UBC Mathematics Colloquium: Heyrim Cho

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 discuss different approaches to develop mathematical models from single-cell data. 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 modeled as directed and random movement on the abstracted graph with PDEs. 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 develop representations of multi-correlated stochastic processes for correlated time series cell data, by releasing the bi-orthogonal condition of Karhunen-Loeve expansion. Convergence and computational efficiency of the methods are addressed. Finally, for fluorescence in situ hybridization data that provides spatial-temporal patterns of cells, we develop tumor growth model incorporating dynamics of drug resistance. It is demonstrated that assuming continuous cell state may result in different dynamics of anti-cancer drug resistance when compared with the predictions of classical discrete models, and its implications in designing therapies are studied.