Applications of Optimal Transport and Stochastic Differential Equations in Single-cell RNA Sequencing Data
Year: 2024
Type: dissertation
Abstract: Recent advances in single-cell sequencing technology have opened new avenues for the mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. A major hurdle, however, is that RNA sequencing requires the destruction of cells, which prevents the continuous tracking of genetic information across different developmental stages. In response to this challenge, Optimal Transport (OT) and Stochastic Differential Equations (SDE) have emerged as significant tools in scRNA-seq data analysis. OT is notable for its innovative approach in computing pairings or joint probabilities among cells from different time points, offering fresh insights into cellular dynamics. However, its inherent static nature limits its effectiveness in continuous data scenarios. This limitation confines OT to inferring just the endpoints and intermediate points of developmental paths, without capturing the full shape of the trajectory in situations involving continuous data such as gene expression. In contrast, SDEs offer a more dynamic and flexible framework, better suited for modeling continuous data such as gene expression. SDEs are capable of capturing non-linear trajectories and detailed path shapes. However, a significant drawback is their reliance on numerical approximations, which can lead to inaccuracies and deviations from true developmental trajectories. This thesis contributes to these methodologies in two significant ways. Firstly, although OT is less suited for modeling continuous data such as gene expression, our research suggests it has potential for effectively modeling multinomial data, such as cell types. This capability is particularly important, as accurately modeling cell types plays a crucial role in unraveling the complexities of cell developmental processes and understanding cell differentiation, potentially opening doors to real-world applications in areas like cell therapy. In our work, we propose the Trajectory Inference with Multinomial Optimal transport (TIMO) to model cell type trajectories, thereby providing both biological and quantitative insights into the differentiation process among various cell types. Furthermore, TIMO is innovatively applied for change point detection, pinpointing biological change points indicative of cellular differentiation, thus providing deeper understanding of developmental trajectories. Secondly, in an effort to address the limitations of traditional SDE models, we introduce a novel Forward-Backward Stochastic Differential Equations (FBSDE) approach. While SDEs have certain advantages over OT in modeling continuous data, our FBSDE model aims to refine the accuracy issues commonly associated with numerical approximations in existing SDE methods. This model integrates forward and backward temporal dynamics, providing a more nuanced representation of single-cell gene expression dynamics. The performance of the TIMO and FBSDE models is evaluated through comprehensive analyses tailored to their respective applications. The OT method is first assessed through simulations, comparing it with other change point detection methods. It is further evaluated using Mouse Embryonic Fibroblast scRNA-seq data, where its performance is contrasted with biological ground truth and existing cell type modeling methods. In parallel, the performance of the FBSDE model is analyzed in comparison to other SDE methods across multiple scRNA-seq datasets. This comparison is focused on the generative modeling capabilities of the FBSDE model, highlighting its potential in accurately capturing the intricacies of single-cell gene expression dynamics.
Source: TSpace (University of Toronto)
Author: Zhang, Kevin
Institution: University of Toronto
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7133054166