An improved method to measure all rate constants in the simplest enzyme kinetics model

Li, Banghe; Li, Bo; Shen, Yuefeng

doi:10.1007/s10910-011-9922-4

Cited by 3 publications

(7 citation statements)

References 23 publications

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“…This article provides another equation which approximates the whole process of the chemical reaction better than dE/dt = 0 does. This replacement is first introduced in our former paper [21]. In [21], we provided an improved method to measure all rate constants in the simplest enzyme kinetics model The mathematical background can be found in many fundamental books on mathematical biology [23,24] or ordinary differential equations [25,26].…”

Section: Michaelis-menten Equation Soon Became the Basic Equation Of mentioning

confidence: 99%

“…For the convenience of the readers, we recap those here. For more information, please read [21]. This paper adopts the same notations.…”

Section: Motivation and Derivation Of The Replacementmentioning

confidence: 99%

“…The replacement of Michaelis-Menten curve was given first in [21]. In Section 4 of [21], we have given the motivation and derivation of the equation. For the convenience of the readers, we recap those here.…”

Section: Motivation and Derivation Of The Replacementmentioning

confidence: 99%

“…This replacement is first introduced in our former paper [21]. In [21], we provided an improved method to measure all rate constants in the simplest enzyme kinetics model using this replacement with the aid of Michaelis-Menten equation. This method improved the approach in [22] greatly.…”

Section: Introductionmentioning

confidence: 99%

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A much better replacement of the Michaelis–Menten equation and its application

Shen

2019

Int. J. Biomath.

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Michaelis-Menten equation is a basic equation of enzyme kinetics andgives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis-Menten curve (15). This curve is derived from Quasi-Steady-State Assumption(QSSA), which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al [19].Here, we found a quartic equation A(S, E) = 0 (22), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady state of a reaction, Michaelis-Menten curve approximates the reaction well, while our quartic equation A(S, E) = 0 gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line same to that of the reaction, while Michaelis-Menten curve does not. In addition, our quartic equation A(S, E) = 0 differs to Michaelis-Menten curve less than the order of 1/S 3 as S approaches +∞.By considering the above merits of A(S, E) = 0, we suggest it as a replacement of Michaelis-Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because its complexity, it provides more information about the rate constants than Michaelis-Menten curve does.Finally, we get a better replacement of the Michaelis-Menten equation by combing A(S, E) = 0 and the equation dP/dt = k2C(t).keywords : rate constants of enzyme kinetics; quasi-steady-state assumption; quasi-steady-state law. a.

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Section: Michaelis-menten Equation Soon Became the Basic Equation Of mentioning

confidence: 99%

“…For the convenience of the readers, we recap those here. For more information, please read [21]. This paper adopts the same notations.…”

Section: Motivation and Derivation Of The Replacementmentioning

confidence: 99%

Section: Motivation and Derivation Of The Replacementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A much better replacement of the Michaelis–Menten equation and its application

Shen

2019

Int. J. Biomath.

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“…Analyses over a wide range of the ratio s 0 /e 0 were pursued in several recent theoretical works [18 -21] with interesting experimental relevance [22]. A route to calculate rate constants also followed [23].…”

Section: Introductionmentioning

confidence: 99%

Single-substrate enzyme kinetics: the quasi-steady-state approximation and beyond

Dhatt

Bhattacharyya

2013

J Math Chem

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We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios by adopting a different scaling scheme. The regions of validity of the quasi-steady-state approximation are noted. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures are highlighted. Some recent observations are rationalized, particularly at moderate and high enzyme concentrations.

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An Analysis of the Kinetics of Enzymatic Systems Based on Computer Algebra Theory

宗凯¹,

于建平²,

吴素萍³

et al. 2015

AAM

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Enzyme plays an important role in the living system as well as life process, and is involved in almost every chemical reaction; thus the enzyme kinetics is fundamental to the research of the chemical reactions. Therefore, from the early part of twentieth century, many researchers were dedicated to the study of the analysis of kinetics of enzymatic system, and a lot of excellent work has been done, because the analysis of the enzyme kinetics can help us find how the activity of enzyme is controlled, how the drug inhibits the enzyme, its role in metabolism, and so on. In this paper, we present a method by rigorous mathematics to analyze the general enzyme kinetics model, which is concerned with a single substrate catalyzed by enzyme and transformed into a single product, and it is based on computer algebra technique and the qualitative theory of dynamical system. Our method does not need any assumption and all the solutions here are analytical. Finally, some examples are given to test this method and make it readable by simulated progress curves, so that almost everyone may understand it. Furthermore, the techniques in this study can be used to the research of other disciplines, such as biophysics, and so on.

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An improved method to measure all rate constants in the simplest enzyme kinetics model

Cited by 3 publications

References 23 publications

A much better replacement of the Michaelis–Menten equation and its application

A much better replacement of the Michaelis–Menten equation and its application

Single-substrate enzyme kinetics: the quasi-steady-state approximation and beyond

An Analysis of the Kinetics of Enzymatic Systems Based on Computer Algebra Theory

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