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Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration

  • Agustín Hernández ORCID logo EMAIL logo
Published/Copyright: September 26, 2022
Biological Chemistry
From the journal Biological Chemistry Volume 404 Issue 1

Abstract

Enzyme behaviour is characterised in the laboratory using diluted solutions of enzyme. However, in vivo processes usually occur at [S T ] ≈ [E T ] ≈ K m . Furthermore, the study of enzyme action involves characterisation of inhibitors and their mechanisms. However, to date, there have been no reports proposing mathematical expressions that can be used to describe enzyme activity at high enzyme concentration apart from the simplest single substrate, irreversible case. Using a continued fraction approach, equations can be easily derived for the most common cases in monosubstrate reactions, such as irreversible or reversible reactions and effector (inhibitor or activator) kinetic interactions. These expressions are an extension of the classical Michaelis-Menten equations. A first analysis using these expressions permits to deduce some differences at high versus low enzyme concentration, such as the greater effectiveness of allosteric inhibitors compared to catalytic ones. Also, they can be used to understand catalyst saturation in a reaction. Although they can be linearised, these equations also show differences that need to be taken into account. For example, the different meaning of line intersection points in Dixon plots. All in all, these expressions may be useful tools for modelling in vivo and biotechnological processes.

Keywords: catalyst saturation; continued fraction; Cornish-Bowden plots; Dixon plots; fast equilibrium; quasi-steady-state
Corresponding author: Agustín Hernández, Unit for Integrated Research on Tropical Biodiversity – BIOTROP, Centre for Biological and Health Sciences, Federal University of Sao Carlos, Sao Carlos (SP), Brazil, E-mail:

Acknowledgements

The author thanks Ms E. A. de Magalhaes, and Dr L. Pino (CNR-ITAE “Nicola Giordano”), for their help in this study, and to late Drs D. T. Cooke and D. T. Clarkson (IACR-Long Ashton Res. Stn) for lifelong teaching through example.

  1. Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

  3. Conflict of interest statement: The author declares to have no conflicts of interest regarding this manuscript.

  4. Compliance with ethical norms: This article does not contain descriptions of studies performed by the authors with participation of humans or using animals as objects.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/hsz-2022-0163).

Received: 2022-04-19
Accepted: 2022-08-18
Published Online: 2022-09-26
Published in Print: 2023-01-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/hsz-2022-0163
Keywords for this article
catalyst saturation; continued fraction; Cornish-Bowden plots; Dixon plots; fast equilibrium; quasi-steady-state

Articles in the same Issue

  1. Frontmatter
  2. Review
  3. A biochemical view on the septins, a less known component of the cytoskeleton
  4. Research Articles/Short Communications
  5. Protein Structure and Function
  6. Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration
  7. Cell Biology and Signaling
  8. MicroRNA-6838-5p suppresses the self-renewal and metastasis of human liver cancer stem cells through downregulating CBX4 expression and inactivating ERK signaling
  9. M2 macrophages-derived exosomal miR-3917 promotes the progression of lung cancer via targeting GRK6
  10. Extracellular stimulation of lung fibroblasts with arachidonic acid increases interleukin 11 expression through p38 and ERK signaling
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