发表机构
University of Cambridge; University of North Carolina at Chapel Hill; Loyola University Chicago; Pomona College; University of Nebraska-Lincoln（剑桥大学; 北卡罗来纳大学教堂山分校; 芝加哥洛约拉大学; 波莫纳学院; 内布拉斯加大学林肯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种统一几何框架，通过GW空间嵌入分析基因表达网络的时空演化，在果蝇时空转录组数据集上验证其可复现曲率动态趋势，为研究动态生物网络提供新手段。
AI 中文摘要
高通量单细胞和空间转录组技术提供了异质细胞状态的高分辨率快照，但它们的破坏性本质无法对同一细胞进行多次测量，因此必须从独立采样、未对齐的细胞群中推断时间和空间动态，这给发育轨迹的重建带来了挑战。最优传输（OT）提供了对齐细胞群和推断发育轨迹的几何框架，但许多现有方法侧重于建模基因表达空间中细胞分布的演化，而非基因表达网络编码的关系结构。为解决这一局限，我们引入了一种几何框架，用于通过在格罗莫夫-瓦瑟斯坦（GW）空间中的嵌入来分析基因表达网络的时空演化。通过将每个发育阶段表示为结合基因表达和空间邻近性的图，我们的方法能够比较不同时间的网络结构、通过GW测地线实现发育阶段之间的连续插值，并使用奥利维尔-里奇曲率量化网络层面的变化。我们在果蝇（Drosophila）时空转录组数据集上评估了该框架，结果显示GW测地线插值能够复现经验基因表达网络中观察到的曲率动态的主要趋势。其与高阶协同最优传输（COOT）距离（联合表示空间和时间信息）的一致性进一步验证了该框架，表明超网络表示成功记录了跨时间的显著生物学变化。总体而言，我们的方法为研究动态演化的生物网络提供了一种统一的几何方法。
英文摘要
High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time. Consequently, temporal and spatial dynamics must be inferred from independently sampled, unaligned cell populations, making it challenging to reconstruct developmental trajectories. Optimal transport (OT) offers a geometric framework for aligning cell populations and inferring developmental trajectories, but many existing approaches focus on modeling the evolution of distributions of cells in gene expression space rather than the relational structure encoded by gene expression networks. To address this limitation, we introduce a geometric framework for analyzing the spatiotemporal evolution of gene expression networks through embeddings in Gromov--Wasserstein (GW) space. By representing each developmental stage as a graph combining gene expression and spatial proximity, our approach enables comparisons of network structure across time, continuous interpolation between developmental stages via GW geodesics, and quantification of network-level changes using Ollivier-Ricci curvature. We evaluate our framework on a spatiotemporal transcriptomic \textit{Drosophila} dataset and show that GW geodesic interpolations reproduce main trends in curvature dynamics observed in empirical gene expression networks. Agreement with higher-order Co-Optimal Transport (COOT) distances, which jointly represent spatial and temporal information, further validates the framework and suggests that hypernetwork representations successfully record salient biological changes across time. In general, our approach provides a unified geometric approach to study dynamically evolving biological networks.
Comments33 pages, 15 figures
