Temporal Topology Provides an Interpretable Framework for Neuronal Morphogenesis.

Neuronal morphogenesis arises through coordinated neurite dynamics that generate cell-type specific dendritic branching during development. Recent advances in high-throughput time-lapse imaging techniques have transformed our ability to track such growth dynamics, yielding comprehensive anatomical datasets of neuronal morphologies. However, quantifying these structural trajectories during neuronal development remains a major challenge. We introduce the Temporal Topological Morphology Descriptor (TTMD), a framework that combines persistent topology with time-resolved neuronal imaging to quantify developmental trajectories of neuronal architecture. Applying TTMD to datasets of Drosophila sensory neurons, we show that developmental stages, branching processes, and mutant-specific growth dynamics can be decoded directly from topology without manual feature selection. Topological Morphology Descriptor (TMD) accurately resolves major developmental transitions in Class I Drosophila neurons, whereas temporal topology (TTMD) is required to uncover subtle alterations in branch dynamics caused by mutations in actin regulatory pathways in Class III Drosophila neurons. TTMD further enables automated topological tracking of branch emergence and retraction across development, overcoming the limitations of labor-intensive manual annotation. These results demonstrate that temporal topology provides a unified and interpretable language for neuronal morphogenesis, enabling the automated analysis of developmental neuroanatomy, and identifying pathological alterations in neuronal structure.