Suzuki Yoko, Lu Mingyang, Ben-Jacob Eshel, Onuchic José N
Department of Physics, School of Science and Engineering, Meisei University, 2-1-1 Hodokubo, Hino-shi, Tokyo 191-8506, Japan.
Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1827, USA.
Sci Rep. 2016 Feb 15;6:21037. doi: 10.1038/srep21037.
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.
调控基因回路基序在执行和维持重要细胞功能方面发挥着关键作用。通常，基因回路的理论研究侧重于稳态行为，并未考虑时间延迟。在本研究中，结果表明，即使对于具有自我调控和交叉调控的最简单的单基因和双基因元件电路，时间延迟的纳入也会完全改变其随时间变化的动力学。这些元件可产生丰富的行为，包括周期性、准周期性、弱混沌、强混沌和间歇性动力学。我们引入了一种基于功率谱的特殊方法来定量表征和区分这些动力学模式。我们的模拟结果表明，虽然单基因或双基因元件的单个负反馈回路只能具有周期性动力学，但具有两个正/负反馈回路的元件是产生混沌动力学的最简元件。这些元件通常有一个产生振荡的负反馈回路，以及另一个允许在多个稳态之间或在振荡和非振荡动力学之间频繁切换的单元。详细介绍了几种简单的单基因和双基因元件可能的动力学特征。讨论了混沌行为在细胞功能稳健性和疾病（例如在癌症背景下）中可能发挥 的作用。
