PhD Thesis Defense

Abstract: Understanding the properties of how cell states transition and diversify during development is fundamental to both basic biology and medical applications. Recent advances in single-cell transcriptomics have enabled the construction of developmental atlases that offer unprecented views of differentiation. However, the structural complexity of these atlases remains poorly understood. In particular, the extent to which topological features—such as clusters, branches, and loops—are present in developmental trajectories and how these relate to gene regulation is an open question.

In this thesis, I present *totopos*, a computational framework for uncovering and quantifying topological motifs in single-cell transcriptome data using tools from algebraic topology. This approach enables the classification of cell state manifolds by their Betti numbers, a metric of topological complexity. *totopos* also enables the identification of "topoGenes"—genetic drivers associated with topological loop signatures. Applying this framework to a broad compendium of developmental atlases across model organisms, I find that developmental trajectories are not universally tree-like: many contain loops indicative of self-renewal and convergent differentiation. Case studies in *C. elegans*, cnidarians, and mammalian systems, reveal that the loop motifs corresponds to biologically meaningful modules and regulatory states.

By leveraging concepts from topology and dynamics, I will discuss global principles found in my work in the context of the Waddington landscape model of development. This work proposes a geometric view of cellular plasticity and organizing principles that govern metazoan multicellular systems.