Evolution of bow-tie architectures in biology.

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PLoS computational biology, ISSN: 1553-7358, Vol: 11, Issue: 3, Page: e1004055

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10.1371/journal.pcbi.1004055; 10.1371/journal.pcbi.1004055.t001; 10.1371/journal.pcbi.1004055.g003; 10.1371/journal.pcbi.1004055.g004; 10.1371/journal.pcbi.1004055.g006; 10.1371/journal.pcbi.1004055.g001; 10.1371/journal.pcbi.1004055.g005; 10.1371/journal.pcbi.1004055.g002
PMC4370773; 4370773
Tamar Friedlander; Avraham E. Mayo; Tsvi Tlusty; Uri Alon; Andrey Rzhetsky
Public Library of Science (PLoS); Figshare; PUBLIC LIBRARY SCIENCE
Agricultural and Biological Sciences; Mathematics; Environmental Science; Biochemistry, Genetics and Molecular Biology; Neuroscience; Computer Science; Biochemistry; Physical Sciences not elsewhere classified; Genetics; Molecular Biology; Biotechnology; Evolutionary Biology; Biological Sciences not elsewhere classified; Information Systems not elsewhere classified; Developmental Biology; Cancer; Infectious Diseases; output biomass components; rank; bow-tie architectures; 69999 Biological Sciences not elsewhere classified; 29999 Physical Sciences not elsewhere classified; 80699 Information Systems not elsewhere classified
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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.