Cells are the smallest operational units of living systems. Through synthesis of various biomolecules and exchange of signals with the environment, cells tightly regulate their composition to realize a specific functional state. The transformation of a cell by internal and external stimuli that alter its biomolecular composition is conceptualized as a cell state transition and plays a critical role in dynamic biological processes, including differentiation, development, and proliferation. Recent advances in technologies that can scrutinize cell states at a single-cell resolution, particularly single-cell RNA sequencing (scRNA-seq), offer the opportunity to assess how underlying molecular properties influence the conversion between states. However, the design of suitable computational methods to aid with interpretation of these data is an active and incomplete area of research. Here, I decode the intricate properties of cell state transitions through quantitative analyses and modeling, tackling three distinct research questions that explore the path, pace, and rules of temporal dynamics in single cells.

First, I examine cell state transitions at the population level, asking which transitions occur in a differentiation protocol where a homogeneous pool of progenitor cells is directed towards a mature cell type. I explore this question in the practical setting of an embryonic stem cell differentiation protocol to generate retinal pigmented epithelium (RPE) for treating age- related macular degeneration. Using scRNA-seq, I conclude that our protocol, rather than progressing along a linear route from stem cells to RPE, can be better explained by a divergence-convergence model of differentiation that largely recapitulates development.

Second, I investigate the pace at which cell state transitions occur, asking how the rate of the cell cycle varies across different tissues and environmental contexts and whether it can be inferred by the gene expression of an ensemble of cells. To this end, I reformulate the RNA velocity algorithm, which extrapolates future cell states from scRNA-seq data, into a unified framework with gene manifold estimation, implementing a Bayesian model for velocity inference of periodic processes. I observe variations in cell cycle speed among diverse samples and in response to chemical or genetic perturbations. I also propose an inferential framework for statistical significance testing and discover that cell cycle velocities can be approximated in real time and validated experimentally.

Third, I consider the maintenance of a steady-state biological system, asking whether the rules that govern transition probabilities among cell states can be defined using non- transcriptional modalities. To explore this, I formulate a Markov model and infer a cell transition matrix using maximum likelihood estimation from reconstructed cell lineage information in a setting where endpoint states are known but past cell states are latent. I apply the method to characterize lipid-state switches in dermal human fibroblasts, finding a remarkable stability of states, termed lipotypes, across cell generations.

In summary, this work advances our understanding of cell state transitions for retinal progenitor differentiation, cell cycle modulations, and fibroblast plasticity, introducing new modeling strategies to tackle these dynamics with modern single-cell omics techniques