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.

Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function

“…Can phenotypic constraints also shape their structural features? The answer is again "yes", as has been shown in both metabolic [113,200,201] and signaling networks [202]. In both of these types of networks, the large scale structure tends to be organized in terms of a core part and two peripheral parts, one feeding into the core and another feeding out of it.…”

Habitat variability does not generally promote metabolic network modularity in flies and mammals

“…Q d is suitable for analyzing metabolic networks because the networks are directed (Clune et al, 2013). For example, unlike Q ud , Q d can characterize input (i.e., nutrient) modules, core modules, and output (i.e., product) modules (Leicht & Newman, 2008) (e.g., a bow-tie structure, which is related to biological robustness (Friedlander, Mayo, Tlusty, & Alon, 2014;Ma & Zeng, 2003)) in metabolic networks by considering edge direction. Nonetheless, some previous studies (Parter et al, 2007;Takemoto & Borjigin, 2011;Takemoto, 2013;Wagner & Fell, 2001) focused on the undirected version of the Q-value because of some apparent problems with Q d ; for example, the reversibility/irreversibility of metabolic reactions may change with environmental conditions (Parter et al, 2007;Wagner & Fell, 2001), and Q d cannot distinguish between situations with and without directed flow (Arenas, Duch, Fernández, & Gómez, 2007) (e.g., Fig.…”

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“…For example, the bow-tie (also called hourglass) architecture, which refers to systems that receive a diversity of inputs and convert the input signals through an intermediate “core”, and finally generate a variety of outputs. Since the intermediate “core” is composed of relatively few universal components, the overall structure of the system resembles a bow-tie or hourglass [7]. For instance, in metabolic networks, multiple input nutrients are converted into multiple biomass components by a small number of mediator factors [7].…”

“…Since the intermediate “core” is composed of relatively few universal components, the overall structure of the system resembles a bow-tie or hourglass [7]. For instance, in metabolic networks, multiple input nutrients are converted into multiple biomass components by a small number of mediator factors [7]. Previous work suggests that the recurrence of bow-tie architecture in various biological systems indicates its significance on enhancing the robustness of the biological systems [8].…”