A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

Schuster, Stefan; Schuster, R.

doi:10.1007/bf01171883

Cited by 62 publications

(58 citation statements)

References 11 publications

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“…For example, the number of independent fluxes in a metabolic network, and the relationships between them at steady state, can be determined from the null space of the stoichiometry matrix (Reder, 1988;Schuster and Schuster, 1989), and those metabolite concentrations constrained by mass conservation can be determined from the left null space of the stoichiometry matrix (Reder, 1988;Schuster and Höfer, 1991).…”

Section: Modeling Metabolism Modeling Approachesmentioning

confidence: 99%

Responses to Light Intensity in a Genome-Scale Model of Rice Metabolism

et al. 2013

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We describe the construction and analysis of a genome-scale metabolic model representing a developing leaf cell of rice (Oryza sativa) primarily derived from the annotations in the RiceCyc database. We used flux balance analysis to determine that the model represents a network capable of producing biomass precursors (amino acids, nucleotides, lipid, starch, cellulose, and lignin) in experimentally reported proportions, using carbon dioxide as the sole carbon source. We then repeated the analysis over a range of photon flux values to examine responses in the solutions. The resulting flux distributions show that (1) redox shuttles between the chloroplast, cytosol, and mitochondrion may play a significant role at low light levels, (2) photorespiration can act to dissipate excess energy at high light levels, and (3) the role of mitochondrial metabolism is likely to vary considerably according to the balance between energy demand and availability. It is notable that these organelle interactions, consistent with many experimental observations, arise solely as a result of the need for mass and energy balancing without any explicit assumptions concerning kinetic or other regulatory mechanisms.

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Section: Modeling Metabolism Modeling Approachesmentioning

confidence: 99%

Responses to Light Intensity in a Genome-Scale Model of Rice Metabolism

et al. 2013

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“…1) with linear kinetics. More-complex biochemical reactions in vivo are nonlinear; they remain to be analyzed in the context of single-molecule enzymology (36). Macroscopically, introducing nonlinearity into the kinetics leads to sustained biochemical oscillation, which does not happen with linear kinetics (46,47).…”

Section: Nonlinear Biochemical Reactions and Nessmentioning

confidence: 99%

“…Mathematically, it can be shown that if and only if Eq. 3 is satisfied for every possible cycle in the kinetic network, then the entire system is at equilibrium, and its stochastic dynamic is time-reversible (10,35,36). There is a branch of probability theory known as reversible (symmetric) Markov process that focuses on such stochastic systems (37).…”

Section: Equilibrium and Symmetry Of The Third-order Time-correlationmentioning

confidence: 99%

Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states

Qian

Elson

2004

Proc. Natl. Acad. Sci. U.S.A.

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In living cells, biochemical reaction networks often function in nonequilibrium steady states. Under these conditions, the networks necessarily have cyclic reaction kinetics that are maintained by sustained constant input and output, i.e., pumping. To differentiate this state from an equilibrium state without flux, we propose a microscopic method based on concentration fluctuation measurements, via fluorescence correlation spectroscopy, and statistical analyses of high-order correlations and cross correlations beyond the standard fluorescence correlation spectroscopy autocorrelation. We show that, for equilibrium systems with time reversibility, the correlation functions possess certain symmetries, the violation of which is a measure of steady-state fluxes in reaction cycles. This result demonstrates the theoretical basis for experimentally measuring reaction fluxes in a biochemical network in situ and the importance of single-molecule measurements in providing fundamental information on nonequilibrium steadystates in biochemistry. recent study on enzyme kinetics of single horseradish peroxidase molecules has observed an oscillatory timecorrelation function, suggesting an irreversible, nonequilibrium nature of the biochemical reaction (4). In single-molecule enzymology (5, 6), the consecutive turnover of substrates to products catalyzed by a single enzyme molecule is recorded in terms of the fluorescence of enzyme-substrate or enzymeproduct complexes. One essential feature of such a measurement is that the concentrations of the substrate, [S], and the product, [P], are approximately constant over the course of the entire experiment. Thus, although the enzyme molecule is subject to stochastic fluctuations, on average it participates in a stationary process with a net circular flux. The flux is zero if and only if the substrate and product concentrations satisfy conditions of [P]͞[S] ϭ K eq , where K eq is the equilibrium constant for the reaction S º P, both in the presence and absence of the enzyme. In this unique situation, the reaction is at a chemical equilibrium.

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“…The appearance of affinities is directly related to that of so-called emergent cycles, through which the external chemical forces can act. In finite chemical networks, if no emergent affinity arises from the chemostatting procedure, the system will always relax to a unique equilibrium state compatible with the chemostats and the non-broken conservation laws 11,16 . When emergent cycles-or equivalently affinities-are generated, the system may evolve towards a non-equilibrium steady state defined byŻ kx = 0, ∀k x andJ nm = 0 (nonequilibrium steady state quantities are denoted by an overbar in the text).…”

Section: Steady States: Conservation Laws Cycles and Dissipationmentioning

confidence: 99%

“…Closed systems always reach an equilibrium steady state 16 defined byŻ kx eq = 0, ∀k x and J nm eq = 0, ∀n, m. Their dynamics is constrained by conservation laws 11,17,18 , which fully characterize the equilibrium concentration distribution. Chemostatting generic chemical species may break these conservation laws and may create chemical forces-also called affinities 11 .…”

Section: Steady States: Conservation Laws Cycles and Dissipationmentioning

confidence: 99%

Glucans monomer-exchange dynamics as an open chemical network

Rao

Lacoste

Esposito

2015

The Journal of Chemical Physics

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We describe the oligosaccharides-exchange dynamics performed by so-called D-enzymes on polysaccharides. To mimic physiological conditions, we treat this process as an open chemical network by assuming some of the polymer concentrations fixed (chemostatting). We show that three different long-time behaviors may ensue: equilibrium states, nonequilibrium steady states, and continuous growth states. We dynamically and thermodynamically characterize these states and emphasize the crucial role of conservation laws in identifying the chemostatting conditions inducing them.

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A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

Cited by 62 publications

References 11 publications

Responses to Light Intensity in a Genome-Scale Model of Rice Metabolism

Responses to Light Intensity in a Genome-Scale Model of Rice Metabolism

Fluorescence correlation spectroscopy with high-order and dual-color correlation to probe nonequilibrium steady states

Glucans monomer-exchange dynamics as an open chemical network

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