Modeling acute myeloid leukemia in a continuum of differentiation states

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 ℝ2 or ℝ3 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 differentiation processes as well as predict the evolution of abnormal differentiation processes such as those observed during pathogenesis of acute myeloid leukemia (AML).

[1]  Fabian J Theis,et al.  Diffusion pseudotime robustly reconstructs lineage branching , 2016, Nature Methods.

[2]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[3]  P. Rigollet,et al.  Reconstruction of developmental landscapes by optimal-transport analysis of single-cell gene expression sheds light on cellular reprogramming , 2017, bioRxiv.

[4]  Fabian J. Theis,et al.  Diffusion maps for high-dimensional single-cell analysis of differentiation data , 2015, Bioinform..

[5]  Ziv Bar-Joseph,et al.  TASIC: determining branching models from time series single cell data , 2017, Bioinform..

[6]  S. Stowell,et al.  Microbial Exposure Regulates the Development of Anti-Blood Group Antibodies , 2016 .

[7]  Hannah A. Pliner,et al.  Reversed graph embedding resolves complex single-cell trajectories , 2017, Nature Methods.

[8]  Lisa Garrett,et al.  The fusion gene Cbfb-MYH11 blocks myeloid differentiation and predisposes mice to acute myelomonocytic leukaemia , 1999, Nature Genetics.

[9]  Elmar Eisemann,et al.  Visual analysis of mass cytometry data by hierarchical stochastic neighbour embedding reveals rare cell types , 2017, Nature Communications.

[10]  Guido Marcucci,et al.  CBFβ-SMMHC creates aberrant megakaryocyte-erythroid progenitors prone to leukemia initiation in mice. , 2016, Blood.

[11]  Wenqing Hu,et al.  On Diffusion in Narrow Random Channels , 2012, 1210.5226.

[12]  Sean C. Bendall,et al.  Wishbone identifies bifurcating developmental trajectories from single-cell data , 2016, Nature Biotechnology.

[13]  F. Collins,et al.  Fusion between transcription factor CBF beta/PEBP2 beta and a myosin heavy chain in acute myeloid leukemia. , 1993, Science.

[14]  Li Wang,et al.  Dimensionality Reduction Via Graph Structure Learning , 2015, KDD.

[15]  Nicola K. Wilson,et al.  A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation. , 2016, Blood.

[16]  L. Steinmetz,et al.  Human haematopoietic stem cell lineage commitment is a continuous process , 2017, Nature Cell Biology.

[17]  Sean C. Bendall,et al.  Data-Driven Phenotypic Dissection of AML Reveals Progenitor-like Cells that Correlate with Prognosis , 2015, Cell.

[18]  Andrew J. Hill,et al.  Single-cell mRNA quantification and differential analysis with Census , 2017, Nature Methods.

[19]  Lisa Garrett,et al.  Cbfβ-SMMHC induces distinct abnormal myeloid progenitors able to develop acute myeloid leukemia , 2006 .

[20]  Mark Freidlin,et al.  SPDEs on narrow domains and on graphs: an asymptotic approach , 2014, 1412.6423.

[21]  Ya-Huei Kuo,et al.  Cbfβ-SMMHC impairs differentiation of common lymphoid progenitors and reveals an essential role for RUNX in early B cell development , 2008 .

[22]  J. Marioni,et al.  Differentiation dynamics of mammary epithelial cells revealed by single-cell RNA sequencing , 2017, Nature Communications.

[23]  Evan Z. Macosko,et al.  Comprehensive Classification of Retinal Bipolar Neurons by Single-Cell Transcriptomics , 2016, Cell.

[24]  C. Waddington,et al.  The strategy of the genes , 1957 .

[25]  Simon M. J. Lyons.  Introduction to stochastic differential equations , 2011 .

[26]  Berthold Göttgens,et al.  Advancing haematopoietic stem and progenitor cell biology through single‐cell profiling , 2016, FEBS letters.

[27]  S. Counce.  The Strategy of the Genes , 1958, The Yale Journal of Biology and Medicine.