VIDEO ABSTRACT.

Many biological systems consist of branching structures that exhibit a wide variety of shapes. Our understanding of their systematic roles is hampered from the start by the lack of a fundamental means of standardizing the description of complex branching patterns, such as those of neuronal trees. To solve this problem, we have invented the Topological Morphology Descriptor (TMD), a method for encoding the spatial structure of any tree as a “barcode”, a unique topological signature. As opposed to traditional morphometrics, the TMD couples the topology of the branches with their spatial extents by tracking their topological evolution in 3-dimensional space. We prove that neuronal trees, as well as stochastically generated trees, can be accurately categorized based on their TMD profiles. The TMD retains sufficient global and local information to create an unbiased benchmark test for their categorization and is able to quantify and characterize the structural differences between distinct morphological groups. The use of this mathematically rigorous method will advance our understanding of the anatomy and diversity of branching morphologies.Electronic supplementary material The online version of this article (10.1007/s12021-017-9341-1) contains supplementary material, which is available to authorized users.

No abstract

There have been few quantitative characterizations of the morphological, biophysical, and cable properties of neurons in the human neocortex. We employed feature-based statistical methods on a rare data set of 60 3D reconstructed pyramidal neurons from L2 and L3 in the human temporal cortex (HL2/L3 PCs) removed after brain surgery. Of these cells, 25 neurons were also characterized physiologically. Thirty-two morphological features were analyzed (e.g., dendritic surface area, 36 333 ± 18 157 μm2; number of basal trees, 5.55 ± 1.47; dendritic diameter, 0.76 ± 0.28 μm). Eighteen features showed a significant gradual increase with depth from the pia (e.g., dendritic length and soma radius). The other features showed weak or no correlation with depth (e.g., dendritic diameter). The basal dendritic terminals in HL2/L3 PCs are particularly elongated, enabling multiple nonlinear processing units in these dendrites. Unlike the morphological features, the active biophysical features (e.g., spike shapes and rates) and passive/cable features (e.g., somatic input resistance, 47.68 ± 15.26 MΩ, membrane time constant, 12.03 ± 1.79 ms, average dendritic cable length, 0.99 ± 0.24) were depth-independent. A novel descriptor for apical dendritic topology yielded 2 distinct classes, termed hereby as “slim-tufted” and “profuse-tufted” HL2/L3 PCs; the latter class tends to fire at higher rates. Thus, our morpho-electrotonic analysis shows 2 distinct classes of HL2/L3 PCs.

A consensus on the number of morphologically different types of pyramidal cells (PCs) in the neocortex has not yet been reached, despite over a century of anatomical studies, due to the lack of agreement on the subjective classifications of neuron types, which is based on expert analyses of neuronal morphologies. Even for neurons that are visually distinguishable, there is no common ground to consistently define morphological types. The objective classification of PCs can be achieved with methods from algebraic topology, and the dendritic arborization is sufficient for the reliable identification of distinct types of cortical PCs. Therefore, we objectively identify 17 types of PCs in the rat somatosensory cortex. In addition, we provide a solution to the challenging problem of whether 2 similar neurons belong to different types or to a continuum of the same type. Our topological classification does not require expert input, is stable, and helps settle the long-standing debate on whether cell-types are discrete or continuous morphological variations of each other.