Substrate concentration dependence of the diffusion-controlled steady-state rate constant

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.

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The Effects of Substrate Concentration on the Mg-Adenosine Triphosphatase Activity of Myosin

Canadian Journal of Biochemistry ◽

10.1139/o75-174 ◽

1975 ◽

Vol 53 (12) ◽

pp. 1282-1287 ◽

Cited By ~ 7

Author(s):

T. Nihei ◽

C. A. Filipenko

Keyword(s):

Steady State ◽

Substrate Concentration ◽

Active Sites ◽

Adenosine Triphosphatase ◽

Kinetic Studies ◽

Heavy Meromyosin ◽

Adenosine Triphosphatase Activity ◽

Steady State Rate ◽

State Rate ◽

Substrate Concentrations

Using myosin, heavy meromyosin, and subfragment-1 the steady state rate of Mg-modified adenosine triphosphatase (Mg-ATPase) was determined over a range of substrate concentrations between 10−8 M and 5 × 10−3 M, at 0.5 M and 0.05 M KCl (pH 7.4 at 20 °C). At the substrate concentrations below 10−5 M, myosin Mg-ATPase was observed to show that two active sites interact, as suggested by the analysis of transient kinetic studies (Walz, F. G., Jr.: J. Theor. Biol. 41, 357–373 (1973)). The increase in the activity at Mg-ATP concentrations higher than 10−4 M corresponds to the binding of Mg-ATP to myosin sites not responsible for the catalytic action. With heavy meromyosin and subfragment-1, the activity was best expressed by the Michaelis equation. With heavy meromyosin, the activation at high ATP concentrations is detectable, though not as pronounced as with myosin, but not with subfragment-1.

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THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS: II. THE CASE OF TWO ENZYME–SUBSTRATE COMPLEXES

Canadian Journal of Chemistry ◽

10.1139/v56-018 ◽

1956 ◽

Vol 34 (2) ◽

pp. 146-150 ◽

Cited By ~ 20

Author(s):

Ludovic Ouellet ◽

Keith J. Laidler

Keyword(s):

Steady State ◽

Substrate Concentration ◽

Kinetic Scheme ◽

Rate Equations ◽

Theoretical Treatment ◽

Transient Phase ◽

Enzyme Substrate ◽

Enzyme Systems ◽

Steady State Rate ◽

State Rate

A theoretical treatment is worked out for the kinetic scheme[Formula: see text]in which two enzyme–substrate complexes are formed consecutively. The steady-state rate equations are obtained, and equations are given for the transient phase subject to the condition that the substrate concentration is greatly in excess of that of the enzyme. Some kinetic consequences of the resulting equations are discussed.

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The kinetics of ox kidney biliverdin reductase in the pre-steady state. Evidence that the dissociation of bilirubin is the rate-determining step

Biochemical Journal ◽

10.1042/bj2590709 ◽

1989 ◽

Vol 259 (3) ◽

pp. 709-713 ◽

Cited By ~ 4

Author(s):

E Rigney ◽

T J Mantle ◽

F M Dickinson

Keyword(s):

Steady State ◽

Rate Constant ◽

Ph Dependence ◽

Order Rate Constant ◽

Protein Fluorescence ◽

Biliverdin Reductase ◽

Rate Determining Step ◽

Steady State Rate ◽

State Rate ◽

Kinetics Of

When the production of bilirubin by biliverdin reductase was monitored at 460 nm by stopped-flow spectrophotometry a ‘burst’ was observed with a first-order rate constant at pH 8 of 20 s-1. The steady-state rate was established on completion of the ‘burst’. When the reaction was monitored at 401 nm there was no observed steady-state rate, but a diminished pre-steady-state ‘burst’ reaction was still seen with a rate constant of 22 s-1. We argue that the rate-limiting reaction is the dissociation of bilirubin from an enzyme.NADP+.bilirubin complex. With NADPH as the cofactor the hydride-transfer step was shown to exhibit pH-dependence associated with an ionizing group with a pK of 7.2. The kinetics of NADPH binding to the enzyme at pH 7.0 were measured by monitoring the quenching of protein fluorescence on binding the coenzyme.

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A rapid burst preceding the steady-state rate of H+-transhydrogenase during illumination of chromatophores ofRhodobacter capsulatus

FEBS Letters ◽

10.1016/0014-5793(90)80806-t ◽

1990 ◽

Vol 277 (1-2) ◽

pp. 45-48 ◽

Cited By ~ 10

Author(s):

Tracy Palmer ◽

J.Baz Jackson

Keyword(s):

Steady State ◽

Steady State Rate ◽

State Rate

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Corticosterone secretion in rats as a function of ACTH input and adrenal blood flow

American Journal of Physiology-Legacy Content ◽

10.1152/ajplegacy.1965.209.4.811 ◽

1965 ◽

Vol 209 (4) ◽

pp. 811-814 ◽

Cited By ~ 30

Author(s):

John C. Porter ◽

M. S. Klaiber

Keyword(s):

Blood Flow ◽

Steady State ◽

Steady Increase ◽

Constant Input ◽

Corticosterone Secretion ◽

Steady State Rate ◽

State Rate

The rate of secretion of corticosterone from the left adrenal of rats receiving a constant input of ACTH was determined for different flows of blood through the adrenal during the 2- to 3-hr interval following hypophysectomy. Two hours after hypophysectomy the secretion of corticosterone was low in all groups regardless of flow. An input of 0.26 mU ACTH/min caused a steady increase in secretion for 30–40 min before a steady-state rate was attained. The average steady-state rate of secretion was 1.1, 2.4, 3.5, 6.2, 7.2, 6.2, and 6.2 µg/5 min for flows of 0.005, 0.012, 0.023, 0.034, 0.039, 0.051, and 0.058 ml/min, respectively. Under the conditions of these experiments where the input of ACTH was 0.26 mU/min the secretion of corticosterone increased significantly with time of input of ACTH and with flow of blood through the adrenal.

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The Natural Rate of Interest and the Optimal Rate of Interest in the Steady State

Saving and Investment in the Twenty-First Century ◽

10.1007/978-3-030-75031-2_2 ◽

2021 ◽

pp. 17-41

Author(s):

Carl Christian von Weizsäcker ◽

Hagen M. Krämer

Keyword(s):

Steady State ◽

Public Debt ◽

Fundamental Equation ◽

Optimal Rate ◽

Natural Rate ◽

Real Rate ◽

Capital Theory ◽

Steady State Rate ◽

Natural Rate Of Interest ◽

State Rate

AbstractThe “natural rate of interest” is the hypothetical, risk-free real rate of interest that would obtain in a closed economy, if net public debt were zero. It is considerably less than the optimal steady-state rate of interest, which is equal to the system’s growth rate. This holds for a very general “meta-model.” The fundamental equation of capital theory holds on the optimal steady-state path: T = Z − D, where T is the overall economic period of production, Z is the representative private “waiting period” of consumers and D is the public debt ratio. Prosperity is at least 30% lower at the natural rate of interest than at the optimal rate.

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