Continuum of Gene-Expression Profiles Provides Spatial Division of Labor within a Differentiated Cell Type

Single-cell gene expression reveals the diversity within a differentiated cell type. Often, cells of the same type show a continuum of gene-expression patterns. The origin of such continuum gene-expression patterns is unclear. To address this, we develop a theory to understand how a continuumprovides division of labor in a tissue in which cells collectively contribute to several tasks. We find that a continuum is optimal when there are spatial gradients in the tissue that affect the performance in each task. The continuum is bounded inside a polyhedron whose vertices are expression profiles optimal at each task. We test this using single-cell gene expression for intestinal villi and liver hepatocytes, which form a curved 1D trajectory and a full 3D tetrahedron in gene-expression space, respectively. We infer the tasks for both cell types and characterize the spatial zonation of the task-specialist cells. This approach can be generally applied to other tissues.