Geometry of the Gene Expression Space of Individual Cells

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.Author Summary: In the past, biological experiments usually pooled together millions of cells, masking the differences between individual cells. Current technology takes a big step forward by measuring gene expression from individual cells. Interpreting this data is challenging because we need to understand how cells are arranged in a high dimensional gene expression space. Here we test recent theory that suggests that cells facing multiple tasks should be arranged in simple low dimensional polygons or polyhedra (generally called polytopes). The vertices of the polytopes are gene expression profiles optimal for each of the tasks. We find evidence for such simplicity in a variety of tissues—spleen, bone marrow, intestine—analyzed by different single-cell technologies. We find that cells are distributed inside polytopes, such as tetrahedrons or four-dimensional simplexes, with cells closest to each vertex responsible for a different key task. For example, intestinal progenitor cells that give rise to the other cell types show a continuous distribution in a tetrahedron whose vertices correspond to several key sub-tasks. Immune dendritic cells likewise are continuously distributed between key immune tasks. This approach of testing whether data falls in polytopes may be useful for interpreting a variety of single-cell datasets in terms of biological tasks.