The integrated Michaelis-Menten equation

Hommes, F.A.

doi:10.1016/0003-9861(62)90444-7

Cited by 35 publications

(14 citation statements)

References 4 publications

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“…Using the early analog computers, Hommes (1962), Morales (1964), andWalter (1966) mapped the range of validity of the sQSSA for both the irreversible and reversible MM reactions, showing notable shortcomings for cases with large reverse bimolecular constants (k À1 ). Wong (1965) made an attempt to develop a continuous description of the initial transient and the steady-state phases of the reaction and concluded that the initial transient must be brief for the sQSSA to be applicable.…”

Section: Validity Of the Quasi-steady-state Approximationmentioning

confidence: 99%

A Century of Enzyme Kinetics: Reliability of the K M and v max Estimates

Schnell¹,

Maini²

2003

Comments� on Theoretical Biology

135

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The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The simplified system yields insights into the behavior of the biochemical reaction, and analytical approximations can be obtained to determine its kinetic parameters. However, this process can lead to inaccuracies due to the inappropriate application of the QSSA. Here we present a number of approximate solutions and determine in which regions of the initial enzyme and substrate concentration parameter space they are valid. In particular, this illustrates that experimentalists must be careful to use the correct approximation appropriate to the initial conditions within the parameter space.

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Section: Validity Of the Quasi-steady-state Approximationmentioning

confidence: 99%

A Century of Enzyme Kinetics: Reliability of the K M and v max Estimates

Schnell¹,

Maini²

2003

Comments� on Theoretical Biology

135

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“…The magnitude of error involved with the PSS assumption for a simple Michaelis-Menten mechanism of Equation (1) has been examined before (Miller and Alberty, 1958;Heineken et al, 1967) for some fixed values of parameters. Hommes (1962) and Walter and Morales (1964) gave maps for some combinations of rate constants. The discrepancies between the true and the PSS solutions are analyzed here.…”

Section: Ratios Of Enzyme To Substratementioning

confidence: 99%

On kinetic behavior at high enzyme concentrations

Lim

1973

AIChE Journal

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The data of Richardson and Ayers (1959) for glass beads and air and Heertjes and McKibbins (1956) for silica gel and air were compared with calculated heat transfer coefficients for the total surface area. A value of = 0.38 was used as a typical void fraction for a fixed bed. Figure 1 shows this comparison with reasonable agreement between calculated and experimental coefficients. N OT A T I ON C, = specific heat D = diffusivity D, D, = particle diameter d = particle cluster diameter g h, h, h,, k = mass transfer coefficient NR, = Deue/u, Reynolds number N s , = Schmidt number u, us = superficial velocity Greek Letters a! = equivalent diameter of channel = acceleration due to gravity = channel heat transfer coefficient = heat transfer coefficient based on total particle = particle cluster coefficient based on channel area surface = actual velocity in packing channels = thermal diffusivity of fluid f = overall bed void fraction = void fraction of bed for particle clusters =ratio of average channelling length to particle €0 .f p = fluid viscosity p = fluid density ps = solids density $ cp = particle shape factor diameter U = kinematic viscosity of fluid = dimensionless temperature or concentration Currently there are considerable interest and activities in potential applications of enzymes in various forms as industrial catalysts, some of which involve a large concentration of enzymes. For details one may refer to the review paper by Carbonell and Kostin (1972). For enzyme kinetics at high enzyme concentrations Carbonell and Kostin also refer to the work of Cha (1970), who compared what he called the true rate equation with a number of approximate rate equations which includes among others the Michaelis-Menten equation.The purpose of this note is twofold: (1) to show that the rate equation which was developed by Reiner (1969) and subsequently used by Cha (1970) as the true rate is based on a misconception and is entirely equivalent to the Michaelis-Menten equation in the form of present day use (or more correctly Briggs-Haldane) and hence the comparisons made by Cha (1970) are incorrect, and ( 2 ) to bring attention to the fact that when the total enzyme concentration is high relative to the initial substrate concentration the pseudo-steady state (PSS) assumption which leads to the Michaelis-Menten (or Eriggs-Haldane) equation may not hold, and therefore a valid comparison would be with the true rate which must be computed without the PSS assumption. This comparison is made using the data reported in the literature on the hydrolysis of acetyl-L-phenyl-alanine ethyl ether by chymotrypsin AlChE Journal (Vol. 19, No. 3 ) (Gutfreund and Hammond, 1959) at various concentration ratios of enzyme to the initial substrate. I t is very important to fully realize the limitations imposed by the PSS assumption as currently there are being developed many potential applications involving use of concentrated enzymes. RATE EQUATIONSsubstrate-one enzyme reaction in a batch reactor,The reaction under consideration is the simplest...

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“…Using the early analog computers, Hommes (1962), Walter and Morales (1964) and Walter (1966) mapped the range of validity of the sQSSA, showing notable shortcomings for the case with large reverse bimolecular velocity constants. Wong (1965) made an attempt to develop a continuous description of the transient-state and the steady-state phase, and concluded that the transient must be brief for the sQSSA to be applicable.…”

Section: Introductionmentioning

confidence: 99%

Enzyme Kinetics at High Enzyme Concentration

Schnell¹,

Maini²

2000

Bulletin of Mathematical Biology

180

197

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We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt approximately 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.

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The integrated Michaelis-Menten equation

Cited by 35 publications

References 4 publications

A Century of Enzyme Kinetics: Reliability of the K M and v max Estimates

A Century of Enzyme Kinetics: Reliability of the K M and v max Estimates

On kinetic behavior at high enzyme concentrations

Enzyme Kinetics at High Enzyme Concentration

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