Research article Special Issues

On the quasi-steady-state approximation in an open Michaelis–Menten reaction mechanism

  • Received: 30 December 2020 Accepted: 09 April 2021 Published: 21 April 2021
  • MSC : 92C45, 34N05, 34C45

  • The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis–Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.

    Citation: Justin Eilertsen, Marc R. Roussel, Santiago Schnell, Sebastian Walcher. On the quasi-steady-state approximation in an open Michaelis–Menten reaction mechanism[J]. AIMS Mathematics, 2021, 6(7): 6781-6814. doi: 10.3934/math.2021398

    Related Papers:

  • The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis–Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.



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