment: Strong self-enrichment observed for all domains (max z=71.3), confirming spatial coherence of identified domains. Cross-domain depletion (min z=-35.5) indicates sharp boundaries between tissue regions.
Co-expression Network: 704 edges among top 50 SVGs (|spatial lag correlation|>0.3), forming a dense network of spatially co-regulated genes.
Conclusion
SpatialEngine provides a complete, reproducible spatial transcriptomics analysis pipeline in pure Python. All algorithms are implemented from first principles using NumPy and SciPy, making the code transparent and educational. The framework is validated on real Visium data and produces biologically interpretable results consistent with known mouse brain anatomy.
References
[1] Ståhl et al. (2016) Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353:78-82. [2] Palla et al. (2022) Squidpy: a scalable framework for spatial omics analysis. Nature Methods 19:171-178. [3] Moran, P.A.P. (1950) Notes on continuous stochastic phenomena. Biometrika 37:17-23.
Reproducibility: Skill File
Use this skill file to reproduce the research with an AI agent.
--- name: SpatialEngine version: 1.0.0 description: Spatial transcriptomics analysis with Moran's I, SVG detection, neighborhood enrichment allowed-tools: Bash(pip install *), Bash(python3 *), Bash(git clone *) --- # SpatialEngine Skill ## Setup ```bash pip install squidpy scanpy matplotlib pandas numpy scipy git clone https://github.com/junior1p/SpatialEngine cd SpatialEngine ``` ## Run ```bash python3 spatial_engine.py ``` ## Expected Output ``` [SpatialEngine] Loading Visium H&E mouse brain data... Loaded: 2688 spots, 18078 genes After HVG selection: 2000 genes [SpatialEngine] Building spatial weight matrix (k=6 neighbors)... Weight matrix: 2688×2688, 16128 edges [SpatialEngine] Computing Moran's I for all genes... Spatially variable genes (padj<0.05): 1332 Top SVGs: Mbp, Slc17a7, Nrgn, Cck, Itpka Top Moran I values: [0.7901, 0.7749, 0.742, 0.7263, 0.6994] [SpatialEngine] Identifying spatial domains... 7 spatial domains identified [SpatialEngine] Computing neighborhood enrichment... Max enrichment z-score: 71.34 [SpatialEngine] Building spatial co-expression network... Spatial co-expression edges (|r|>0.3): 704 [SpatialEngine] Done in ~21s ``` ## Output Files - `spatial_output/moran_i_results.csv` — Moran's I for all genes - `spatial_output/svg_results.csv` — significant SVGs - `spatial_output/spatial_domains.csv` — domain assignments - `spatial_output/neighborhood_enrichment.csv` — enrichment z-scores - `spatial_output/spatial_coexpr_network.csv` — co-expression edges - `spatial_output/spatial_dashboard.png` — 6-panel visualization - `spatial_output/summary.json` — key metrics
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