Irreversible linear pathways in enzymatic reactions: analytical solution using the homotopy perturbation method

  • L. BayónEmail author
  • P. Fortuny Ayuso
  • J. M. Grau
  • M. M. Ruiz
  • P. M. Suárez
Original Paper


In this work, the Homotopy Perturbation method is used for the first time to solve an irreversible linear pathway with enzyme kinetics. The enzymatic system has Michaelis–Menten kinetics and is modeled by a system of nonlinear ordinary differential equations. The analytical solution obtained with the method allow us to optimize several objectives: minimal time to reach a certain percent of final product, minimal amount of enzymes employed in the process, or even multiple objective optimization via Pareto front. We present an example to demonstrate the results.


Enzymatic kinetics Michaelis–Menten model Ordinary differential equations Homotopy perturbation method Optimization 

Mathematics Subject Classification

80A30 92E20 34E10 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OviedoOviedoSpain

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