Dissecting Sholl Analysis into Its Functional Components

Bird, Alex D.; Cuntz, Hermann

doi:10.1016/j.celrep.2019.04.097

Cited by 69 publications

(56 citation statements)

References 76 publications

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“…It is indicative of the preferred growing direction of the neural arbor. For more details see Bird and Cuntz ( 2019 ). Euler root angles , α Histogram of the Euler root angles ( α ).…”

Section: Methodsmentioning

confidence: 99%

A Systematic Evaluation of Interneuron Morphology Representations for Cell Type Discrimination

2020

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Quantitative analysis of neuronal morphologies usually begins with choosing a particular feature representation in order to make individual morphologies amenable to standard statistics tools and machine learning algorithms. Many different feature representations have been suggested in the literature, ranging from density maps to intersection profiles, but they have never been compared side by side. Here we performed a systematic comparison of various representations, measuring how well they were able to capture the difference between known morphological cell types. For our benchmarking effort, we used several curated data sets consisting of mouse retinal bipolar cells and cortical inhibitory neurons. We found that the best performing feature representations were two-dimensional density maps, two-dimensional persistence images and morphometric statistics, which continued to perform well even when neurons were only partially traced. Combining these feature representations together led to further performance increases suggesting that they captured non-redundant information. The same representations performed well in an unsupervised setting, implying that they can be suitable for dimensionality reduction or clustering.

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“…It is indicative of the preferred growing direction of the neural arbor. For more details see Bird and Cuntz ( 2019 ). Euler root angles , α Histogram of the Euler root angles ( α ).…”

Section: Methodsmentioning

confidence: 99%

A Systematic Evaluation of Interneuron Morphology Representations for Cell Type Discrimination

2020

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“…A large palette of branching statistics were collected for each dendrite reconstruction separately using simple combinations of TREES toolbox functions: (1) Total dendrite length L was the sum of all internode lengths (len tree), (2) number of branch points B were calculated as the sum of all nodes that are branch points (B tree), (3) covered surface area S was calculated with a novel custom written TREES toolbox function span tree that counts 1 − bins after morphological closing with a disc of 4µm radius of a binary matrix with 1 − bins at tree node locations after resampling the trees to 1µm internode distances -similarly to previous work on fly lobula plate tangential cells (Cuntz et al, 2008), (4) Sholl analysis (Bird and Cuntz, 2019) that calculates the number of intersections of a tree with a growing circle centred on the dendrite root was done by using the dedicated TREES toolbox function sholl tree, (5) normalised Sholl analysis was done by normalising the Sholl radii to 6× the mean Euclidean distance in the tree (eucl tree) and normalising the number of intersections with the integral over the Sholl intersections diagram, (6) branch order distributions were calculated by identifying how many nodes and the overall dendritic cable length of their connected segments in the tree had a given branch order (BO tree), (7) normalised branch orders were normalised to the next integer of 2.5× the mean branch order in any given tree and the cable distribution was normalised to the total length of dendrite, (8) branch length distributions were obtained by combining two TREES toolbox functions that calculate the path length from each node to the root (Pvec tree) and that dissect the trees into their individual branches (dissect tree), (9) normalised branch lengths were normalised to 3× the mean branch length in the tree and branch length frequency was normalised to the integral over the distribution, (10) compression value distributions were calculated as the ratio between Euclidean distances (eucl tree) and the path distances (Pvec tree) to the root for all nodes, (11) the Strahler order distributions were calculated as the percentages of dendrite length per given Strahler order (strahler tree) (Vormberg et al, 2017), (12) branch angle distributions were obtained by calculating the angles in the branching plane of each branch point (angleB tree).…”

Section: Classical Branching Statisticsmentioning

confidence: 99%

A developmental stretch-and-fill process that optimises dendritic wiring

Baltruschat

Tavosanis

Cuntz

2020

Preprint

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AbstractThe way in which dendrites spread within neural tissue determines the resulting circuit connectivity and computation. However, a general theory describing the dynamics of this growth process does not exist. Here we obtain the first time-lapse reconstructions of neurons in living fly larvae over the entirety of their developmental stages. We show that these neurons expand in a remarkably regular stretching process that conserves their shape. Newly available space is filled optimally, a direct consequence of constraining the total amount of dendritic cable. We derive a mathematical model that predicts one time point from the previous and use this model to predict dendrite morphology of other cell types and species. In summary, we formulate a novel theory of dendrite growth based on detailed developmental experimental data that optimises wiring and space filling and serves as a basis to better understand aspects of coverage and connectivity for neural circuit formation.In briefWe derive a detailed mathematical model that describes long-term time-lapse data of growing dendrites; it optimises total wiring and space-filling.HighlightsDendrite growth iterations guarantee optimal wiring at each iteration.Optimal wiring guarantees optimal space filling.The growth rule from fly predicts dendrites of other cell types and species.Fly neurons stretch-and-fill target area with precise scaling relations.Phase transition of growth process between fly embryo and larval stages.

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“…For all the dendrites intersecting that sphere it associates to r the sum of the angles between dendrites and normal directions to the sphere. The flux construction is related to, and can be viewed as an extension of the root-angle construction in [44]. This construction associates to a leaf the angle between the radial normal and the main branch ending at that leaf.…”

Section: Methodsmentioning

confidence: 99%

“…(3) Flux: This associates to a given radius r the sum of the angles between dendrites and normal directions to the sphere of radius r centered at the soma, at the points where the dendrites intersect with that sphere.The flux construction is related to, and can be viewed as an extension of the root-angle construction in [43]. This construction considers, at any given leaf, the angle between the radial normal and the main branch ending at that point.…”

Section: Sholl Descriptorsmentioning

confidence: 99%

Topological Sholl Descriptors For Neuronal Clustering and Classification

Khalil

Kallel

Farhat

et al. 2021

Preprint

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Variations in neuronal morphology among cell classes, brain regions, and animal species are thought to underlie known heterogeneities in neuronal function. Thus, accurate quantitative descriptions and classification of large sets of neurons is essential for functional characterization. However, unbiased computational methods to classify groups of neurons are currently scarce. We introduce a novel, robust, and unbiased method to study neuronal morphologies. We develop mathematical descriptors that quantitatively characterize structural differences among neuronal cell types and thus classify them. Each descriptor that is assigned to a neuron is a function of a distance from the soma with values in real numbers or more general metric spaces. Standard clustering methods enhanced with detection and metric learning algorithms are then used to objectively cluster and classify neurons. Our results illustrate a practical and effective approach to the classification of diverse neuronal cell types, with the potential for discovery of putative subclasses of neurons.

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Dissecting Sholl Analysis into Its Functional Components

Abstract: Graphical Abstract Highlights d Root angle measure quantifies a dendrite's centripetal bias d Functional interpretation of dendrites without full reconstruction d Parameter estimation for optimal wiring-based dendrite models d Simple relation between dendrite length and Sholl profile

Cited by 69 publications

References 76 publications

A Systematic Evaluation of Interneuron Morphology Representations for Cell Type Discrimination

A Systematic Evaluation of Interneuron Morphology Representations for Cell Type Discrimination

A developmental stretch-and-fill process that optimises dendritic wiring

Topological Sholl Descriptors For Neuronal Clustering and Classification

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