A Topological Representation of Branching Neuronal Morphologies

Lida Kanari; Pawel Dlotko; Martina Scolamiero; Ran Levi; Julian Charles Shillcock; Kathryn Hess; Henry Markram

doi:10.1007/s12021-017-9341-1

A Topological Representation of Branching Neuronal Morphologies

Lida Kanari, Pawel Dlotko, Martina Scolamiero, Ran Levi, Julian Charles Shillcock, Kathryn Hess, Henry Markram

Mathematical Science

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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.

Original language	English
Pages (from-to)	3-13
Number of pages	11
Journal	Neuroinformatics
Volume	16
Issue number	1
Early online date	3 Oct 2017
DOIs	https://doi.org/10.1007/s12021-017-9341-1
Publication status	Published - Jan 2018

Bibliographical note

The online version of this article (https://doi.org/10.1007/s12021-017-9341-1) contains supplementary material, which is available to authorized users.

Among others, we thank Athanassia Chalimourda and Katherine Turner for helpful conversations in various stages of this research and Jay Coggan for a critical reading of the manuscript. We also thank Hanchuan Peng and Xiaoxiao Liu for providing and curating the BigNeuron datasets. This work was supported by funding for the Blue Brain Project (BBP) from the ETH Domain. P.D. and R.L. were supported part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR “Synapsy”.

Keywords

topological data analysis
neuronal morphologies
branching morphology
clustering trees

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A Topological Representation of Branching Neuronal Morphologies
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Cite this

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title = "A Topological Representation of Branching Neuronal Morphologies",

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.",

keywords = "topological data analysis, neuronal morphologies, branching morphology , clustering trees ",

author = "Lida Kanari and Pawel Dlotko and Martina Scolamiero and Ran Levi and Shillcock, {Julian Charles} and Kathryn Hess and Henry Markram",

note = "The online version of this article (https://doi.org/10.1007/s12021-017-9341-1) contains supplementary material, which is available to authorized users. Among others, we thank Athanassia Chalimourda and Katherine Turner for helpful conversations in various stages of this research and Jay Coggan for a critical reading of the manuscript. We also thank Hanchuan Peng and Xiaoxiao Liu for providing and curating the BigNeuron datasets. This work was supported by funding for the Blue Brain Project (BBP) from the ETH Domain. P.D. and R.L. were supported part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR “Synapsy”.",

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A Topological Representation of Branching Neuronal Morphologies

Abstract

Bibliographical note

Keywords

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