Geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat
| Autor: | Jaap A. Kaandorp, Erik De Schutter, Robert Sinclair, Nol Chindapol, Yihwa Kim |
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| Přispěvatelé: | Computational Science Lab (IVI, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Models
Anatomic Anatomy and Physiology Plant Science Cardiovascular System Steiner tree problem Trees 0302 clinical medicine Bifurcation theory Morphogenesis lcsh:QH301-705.5 0303 health sciences Ecology Plants Anthozoa Mathematical theory Tree structure Computational Theory and Mathematics Geometric group theory Modeling and Simulation Corals symbols Medicine Research Article Geometry Marine Biology Topology Models Biological 03 medical and health sciences Cellular and Molecular Neuroscience symbols.namesake Euclidean geometry Genetics Animals Computer Simulation Biology Theoretical Biology Molecular Biology Ecology Evolution Behavior and Systematics 030304 developmental biology Computational Neuroscience Computational Biology Function (mathematics) Tree (graph theory) Neuroanatomy lcsh:Biology (General) Euclidean Geometry Cardiovascular Anatomy Mathematics 030217 neurology & neurosurgery Neuroscience |
| Zdroj: | PLoS Computational Biology, Vol 8, Iss 4, p e1002474 (2012) PLoS Computational Biology PLoS Computational Biology, 8(4). Public Library of Science |
| ISSN: | 1553-7358 1553-734X |
| Popis: | 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. Author Summary Morphology is constrained by function and vice-versa. Often, intricate morphology can be explained by optimization of a cost. However, in biology, the exact form of the cost function is seldom clear. Previously, for many different natural trees authors have reported that most bifurcations are planar and we confirm this here for branching corals and mammalian neurons. In a three-dimensional space, where bifurcations can have many shapes, it is not clear why they are mostly planar. We show, using a geometric proof, that bifurcations that are part of an optimal wiring cost tree should be planar. We demonstrate this by proving that a bifurcation that is not planar cannot be part of an optimal wiring cost tree, using a very general form of wiring cost which applies even when the exact form of the cost function is not known. We conclude that nature selects for developmental mechanisms which produce planar bifurcations. |
| Databáze: | OpenAIRE |
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