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The topological requirements for robust perfect adaptation in networks of any size

Robyn P. Araujo & Lance A. Liotta

Nature Communications volume 9, Article number: 1757 (2018)

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Biochemical networks Complexity Modularity Robustness

Received: 28 February 2017 Accepted: 03 April 2018

Published: 01 May 2018


Robustness, and the ability to function and thrive amid changing and unfavorable environments, is a fundamental requirement for living systems. Until now it has been an open question how large and complex biological networks can exhibit robust behaviors, such as perfect adaptation to a variable stimulus, since complexity is generally associated with fragility. Here we report that all networks that exhibit robust perfect adaptation (RPA) to a persistent change in stimulus are decomposable into well-defined modules, of which there exist two distinct classes. These two modular classes represent a topological basis for all RPA-capable networks, and generate the full set of topological realizations of the internal model principle for RPA in complex, self-organizing, evolvable bionetworks. This unexpected result supports the notion that evolutionary processes are empowered by simple and scalable modular design principles that promote robust performance no matter how large or complex the underlying networks become.


This study was partially supported by NIH grants R33CA206937 and R01AR068436.

Author information


School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, 4000, Australia

Robyn P. Araujo

Institute of Health and Biomedical Innovation (IHBI), 60 Musk Avenue, Kelvin Grove, Brisbane, QLD, 4059, Australia

Robyn P. Araujo

Center for Applied Proteomics and Molecular Medicine, George Mason University, 10920 George Mason Circle, Manassas, Virginia, 20110, USA

Lance A. Liotta


R.P.A. conceived of the analytical methodology, and performed all derivations, proofs and computational simulations. R.P.A. and L.A.L. wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Robyn P. Araujo.