Phase reversal in the Selkov model with inhomogeneous influx

Lavrova, Anastasia I.; Schimansky‐Geier, Lutz; Postnikov, Eugene B.

doi:10.1103/physreve.79.057102

Cited by 15 publications

(21 citation statements)

References 13 publications

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“…Recently the 2D case without taking into account the thickness of finite reactor is considered [16]. Here we generalize proposed approach for 3D case.…”

Section: Introductionmentioning

confidence: 93%

Model of glycolytic traveling waves control in 3D spatial reactor

Verisokin

Verveyko

Postnikov

et al. 2009

2009 IEEE International Conference on Control Applications

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We present the 3D mathematical model of glycolysis reaction in an open reactor based on the Selkov equations. It has been shown that this relatively simple model adequately reproduce the main features of the experimentally observed glycolytic traveling waves. The analysis of the wave generation conditions shows that the emergence, direction of motion and shape of these reaction-diffusion waves can be effectively regulated via the spatial heterogeneity of a substrate influx.978-1-4244-4603-2/09/$25.00 ©2009 IEEE

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“…Recently the 2D case without taking into account the thickness of finite reactor is considered [16]. Here we generalize proposed approach for 3D case.…”

Section: Introductionmentioning

confidence: 93%

Model of glycolytic traveling waves control in 3D spatial reactor

Verisokin

Verveyko

Postnikov

et al. 2009

2009 IEEE International Conference on Control Applications

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“…To take into account the effect of non-negative term 2λc 1 in eq. ( 19) that generates unidirectional acceleration from unstable stationary point, correction factors, p 2 and p 1 in phase shift and limit cycle radius expression needs to be introduced [47].…”

Section: B Hopf Instabilitymentioning

confidence: 99%

Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in the presence of cross diffusion

Kumar

Gangopadhyay

2020

Phys. Rev. E

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A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion can be best viewed in terms of critical control parameter and wave number containing both the self and cross diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction diffusion equation it clarifies two aspects: energy cost of pattern formation, specially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogoiubov averaging method. Due to Hopf instability it is observed that the cross diffusion parameters can be a source of huge change in free energy and concentration profiles.

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“…2). Valuable contributions to explain and model, on an experimental basis, the glycolytic oscillations "engine" and their self-control, have been done on E. coli, 27,28,[30][31][32][33] or on yeast. 34 Glycolytic oscillation occurrence and characteristics (period) are influenced by both external (environmental) and internal (genomic) factors, that is: 35,36 I) From one side it is the glucose (Glc) import driving force through the phosphotransferase (PTS)-system ( Fig.…”

Section: How Glycolytic Oscillations Occurmentioning

confidence: 99%

“…Valuable contributions to model the glycolytic oscillations related to the system characteristics and environmental conditions have been reported. 27,28,[30][31][32][33] The advantage of the mTRM model of Maria 4 is its capacity to reproduce glycolytic oscillations using a reduced kinetic model but still preserving the essential glycolytic and environmental parameters with a major influence on the process (see the next chapter on oscillation conditions).…”

Section: How Glycolytic Oscillations Occurmentioning

confidence: 99%

Model-based Identification of Some Conditions Leading to Glycolytic Oscillations in E. coli Cells

Maria

Mihalachi

Gîjiu

2019

Chem.Biochem.Eng.Q.

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Autonomous oscillations of glycolytic intermediate concentrations reflect the dynamics of the control and regulation of this major catabolic pathway, and this phenomenon has been reported in a broad range of bacteria. Understanding glycolytic oscillations might therefore prove crucial for the general understanding of the regulation of cell metabolism with immediate practical applications, allowing in silico design of modified cells with desirable 'motifs' of practical applications in the biosynthesis industry, environmental engineering, and medicine. By using a kinetic model from literature, this paper is aiming at in silico (model-based) identification of some conditions leading to the occurrence of stable glycolytic oscillations in the E. coli cells.

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Phase reversal in the Selkov model with inhomogeneous influx

Cited by 15 publications

References 13 publications

Model of glycolytic traveling waves control in 3D spatial reactor

Model of glycolytic traveling waves control in 3D spatial reactor

Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in the presence of cross diffusion

Model-based Identification of Some Conditions Leading to Glycolytic Oscillations in E. coli Cells

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