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Wang J, Gu C, Xu Y, Zou W. Discontinuous phase transition switching induced by a power-law function between dynamical parameters in coupled oscillators. CHAOS (WOODBURY, N.Y.) 2024; 34:023106. [PMID: 38341760 DOI: 10.1063/5.0189672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Accepted: 01/09/2024] [Indexed: 02/13/2024]
Abstract
In biological or physical systems, the intrinsic properties of oscillators are heterogeneous and correlated. These two characteristics have been empirically validated and have garnered attention in theoretical studies. In this paper, we propose a power-law function existed between the dynamical parameters of the coupled oscillators, which can control discontinuous phase transition switching. Unlike the special designs for the coupling terms, this generalized function within the dynamical term reveals another path for generating the first-order phase transitions. The power-law relationship between dynamic characteristics is reasonable, as observed in empirical studies, such as long-term tremor activity during volcanic eruptions and ion channel characteristics of the Xenopus expression system. Our work expands the conditions that used to be strict for the occurrence of the first-order phase transitions and deepens our understanding of the impact of correlation between intrinsic parameters on phase transitions. We explain the reason why the continuous phase transition switches to the discontinuous phase transition when the control parameter is at a critical value.
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Affiliation(s)
- Jiangsheng Wang
- Department of Systems Science, Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Changgui Gu
- Department of Systems Science, Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Yan Xu
- Department of Systems Science, Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Jin J, Xu F, Liu Z, Qi H, Yao C, Shuai J, Li X. Biphasic amplitude oscillator characterized by distinct dynamics of trough and crest. Phys Rev E 2023; 108:064412. [PMID: 38243441 DOI: 10.1103/physreve.108.064412] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 11/28/2023] [Indexed: 01/21/2024]
Abstract
Biphasic amplitude dynamics (BAD) of oscillation have been observed in many biological systems. However, the specific topology structure and regulatory mechanisms underlying these biphasic amplitude dynamics remain elusive. Here, we searched all possible two-node circuit topologies and identified the core oscillator that enables robust oscillation. This core oscillator consists of a negative feedback loop between two nodes and a self-positive feedback loop of the input node, which result in the fast and slow dynamics of the two nodes, thereby achieving relaxation oscillation. Landscape theory was employed to study the stochastic dynamics and global stability of the system, allowing us to quantitatively describe the diverse positions and sizes of the Mexican hat. With increasing input strength, the size of the Mexican hat exhibits a gradual increase followed by a subsequent decrease. The self-activation of input node and the negative feedback on input node, which dominate the fast dynamics of the input node, were observed to regulate BAD in a bell-shaped manner. Both deterministic and statistical analysis results reveal that BAD is characterized by the linear and nonlinear dependence of the oscillation trough and crest on the input strength. In addition, combining with computational and theoretical analysis, we addressed that the linear response of trough to input is predominantly governed by the negative feedback, while the nonlinear response of crest is jointly regulated by the negative feedback loop and the self-positive feedback loop within the oscillator. Overall, this study provides a natural and physical basis for comprehending the occurrence of BAD in oscillatory systems, yielding guidance for the design of BAD in synthetic biology applications.
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Affiliation(s)
- Jun Jin
- Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
| | - Fei Xu
- Department of Physics, Anhui Normal University, Wuhu, Anhui 241002, China
| | - Zhilong Liu
- Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
| | - Hong Qi
- Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Chenggui Yao
- College of Data Science, Jiaxing University, Jiaxing, Zhejiang 314000, China
| | - Jianwei Shuai
- Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
- Oujiang Laboratory (Zhejiang Lab for Regenerative Medicine, Vision and Brain Health) and Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China
| | - Xiang Li
- Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
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Zhong Z, Lin W, Qin BW. Modulating Biological Rhythms: A Noncomputational Strategy Harnessing Nonlinearity and Decoupling Frequency and Amplitude. PHYSICAL REVIEW LETTERS 2023; 131:138401. [PMID: 37832005 DOI: 10.1103/physrevlett.131.138401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Revised: 07/17/2023] [Accepted: 08/30/2023] [Indexed: 10/15/2023]
Abstract
Understanding and achieving concurrent modulation of amplitude and frequency, particularly adjusting one quantity and simultaneously sustaining the other at an invariant level, are of paramount importance for complex biophysical systems, including the signal pathway where different frequency indicates different upstream signal yielding a certain downstream physiological function while different amplitude further determines different efficacy of a downstream output. However, such modulators with clearly described and universally valid mechanisms are still lacking. Here, we rigorously propose an easy-to-use control strategy containing only one or two steps, leveraging the nonlinearity in the modulated systems to decouple frequency and amplitude in a noncomputational manner. The strategy's efficacy is demonstrated using representative biochemical systems and, thus, it could be potentially applicable to modulating rhythms in experiments of biochemistry and synthetic biology.
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Affiliation(s)
- Zhaoyue Zhong
- School of Mathematical Sciences and Shanghai Center for Mathematical Sciences, Fudan University, 200433 Shanghai, China
| | - Wei Lin
- School of Mathematical Sciences and Shanghai Center for Mathematical Sciences, Fudan University, 200433 Shanghai, China
- Research Institute of Intelligent Complex Systems, Fudan University, 200433 Shanghai, China
- Shanghai Artificial Intelligence Laboratory, 200232 Shanghai, China
- State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institute of Brain Science, Fudan University, 200032 Shanghai, China
| | - Bo-Wei Qin
- Research Institute of Intelligent Complex Systems, Fudan University, 200433 Shanghai, China
- Shanghai Artificial Intelligence Laboratory, 200232 Shanghai, China
- State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institute of Brain Science, Fudan University, 200032 Shanghai, China
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Liu W, Xie J, Liu H, Xiao J. Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:123117. [PMID: 36587328 DOI: 10.1063/5.0130753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 11/11/2022] [Indexed: 06/17/2023]
Abstract
Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength ϵ and the frequency mismatches Δω for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.
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Affiliation(s)
- Weiqing Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Jiangnan Xie
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Hanchang Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Jinghua Xiao
- School of Science, Beijing University of Posts and Communications, Beijing 100876, China
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Qiao L, Zhang ZB, Zhao W, Wei P, Zhang L. Network design principle for robust oscillatory behaviors with respect to biological noise. eLife 2022; 11:76188. [PMID: 36125857 PMCID: PMC9489215 DOI: 10.7554/elife.76188] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 08/22/2022] [Indexed: 11/13/2022] Open
Abstract
Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus, a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive autoregulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive autoregulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive autoregulation—improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.
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Affiliation(s)
- Lingxia Qiao
- Beijing International Center for Mathematical Research, Peking University, Beijing, China
| | - Zhi-Bo Zhang
- Center for Quantitative Biology, Peking University, Beijing, China.,Peking-Tsinghua Joint Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China
| | - Wei Zhao
- Center for Quantitative Biology, Peking University, Beijing, China
| | - Ping Wei
- Center for Quantitative Biology, Peking University, Beijing, China.,Center for Cell and Gene Circuit Design, CAS Key Laboratory of Quantitative Engineering Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Peking University, Beijing, China.,Center for Quantitative Biology, Peking University, Beijing, China
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Liu H, Liu W, Fu C, Zhan M. Sinusoidal and nonsinusoidal patterns in amplitude envelope synchronization. Phys Rev E 2022; 105:044209. [PMID: 35590590 DOI: 10.1103/physreve.105.044209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Accepted: 04/03/2022] [Indexed: 06/15/2023]
Abstract
In this work, amplitude envelope synchronization (AES), as a general phenomenon characterized with highly correlated amplitude envelope but uncorrelated phases and frequencies in coupled nonidentical nonlinear systems, is investigated theoretically and numerically. Two different types of AES patterns, including sinusoidal and nonsinusoidal, are widely observable in coupled periodic and/or chaotic oscillators. They both come from modulation of phase mismatch on amplitude but show different patterns due to different behaviors of phase mismatch. With increase of frequency mismatch, the system tends to crossover from nonsinusoidal to sinusoidal AES. With the aid of synchronization manifold and transverse stability analyses of the AES state, the physical mechanism and scale relations for the AES are well revealed. We expect that all these results could uncover the generality of AES in coupled nonlinear oscillators and help to understand the rich dynamics of phase and amplitude coupling in multidisciplinary fields.
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Affiliation(s)
- Hanchang Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Weiqing Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Chaoxin Fu
- School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Meng Zhan
- State Key Laboratory of Advanced Electromagnetic Engineering and Technology, and School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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