title: Scaling Laws in Spatial Network Formation.
abstract: Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such systems is far from fully understood. Here, we analyze a class of spatial network formation processes by introducing a mapping from geometric to graph-theoretic constraints. Combining stochastic and mean field analyses yields an algebraic scaling law for the extent (graph diameter) of the resulting networks with system size, in contrast to logarithmic scaling known for networks without constraints. Intriguingly, the exponent falls between that of self-avoiding random walks and that of space filling arrangements, consistent with experimentally observed scaling of the radius of gyration of protein tertiary structures with their chain length.
authors: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.|Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany.|Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, 37077 Göttingen, Germany.
authors: Nora
authors: N
authors: Molkenthin
authors: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.|Department of Physics, Technical University of Darmstadt, 64289 Darmstadt, Germany.|Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, 37077 Göttingen, Germany.
authors: Marc
authors: M
authors: Timme
mesh_terms: D000465:Algorithms; D017434:Protein Structure, Tertiary; D011506:Proteins / Q000737:chemistry*
chemical_list: D011506:Proteins