Geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat.

PLoS Computational Biology
Yihwa KimErik De Schutter

Abstract

The complex three-dimensional shapes of tree-like structures in biology are constrained by optimization principles, but the actual costs being minimized can be difficult to discern. We show that despite quite variable morphologies and functions, bifurcations in the scleractinian coral Madracis and in many different mammalian neuron types tend to be planar. We prove that in fact bifurcations embedded in a spatial tree that minimizes wiring cost should lie on planes. This biologically motivated generalization of the classical mathematical theory of Euclidean Steiner trees is compatible with many different assumptions about the type of cost function. Since the geometric proof does not require any correlation between consecutive planes, we predict that, in an environment without directional biases, consecutive planes would be oriented independently of each other. We confirm this is true for many branching corals and neuron types. We conclude that planar bifurcations are characteristic of wiring cost optimization in any type of biological spatial tree structure.

References

Jan 1, 1977·Bulletin of Mathematical Biology·H B Uylings
Apr 4, 1975·Brain Research·H B Uylings, G J Smit
Jan 1, 1992·Biological cybernetics·C Cherniak
Mar 1, 1968·Journal of Applied Physiology·K Horsfield, G Cumming
Jun 1, 1967·The Bulletin of Mathematical Biophysics·K Horsfield, G Cumming
Mar 1, 1983·The Journal of General Physiology·M ZamirB L Langille
Sep 24, 1998·Journal of Theoretical Biology·D L TurcotteW I Newman
Jun 26, 1999·Science·R J Metzger, M A Krasnow
Apr 26, 2001·Journal of Theoretical Biology·W ZhiY Qi-Xing
Sep 12, 2002·Network : Computation in Neural Systems·Harry B M Uylings, Jaap van Pelt
Apr 18, 2003·Journal of Theoretical Biology·Juan Armando SánchezCarl Simpson
May 15, 2003·Trends in Neurosciences·Fen-Biao Gao, Brigitte A Bogert
Aug 30, 2003·BMC Neuroscience·Dmitri B Chklovskii, Armen Stepanyants
Feb 6, 2004·Nature Neuroscience·Cristopher M NiellStephen J Smith
Jun 26, 2004·Annual Review of Neuroscience·Dmitri B Chklovskii, Alexei A Koulakov
Jul 19, 2005·Annual Review of Neuroscience·Liqun Luo, Dennis D M O'Leary
Jan 4, 2006·PLoS Computational Biology·Quan Wen, Dmitri B Chklovskii
Mar 1, 1926·Proceedings of the National Academy of Sciences of the United States of America·C D Murray
Sep 21, 2006·Microscopy and Microanalysis : the Official Journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada·Bernhard StöttingerAlois Lametschwandtner
May 8, 2007·Cell·Benjamin J MatthewsWesley B Grueber
Jun 15, 2007·Theoretical Biology & Medical Modelling·Hermann CuntzIdan Segev
Aug 31, 2007·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Giorgio A AscoliMaryam Halavi
Feb 29, 2008·Journal of Neurophysiology·Quan Wen, Dmitri B Chklovskii
May 9, 2008·Nature·Ross J MetzgerMark A Krasnow
Nov 4, 2008·Biological Reviews of the Cambridge Philosophical Society·Peter A Todd
Dec 30, 2008·PLoS Computational Biology·Hermann CuntzAlexander Borst
Jul 23, 2009·Proceedings of the National Academy of Sciences of the United States of America·Quan WenDmitri B Chklovskii
Mar 20, 2010·PLoS Computational Biology·Julian M L BuddZoltán F Kisvárday
Apr 21, 2010·Nature Reviews. Neuroscience·Yuh-Nung Jan, Lily Yeh Jan
Jun 25, 2010·Proceedings. Biological Sciences·Maxim V FilatovRolf P M Bak
Aug 12, 2010·PLoS Computational Biology·Hermann CuntzMichael Häusser
Aug 31, 2010·Current Opinion in Neurobiology·Tiago Branco, Michael Häusser
Feb 4, 2011·Journal of the Royal Society, Interface·Tanya LattyMadeleine Beekman
Oct 1, 1976·The Biological Bulletin·Gordon J Leversee

❮ Previous
Next ❯

Citations

Feb 7, 2017·ELife·Adriane G OtopalikEve Marder
Feb 7, 2016·The Journal of Comparative Neurology·Ignacio LegueyJavier DeFelipe
May 2, 2019·Proceedings. Biological Sciences·Arjun Chandrasekhar, Saket Navlakha
Jul 12, 2017·Current Biology : CB·Adam ConnSaket Navlakha

❮ Previous
Next ❯

Related Concepts

Related Feeds

Barrel cortex

Here is the latest research on barrel cortex, a region of somatosensory and motor corticies in the brain, which are used by animals that rely on whiskers for world exploration.

Related Papers

Bulletin of Mathematical Biology
A G Roy, M J Woldenberg
Proceedings of the National Academy of Sciences of the United States of America
Hermann CuntzMichael Häusser
Neuroscience Letters
H B Uylings, W A Veltman
Journal of Theoretical Biology
W ZhiY Qi-Xing
© 2021 Meta ULC. All rights reserved