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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: 0] [Impact Index Per Article: 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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Chen X, Wang T, Guan Y, Ouyang Q, Lou C, Qian L. The Topological Characteristics of Biological Ratio-Sensing Networks. Life (Basel) 2023; 13:life13020351. [PMID: 36836707 PMCID: PMC9965423 DOI: 10.3390/life13020351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 01/12/2023] [Accepted: 01/21/2023] [Indexed: 01/31/2023] Open
Abstract
Ratio sensing is a fundamental biological function observed in signal transduction and decision making. In the synthetic biology context, ratio sensing presents one of the elementary functions for cellular multi-signal computation. To investigate the mechanism of the ratio-sensing behavior, we explored the topological characteristics of biological ratio-sensing networks. With exhaustive enumeration of three-node enzymatic and transcriptional regulatory networks, we found that robust ratio sensing was highly dependent on network structure rather than network complexity. Specifically, a set of seven minimal core topological structures and four motifs were deduced to be capable of robust ratio sensing. Further investigations on the evolutionary space of robust ratio-sensing networks revealed highly clustered domains surrounding the core motifs which suggested their evolutionary plausibility. Our study revealed the network topological design principles of ratio-sensing behavior and provided a design scheme for constructing regulatory circuits with ratio-sensing behavior in synthetic biology.
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Affiliation(s)
- Xinmao Chen
- School of Physics, Peking University, Beijing 100871, China
| | - Tianze Wang
- Center for Quantitative Biology, Peking University, Beijing 100871, China
| | - Ying Guan
- Center for Cell and Gene Circuit Design, CAS Key Laboratory of Quantitative Engineering Biology, Guangdong Provincial Key Laboratory of Synthetic Genomics, Shenzhen Key Laboratory of Synthetic Genomics, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Qi Ouyang
- School of Physics, Peking University, Beijing 100871, China
- Center for Quantitative Biology, Peking University, Beijing 100871, China
- Correspondence: (Q.O.); (C.L.); (L.Q.)
| | - Chunbo Lou
- Center for Cell and Gene Circuit Design, CAS Key Laboratory of Quantitative Engineering Biology, Guangdong Provincial Key Laboratory of Synthetic Genomics, Shenzhen Key Laboratory of Synthetic Genomics, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
- Correspondence: (Q.O.); (C.L.); (L.Q.)
| | - Long Qian
- Center for Quantitative Biology, Peking University, Beijing 100871, China
- Correspondence: (Q.O.); (C.L.); (L.Q.)
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Wang J, Belta C, Isaacson SA. How Retroactivity Affects the Behavior of Incoherent Feedforward Loops. iScience 2020; 23:101779. [PMID: 33305173 PMCID: PMC7711281 DOI: 10.1016/j.isci.2020.101779] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 09/24/2020] [Accepted: 11/02/2020] [Indexed: 10/27/2022] Open
Abstract
An incoherent feedforward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. It remains an open question to understand the behavior of IFFLs in contexts with high levels of retroactivity, where an upstream transcription factor binds to numerous downstream binding sites. Here we study the behavior of IFFLs by simulating and comparing ODE models with different levels of retroactivity. We find that increasing retroactivity in an IFFL can increase, decrease, or keep the network's response time and pulse amplitude constant. This suggests that increasing retroactivity, traditionally considered an impediment to designing robust synthetic systems, could be exploited to improve the performance of IFFLs. In contrast, we find that increasing retroactivity in a negative autoregulated circuit can only slow the response. The ability of an IFFL to flexibly handle retroactivity may have contributed to its significant abundance in both bacterial and eukaryotic regulatory networks.
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Affiliation(s)
- Junmin Wang
- The Bioinformatics Graduate Program, Boston University, Boston, MA 02215, USA
| | - Calin Belta
- The Bioinformatics Graduate Program, Boston University, Boston, MA 02215, USA
| | - Samuel A. Isaacson
- Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA
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Tareen A, Wingreen NS, Mukhopadhyay R. Asymmetry between Activators and Deactivators in Functional Protein Networks. Sci Rep 2020; 10:10131. [PMID: 32576941 PMCID: PMC7311538 DOI: 10.1038/s41598-020-66699-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 05/18/2020] [Indexed: 12/04/2022] Open
Abstract
Are “turn-on” and “turn-off” functions in protein-protein interaction networks exact opposites of each other? To answer this question, we implement a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. We study the roles of activators and deactivators, two core components of oscillatory protein interaction networks, and find a striking asymmetry in the roles of activating and deactivating proteins, where activating proteins tend to be synergistic and deactivating proteins tend to be competitive.
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Affiliation(s)
- Ammar Tareen
- Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA.,Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, New York, 11724, USA
| | - Ned S Wingreen
- Lewis-Sigler Institute for Integrative Genomics, Carl Icahn Laboratory, Washington Road, Princeton, New Jersey, 08544, USA. .,Department of Molecular Biology, Princeton University, Princeton, NJ, 08544, USA.
| | - Ranjan Mukhopadhyay
- Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA.
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Li Z, Liu S, Yang Q. Incoherent Inputs Enhance the Robustness of Biological Oscillators. Cell Syst 2019; 5:72-81.e4. [PMID: 28750200 DOI: 10.1016/j.cels.2017.06.013] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Revised: 03/30/2017] [Accepted: 06/22/2017] [Indexed: 11/25/2022]
Abstract
Robust biological oscillators retain the critical ability to function in the presence of environmental perturbations. Although central architectures that support robust oscillations have been extensively studied, networks containing the same core vary drastically in their potential to oscillate, and it remains elusive what peripheral modifications to the core contribute to this functional variation. Here, we have generated a complete atlas of two- and three-node oscillators computationally, then systematically analyzed the association between network structure and robustness. We found that, while certain core topologies are essential for producing a robust oscillator, local structures can substantially modulate the robustness of oscillations. Notably, local nodes receiving incoherent or coherent inputs respectively promote or attenuate the overall network robustness in an additive manner. We validated these relationships in larger-scale networks reflective of real biological oscillators. Our findings provide an explanation for why auxiliary structures not required for oscillation are evolutionarily conserved and suggest simple ways to evolve or design robust oscillators.
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Affiliation(s)
- Zhengda Li
- Department of Biophysics, University of Michigan, Ann Arbor, MI, USA; Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI, USA
| | - Shixuan Liu
- Cell Biology Program, The Hospital for Sick Children, Toronto, ON, Canada; Department of Molecular Genetics, University of Toronto, Toronto, ON, Canada
| | - Qiong Yang
- Department of Biophysics, University of Michigan, Ann Arbor, MI, USA; Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI, USA.
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Wu L, Wang H, Ouyang Q. Constructing network topologies for multiple signal-encoding functions. BMC SYSTEMS BIOLOGY 2019; 13:6. [PMID: 30634968 PMCID: PMC6330498 DOI: 10.1186/s12918-018-0676-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/29/2018] [Accepted: 12/28/2018] [Indexed: 11/17/2022]
Abstract
Background Cells use signaling protein networks to sense their environment and mediate specific responses. Information about environmental stress is usually encoded in the dynamics of the signaling molecules, and qualitatively distinct dynamics of the same signaling molecule can lead to dramatically different cell fates. Exploring the design principles of networks with multiple signal-encoding functions is important for understanding how distinct dynamic patterns are shaped and integrated by real cellular networks, and for building cells with targeted sensing–response functions via synthetic biology. Results In this paper, we investigate multi-node enzymatic regulatory networks with three signal-encoding functions, i.e., dynamic responses of oscillation, transient activation, and sustained activation upon step stimulation by three different inducers, respectively. Taking into account competition effects of the substrates for the same enzyme in the enzymatic reactions, we searched for robust subnetworks for each signal-encoding function by three-node-network enumeration and then integrated the three subnetworks together via node-merging. The obtained tri-functional networks consisted of four to six nodes, and the core structures of these networks were hybrids of the motifs for the subfunctions. Conclusions The simplest but relatively robust tri-functional networks demonstrated that the three functions were compatible within a simple negative feedback loop. Depending on the network structure, the competition effects of the substrates for the same enzyme within the networks could promote or hamper the target functions, and can create implicit functional motifs. Overall, the networks we obtained could in principle be synthesized to construct dynamic control circuits with multiple target functions. Electronic supplementary material The online version of this article (10.1186/s12918-018-0676-5) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Lili Wu
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
| | - Hongli Wang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China. .,Center for Quantitative Biology, Peking University, Beijing, 100871, China.
| | - Qi Ouyang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China. .,Center for Quantitative Biology, Peking University, Beijing, 100871, China. .,Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, 100871, China.
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Abstract
Background Self-sustained oscillations are a ubiquitous and vital phenomenon in living systems. From primitive single-cellular bacteria to the most sophisticated organisms, periodicities have been observed in a broad spectrum of biological processes such as neuron firing, heart beats, cell cycles, circadian rhythms, etc. Defects in these oscillators can cause diseases from insomnia to cancer. Elucidating their fundamental mechanisms is of great significance to diseases, and yet challenging, due to the complexity and diversity of these oscillators. Results Approaches in quantitative systems biology and synthetic biology have been most effective by simplifying the systems to contain only the most essential regulators. Here, we will review major progress that has been made in understanding biological oscillators using these approaches. The quantitative systems biology approach allows for identification of the essential components of an oscillator in an endogenous system. The synthetic biology approach makes use of the knowledge to design the simplest, de novo oscillators in both live cells and cell-free systems. These synthetic oscillators are tractable to further detailed analysis and manipulations. Conclusion With the recent development of biological and computational tools, both approaches have made significant achievements.
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Vasylchenkova A, Mraz M, Zimic N, Moskon M. Classical Mechanics Approach Applied to Analysis of Genetic Oscillators. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2017; 14:721-727. [PMID: 27076464 DOI: 10.1109/tcbb.2016.2550456] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Biological oscillators present a fundamental part of several regulatory mechanisms that control the response of various biological systems. Several analytical approaches for their analysis have been reported recently. They are, however, limited to only specific oscillator topologies and/or to giving only qualitative answers, i.e., is the dynamics of an oscillator given the parameter space oscillatory or not. Here, we present a general analytical approach that can be applied to the analysis of biological oscillators. It relies on the projection of biological systems to classical mechanics systems. The approach is able to provide us with relatively accurate results in the meaning of type of behavior system reflects (i.e., oscillatory or not) and periods of potential oscillations without the necessity to conduct expensive numerical simulations. We demonstrate and verify the proposed approach on three different implementations of amplified negative feedback oscillator.
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Robust network topologies for generating oscillations with temperature-independent periods. PLoS One 2017; 12:e0171263. [PMID: 28152061 PMCID: PMC5289577 DOI: 10.1371/journal.pone.0171263] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 01/17/2017] [Indexed: 11/26/2022] Open
Abstract
Nearly all living systems feature a temperature-independent oscillation period in circadian clocks. This ubiquitous property occurs at the system level and is rooted in the network architecture of the clock machinery. To investigate the mechanism of this prominent property of the circadian clock and provide general guidance for generating robust genetic oscillators with temperature-compensated oscillations, we theoretically explored the design principle and core network topologies preferred by oscillations with a temperature-independent period. By enumerating all topologies of genetic regulatory circuits with three genes, we obtained four network motifs, namely, a delayed negative feedback oscillator, repressilator, activator-inhibitor oscillator and substrate-depletion oscillator; hybrids of these motifs constitute the vast majority of target network topologies. These motifs are biased in their capacities for achieving oscillations and the temperature sensitivity of the period. The delayed negative feedback oscillator and repressilator are more robust for oscillations, whereas the activator-inhibitor and substrate-depletion oscillators are superior for maintaining a temperature-independent oscillation period. These results suggest that thermally robust oscillation can be more plausibly achieved by hybridizing these two categories of network motifs. Antagonistic balance and temperature insulation mechanisms for achieving temperature compensation are typically found in these topologies with temperature robustness. In the temperature insulation approach, the oscillation period relies on very few parameters, and these parameters are influenced only slightly by temperature. This approach prevents the temperature from affecting the oscillation period and generates circadian rhythms that are robust against environmental perturbations.
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Woods ML, Leon M, Perez-Carrasco R, Barnes CP. A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators. ACS Synth Biol 2016; 5:459-70. [PMID: 26835539 PMCID: PMC4914944 DOI: 10.1021/acssynbio.5b00179] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology.
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Affiliation(s)
- Mae L. Woods
- Department of Cell and Developmental Biology, ‡Department of Mathematics, and ¶Department of Genetics,
Evolution and Environment, University College London, London, WC1E 6BT, U.K
| | - Miriam Leon
- Department of Cell and Developmental Biology, ‡Department of Mathematics, and ¶Department of Genetics,
Evolution and Environment, University College London, London, WC1E 6BT, U.K
| | - Ruben Perez-Carrasco
- Department of Cell and Developmental Biology, ‡Department of Mathematics, and ¶Department of Genetics,
Evolution and Environment, University College London, London, WC1E 6BT, U.K
| | - Chris P. Barnes
- Department of Cell and Developmental Biology, ‡Department of Mathematics, and ¶Department of Genetics,
Evolution and Environment, University College London, London, WC1E 6BT, U.K
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