A Biophysical Approach to Normalization and Trajectory Inference in Single-Cell RNA Sequencing Data Analysis

Author: Fang, Meichen

Year: 2025

Degree: Dissertation (Ph.D.)

Advisor: Pachter, Lior S.

Committee Members: Thomson, Matthew; Pachter, Lior S.; Bois, Justin S.; Chong, Shasha

Option: Bioengineering; Applied And Computational Mathematics

DOI: 10.7907/asek-t904

Abstract

Single-cell genomics assays, particularly single-cell RNA sequencing that enables genome-wide profiling of gene expression, have been driven forward by a combination of technological and computational advances. While producing extraordinary large amounts of data for biological discovery, methods for mining results currently rely heavily on heuristics and lack of modeling has resulted in limited mechanistic biological insight. This thesis presents two models for normalization and trajectory inference in single-cell RNA sequencing analysis to demonstrate how biophysical modeling, when combined with principled statistical inference, can yield interpretable insights grounded in rigorous theoretical frameworks.

We begin by explaining the two cultures in single-cell RNA sequencing analysis. Next, we present the chemical master equation, which forms the theoretical foundation for biophysically informed stochastic models of gene expression, and explore an existing gap in developing uniform approximations over time under the large-volume limit. Returning to single-cell RNA sequencing data analysis, we introduce two mechanistic models for normalization and trajectory inference, which are essential components of single-cell RNA sequencing analysis.

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