geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat几何理论预测最小的布线成本树生物学的分支,是平的.pdfVIP

Geometric Theory Predicts Bifurcations in Minimal Wiring Cost Trees in Biology Are Flat 1. 2. 3 3 1 Yihwa Kim , Robert Sinclair , Nol Chindapol , Jaap A. Kaandorp , Erik De Schutter * 1 Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan, 2 Mathematical Biology Unit, Okinawa Institute of Science and Technology, Okinawa, Japan, 3 Section Computational Science, Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands 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. Citation: Kim Y, Sinclair R, Chindapol N, Kaandorp JA, De Schutter E (2012) Geometric Theory Predicts Bifurcations in Minimal Wiring Cost Tree