Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I will discuss different approaches to develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states in the reduced differentiation space. Then, we develop PDE models that describe the cell differentiation as directed and random movement on the abstracted graph or on the reduced space. Normal hematopoiesis differentiation and abnormal processes of acute myeloid leukemia (AML) progression are simulated, and the model can predict the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of AML. In addition, we demonstrate that our model is capable to illustrate the reconstitution of impaired Hematopoiesis, for instance, after chemotherapy.
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