1,354,374 research outputs found
Bistability without hysteresis in chemical reaction systems: A theoretical analysis of irreversible transitions between multiple steady states
No full textSCOPUS: ar.jinfo:eu-repo/semantics/publishe
Bistability without hysteresis in chemical reaction systems: The case of nonconnected branches of coexisting steady states
No full textSCOPUS: ar.jinfo:eu-repo/semantics/publishe
Oscillations and bistability predicted by a model for a cyclical bienzymatic system involving the regulated isocitrate dehydrogenase reaction
No full textWe analyze the dynamics of a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC. 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model showed the possibility of a coexistence between two stable steady states in this reaction system [G.M. Guidi et al. Biophys. J. 74 (1998) 1229-1240], owing to the regulatory properties of IDH. Here we extend this analysis by considering the behavior of the model proposed for the IDH-DIA bienzymatic system in conditions where the system is open to an influx of its substrates isocitrate and NADP+ and to an efflux of all metabolic species. The analysis indicates that in addition to different modes of bistability (including mushrooms and isolas), sustained oscillations can be observed in such conditions. These results point to the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems. The results obtained in this particular bienzymatic system bear on other enzymatic systems possessing a cyclical nature, which are known to play significant roles in a variety of metabolic and cellular regulatory processes. Copyright (C) 2000 Elsevier Science B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
From bistability to oscillations in a model for the isocitrate dehydrogenase reaction
No full textConsidered is a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model show the possibility of a coexistence between two stable steady states in this reaction system. The phenomenon originates from the regulatory properties of IDH. We extend the analysis of a theoretical model proposed for the IDH-DIA bienzymatic system and investigate the occurrence of different modes of bistability, with or without hysteresis, i.e. in the presence of two or only one limit point bounding the domain of multiple steady states. The analysis indicates that the two types of bistability may sometimes be observed sequentially as a given control parameter is progressively increased. We further obtain conditions in which sustained oscillations develop in the model. These results establish the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems.SCOPUS: cp.jinfo:eu-repo/semantics/publishe
Dynamical Behavior of the Fractional Goldbeter-Lefever Model
No full textDue to the importance of the historical memory in the analysis of a class of dynamical systems, weintroduce in this paper a time fractional-order derivative into the Goldbeter-Lefever model, which is a generalized form of its corresponding first-derivative model. For this system, we investigate the local stability of the proposed system, and we discuss the Hopf bifurcation. Some numerical simulations are performed to confirm the analytical obtained results
Alternating oscillations and chaos in a skeleton model of two coupled biochemical oscillators driving successive phases of the cell cycle
No full textBistability in the isocitrate dehydrogenase reaction: an experimentally based theoretical study
No full textUniform asymptotic expansions beyond the TQSSA for the Goldbeter-Koshland switch
No full textIn this paper we study the mathematical model of the Goldbeter-Koshland switch, or futile cycle, which is a mechanism that describes several chemical reactions, in particular the so-called phosphorylation-dephosphorylation cycle. We determine the appropriate perturbation parameter epsilon (related to the kinetic constants and initial conditions of the model) for the application of singular perturbation techniques. We also determine the inner and outer solutions and the corresponding uniform expansions, up to the first order in epsilon , beyond the total quasi-steady state approximation (tQSSA). These expansions, in particular the inner ones, can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data. Some numerical results are discussed. Moreover, in a study case, we determine the center manifold of the system and show that, at zero order, it is asymptotically equivalent to the tQSSA of the system
The cell cycle is a limit cycle
No full textProgression along the successive phases of the mammalian cell cycle is driven by a network of cyclin-dependent kinases (Cdks). This network is regulated by a variety of negative and positive feedback loops. We previously proposed a detailed, 39-variable model for the Cdk network and showed that it is capable of temporal self-organization in the form of sustained oscillations, which correspond to the repetitive, transient, sequential activation of the cyclin- Cdk complexes that govern the successive phases of the cell cycle [gérard and Goldbeter (2009) Proc Natl Acad Sci 106, 21643-8]. Here we compare the dynamical behavior of three models of dikrent complexity for the Cdk network driving the mammalian cell cycle. The rst is the detailed model that counts 39 variables and is based on Michaelis-Menten kinetics for the enzymatic steps. From this detailed model, we build a version based only on mass-action kinetics, which counts 80 variables. In this version we do not need to assume that enzymes are present in much smaller amounts that their substrates, which is not necessarily the case in the cell cycle. We show that these two versions of the model for the Cdk network yield similar results. In particular they predict sustained oscillations of the limit cycle type. We show that the model for the Cdk network can be reduced to a version containing only 5 variables, which is more amenable to stochastic simulations. This skeleton version retains the dynamic properties of the more complex versions of the model for the Cdk network in regard to Cdk oscillations. The regulatory wiring of the Cdk network therefore governs its dynamic behavior, regardless of the degree of molecular detail. We discuss the relative advantages of each version of the model, all of which support the view that the mammalian cell cycle behaves as a limit cycle oscillator. © EDP Sciences, 2012.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Regions of multistationarity in cascades of Goldbeter–Koshland loops
No full textWe consider cascades of enzymatic Goldbeter-Koshland loops (Goldbeter and Koshland in Proc Natl Acad Sci 78(11):6840-6844, 1981) with any number n of layers, for which there exist two layers involving the same phosphatase. Even if the number of variables and the number of conservation laws grow linearly with n, we find explicit regions in reaction rate constant and total conservation constant space for which the associated mass-action kinetics dynamical system is multistationary. Our computations are based on the theoretical results of our companion paper (Bihan, Dickenstein and Giaroli 2018, preprint: arXiv:1807.05157) which are inspired by results in real algebraic geometry by Bihan et al. (SIAM J Appl Algebra Geom, 2018).Fil: Giaroli, Magalí Paola. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Bihan, Frédéric. Université Savoie Mont Blanc. Laboratoire de Mathématiques; FranciaFil: Dickenstein, Alicia Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
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