title: Geometry of the Gene Expression Space of Individual Cells.
abstract: 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.
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Yael
authors.initials: Y
authors.lastname: Korem
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Pablo
authors.initials: P
authors.lastname: Szekely
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Yuval
authors.initials: Y
authors.lastname: Hart
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Hila
authors.initials: H
authors.lastname: Sheftel
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Jean
authors.initials: J
authors.lastname: Hausser
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Avi
authors.initials: A
authors.lastname: Mayo
authors.affiliation: Department of Medicine, Division of Gastroenterology and Hepatology, and Institute for Stem Cell Biology and Regenerative Medicine, Stanford University, Stanford, California, United States of America.
authors.forename: Michael E
authors.initials: ME
authors.lastname: Rothenberg
authors.affiliation: Faculty of Engineering, Bar Ilan University, Ramat Gan, Israel.
authors.forename: Tomer
authors.initials: T
authors.lastname: Kalisky
authors.affiliation: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Uri
authors.initials: U
authors.lastname: Alon
mesh_terms: D000818:Animals; D002454:Cell Differentiation / Q000502:physiology*; D002478:Cells, Cultured / Q000166:cytology* / Q000502:physiology*; D003198:Computer Simulation; D005786:Gene Expression Regulation / Q000502:physiology*; D006801:Humans; D051379:Mice; D008954:Models, Biological; D015233:Models, Statistical; D011506:Proteins / Q000378:metabolism*; D062211:Spatio-Temporal Analysis
chemical_list: D011506:Proteins