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Analysis of a genetic-metabolic oscillator with piecewise linear models. J Theor Biol 2019; 462:259-269. [DOI: 10.1016/j.jtbi.2018.10.026] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Revised: 09/10/2018] [Accepted: 10/09/2018] [Indexed: 11/21/2022]
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Ropers D, Métris A. Data for the qualitative modeling of the osmotic stress response to NaCl in Escherichia coli. Data Brief 2016; 9:606-612. [PMID: 27766288 PMCID: PMC5066198 DOI: 10.1016/j.dib.2016.09.028] [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: 06/23/2016] [Revised: 09/09/2016] [Accepted: 09/19/2016] [Indexed: 11/30/2022] Open
Abstract
Qualitative modeling approaches allow to provide a coarse-grained description of the functioning of cellular networks when experimental data are scarce and heterogeneous. We translate the primary literature data on the response of Escherichia coli to hyperosmotic stress caused by NaCl addition into a piecewise linear (PL) model. We provide a data file of the qualitative model, which can be used for simulation of changes of protein concentrations and of DNA coiling during the physiological response of the bacterium to the stress. The qualitative model predictions are directly comparable to the available experimental data. This data is related to the research article entitled “Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens” (Metris et al., 2016) [1].
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Affiliation(s)
- Delphine Ropers
- Inria, Grenoble - Rhône-Alpes Research Center, Saint Ismier, France
| | - Aline Métris
- Institute of Food Research, Norwich Research Park, Norwich NR4 7UA, UK
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3
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Abstract
Bistable switches are widely used in synthetic biology to trigger cellular functions in response to environmental signals. All bistable switches developed so far, however, control the expression of target genes without access to other layers of the cellular machinery. Here, we propose a bistable switch to control the rate at which cells take up a metabolite from the environment. An uptake switch provides a new interface to command metabolic activity from the extracellular space and has great potential as a building block in more complex circuits that coordinate pathway activity across cell cultures, allocate metabolic tasks among different strains or require cell-to-cell communication with metabolic signals. Inspired by uptake systems found in nature, we propose to couple metabolite import and utilization with a genetic circuit under feedback regulation. Using mathematical models and analysis, we determined the circuit architectures that produce bistability and obtained their design space for bistability in terms of experimentally tuneable parameters. We found an activation-repression architecture to be the most robust switch because it displays bistability for the largest range of design parameters and requires little fine-tuning of the promoters' response curves. Our analytic results are based on on-off approximations of promoter activity and are in excellent qualitative agreement with simulations of more realistic models. With further analysis and simulation, we established conditions to maximize the parameter design space and to produce bimodal phenotypes via hysteresis and cell-to-cell variability. Our results highlight how mathematical analysis can drive the discovery of new circuits for synthetic biology, as the proposed circuit has all the hallmarks of a toggle switch and stands as a promising design to control metabolic phenotypes across cell cultures.
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Affiliation(s)
- Diego A Oyarzún
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | - Madalena Chaves
- BioCore team, INRIA Sophia Antipolis 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis, France
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Métris A, George SM, Ropers D. Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens. Int J Food Microbiol 2016; 240:63-74. [PMID: 27377009 DOI: 10.1016/j.ijfoodmicro.2016.06.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Revised: 06/09/2016] [Accepted: 06/19/2016] [Indexed: 01/08/2023]
Abstract
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available, and the more abstract Boolean methods.
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Affiliation(s)
- Aline Métris
- Institute of Food Research, Norwich Research Park, Norwich NR4 7UA, UK.
| | - Susie M George
- Institute of Food Research, Norwich Research Park, Norwich NR4 7UA, UK.
| | - Delphine Ropers
- Inria Grenoble - Rhône-Alpes Research Center, Saint Ismier, France.
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Halász ÁM, Lai HJ, McCabe MM, Radhakrishnan K, Edwards JS. Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013; 10:957-69. [PMID: 24334389 PMCID: PMC4090023 DOI: 10.1109/tcbb.2013.41] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
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Affiliation(s)
- Ádám M. Halász
- Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310
- corresponding author (, )
| | - Hong-Jian Lai
- Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310
| | - Meghan M. McCabe
- Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131 ()
| | - Krishnan Radhakrishnan
- Preventive Medicine and Environmental Health, College of Public Health, University of Kentucky, Lexington, KY 40536 ()
| | - Jeremy S. Edwards
- Department of Molecular Genetics and Microbiology, University of New Mexico Health Science Center, Albuquerque, NM 87131 ()
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Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks. Biosystems 2013; 112:171-9. [PMID: 23499821 DOI: 10.1016/j.biosystems.2013.03.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models. We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model.
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Apri M, de Gee M, Molenaar J. Complexity reduction preserving dynamical behavior of biochemical networks. J Theor Biol 2012; 304:16-26. [DOI: 10.1016/j.jtbi.2012.03.019] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2011] [Revised: 02/13/2012] [Accepted: 03/15/2012] [Indexed: 12/31/2022]
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Holzhütter HG, Drasdo D, Preusser T, Lippert J, Henney AM. The virtual liver: a multidisciplinary, multilevel challenge for systems biology. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2012; 4:221-35. [PMID: 22246674 DOI: 10.1002/wsbm.1158] [Citation(s) in RCA: 81] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
The liver is the central metabolic organ in human physiology, with functions that are fundamentally important to the detoxification of xenobiotics (drugs), the maintenance of homeostasis of numerous blood metabolites, and the production of mediators of the acute phase response. Liver toxicity, whether actual or implied is the reason for the failure of a significant proportion of many promising novel medicines that consequently never reach the market, and diseases such as atherosclerosis, diabetes, and fatty liver diseases, that are a major burden on current health resources, are directly linked to functional and structural disorders of the liver. This article presents the concepts and approaches underpinning one of the most exciting and ambitious modeling projects in the field of systems biology and systems medicine. This major multidisciplinary research program is aimed at developing a whole-organ model of the human liver, representing its central physiological functions under normal and pathological conditions The model will be composed of a larger battery of interconnected submodels representing liver anatomy and physiology, integrating processes across hierarchical levels in space, time, and structural organization. In this article, we outline the general architecture of the liver model and present first step taken to reach this ambitious goal.
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Batt G, Besson B, Ciron PE, de Jong H, Dumas E, Geiselmann J, Monte R, Monteiro PT, Page M, Rechenmann F, Ropers D. Genetic network analyzer: a tool for the qualitative modeling and simulation of bacterial regulatory networks. Methods Mol Biol 2012; 804:439-462. [PMID: 22144166 DOI: 10.1007/978-1-61779-361-5_22] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Genetic Network Analyzer (GNA) is a tool for the qualitative modeling and simulation of gene regulatory networks, based on so-called piecewise-linear differential equation models. We describe the use of this tool in the context of the modeling of bacterial regulatory networks, notably the network of global regulators controlling the adaptation of Escherichia coli to carbon starvation conditions. We show how the modeler, by means of GNA, can define a regulatory network, build a model of the network, determine the steady states of the system, perform a qualitative simulation of the network dynamics, and analyze the simulation results using model-checking tools. The example illustrates the interest of qualitative approaches for the analysis of the dynamics of bacterial regulatory networks.
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Affiliation(s)
- Grégory Batt
- INRIA Paris - Rocquencourt, Domaine de Voluceau, Le Chesnay, France
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Monteiro PT, Dias PJ, Ropers D, Oliveira AL, Sá-Correia I, Teixeira MC, Freitas AT. Qualitative modelling and formal verification of the FLR1 gene mancozeb response in Saccharomyces cerevisiae. IET Syst Biol 2011; 5:308-16. [PMID: 22010757 DOI: 10.1049/iet-syb.2011.0001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
BACKGROUND Qualitative models allow understanding the relation between the structure and the dynamics of gene regulatory networks. The dynamical properties of these models can be automatically analysed by means of formal verification methods, like model checking. This facilitates the model-validation process and the test of new hypotheses to reconcile model predictions with the experimental data. RESULTS The authors report in this study the qualitative modelling and simulation of the transcriptional regulatory network controlling the response of the model eukaryote Saccharomyces cerevisiae to the agricultural fungicide mancozeb. The model allowed the analysis of the regulation level and activity of the components of the gene mancozeb-induced network controlling the transcriptional activation of the FLR1 gene, which is proposed to confer multidrug resistance through its putative role as a drug eflux pump. Formal verification analysis of the network allowed us to confront model predictions with the experimental data and to assess the model robustness to parameter ordering and gene deletion. CONCLUSIONS This analysis enabled us to better understand the mechanisms regulating the FLR1 gene mancozeb response and confirmed the need of a new transcription factor for the full transcriptional activation of YAP1. The result is a computable model of the FLR1 gene response to mancozeb, permitting a quick and cost-effective test of hypotheses prior to experimental validation.
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Affiliation(s)
- P T Monteiro
- INESC-ID/IST, Rua Alves Redol 9, Lisboa 1000-029, Portugal.
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Baldazzi V, Ropers D, Geiselmann J, Kahn D, de Jong H. Importance of metabolic coupling for the dynamics of gene expression following a diauxic shift in Escherichia coli. J Theor Biol 2011; 295:100-15. [PMID: 22138386 DOI: 10.1016/j.jtbi.2011.11.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2011] [Revised: 11/07/2011] [Accepted: 11/08/2011] [Indexed: 11/27/2022]
Abstract
Gene regulatory networks consist of direct interactions, but also include indirect interactions mediated by metabolism. We investigate to which extent these indirect interactions arising from metabolic coupling influence the dynamics of the system. To this end, we build a qualitative model of the gene regulatory network controlling carbon assimilation in Escherichia coli, and use this model to study the changes in gene expression following a diauxic shift from glucose to acetate. In particular, we compare the relative variation in the steady-state concentrations of enzymes and transcription regulators during growth on glucose and acetate, as well as the dynamic response of gene expression to the exhaustion of glucose and the subsequent assimilation of acetate. We find significant differences between the dynamics of the system in the absence and presence of metabolic coupling. This shows that interactions arising from metabolic coupling cannot be ignored when studying the dynamics of gene regulatory networks.
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Affiliation(s)
- Valentina Baldazzi
- INRA, Plantes et Systèmes de Culture Horticoles, Domaine St Paul, Site Agroparc, 84941 Avignon Cedex 9, France.
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Silva-Rocha R, de Jong H, Tamames J, de Lorenzo V. The logic layout of the TOL network of Pseudomonas putida pWW0 plasmid stems from a metabolic amplifier motif (MAM) that optimizes biodegradation of m-xylene. BMC SYSTEMS BIOLOGY 2011; 5:191. [PMID: 22078029 PMCID: PMC3253710 DOI: 10.1186/1752-0509-5-191] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/09/2011] [Accepted: 11/11/2011] [Indexed: 12/13/2022]
Abstract
Background The genetic network of the TOL plasmid pWW0 of the soil bacterium Pseudomonas putida mt-2 for catabolism of m-xylene is an archetypal model for environmental biodegradation of aromatic pollutants. Although nearly every metabolic and transcriptional component of this regulatory system is known to an extraordinary molecular detail, the complexity of its architecture is still perplexing. To gain an insight into the inner layout of this network a logic model of the TOL system was implemented, simulated and experimentally validated. This analysis made sense of the specific regulatory topology out on the basis of an unprecedented network motif around which the entire genetic circuit for m-xylene catabolism gravitates. Results The most salient feature of the whole TOL regulatory network is the control exerted by two distinct but still intertwined regulators (XylR and XylS) on expression of two separated catabolic operons (upper and lower) for catabolism of m-xylene. Following model reduction, a minimal modular circuit composed by five basic variables appeared to suffice for fully describing the operation of the entire system. In silico simulation of the effect of various perturbations were compared with experimental data in which specific portions of the network were activated with selected inducers: m-xylene, o-xylene, 3-methylbenzylalcohol and 3-methylbenzoate. The results accredited the ability of the model to faithfully describe network dynamics. This analysis revealed that the entire regulatory structure of the TOL system enables the action an unprecedented metabolic amplifier motif (MAM). This motif synchronizes expression of the upper and lower portions of a very long metabolic system when cells face the head pathway substrate, m-xylene. Conclusion Logic modeling of the TOL circuit accounted for the intricate regulatory topology of this otherwise simple metabolic device. The found MAM appears to ensure a simultaneous expression of the upper and lower segments of the m-xylene catabolic route that would be difficult to bring about with a standard substrate-responsive single promoter. Furthermore, it is plausible that the MAM helps to avoid biochemical conflicts between competing plasmid-encoded and chromosomally-encoded pathways in this bacterium.
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Affiliation(s)
- Rafael Silva-Rocha
- Systems Biology Program, Centro Nacional de Biotecnología CSIC Cantoblanco-Madrid, 28049, Spain
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Monteiro PT, Dumas E, Besson B, Mateescu R, Page M, Freitas AT, de Jong H. A service-oriented architecture for integrating the modeling and formal verification of genetic regulatory networks. BMC Bioinformatics 2009; 10:450. [PMID: 20042075 PMCID: PMC2813247 DOI: 10.1186/1471-2105-10-450] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2009] [Accepted: 12/30/2009] [Indexed: 01/24/2023] Open
Abstract
Background The study of biological networks has led to the development of increasingly large and detailed models. Computer tools are essential for the simulation of the dynamical behavior of the networks from the model. However, as the size of the models grows, it becomes infeasible to manually verify the predictions against experimental data or identify interesting features in a large number of simulation traces. Formal verification based on temporal logic and model checking provides promising methods to automate and scale the analysis of the models. However, a framework that tightly integrates modeling and simulation tools with model checkers is currently missing, on both the conceptual and the implementational level. Results We have developed a generic and modular web service, based on a service-oriented architecture, for integrating the modeling and formal verification of genetic regulatory networks. The architecture has been implemented in the context of the qualitative modeling and simulation tool GNA and the model checkers NUSMV and CADP. GNA has been extended with a verification module for the specification and checking of biological properties. The verification module also allows the display and visual inspection of the verification results. Conclusions The practical use of the proposed web service is illustrated by means of a scenario involving the analysis of a qualitative model of the carbon starvation response in E. coli. The service-oriented architecture allows modelers to define the model and proceed with the specification and formal verification of the biological properties by means of a unified graphical user interface. This guarantees a transparent access to formal verification technology for modelers of genetic regulatory networks.
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Affiliation(s)
- Pedro T Monteiro
- INRIA Grenoble-Rhône-Alpes, 655 Avenue de l'Europe, Montbonnot, 38334 St Ismier Cedex, France.
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