Criticality Distinguishes the Ensemble of Biological Regulatory Networks

Daniels, Bryan C.; Kim, Hyun-Ju; Moore, Douglas; Zhou, Siyu; Smith, Harrison B.; Karas, Bradley; Kauffman, Stuart; Walker, Sara Imari

doi:10.1103/physrevlett.121.138102

Cited by 101 publications

(117 citation statements)

References 49 publications

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“…This can be understood because immune cells probably not only have a variable environment, but actually have evolved to thrive on it. The finding on the ordered dynamics of the CD4+ Tcell network is consistent with many research findings exhibiting that gene regulatory networks of biological systems have ordered or critical dynamics [49][50][51][52].…”

Section: Comparison Of Antifragility Between Multilayer and Single-lasupporting

confidence: 90%

A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models

2019

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Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks. Here we study how the multilayer structure affects the antifragility of the whole system. By comparing single-layer and multilayer Boolean networks based on our recently proposed antifragility measure, we found that the multilayer structure facilitated the production of antifragile systems. Our measure and findings will be useful for various applications such as exploring properties of biological systems with multilayer structures and creating more antifragile engineered systems.

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Section: Comparison Of Antifragility Between Multilayer and Single-lasupporting

confidence: 90%

A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models

2019

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“…We found that A. thaliana cell-cycle repeatedly produces antifragile networks at regular intervals depending on the values of . Based on many studies demonstrating living organisms are ordered or critical [47][48][49][50], we can infer that A. thaliana might have been evolved in environments where particular dimensions of perturbations are added more frequently than other biological systems. We also found that CD4+ T cell differentiation and plasticity is the most antifragile of the ones studied, probably because it has the most variable environment.…”

Section: Antifragility In Biological Bnsmentioning

confidence: 99%

A Novel Antifragility Measure Based on Satisfaction and Its Application to Random and Biological Boolean Networks

2019

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Antifragility is a property that enhances the capability of a system in response to external perturbations. Although the concept has been applied in many areas, a practical measure of antifragility has not been developed yet. Here we propose a simply calculable measure of antifragility, based on the change of "satisfaction" before and after adding perturbations, and apply it to random Boolean networks (RBNs). Using the measure, we found that ordered RBNs are the most antifragile. Also, we demonstrated that seven biological systems are antifragile. Our measure and results can be used in various applications of Boolean networks (BNs) including creating antifragile engineering systems, identifying the genetic mechanism of antifragile biological systems, and developing new treatment strategies for various diseases.

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“…The precise statistical properties of functional ensembles, and of ensembles of networks reliable under noise, are mostly open questions at present. Daniels at al. (2018) give a first account of how natural critical networks dramatically differ from random critical networks in their mean connectivity K, but also in their local causal and logical structures.…”

Section: Resultsmentioning

confidence: 99%

“…There is now solid evidence that evolution indeed has achieved and is maintaining genetic networks near dynamical criticality (Balleza et al 2008;Daniels et al 2018). Is this a curiosity or a biological necessity as early models suggest?…”

Section: Introductionmentioning

confidence: 99%

Ensembles, dynamics, and cell types: Revisiting the statistical mechanics perspective on cellular regulation

Bornholdt

Kauffman

2019

Journal of Theoretical Biology

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Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this subensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.* bornholdt@uni-bremen.de

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Criticality Distinguishes the Ensemble of Biological Regulatory Networks

Cited by 101 publications

References 49 publications

A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models

A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models

A Novel Antifragility Measure Based on Satisfaction and Its Application to Random and Biological Boolean Networks

Ensembles, dynamics, and cell types: Revisiting the statistical mechanics perspective on cellular regulation

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