Recent advancements in spatial transcriptomics (ST) technologies offer unprecedented opportunities to unveil the spatial heterogeneity of gene expression and cell states within tissues. Despite these capabilities of the ST data, accurately dissecting spatiotemporal structures (e.g., spatial domains, temporal trajectories, and functional interactions) remains challenging. Here, we introduce a computational framework, PearlST (partial differential equation [PDE]-enhanced adversarial graph autoencoder of ST), for accurate inference of spatiotemporal structures from the ST data using PDE-enhanced adversarial graph autoencoder. PearlST employs contrastive learning to extract histological image features, integrates a PDE-based diffusion model to enhance characterization of spatial features at domain boundaries, and learns the latent low-dimensional embeddings via Wasserstein adversarial regularized graph autoencoders. Comparative analyses across multiple ST datasets with varying resolutions demonstrate that PearlST outperforms existing methods in spatial clustering, trajectory inference, and pseudotime analysis. Furthermore, PearlST elucidates functional regulations of the latent features by linking intercellular ligand-receptor interactions to most contributing genes of the low-dimensional embeddings, as illustrated in a human breast cancer dataset. Overall, PearlST proves to be a powerful tool for extracting interpretable latent features and dissecting intricate spatiotemporal structures in ST data across various biological contexts.

Unraveling molecular regulatory networks underlying disease progression is critically important for understanding disease mechanisms and identifying drug targets. The existing methods for inferring gene regulatory networks (GRNs) rely mainly on time-course gene expression data. However, most available omics data from cross-sectional studies of cancer patients often lack sufficient temporal information, leading to a key challenge for GRN inference. Through quantifying the latent progression using random walks-based manifold distance, we propose a latent-temporal progression-based Bayesian method, PROB, for inferring GRNs from the cross-sectional transcriptomic data of tumor samples. The robustness of PROB to the measurement variabilities in the data is mathematically proved and numerically verified. Performance evaluation on real data indicates that PROB outperforms other methods in both pseudotime inference and GRN inference. Applications to bladder cancer and breast cancer demonstrate that our method is effective to identify key regulators of cancer progression or drug targets. The identified ACSS1 is experimentally validated to promote epithelial-to-mesenchymal transition of bladder cancer cells, and the predicted FOXM1-targets interactions are verified and are predictive of relapse in breast cancer. Our study suggests new effective ways to clinical transcriptomic data modeling for characterizing cancer progression and facilitates the translation of regulatory network-based approaches into precision medicine.

The first Lewis acid-catalyzed intramolecular interrupted Nazarov cyclization of 1,4-pentadien-3-ols is described. Using FeBr3 as the catalyst, a series of new substituted cyclopenta[b]indoles was prepared-through a sequence of Nazarov cyclization, nucleophilic amination, and isomerization-with good yields and high diastereo- and regioselectivities. A similar catalytic process was also developed for the synthesis of structurally interesting spiro[indene-1,4'-quinoline]s.