Modelling acute myeloid leukaemia in a continuum of differentiation states

• Published in: Letters in biomathematics Vol. 5; no. Suppl 1; pp. S69 - S98
• Main Authors: Cho, H., Ayers, K., de Pills, L., Kuo, Y.-H., Park, J., Radunskaya, A., Rockne, R. C.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.01.2018; Taylor & Francis Ltd; Intercollegiate Biomathematics Alliance
• Subjects: acute myeloid leukaemia; Acute myeloid leukemia; Cell differentiation; cellular differentiation; Computer simulation; developmental trajectories; Differential equations; Differentiation (biology); differentiation continuum; Diffusion mapping; Gene sequencing; haematopoiesis; Leukemia; Mathematical analysis; Mathematical models; nonlinear dimension reduction; Partial differential equations; Pathogenesis; Ribonucleic acid; RNA; single-cell RNA-sequencing; AML; developmental trajectories; differentiation continuum; hematopoiesis; acute myeloid leukemia; diffusion mapping; nonlinear dimension reduction; single cell RNA-Sequencing; cellular differentiation
• ISSN: 2373-7867; 2373-7867
• DOI: 10.1080/23737867.2018.1472532

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.