Chaotic gene regulatory networks can be robust against mutations and noise

Sevi̇m, Volkan; Rikvold, Per Arne

doi:10.1016/j.jtbi.2008.03.003

Cited by 38 publications

(43 citation statements)

References 39 publications

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“…Another extension is the use of fitness favoring for dynamic attractors. As the model (1), with suitable choice of J ij , shows periodic or chaotic attractors [41], study on the evolution of robust dynamic system is also of importance ( see also [42]). …”

Section: Summary and Discussionmentioning

confidence: 99%

Shaping robust system through evolution

Kaneko

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network's robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is derived, akin to the fluctuation-dissipation relationship known in physics. Lead paragraphBiological function is generally robust to noise in dynamical systems and to mutation to structure of the system. How are these two types of robustness related? Through numerical simulations of a minimal model that captures the essence of a gene expression dynamics that undergoes a mutation and selection process, we demonstrate that the evolved networks acquire robustness to mutation only when gene expression is sufficiently noisy -a physical constraint highlighted by a series of experimental studies in recent 1 years. We derive a quantitative condition for evolution of robustness which ultimately links robustness to mutation in the evolutionary time-scale and robustness to noise in development in the reproductive time-scale. Our model simulations predict correlation between the two robustness, which lead to a universal proportionality relationship between variances of genetic and epigenetic phenotype fluctuations, which remind us of fluctuation-dissipation relationship in statistical physics.

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Section: Summary and Discussionmentioning

confidence: 99%

Shaping robust system through evolution

Kaneko

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Threshold networks can be used to model gene regulatory networks [1]- [3]. The nodes of the network represent genes, and the directed links between them represent interactions between genes.…”

Section: Introductionmentioning

confidence: 99%

The phase diagram of random threshold networks

Szejka¹,

Mihaljev

Drossel

2008

New J. Phys.

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Abstract. Threshold networks are used as models for neural or gene regulatory networks. They show rich dynamical behaviour with a transition between a frozen phase and a chaotic phase. We investigate the phase diagram of randomly connected threshold networks with real-valued thresholds h and a fixed number of inputs per node. The nodes are updated according to the same rules as in a model of the cell-cycle network of Saccharomyces cereviseae (Li et al 2004 Proc. Natl Acad. Sci. USA 101 4781-6). Using the annealed approximation, we derive expressions for the time evolution of the proportion of nodes in the 'on' and 'off' states, and for the sensitivity λ. The results are compared with simulations of quenched networks. We find that for integer values of h the simulations show marked deviations from the annealed approximation even for large networks. This can be attributed to the particular choice of the updating rule. Contents

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“…Very complex dynamic behavior has been extensively reported in biological GRNs and network models, including in certain regulatory motifs [37], in statistical analyses [15], and in systems of differential equations used to model such networks [16][17][18]. Payne et al [19] used Random Boolean Circuits [55] to explore the effect of chaotic dynamics on robustness and evolvability.…”

Section: Discussionmentioning

confidence: 99%

“…Mathematical analysis of random Boolean networks and other models has provided some insights into the expected dynamical behavior of networks in ordered, periodic, and chaotic regions [15][16][17][18][19] based on network genotype and interactive rules.…”

Section: Introductionmentioning

confidence: 99%