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Stable maintenance of hidden switches as a strategy to increase the gene expression stability

A preprint version of the article is available at bioRxiv.


In response to severe genetic and environmental perturbations, wild-type organisms can express hidden alternative phenotypes adaptive to such adverse conditions. While our theoretical understanding of the population-level fitness advantage and evolution of phenotypic switching under variable environments has grown, the mechanism by which these organisms maintain phenotypic switching capabilities under static environments remains to be elucidated. Here, using computational simulations, we analyzed the evolution of gene circuits under natural selection and found that different strategies evolved to increase the gene expression stability near the optimum level. In a population comprising bistable individuals, a strategy of maintaining bistability and raising the potential barrier separating the bistable regimes was consistently taken. Our results serve as evidence that hidden bistable switches can be stably maintained during environmental stasis—an essential property enabling the timely release of adaptive alternatives with small genetic changes in the event of substantial perturbations.

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Fig. 1: Comparison of genotypic characteristics among different phases.
Fig. 2: Association of bistable populations from different phases.
Fig. 3: Evolution of gene expression stability.
Fig. 4: Evolutionary simulation results of Gaussian-based models.

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Data availability

The simulation data along with the data analysis scripts associated with the current submission and the source data for Figs. 1–4 are available in the Zenodo repository48.

Code availability

The simulator source code and data analysis scripts have been deposited in GitHub, and they can be accessed at The tool package has also been deposited in Zenodo48.


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We thank O. Soyer and T. Gojobori for their comments on an earlier version of the manuscript. X.G. was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under award numbers BAS/1/1624-01, URF/1/3412-01, URF/1/3450-01, FCC/1/1976-18, FCC/1/1976-23, FCC/1/1976-25, FCC/1/1976-26 and FCS/1/4102-02.

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Authors and Affiliations



H.K. conceived and designed the study, developed tools, performed analysis and wrote the paper. X.G. oversaw the project and wrote the paper. All authors reviewed the final manuscript.

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Correspondence to Xin Gao.

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The authors declare no competing interests.

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Peer review information Nature Computational Science thanks Gábor Balázsi and Xiaojun Tian for their contribution to the peer review of this work. Fernando Chirigati was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Supplementary Sections 1–4 and Figs. 1–18.

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Kuwahara, H., Gao, X. Stable maintenance of hidden switches as a strategy to increase the gene expression stability. Nat Comput Sci 1, 62–70 (2021).

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