ABSTRACT Morphology is an essential phenotype in the characterization of cells and their states. It reflects the progression of functional cellular processes, such as morphogenesis, migration, or dendrite arborization, and can be indicative of disease. Delineating the molecular pathways that underlie morphological phenotypes is critical to understanding the relation between genetic pathways, morphology, and function of cells in the brain. Recent techniques like Patch-seq can be used to simultaneously profile cell morphology, gene expression, and electrophysiological properties of individual cells. However, there is a lack of computational methods that can summarize the great diversity of complex cell morphologies found in the brain and statistically infer relations with gene expression and physiological properties. To overcome this impediment, we have pioneered a novel approach for cell morphometry and multi-modal analysis based on concepts from metric geometry. Our studies show that this approach can be efficiently used with single-cell morphological, transcriptomic, and physiological data from the BRAIN Initiative Cell Census Network to delineate the molecular pathways that underlie the morphological and physiological phenotypes of brain cells. Our goal is to build upon this approach to establish a scalable algorithmic framework and a software for the combined analysis of 3D cell morphologies and single-cell transcriptomic and physiological data. Aim 1 of this proposal will establish a general and interpretable algorithm for the characterization, classification, and integration of complex and heterogeneous 3D cell morphologies. We will use metric geometry to construct accurate cell morphology summary spaces, where cells are represented by points, and distances between cells indicate the amount of deformation needed to change the 3D morphology of one cell into that of another. We will also address the integration and batch correction of these spaces. Aim 2 will build upon clustering-independent spectral methods to develop a statistical framework for establishing associations between cell morphology and single cell transcriptomic and electrophysiological data. We will use Patch-seq, fMOST, MORF, MouseLight, and serial electron microscopy data from the BRAIN Initiative cell Census Network, the Allen Brain Atlas Cell Types Database, and the MICrONS consortium, as well as simulated data, to evaluate and optimize these algorithms. We will disseminate these methods by implementing them into an open-source, cloud-enabled, software for the combined morphometric, molecular, and physiological analysis of cells, and by organizing several workshops and tutorials to foster an active community of users. Taken together, the outcomes of our research program will fill a critical gap in the integrative analysis of single-cell morphological, molecular, and physiological data and will contribute to establishing the foundations of the new field of single-cell morpho...