ArticleScientific reports2016
Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays.
Article in Scientific reports, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- How nature discovers rare Turing islands: Exploration by common limit cycles.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
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- Extreme events in gene regulatory networks with time-delays.Scientific reports · 2025Article
- A mathematical model for pancreatic cancer during intraepithelial neoplasia.Royal Society open science · 2024Article
- Article
- Nonlinear delay differential equations and their application to modeling biological network motifs.Nature communications · 2021Article
- Developing an Embedding, Koopman and Autoencoder Technologies-Based Multi-Omics Time Series Predictive Model (EKATP) for Systems Biology research.Frontiers in genetics · 2021Article
- Limit cycles in models of circular gene networks regulated by negative feedback loops.BMC bioinformatics · 2020Article
- On the dynamical aspects of local translation at the activated synapse.BMC bioinformatics · 2020Article
- Toward New Modalities in VEP-Based BCI Applications Using Dynamical Stimuli: Introducing Quasi-Periodic and Chaotic VEP-Based BCI.Frontiers in neuroscience · 2020Article
- Identification of self-regulatory network motifs in reverse engineering gene regulatory networks using microarray gene expression data.IET systems biology · 2019Article
- Bistable emergence of oscillations in growingProceedings of the National Academy of Sciences of the United States of America · 2018Article
- Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis.Scientific reports · 2016Article
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Authors and funding
4 authors.
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No grant is acknowledged in the PubMed record.
Abstract
Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.
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