scholarly journals Deviations from Michaelis-Menten kinetics. The possibility of complicated curves for simple kinetic schemes and the computer fitting of experimental data for acetylcholinesterase, acid phosphatase, adenosine deaminase, arylsulphatase, benzylamine oxidase, chymotrypsin, fumarase, galactose dehydrogenase, β-galactosidase, lactate dehydrogenase, peroxidase and xanthine oxidase

1980 ◽  
Vol 187 (3) ◽  
pp. 739-765 ◽  
Author(s):  
W G Bardsley ◽  
P Leff ◽  
J Kavanagh ◽  
R D Waight
Keyword(s):  
Experimental Data ◽  
Rate Equation ◽  
Substrate Inhibition ◽  
Rate Equations ◽  
Double Reciprocal Plot ◽  
Binding Model ◽  
Steady State Rate ◽  
Benzylamine Oxidase ◽  
S Curve ◽  
Galactose Dehydrogenase

The possible graph shapes for one-site/two-state and substrate-modifier models are discussed. The two-state model is a version of the Monod-Wyman-Changeux model and gives a rate equation with 240 denominator terms. Discussion in terms of K and V effects is not possible. A simplified version of the mechanism can be shown to give v-versus-[S] curves that are either sigmoid or non-sigmoid. They may show substrate inhibition or no final maximum, and the double-reciprocal plots can be concave up or down. The corresponding binding model is determined by only two constants and gives a linear double-reciprocal plot. The substrate-modifier mechanism is a simple example of a mechanism where inclusion of catalytic steps leads to a genuine increase in degree of the rate equation. The v-versus-[S] curve can show such complexities as two maxima and a minimum, and the double-reciprocal plot can cross its asymptote twice, proving the rate equation to be 4:4. A simplified version is 3:3, and analysis shows that at least 18 of the 27 double-reciprocal plots that can arise with 3:3 functions are possible with this particular mechanism. Representative double-reciprocal and Scatchard plots are presented for several sets of rate-constant values. It is concluded that relatively simple mechanisms give pseudo-steady-state rate equations of high degree and considerable complexity. With extended ranges of substrate concentrations there is every reason to believe that experimental data would show the sort of deviations from Michaelis-Menten kinetics seen with calculated curves for such simple mechanisms. Narrow ranges of substrate concentration, on the other hand, would lead to inflexions and curvature being overlooked. It is not possible to discuss such deviations from Michaelis-Menten kinetics in terms of kinetic constants such as Km and V, and, in general, it is also difficult to see any simple way to explain intuitively such features as sigmoidicity, substrate inhibition, double-reciprocal convexity and decrease in degree by cancellation of common factors between numerator and denominator of rate equations. These conclusions apply with even more force when catalytic steps are included, for then the rate equations, are for multi-site mechanisms, of higher degree, allowing increasingly complex curve shapes. A number of enzymes were studied and initial-rate data were fitted by computer.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Rates of reactions catalysed by a dimeric enzyme. Effects of the reaction scheme and the kinetic parameters on co-operativity

1991 ◽  
Vol 280 (1) ◽  
pp. 131-137 ◽  
Author(s):  
H Ishikawa ◽  
H Ogino ◽  
H Oshida
Keyword(s):  
Substrate Inhibition ◽  
Reaction Scheme ◽  
Rate Equations ◽  
Kinetic Behaviour ◽  
Hill Coefficients ◽  
S Curve ◽  
Almost All ◽  
The Hill ◽  
Rate Behaviour ◽  
Reaction Schemes

For the reaction S in equilibrium P catalysed by a dimeric enzyme, the reaction schemes are considered on the basis of the KNF model. For each of the ten possible schemes, the rate equation is derived on the basis of the combined steady-state and rapid-equilibrium assumptions. The curves of the plots of initial velocity v versus the substrate concentration [S] and the Hill coefficients h calculated from the rate equations depend strongly on the reaction scheme and the parameter X1. This parameter is defined by log (KS2/KS1) and is a measure of the relative affinities of the first and second protomers for the substrate. When X1 less than 0, v-[S] curves for some schemes exhibit negative co-operativity (h less than 1.0) and v-[S] curves for other schemes are similar to that of the Michaelis-Menten scheme, indicating that, even if there is interaction between the distinct protomers, sigmoidal rate behaviour is not necessarily observed. When X1 greater than 0, all the reaction schemes except one, which shows substrate-inhibition kinetic behaviour, exhibit sigmoidal kinetic behaviour (h greater than 1.0), and at the limit of X1 much greater than 0 the Hill coefficients attain the maximum possible value of 2.0. Furthermore, we have found that, even if X1 = 0, the v-[S] curve for almost all the schemes considered in the present work does not necessarily agree with that for the Michaelis-Menten scheme. This means that the deviation of the v-[S] curve from a hyperbola can be observed even if there is no interaction between the distinct protomers.

A COMPARISON BETWEEN THE INITIAL RATE EXPRESSIONS OBTAINED UNDER STRICT CONDITIONS AND THE RAPID EQUILIBRIUM ASSUMPTION USING, AS EXAMPLE, A FOUR SUBSTRATE ENZYME REACTION

2011 ◽  
Vol 10 (05) ◽  
pp. 659-678
Author(s):  
J. M. YAGO ◽  
C. GARRIDO-DEL SOLO ◽  
M. GARCIA-MORENO ◽  
R. VARON ◽  
F. GARCIA-SEVILLA ◽  
...  
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Initial Rate ◽  
Enzyme Reaction ◽  
Rate Equations ◽  
Steady State Rate ◽  
State Rate ◽  
Rapid Equilibrium ◽  
Kinetics Of ◽  
Substrate Concentrations

The software WinStes, developed by our group, is used to derive the strict steady-state initial rate equation of the reaction mechanism of CTP:sn-glycerol-3-phosphate cytidylyltransferase [EC 2.7.7.39] from Bacillus subtilis. This enzyme catalyzes a reaction with two substrates and operates by a random ordered binding mechanism with two molecules of each substrate. The accuracy of the steady-state rate equation derived is checked by comparing the rate values it provides with those obtained from the simulated progress curves. To analyze the kinetics of this enzyme using the strict steady-state initial rate equation, several curves for different substrate concentrations and different rate constants are generated. A comparison of these curves with the curves obtained from the rapid equilibrium initial rate equation, with different substrate concentration values, serves to analyze how the strict steady-state rate equation values are closer to those of rapid equilibrium rate equations when rapid equilibrium conditions are fulfilled.

A New Adsorption Rate Equation in Batch Systems

2018 ◽  
Author(s):  
yongson hong ◽  
Kye-Ryong Sin ◽  
Jong-Su Pak ◽  
Chol-Min Pak
Keyword(s):  
Experimental Data ◽  
Kinetic Analysis ◽  
Adsorption Kinetics ◽  
Rate Equation ◽  
Kinetic Models ◽  
Adsorption Kinetic ◽  
Adsorption Rate ◽  
Batch Systems ◽  
New View

<p><b>In this paper, the deficiencies and cause of previous adsorption kinetic models were revealed, new adsorption rate equation has been proposed and its validities were verified by kinetic analysis of various experimental data.</b> <b>This work is a new view on the adsorption kinetics rather than a comment on the previous adsorption papers.</b></p>

Kinetic modelling of microalgal growth and fucoxanthin synthesis in photobioreactor

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaojuan Zhang ◽  
Junru Zhao ◽  
Jie Zhang ◽  
Shijing Su ◽  
Luqiang Huang ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Kinetic Parameters ◽  
Kinetic Modelling ◽  
Inhibitory Effect ◽  
Rate Equations ◽  
Phosphorus Concentration ◽  
Model Output ◽  
Nitrogen And Phosphorus ◽  
Nitrogen Phosphorus

Abstract This paper presented a mathematical model to describe the production of fucoxanthin by alga Thalassiosira weissflogi ND-8 in photobioreactor. Our interest was focused on characterizing the effects of nitrogen and phosphorus on the growth of microalgae and on the synthesis of fucoxanthin. The rate equations of microalgal growth, fucoxanthin synthesis and substrate consumptions were formulated. Kinetic parameters of the model and their sensitivities with respect to model output were estimated. The predicted results were compared with experimental data, which showed that this model closely agrees with actual experiment and is able to reflect the growth and metabolism characteristics of microalgae. Our results also indicated that nitrogen plays a major role in the synthesis of fucoxanthin, and the synthesis of fucoxanthin is partially linearly related to the consumption of nitrogen. Phosphorus is primarily consumed in the growth and metabolism of microalgal cells, while excessive phosphorus concentration has an inhibitory effect on the growth of microalgae.

A Comparative Experiment on the Bond-Slip of Reinforced Concrete

2012 ◽  
Vol 226-228 ◽  
pp. 1795-1799
Author(s):  
Chuan Guo Cai ◽  
Guo Liang Chen
Keyword(s):  
Experimental Data ◽  
Reinforced Concrete ◽  
Concrete Columns ◽  
Comparative Experiment ◽  
Test Device ◽  
Static Test ◽  
Bond Slip ◽  
Repeated Load ◽  
S Curve ◽  
The One

A new test device, which can be used for measuring the stain and the displacement on the adhesive interface while the slip occurs within the reinforced concrete, is proposed and designed. With that, a comparative experiment is carried out on a group of the reinforced concrete columns bearing alternating load to obtain the τ-s curve. The hysteretic curves of these specimens are recorded timely. The result from the one-way repeated load is similar with several well-known expressions which are commonly cited at home and abroad. That from the low cycle load reveals some certain characteristic of the alternating slip, which there isn't in the static test. The experimental data could make contribution for the numerical simulation on bridge and seismic building.

Kinetic Study Of Crystallisation In Amorphous Thin Lpcvd Si Films

1993 ◽  
Vol 321 ◽  
Author(s):  
B. Pieraggi ◽  
J. P. Guillemet ◽  
B. de Mauduit
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Isothermal Annealing ◽  
Nucleation Kinetics ◽  
Crystallisation Kinetics ◽  
Crystallisation Behaviour ◽  
Steady State Rate ◽  
State Rate ◽  
Si Films

ABSTRACTThe crystallisation behaviour of LPCVD silicon films has been investigated by TEM from in situ isothermal annealing of undoped a-Si films deposited from disilane (Si2H6) at temperatures 450,465 and 480 °C and at gas pressure of 200 MTorr. Nucleation kinetics, grain growth rates and crystallisation kinetics were determined for temperatures ranging from 600 to 675 °C. Nucleation kinetics have been experimentally determined in the early first stages of annealing : they do not show any steady-state rate and are fitted according to a power law. Experimental data for crystallisation kinetics are fitted by an Avrami law without introducing any incubation time.

Modeling of Gas Turbine Combustors—A Convenient Reaction Rate Equation

1972 ◽  
Vol 94 (3) ◽  
pp. 173-180 ◽  
Author(s):  
D. Kretschmer ◽  
J. Odgers
Keyword(s):  
Rate Equation ◽  
Reaction Rate ◽  
Reaction Order ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Combustion System ◽  
Wide Range ◽  
Simple Mass ◽  
Rich Mixtures ◽  
Reaction Rate Equation

In order to model a practical combustion system successfully, it is necessary to develop one or more reaction rate equations which will describe performance over a wide range of conditions. The equations should be kept as simple as possible and commensurate with the accuracy needed. In this paper a bimolecular reaction is assumed, based upon a simple mass balance. Temperatures derived from the latter are related to measured practical ones such that, if required, an evaluation of the partly burned product composition can be made. A convenient reaction rate equation is given which describes a wide range of blow-out data for spherical reactors at weak mixture conditions. NVP2φ={1.29×1010(m+1)[5(1−yε)]φ[φ−yε]φe−C/(Ti+εΔT)}/{0.082062φyε[5(m+1)+φ+yε]2φ[Ti+εΔT]2φ−0.5} Analysis of the components used in the above equation (especially the variation of activation energy) clearly shows its empirical nature but does not detract from its engineering value. Rich mixtures are considered also, but lack of data precludes a reliable analysis. One of the major results obtained is the variation of the reaction order (n) with equivalence ratio (φ): weak mixtures, n = 2φ; rich mixtures, n = 2/φ. Some support for this variation has been noticed in published literature of other workers.

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