The Structure and Analysis of Complex Reaction Systems

Wei, James Cheng‐Chung; Prater, C. D.

doi:10.1016/s0360-0564(08)60289-8

Cited by 222 publications

(136 citation statements)

References 31 publications

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“…1 are all real and nonpositive (7,8). We can rewrite the equation P i eq k ij ϭ P j eq k ji in a matrix form and then show…”

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

confidence: 99%

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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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“…1 are all real and nonpositive (7,8). We can rewrite the equation P i eq k ij ϭ P j eq k ji in a matrix form and then show…”

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

confidence: 99%

“…In this unique situation, the reaction is at a chemical equilibrium. A biochemical reaction with oscillatory kinetics is necessarily nonequilibrium (7)(8)(9)(10). However, the converse is not true: A reaction in a nonequilibrium steady state (NESS) can be without oscillation.…”

mentioning

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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“…This paper is devoted to a qualitative analysis of how the properties of a network can be restricted so as to provide a variety of control mechanisms. Several other investigators have examined this very problem (2)(3)(4). Their considerations, which have been based on the dynamic consequences of physical constraints such as conservation of mass and positivity of concentrations of all species, or on the properties of the topological dynamics of appropriate vector fields, have not taken into account the possibility of regulation of enzyme activity through substrate dependency and allosteric control.…”

Section: Introductionmentioning

confidence: 99%

Model for Constraint and Control in Biochemical Networks

Newman

Rice

1971

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

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A model is proposed for biochemical networks which takes into account substrate and modifier effects on enzyme activity and the different time scales on which the relevant processes occur. Sources of global constraint that can be utilized in metabolic regulation are indicated, and the relation of the model to the experiments of Kauffman on switching networks is analyzed. The biological significance of the model and possible systems in which it might be tested are discussed.

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“…Az elsőrendű reakcióhálózatok (FCRN) vizsgálatával számos cikk [39][40][41][42][43][44][45][46][47][48][49][50][51] foglalkozik. Ennek oka abban rejlik, hogy látszólagos egyszerűségük dacára a reakciókinetika és a kémiai dinamika jónéhány effektusát (pl.…”

Section: Irodalmi áTtekintés 31 a Kémiai Reakcióhálózatok Irodalmi unclassified

“…[56]) esetére korlátozódik [39]. A kérdéses dolgozatban Wei és Prater megmutatta, hogy ha az együttható mátrix diagonalizálható, akkor a koncentráció-idő függvények a spektrálfelbontás segítségével számíthatók.…”

Section: Irodalmi áTtekintés 31 a Kémiai Reakcióhálózatok Irodalmi unclassified

Konformációváltozások kinetikájának modellezése elsőrendű reakcióhálózatokkal

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The Structure and Analysis of Complex Reaction Systems

Cited by 222 publications

References 31 publications

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

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

Model for Constraint and Control in Biochemical Networks

Konformációváltozások kinetikájának modellezése elsőrendű reakcióhálózatokkal

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