Modelling acute myeloid leukaemia in a continuum of differentiation states

Authors

  • H. Cho Department of Mathematics, University of Maryland, College Park, MD, USA ORCID: http://orcid.org/0000-0003-3005-8943 Author
  • K. Ayers Department of Mathematics, Pomona College, Claremont, CA, USA Author
  • L. de Pills Department of Mathematics, Harvey Mudd College, Claremont, CA, USA Author
  • 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 Author
  • J. Park Department of Mathematics, Harvey Mudd College, Claremont, CA, USA Author
  • A. Radunskaya Department of Mathematics, Pomona College, Claremont, CA, USA ORCID: http://orcid.org/0000-0002-2353-5046 Author
  • R. C. Rockne Division of Mathematical Oncology, City of Hope, Duarte, CA, USA ORCID: http://orcid.org/0000-0002-1557-159X Author

DOI:

https://doi.org/10.30707/LiB5.2Cho

Keywords:

Diffusion mapping, Haematopoiesis, Single-cell RNA-sequencing, Developmental trajectories, Nonlinear dimension reduction, Cellular differentiation, Acute myeloid leukaemia, Differentiation continuum

Abstract

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 tlib_a_1472532_ilm0001.gif  or  tlib_a_1472532_ilm0002.gif 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.

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Published

2018-06-30

How to Cite

Modelling acute myeloid leukaemia in a continuum of differentiation states. (2018). Letters in Biomathematics, 5(2), 69-98. https://doi.org/10.30707/LiB5.2Cho

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