While several tools have been developed to map axes of variation among individual cells, no analogous approaches exist for identifying axes of variation among multicellular biospecimens profiled at single-cell resolution. For this purpose, we developed ‘phenotypic earth mover’s distance’ (PhEMD). PhEMD is a general method for embedding a ‘manifold of manifolds’, in which each datapoint in the higher-level manifold (of biospecimens) represents a collection of points that span a lower-level manifold (of cells). We apply PhEMD to a newly generated drug-screen dataset and demonstrate that PhEMD uncovers axes of cell subpopulational variation among a large set of perturbation conditions. Moreover, we show that PhEMD can be used to infer the phenotypes of biospecimens not directly profiled. Applied to clinical datasets, PhEMD generates a map of the patient-state space that highlights sources of patient-to-patient variation. PhEMD is scalable, compatible with leading batch-effect correction techniques and generalizable to multiple experimental designs.

虽然已经开发了几种工具来绘制单个细胞之间的变异轴，但不存在类似的方法来识别以单细胞分辨率分析的多细胞生物样本之间的变异轴。为此，我们开发了“表型推土机距离”（PhEMD）。PhEMD 是一种嵌入“流形流形”的通用方法，其中高级流形（生物样本）中的每个数据点表示跨越较低级流形（细胞）的点的集合。我们将 PhEMD 应用于新生成的药物筛选数据集，并证明 PhEMD 揭示了在大量扰动条件下细胞亚群变化的轴。此外，我们表明 PhEMD 可用于推断未直接分析的生物样本的表型。应用于临床数据集，PhEMD 生成患者状态空间的地图，突出显示患者间差异的来源。PhEMD 具有可扩展性，与领先的批次效应校正技术兼容，并可推广到多个实验设计。