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Fibration symmetries uncover the building blocks of biological networks.

ABSTRACT: A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these networks as a set of input trees, one for each node, which contains all pathways along which information can be transmitted in the network. In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional building blocks called fibers. Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity. Each fiber can then be collapsed into a single representative base node through an information-preserving transformation called "symmetry fibration," introduced by Grothendieck in the context of algebraic geometry. We exemplify the symmetry fibrations in gene regulatory networks and then show that they universally apply across species and domains from biology to social and infrastructure networks. The building blocks are classified into topological classes of input trees characterized by integer branching ratios and fractal golden ratios of Fibonacci sequences representing cycles of information. Thus, symmetry fibrations describe how complex networks are built from the bottom up to process information through the synchronization of their constitutive building blocks.

SUBMITTER: Morone F

PROVIDER: S-EPMC7165483 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature

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Fibration symmetries uncover the building blocks of biological networks.

Morone Flaviano F Leifer Ian I Makse Hernán A HA

Proceedings of the National Academy of Sciences of the United States of America 20200331 15

A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these networks as a set of input trees, one for each node, which contains all pathways along which information can be transmitted in the network. In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional buil ...[more]

PMID: 32234788

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Project description:The development of new biological and chemical instruments for research and diagnostic applications is often slowed by the cost, specialization, and custom nature of these instruments. New instruments are built from components that are drawn from a host of different disciplines and not designed to integrate together, and once built, an instrument typically performs a limited number of tasks and cannot be easily adapted for new applications. Consequently, the process of inventing new instruments is very inefficient, especially for researchers or clinicians in resource-limited settings. To improve this situation, we propose that a family of standardized multidisciplinary components is needed, a set of "building blocks" that perform a wide array of different tasks and are designed to integrate together. Using these components, scientists, engineers, and clinicians would be able to build custom instruments for their own unique needs quickly and easily. In this work we present the foundation of this set of components, a system we call Multifluidic Evolutionary Components (MECs). "Multifluidic" conveys the wide range of fluid volumes MECs operate upon (from nanoliters to milliliters and beyond); "multi" also reflects the multiple disciplines supported by the system (not only fluidics but also electronics, optics, and mechanics). "Evolutionary" refers to the design principles that enable the library of MEC parts to easily grow and adapt to new applications. Each MEC "building block" performs a fundamental function that is commonly found in biological or chemical instruments, functions like valving, pumping, mixing, controlling, and sensing. Each MEC also has a unique symbol linked to a physical definition, which enables instruments to be designed rapidly and efficiently using schematics. As a proof-of-concept, we use MECs to build a variety of instruments, including a fluidic routing and mixing system capable of manipulating fluid volumes over five orders of magnitude, an acid-base titration instrument suitable for use in schools, and a bioreactor suitable for maintaining and analyzing cell cultures in research and diagnostic applications. These are the first of many instruments that can be built by researchers, clinicians, and students using the MEC system.

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Fibration symmetries uncover the building blocks of biological networks.

Publications

Fibration symmetries uncover the building blocks of biological networks.

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