Spatial regression of morphology-protein coupling in tumour proteomics

Spatial proteomics has enabled high-resolution characterization of protein organization within tumor microenvironments, yet most computational approaches implicitly assume spatial homogeneity and focus on clustering rather than diffusion constraints imposed by tissue morphology. Here, we model morphology-protein coupling in triple- negative breast cancer using geographically weighted regression (GWR) applied to 41 publicly available Multiplexed Ion Beam Imaging (MIBI) samples comprising 36 protein markers. Single-cell morphometric features were extracted from MIBI spots and combined with spatial adjacency graphs to model location-specific protein dispersion. Compared with ordinary least squares and ridge regression baselines, GWR consistently demonstrated superior performance across regression metrics, explaining substantially greater spatial variance in protein intensity (+.4 R² improvements across markers) while reducing mean absolute and squared errors. Information-theoretic analysis showed lower (Aikake Information Criterion Corrected) AICc values for GWR across the majority of markers, indicating improved model fit. Spatial autocorrelation diagnostics further confirmed that GWR residuals exhibited near-random structure, with significant reductions in Moran's I and Geary's C relative to global models, demonstrating effective capture of local heterogeneity. Eight proteins with significant spatial autocorrelation, including B7-H3 and Beta-catenin, showed pronounced morphology- dependent dispersion patterns that were not recoverable using global regression. These results indiate that explicitly modeling spatial heterogeneity yields more accurate and interpretable representations of protein organization and is consistent with a diffusion- barrier view of pathoproteomics beyond agglomeration alone.