H. Cho
Department of Mathematics, University of Maryland, College Park, MD, USA ORCID: http://orcid.org/0000-0003-3005-8943
K. Ayers
Department of Mathematics, Pomona College, Claremont, CA, USA
L. de Pills
Department of Mathematics, Harvey Mudd College, Claremont, CA, USA
Y.-H. Kuo
Department of Hematological Malignancies Translational Science, Gehr Family Center for Leukemia Research, City of Hope, Duarte, CA, USA ORCID:http://orcid.org/0000-0003-2595-0419
J. Park
Department of Mathematics, Harvey Mudd College, Claremont, CA, USA
A. Radunskaya
Department of Mathematics, Pomona College, Claremont, CA, USA ORCID: http://orcid.org/0000-0002-2353-5046
R. C. Rockne
Division of Mathematical Oncology, City of Hope, Duarte, CA, USA ORCID: http://orcid.org/0000-0002-1557-159X
Here we present a mathematical model of movement in an abstract space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single-cell RNA-sequencing data to characterize cellular states in a high-dimensional space, which is then mapped into 
or 
with dimension reduction techniques. We represent trajectories in the differentiation space as a graph, and model directed and random movement on the graph with partial differential equations. We hypothesize that flow in this space can be used to model normal and abnormal differentiation processes. We present a mathematical model of haematopoiesis parameterized with publicly available single-cell RNA-Seq data and use it to simulate the pathogenesis of acute myeloid leukaemia (AML). The model predicts the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of a mouse model of AML.
