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Manser CL, Perez-Carrasco R. A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks. Development 2024; 151:dev202950. [PMID: 38780527 PMCID: PMC11234385 DOI: 10.1242/dev.202950] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 05/13/2024] [Indexed: 05/25/2024]
Abstract
Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. Here, we address this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). This unlocks the ability to find tempo differences as perturbations in the dynamical system that preserve its orbits. We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo, through both numerical and analytical methods. Our exploration includes two case studies: a generic network featuring coupled production and degradation, with a particular application to neural progenitor differentiation; and the repressilator. In the latter, we illustrate how altering the dimerisation rates of transcription factors can decouple the tempo from the shape of the resulting orbits. We conclude by highlighting how the identification of orthogonal molecular mechanisms for tempo control can inform the design of circuits with specific orbits and tempos.
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Affiliation(s)
- Charlotte L. Manser
- Department of Life Sciences, Imperial College London, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
| | - Ruben Perez-Carrasco
- Department of Life Sciences, Imperial College London, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
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Sun Y, Zhang F, Ouyang Q, Luo C. The dynamic-process characterization and prediction of synthetic gene circuits by dynamic delay model. iScience 2024; 27:109142. [PMID: 38384832 PMCID: PMC10879701 DOI: 10.1016/j.isci.2024.109142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 01/17/2024] [Accepted: 02/01/2024] [Indexed: 02/23/2024] Open
Abstract
Differential equation models are widely used to describe genetic regulations, predict multicomponent regulatory circuits, and provide quantitative insights. However, it is still challenging to quantitatively link the dynamic behaviors with measured parameters in synthetic circuits. Here, we propose a dynamic delay model (DDM) which includes two simple parts: the dynamic determining part and the doses-related steady-state-determining part. The dynamic determining part is usually supposed as the delay time but without a clear formula. For the first time, we give the detail formula of the dynamic determining function and provide a method for measuring all parameters of synthetic elements (include 8 activators and 5 repressors) by microfluidic system. Three synthetic circuits were built to show that the DDM can notably improve the prediction accuracy and can be used in various synthetic biology applications.
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Affiliation(s)
- Yanhong Sun
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Fengyu Zhang
- Wenzhou Institute University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, 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, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
| | - Chunxiong Luo
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
- Wenzhou Institute University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China
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Hellerstein J. An oscillating reaction network with an exact closed form solution in the time domain. BMC Bioinformatics 2023; 24:466. [PMID: 38071308 PMCID: PMC10710734 DOI: 10.1186/s12859-023-05600-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Accepted: 12/04/2023] [Indexed: 12/18/2023] Open
Abstract
BACKGROUND Oscillatory behavior is critical to many life sustaining processes such as cell cycles, circadian rhythms, and notch signaling. Important biological functions depend on the characteristics of these oscillations (hereafter, oscillation characteristics or OCs): frequency (e.g., event timings), amplitude (e.g., signal strength), and phase (e.g., event sequencing). Numerous oscillating reaction networks have been documented or proposed. Some investigators claim that oscillations in reaction networks require nonlinear dynamics in that at least one rate law is a nonlinear function of species concentrations. No one has shown that oscillations can be produced for a reaction network with linear dynamics. Further, no one has obtained closed form solutions for the frequency, amplitude and phase of any oscillating reaction network. Finally, no one has published an algorithm for constructing oscillating reaction networks with desired OCs. RESULTS This is a theoretical study that analyzes reaction networks in terms of their representation as systems of ordinary differential equations. Our contributions are: (a) construction of an oscillating, two species reaction network [two species harmonic oscillator (2SHO)] that has no nonlinearity; (b) obtaining closed form formulas that calculate frequency, amplitude, and phase in terms of the parameters of the 2SHO reaction network, something that has not been done for any published oscillating reaction network; and (c) development of an algorithm that parameterizes the 2SHO to achieve desired oscillation, a capability that has not been produced for any published oscillating reaction network. CONCLUSIONS Our 2SHO demonstrates the feasibility of creating an oscillating reaction network whose dynamics are described by a system of linear differential equations. Because it is a linear system, we can derive closed form expressions for the frequency, amplitude, and phase of oscillations, something that has not been done for other published reaction networks. With these formulas, we can design 2SHO reaction networks to have desired oscillation characteristics. Finally, our sensitivity analysis suggests an approach to constructing a 2SHO for a biochemical system.
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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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Sun Y, Zhang F, Li L, Chen K, Wang S, Ouyang Q, Luo C. Two-Layered Microfluidic Devices for High-Throughput Dynamic Analysis of Synthetic Gene Circuits in E. coli. ACS Synth Biol 2022; 11:3954-3965. [PMID: 36283074 DOI: 10.1021/acssynbio.2c00307] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Escherichia coli is a common chassis for synthetic gene circuit studies. In addition to the dose-response of synthetic gene circuits, the analysis of dynamic responses is also an important part of the future design of more complicated synthetic systems. Recently, microfluidic-based methods have been widely used for the analysis of gene expression dynamics. Here, we established a two-layered microfluidic platform for the systematic characterization of synthetic gene circuits (eight strains in eight different culture environments could be observed simultaneously with a 5 min time resolution). With this platform, both dose responses and dynamic responses with a high temporal resolution could be easily derived for further analysis. A controlled environment ensures the stability of the bacterial growth rate, excluding changes in gene expression dynamics caused by changes of the growth dilution rate. The precise environmental switch and automatic micrograph shooting ensured that there was nearly no time lag between the inducer addition and the data recording. We studied four four-node incoherent-feedforward-loop (IFFL) networks with different operators using this device. The experimental results showed that as the effect of inhibition increased, two of the IFFL networks generated pulselike dynamic gene expressions in the range of the inducer concentrations, which was different from the dynamics of the two other circuits with only a simple pattern of rising to the platform. Through fitting the dose-response curves and the dynamic response curves, corresponding parameters were derived and introduced to a simple model that could qualitatively explain the generation of pulse dynamics.
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Affiliation(s)
- Yanhong Sun
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics School of Physics, Peking University, Beijing100871, China
| | - Fengyu Zhang
- School of Life Sciences and Peking-Tsinghua Center for Life Sciences, Peking University, Beijing100871, China
| | - Lusi Li
- Academy of Advanced Interdisciplinary Studies, Peking University, Beijing100871, China
| | - Kaiyue Chen
- Wenzhou Institute University of Chinese Academy of Sciences, Wenzhou, Zhejiang325001, China
| | - Shujing Wang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics School of Physics, Peking University, Beijing100871, China
| | - Qi Ouyang
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics School of Physics, Peking University, Beijing100871, China.,Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing100871, China
| | - Chunxiong Luo
- The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics School of Physics, Peking University, Beijing100871, China.,Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing100871, China.,Wenzhou Institute University of Chinese Academy of Sciences, Wenzhou, Zhejiang325001, China
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Allard P, Papazotos F, Potvin-Trottier L. Microfluidics for long-term single-cell time-lapse microscopy: Advances and applications. Front Bioeng Biotechnol 2022; 10:968342. [PMID: 36312536 PMCID: PMC9597311 DOI: 10.3389/fbioe.2022.968342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/21/2022] [Indexed: 11/13/2022] Open
Abstract
Cells are inherently dynamic, whether they are responding to environmental conditions or simply at equilibrium, with biomolecules constantly being made and destroyed. Due to their small volumes, the chemical reactions inside cells are stochastic, such that genetically identical cells display heterogeneous behaviors and gene expression profiles. Studying these dynamic processes is challenging, but the development of microfluidic methods enabling the tracking of individual prokaryotic cells with microscopy over long time periods under controlled growth conditions has led to many discoveries. This review focuses on the recent developments of one such microfluidic device nicknamed the mother machine. We overview the original device design, experimental setup, and challenges associated with this platform. We then describe recent methods for analyzing experiments using automated image segmentation and tracking. We further discuss modifications to the experimental setup that allow for time-varying environmental control, replicating batch culture conditions, cell screening based on their dynamic behaviors, and to accommodate a variety of microbial species. Finally, this review highlights the discoveries enabled by this technology in diverse fields, such as cell-size control, genetic mutations, cellular aging, and synthetic biology.
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Affiliation(s)
- Paige Allard
- Department of Biology, Concordia University, Montréal, QC, Canada
| | - Fotini Papazotos
- Department of Biology, Concordia University, Montréal, QC, Canada
| | - Laurent Potvin-Trottier
- Department of Biology, Concordia University, Montréal, QC, Canada
- Department of Physics, Concordia University, Montréal, QC, Canada
- Centre for Applied Synthetic Biology, Concordia University, Montréal, QC, Canada
- *Correspondence: Laurent Potvin-Trottier,
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Abstract
Bacterial proteases are a promising post-translational regulation strategy in synthetic circuits because they recognize specific amino acid degradation tags (degrons) that can be fine-tuned to modulate the degradation levels of tagged proteins. For this reason, recent efforts have been made in the search for new degrons. Here we review the up-to-date applications of degradation tags for circuit engineering in bacteria. In particular, we pay special attention to the effects of degradation bottlenecks in synthetic oscillators and introduce mathematical approaches to study queueing that enable the quantitative modelling of proteolytic queues.
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Affiliation(s)
- Prajakta Jadhav
- Department of Biology and Microbiology, South Dakota State University, Brookings, SD, USA
| | - Yanyan Chen
- Program for Computational and Systems Biology, Memorial Sloan Kettering Cancer Center, New York, NY, USA
| | - Nicholas Butzin
- Department of Biology and Microbiology, South Dakota State University, Brookings, SD, USA
| | - Javier Buceta
- Institute for Integrative Systems Biology (I2SysBio, CSIC-UV), Paterna, Valencia 46980, Spain
| | - Arantxa Urchueguía
- Department of Biology and Microbiology, South Dakota State University, Brookings, SD, USA.,Institute for Integrative Systems Biology (I2SysBio, CSIC-UV), Paterna, Valencia 46980, Spain
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