title: Evolution of bow-tie architectures in biology.
abstract: Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the network-that is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.
authors: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel; Institute of Science and Technology Austria, Klosterneuburg, Austria.
authors: Tamar
authors: T
authors: Friedlander
authors: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors: Avraham E
authors: AE
authors: Mayo
authors: Simons Center for Systems Biology, Institute for Advanced Study, Princeton, New Jersey, United States of America.
authors: Tsvi
authors: T
authors: Tlusty
authors: Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
authors: Uri
authors: U
authors: Alon
mesh_terms: D005075:Biological Evolution; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D015398:Signal Transduction