Journal of Mathematical Chemistry

, Volume 51, Issue 1, pp 144–152 | Cite as

Substrate and enzyme concentration dependence of the Henri–Michaelis–Menten model probed by numerical simulation

  • Jose Ailton Conceicao Bispo
  • Carlos Francisco Sampaio Bonafe
  • Maria Gabriela Bello Koblitz
  • Carlos Geilson Santana Silva
  • Ancelmo Rabelo de Souza
Original Paper


The use of the classic Henry–Michaelis–Menten (HMM) model (or simply, Michaelis–Menten model) to study the substrate and enzyme concentration dependence of enzyme catalysis is a very important step in understanding many biochemical processes, including microbial growth. Although the HMM model has been extensively studied, the conditions in which the substrate concentration is not in excess have still not been adequately defined mathematically. This lack of definition occurs despite at the cellular and molecular levels most systems generally do not operate in a state of substrate excess. In the present work, we describe an approach for studying enzyme reactions in which substrate concentrations are not in excess. Our results show that the use of extent of reactions and numerical simulation of the velocities of reaction provides an important advance in this field and furnishes results not obtained in previous studies involving these aspects. This approach, in association with knowledge of the rate constants, provides a direct and easy means of examining the single substrate–enzyme profile during product formation at any enzyme–substrate ratio. This approach is more direct than previous models that required the use of empirical equations with arbitrary constants.


Enzyme concentration Enzyme kinetics Michaelis–Menten model Time dependence of species concentration 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jose Ailton Conceicao Bispo
    • 1
  • Carlos Francisco Sampaio Bonafe
    • 2
  • Maria Gabriela Bello Koblitz
    • 3
  • Carlos Geilson Santana Silva
    • 1
  • Ancelmo Rabelo de Souza
    • 2
  1. 1.Departamento de Tecnologia (DTEC), Faculdade de Engenharia de AlimentosUniversidade Estadual de Feira de Santana (UEFS)Feira de SantanaBrazil
  2. 2.Laboratório de Termodinâmica de Proteínas, Departamento de Bioquímica, Instituto de BiologiaUniversidade Estadual de Campinas (UNICAMP)CampinasBrazil
  3. 3.Departamento de Tecnologia de Alimentos, Escola de Nutrição, Centro de Ciências Biológicas e da SaúdeUniversidade Federal do Estado do Rio de Janeiro (UNIRIO)Rio de JaneiroBrazil

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