Michaelis - Menten equation for degradation of insoluble substrate

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Resumé

Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis–Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed.
OriginalsprogEngelsk
TidsskriftMathematical Biosciences
Vol/bind296
Sider (fra-til)93-97
Antal sider5
ISSN0025-5564
DOI
StatusUdgivet - 2018

Emneord

  • Enzyme kinetics
  • Michaelis–Menten
  • parameter estimation

Citer dette

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title = "Michaelis - Menten equation for degradation of insoluble substrate",
abstract = "Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis–Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed.",
keywords = "Enzyme kinetics, Michaelis–Menten, parameter estimation, Enzyme kinetics, Michaelis–Menten, parameter estimation",
author = "Morten Andersen and Jeppe Kari and Kim Borch and Peter Westh",
year = "2018",
doi = "10.1016/j.mbs.2017.11.011",
language = "English",
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pages = "93--97",
journal = "Mathematical Biosciences",
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Michaelis - Menten equation for degradation of insoluble substrate. / Andersen, Morten; Kari, Jeppe; Borch, Kim; Westh, Peter.

I: Mathematical Biosciences, Bind 296, 2018, s. 93-97.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Michaelis - Menten equation for degradation of insoluble substrate

AU - Andersen, Morten

AU - Kari, Jeppe

AU - Borch, Kim

AU - Westh, Peter

PY - 2018

Y1 - 2018

N2 - Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis–Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed.

AB - Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis–Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed.

KW - Enzyme kinetics

KW - Michaelis–Menten

KW - parameter estimation

KW - Enzyme kinetics

KW - Michaelis–Menten

KW - parameter estimation

U2 - 10.1016/j.mbs.2017.11.011

DO - 10.1016/j.mbs.2017.11.011

M3 - Journal article

VL - 296

SP - 93

EP - 97

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -