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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: 17] [Impact Index Per Article: 17.0] [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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Cao P, Falcke M, Sneyd J. Mapping Interpuff Interval Distribution to the Properties of Inositol Trisphosphate Receptors. Biophys J 2017; 112:2138-2146. [PMID: 28538151 DOI: 10.1016/j.bpj.2017.03.019] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 03/14/2017] [Accepted: 03/24/2017] [Indexed: 01/24/2023] Open
Abstract
Tightly clustered inositol trisphosphate receptors (IP3Rs) control localized Ca2+ liberation from the endoplasmic reticulum to generate repetitive Ca2+ puffs. Distributions of the interpuff interval (IPI), i.e., the waiting time between successive puffs, are found to be well characterized by a probability density function involving only two parameters, λ and ξ, which represent the basal rate of puff generation and the recovery rate from refractoriness, respectively. However, how the two parameters depend on the kinetic parameters of single IP3Rs in a cluster is still unclear. In this article, using a stochastic puff model and a single-channel data-based IP3R model, we establish the dependencies of λ and ξ on two important IP3R model parameters, IP3 concentration ([IP3]) and the recovery rate from Ca2+ inhibition (rlow). By varying [IP3] and rlow in physiologically plausible ranges, we find that the ξ-λ plane is comprised of only two disjoint regions, a biologically impermissible region and a region where each parameter set (ξ, λ) can be caused by using two different combinations of [IP3] and rlow. The two combinations utilize very different mechanisms to maintain the same IPI distribution, and the mechanistic difference provides a way of identifying IP3R kinetic parameters by observing properties of the IPI.
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Affiliation(s)
- Pengxing Cao
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, Australia
| | - Martin Falcke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Auckland, New Zealand.
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