2026 Theses Doctoral

Kernel Methods for Spatial RNA Biology

Su, Jiayu

Biological function is organized in space, and molecular programs including RNA processing vary dynamically across anatomical and microenvironmental contexts. In glioblastoma, for example, microenvironmental pH triggers isoform switching in ribosomal genes that drives tumor stemness and correlates with worse patient outcome. Spatial transcriptomics and related technologies now measure thousands of molecular features across intact tissues, but our ability to interpret these measurements lags behind. Methods for identifying spatially structured variation lack consensus and clear theoretical properties, while tools for analyzing transcript diversity beyond gene-level summaries remain scarce.

This thesis develops kernel-based statistical methods that integrate spatial information to detect patterns, model dependencies, and resolve isoform-level regulation in tissue context. I begin by establishing theoretical foundations for spatial pattern detection through a universal quadratic-form statistic. We demonstrate that virtually all existing spatial variability tests are equivalent up to their choice of kernel, and use spectral analysis to identify when and why widely used methods such as Moran's I fail. The resulting graph Laplacian-based corrections enable robust, scalable detection of spatial patterns across millions of locations and single-cell lineage-tracing data. Building on these foundations, I develop Smoother, a framework that explicitly models spatial dependency by incorporating tissue structure through priors and regularization.

This approach converts non-spatial models into spatially aware versions, improving imputation, cell-type deconvolution, and dimensionality reduction. Applications show that joint modeling of spatial and single-cell data improves label transfer accuracy, and reveal tissue restructuring and plasma cell localizations in colorectal cancer. I then address challenges in analyzing in situ RNA processing, a largely unexplored dimension of spatial biology. SPLISOSM detects spatial patterns and regulatory associations at transcript resolution while overcoming data sparsity and platform-specific limitations.

Analysis of adult mouse and human brain reveals widespread spatially variable transcript diversity with conserved regulatory programs, while application to glioblastoma uncovers transcript variation in antigen presentation and adhesion genes linked to microenvironmental conditions. Together, these contributions provide theoretical understanding and practical tools for detecting and interpreting spatial patterns of RNA biology, unlocking new directions and potentials in isoform-resolution analysis for complex tissues.