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Zhang, Jingqi

University of British Columbia

The thesis proposes a computational method to solve cellular inference problems on stochastic biological processes. In biological systems, cells can divide, die, and develop from naive to mature states. Many researchers are interested in exploring how a cell would move or differentiate over time under certain perturbations. However, it is often necessary to destroy cells to measure them. Since a cell could only be measured once, we cannot directly record multiple states of a cell at different time points while it is developing and answer questions about cellular fates. Hence, many inference technologies have been developed to make predictions with the observed data. In this thesis, we introduce the optimal transport theory and discuss the possibility to employ it as the mathematical foundation for an analysis framework of trajectory inference. We propose an approach of cellular inference for stationary biological systems where the cell type proportions remain relatively constant over time. We start by the background information on single-cell measurement technologies. Also, we discuss why we need trajectory inference methods, how trajectory inference could be practically useful, and why single-cell measurement technologies are important to the computational methods. Then, we describe the optimal transportation problem and its variation, entropy-regularized optimal transport, with necessary mathematical preliminaries, since optimal transport theory will be the computational foundation of the method we propose in the following sections. Our problem setting focuses on the case where the biological systems are in equilibrium, where the components in the systems are changing, but the populations stay dynamically constant. We introduce Stationary LineageOT (statLOT), which is a computational workflow to solve inference problems for such biological systems where we have access to or can reconstruct the lineage information. We experiment our method on simulated data and real B cell receptor data.

Text

2024-07-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88677

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/