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Impact of Negative Feedbacks on De Novo Pyrimidines Biosynthesis in Escherichia coli. Int J Mol Sci 2023; 24:ijms24054806. [PMID: 36902235 PMCID: PMC10003070 DOI: 10.3390/ijms24054806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 02/25/2023] [Accepted: 02/28/2023] [Indexed: 03/06/2023] Open
Abstract
Earlier studies aimed at investigating the metabolism of endogenous nucleoside triphosphates in synchronous cultures of E. coli cells revealed an auto-oscillatory mode of functioning of the pyrimidine and purine nucleotide biosynthesis system, which the authors associated with the dynamics of cell division. Theoretically, this system has an intrinsic oscillatory potential, since the dynamics of its functioning are controlled through feedback mechanisms. The question of whether the nucleotide biosynthesis system has its own oscillatory circuit is still open. To address this issue, an integral mathematical model of pyrimidine biosynthesis was developed, taking into account all experimentally verified negative feedback in the regulation of enzymatic reactions, the data of which were obtained under in vitro conditions. Analysis of the dynamic modes of the model functioning has shown that in the pyrimidine biosynthesis system, both the steady-state and oscillatory functioning modes can be realized under certain sets of kinetic parameters that fit in the physiological boundaries of the investigated metabolic system. It has been demonstrated that the occurrence of the oscillatory nature of metabolite synthesis depended on the ratio of two parameters: the Hill coefficient, hUMP1-the nonlinearity of the UMP effect on the activity of carbamoyl-phosphate synthetase, and the parameter r characterizing the contribution of the noncompetitive mechanism of UTP inhibition to the regulation of the enzymatic reaction of UMP phosphorylation. Thus, it has been theoretically shown that the E. coli pyrimidine biosynthesis system possesses its own oscillatory circuit whose oscillatory potential depends to a significant degree on the mechanism of regulation of UMP kinase activity.
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Lan Y, Nguyen LK. Multi-Dimensional Analysis of Biochemical Network Dynamics Using pyDYVIPAC. Methods Mol Biol 2023; 2634:33-58. [PMID: 37074573 DOI: 10.1007/978-1-0716-3008-2_2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2023]
Abstract
Biochemical networks are dynamic, nonlinear, and high-dimensional systems. Realistic kinetic models of biochemical networks often comprise a multitude of kinetic parameters and state variables. Depending on the specific parameter values, a network can display one of a variety of possible dynamic behaviors such as monostable fixed point, damped oscillation, sustained oscillation, and/or bistability. Understanding how a network behaves under a particular parametric condition, and how its behavior changes as the model parameters are varied within the multidimensional parameter space are imperative for gaining a holistic understanding of the network dynamics. Such knowledge helps elucidate the parameter-to-dynamics mapping, uncover how cells make decisions under various pathophysiological contexts, and inform the design of biological circuits with desired behavior, where the latter is critical to the field of synthetic biology. In this chapter, we will present a practical guide to the multidimensional exploration, analysis, and visualization of network dynamics using pyDYVIPAC, which is a tool ideally suited to these purposes implemented in Python. The utility of pyDYVIPAC will be demonstrated using specific examples of biochemical networks with differing structures and dynamic properties via the interactive Jupyter Notebook environment.
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Affiliation(s)
- Yunduo Lan
- Department of Biochemistry and Molecular Biology, School of Biomedical Sciences, Monash University, Clayton, VIC, Australia
- Biomedicine Discovery Institute, Monash University, Clayton, VIC, Australia
| | - Lan K Nguyen
- Department of Biochemistry and Molecular Biology, School of Biomedical Sciences, Monash University, Clayton, VIC, Australia.
- Biomedicine Discovery Institute, Monash University, Clayton, VIC, Australia.
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A Modeling Study on Vaccination and Spread of SARS-CoV-2 Variants in Italy. Vaccines (Basel) 2021; 9:vaccines9080915. [PMID: 34452040 PMCID: PMC8402493 DOI: 10.3390/vaccines9080915] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 07/29/2021] [Accepted: 08/12/2021] [Indexed: 12/16/2022] Open
Abstract
From the end of 2020, different vaccines against COVID-19 have been approved, offering a glimmer of hope and relief worldwide. However, in late 2020, new cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) started to re-surge, worsened by the emergence of highly infectious variants. To study this scenario, we extend the Susceptible-Exposed-Infectious-Removed model with lockdown measures used in our previous work with the inclusion of new lineages and mass vaccination campaign. We estimate model parameters using the Bayesian method Conditional Robust Calibration in two case studies: Italy and the Umbria region, the Italian region being worse affected by the emergence of variants. We then use the model to explore the dynamics of COVID-19, given different vaccination paces and a policy of gradual reopening. Our findings confirm the higher reproduction number of Umbria and the increase of transmission parameters due to the presence of new variants. The results illustrate the importance of preserving population-wide interventions, especially during the beginning of vaccination. Finally, under the hypothesis of waning immunity, the predictions show that a seasonal vaccination with a constant rate would probably be necessary to control the epidemic.
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Giaretta A. Stochastic Modeling of the Co-Regulation between Early and E8 Promoters in Human Papillomavirus. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2018; 2018:5026-5029. [PMID: 30441470 DOI: 10.1109/embc.2018.8513406] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
High risk HPV can induce cervical and oropharyngeal cancerous Iesions. The initial phase of the infection is characterized by a fine regulation of the viral DNA replication, in order to maintain 10-100 DNA copies per cell. Such regulation is primarily controlled by El and E2 proteins produced by the early promoter. The recently discovered E8 promoter is capable to co-regulate the early one in order to maintain a low and constant viral DNA copy number.The aim of this study is to develop a novel stochastic mathematical model of the co-regulation between the E8 and the early promoter, with the main purpose to rigorously show the E8 promoter capability to finely regulate the HPV transcripts which control the DNA replication in the first stages of the infection.The model, condensing the biological knowledge present in literature, describes the interaction between the two promoters and shows how the E8 co-regulation is capable to reject the stochastic noise of E2 gene expression to a higher extent than the early promoter negative auto-feedback. This proves the capability of the E8 promoter to finely control the HPV genomes copy number.
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Fagerlund R, Behar M, Fortmann KT, Lin YE, Vargas JD, Hoffmann A. Anatomy of a negative feedback loop: the case of IκBα. J R Soc Interface 2016; 12:0262. [PMID: 26311312 DOI: 10.1098/rsif.2015.0262] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The magnitude, duration and oscillation of cellular signalling pathway responses are often limited by negative feedback loops, defined as an 'activator-induced inhibitor' regulatory motif. Within the NFκB signalling pathway, a key negative feedback regulator is IκBα. We show here that, contrary to current understanding, NFκB-inducible expression is not sufficient for providing effective negative feedback. We then employ computational simulations of NFκB signalling to identify IκBα molecular properties that are critical for proper negative feedback control and test the resulting predictions in biochemical and single-cell live-imaging studies. We identified nuclear import and nuclear export of IκBα and the IκBα-NFκB complex, as well as the free IκBα half-life, as key determinants of post-induction repression of NFκB and the potential for subsequent reactivation. Our work emphasizes that negative feedback is an emergent systems property determined by multiple molecular and biophysical properties in addition to the required 'activator-induced inhibitor' relationship.
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Affiliation(s)
- Riku Fagerlund
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA
| | - Marcelo Behar
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA
| | - Karen T Fortmann
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA
| | - Y Eason Lin
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, CA 90095, USA Institute for Quantitative and Computational Biosciences, University of California, Los Angeles, CA 90095, USA
| | - Jesse D Vargas
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, CA 90095, USA Institute for Quantitative and Computational Biosciences, University of California, Los Angeles, CA 90095, USA
| | - Alexander Hoffmann
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA 92093, USA Department of Microbiology, Immunology, and Molecular Genetics, University of California, Los Angeles, CA 90095, USA Institute for Quantitative and Computational Biosciences, University of California, Los Angeles, CA 90095, USA
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DYVIPAC: an integrated analysis and visualisation framework to probe multi-dimensional biological networks. Sci Rep 2015. [PMID: 26220783 PMCID: PMC4518224 DOI: 10.1038/srep12569] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Biochemical networks are dynamic and multi-dimensional systems, consisting of tens or hundreds of molecular components. Diseases such as cancer commonly arise due to changes in the dynamics of signalling and gene regulatory networks caused by genetic alternations. Elucidating the network dynamics in health and disease is crucial to better understand the disease mechanisms and derive effective therapeutic strategies. However, current approaches to analyse and visualise systems dynamics can often provide only low-dimensional projections of the network dynamics, which often does not present the multi-dimensional picture of the system behaviour. More efficient and reliable methods for multi-dimensional systems analysis and visualisation are thus required. To address this issue, we here present an integrated analysis and visualisation framework for high-dimensional network behaviour which exploits the advantages provided by parallel coordinates graphs. We demonstrate the applicability of the framework, named "Dynamics Visualisation based on Parallel Coordinates" (DYVIPAC), to a variety of signalling networks ranging in topological wirings and dynamic properties. The framework was proved useful in acquiring an integrated understanding of systems behaviour.
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Maeda K, Kurata H. Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity. BMC SYSTEMS BIOLOGY 2014; 8 Suppl 5:S1. [PMID: 25605374 PMCID: PMC4305980 DOI: 10.1186/1752-0509-8-s5-s1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Background One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators. Results We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop). Conclusions Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period.
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Sturrock M, Murray PJ, Matzavinos A, Chaplain MAJ. Mean field analysis of a spatial stochastic model of a gene regulatory network. J Math Biol 2014; 71:921-59. [PMID: 25323318 DOI: 10.1007/s00285-014-0837-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2013] [Revised: 09/05/2014] [Indexed: 01/21/2023]
Abstract
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
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Affiliation(s)
- M Sturrock
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, 43210, USA,
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Wolfrom CM, Laurent M, Deschatrette J. Can we negotiate with a tumor? PLoS One 2014; 9:e103834. [PMID: 25084359 PMCID: PMC4118912 DOI: 10.1371/journal.pone.0103834] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Accepted: 07/08/2014] [Indexed: 12/18/2022] Open
Abstract
Recent progress in deciphering the molecular portraits of tumors promises an era of more personalized drug choices. However, current protocols still follow standard fixed-time schedules, which is not entirely coherent with the common observation that most tumors do not grow continuously. This unpredictability of the increases in tumor mass is not necessarily an obstacle to therapeutic efficiency, particularly if tumor dynamics could be exploited. We propose a model of tumor mass evolution as the integrated result of the dynamics of two linked complex systems, tumor cell population and tumor microenvironment, and show the practical relevance of this nonlinear approach.
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Affiliation(s)
- Claire M. Wolfrom
- Equipe « Dynamiques cellulaires et modélisation », Inserm Unité 757, Université Paris-Sud, Orsay, France
| | - Michel Laurent
- Equipe « Dynamiques cellulaires et modélisation », Inserm Unité 757, Université Paris-Sud, Orsay, France
| | - Jean Deschatrette
- Equipe « Dynamiques cellulaires et modélisation », Inserm Unité 757, Université Paris-Sud, Orsay, France
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Budinsky RA, Schrenk D, Simon T, Van den Berg M, Reichard JF, Silkworth JB, Aylward LL, Brix A, Gasiewicz T, Kaminski N, Perdew G, Starr TB, Walker NJ, Rowlands JC. Mode of action and dose–response framework analysis for receptor-mediated toxicity: The aryl hydrocarbon receptor as a case study. Crit Rev Toxicol 2013; 44:83-119. [DOI: 10.3109/10408444.2013.835787] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
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Zhang Q, Bhattacharya S, Andersen ME. Ultrasensitive response motifs: basic amplifiers in molecular signalling networks. Open Biol 2013; 3:130031. [PMID: 23615029 PMCID: PMC3718334 DOI: 10.1098/rsob.130031] [Citation(s) in RCA: 131] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.
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Affiliation(s)
- Qiang Zhang
- Center for Dose Response Modeling, Institute for Chemical Safety Sciences, The Hamner Institutes for Health Sciences, Research Triangle Park, NC 27709, USA.
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12
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Non-transcriptional regulatory processes shape transcriptional network dynamics. Nat Rev Microbiol 2011; 9:817-28. [PMID: 21986901 DOI: 10.1038/nrmicro2667] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Information about the extra- or intracellular environment is often captured as biochemical signals that propagate through regulatory networks. These signals eventually drive phenotypic changes, typically by altering gene expression programmes in the cell. Reconstruction of transcriptional regulatory networks has given a compelling picture of bacterial physiology, but transcriptional network maps alone often fail to describe phenotypes. Cellular response dynamics are ultimately determined by interactions between transcriptional and non-transcriptional networks, with dramatic implications for physiology and evolution. Here, we provide an overview of non-transcriptional interactions that can affect the performance of natural and synthetic bacterial regulatory networks.
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Nguyen LK, Kulasiri D. Distinct noise-controlling roles of multiple negative feedback mechanisms in a prokaryotic operon system. IET Syst Biol 2011; 5:145-56. [PMID: 21405203 DOI: 10.1049/iet-syb.2010.0020] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
Molecular fluctuations are known to affect dynamics of cellular systems in important ways. Studies aimed at understanding how molecular systems of certain regulatory architectures control noise therefore become essential. The interplay between feedback regulation and noise has been previously explored for cellular networks governed by a single negative feedback loop. However, similar issues within networks consisting of more complex regulatory structures remain elusive. The authors investigate how negative feedback loops manage noise within a biochemical cascade concurrently governed by multiple negative feedback loops, using the prokaryotic tryptophan (trp) operon system in Escherechia coli as the model system. To the authors knowledge, this is the first study of noise in the trp operon system. They show that the loops in the trp operon system possess distinct, even opposing, noise-controlling effects despite their seemingly analogous feedback structures. The enzyme inhibition loop, although controlling the last reaction of the cascade, was found to suppress noise not only for the tryptophan output but also for other upstream components. In contrast, the Repression (Rep) loop enhances noise for all systems components. Attenuation (Att) poses intermediate effects by attenuating noise for the upstream components but promoting noise for components downstream of its target. Regarding noise at the output tryptophan, Rep and Att can be categorised as noise-enhancing loops whereas Enzyme Inhibition as a noise-reducing loop. These findings suggest novel implications in how cellular systems with multiple feedback mechanisms control noise. [Includes supplementary material].
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Panis G, Duverger Y, Courvoisier-Dezord E, Champ S, Talla E, Ansaldi M. Tight regulation of the intS gene of the KplE1 prophage: a new paradigm for integrase gene regulation. PLoS Genet 2010; 6. [PMID: 20949106 PMCID: PMC2951348 DOI: 10.1371/journal.pgen.1001149] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2010] [Accepted: 09/02/2010] [Indexed: 11/18/2022] Open
Abstract
Temperate phages have the ability to maintain their genome in their host, a process called lysogeny. For most, passive replication of the phage genome relies on integration into the host's chromosome and becoming a prophage. Prophages remain silent in the absence of stress and replicate passively within their host genome. However, when stressful conditions occur, a prophage excises itself and resumes the viral cycle. Integration and excision of phage genomes are mediated by regulated site-specific recombination catalyzed by tyrosine and serine recombinases. In the KplE1 prophage, site-specific recombination is mediated by the IntS integrase and the TorI recombination directionality factor (RDF). We previously described a sub-family of temperate phages that is characterized by an unusual organization of the recombination module. Consequently, the attL recombination region overlaps with the integrase promoter, and the integrase and RDF genes do not share a common activated promoter upon lytic induction as in the lambda prophage. In this study, we show that the intS gene is tightly regulated by its own product as well as by the TorI RDF protein. In silico analysis revealed that overlap of the attL region with the integrase promoter is widely encountered in prophages present in prokaryotic genomes, suggesting a general occurrence of negatively autoregulated integrase genes. The prediction that these integrase genes are negatively autoregulated was biologically assessed by studying the regulation of several integrase genes from two different Escherichia coli strains. Our results suggest that the majority of tRNA-associated integrase genes in prokaryotic genomes could be autoregulated and that this might be correlated with the recombination efficiency as in KplE1. The consequences of this unprecedented regulation for excessive recombination are discussed.
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Affiliation(s)
- Gaël Panis
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
- Aix-Marseille Université, Marseille, France
| | - Yohann Duverger
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
| | - Elise Courvoisier-Dezord
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
| | - Stéphanie Champ
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
| | - Emmanuel Talla
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
- Aix-Marseille Université, Marseille, France
- * E-mail: (MA); (ET)
| | - Mireille Ansaldi
- Laboratoire de Chimie Bactérienne, CNRS UPR9043, Institut de Microbiologie de la Méditerranée, Marseille, France
- Aix-Marseille Université, Marseille, France
- * E-mail: (MA); (ET)
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Distributions for negative-feedback-regulated stochastic gene expression: dimension reduction and numerical solution of the chemical master equation. J Theor Biol 2010; 264:377-85. [PMID: 20144620 DOI: 10.1016/j.jtbi.2010.02.004] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2009] [Revised: 01/29/2010] [Accepted: 02/03/2010] [Indexed: 11/22/2022]
Abstract
In this work we introduce a novel approach to study biochemical noise. It comprises a simplification of the master equation of complex reaction schemes (via an adiabatic approximation) and the numerical solution of the reduced master equation. The accuracy of this procedure is tested by comparing its results with analytic solutions (when available) and with Gillespie stochastic simulations. We further employ our approach to study the stochastic expression of a simple gene network, which is subject to negative feedback regulation at the transcriptional level. Special attention is paid to the influence of negative feedback on the amplitude of intrinsic noise, as well as on the relaxation rate of the system probability distribution function to the steady solution. Our results suggest the existence of an optimal feedback strength that maximizes this relaxation rate.
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