The Status of the QSSA Approximation in Stochastic Simulations of Reaction Networks

Bobadilla, Ana Victoria Ponce; Bartmanski, Bartosz J.; Grima, Ramon; Othmer, Hans G.

doi:10.1007/978-3-030-38230-8_10

Cited by 5 publications

(7 citation statements)

References 20 publications

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“…Here we consider only the deterministic ODE model that follows the law of mass action near the thermodynamic limit. For a thorough analysis of the chemical master equation corresponding to (2.1) , we invite the reader to consult [ 1 , 45 ].…”

Section: An Open Michaelis–menten Reaction Mechanismmentioning

confidence: 99%

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

Eilertsen¹,

Roussel²,

Schnell³

et al. 2021

AIMS Mathematics

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There is a vast amount of literature concerning the appropriateness of various perturbation parameters for the standard quasi-steady state approximation in the Michaelis-Menten reaction mechanism, and also concerning the relevance of these parameters for the accuracy of the approximation by the familiar Michaelis-Menten equation. Typically, the arguments in the literature are based on (heuristic) timescale estimates, from which one cannot obtain reliable quantitative estimates for the error of the quasi-steady state approximation. We take a different approach. By combining phase plane analysis with differential inequalities, we derive sharp explicit upper and lower estimates for the duration of the initial transient and substrate depletion during this transitory phase. In addition, we obtain rigorous bounds on the accuracy of the standard quasi-steady state approximation in the slow dynamics regime. Notably, under the assumption that the quasi-steady state approximation is valid over the entire time course of the reaction, our error estimate is of order one in the Segel-Slemrod parameter.

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Section: An Open Michaelis–menten Reaction Mechanismmentioning

confidence: 99%

“…While the QSS reductions of the closed Michaelis–Menten reaction are well-studied, analyses pertaining to the validity of the QSSA in open reaction environments are somewhat sparse [ 1 , 18 , 44 , 45 ]. The question we address is therefore: when is further reduction of (2.4) possible?…”

Section: An Open Michaelis–menten Reaction Mechanismmentioning

confidence: 99%

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

Eilertsen¹,

Roussel²,

Schnell³

et al. 2021

AIMS Mathematics

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show abstract

“…Perhaps most surprisingly, the conditions that support the validity of the stochastic QSSA have been show to be the homologous conditions that permit the authorization of the deterministic QSSA [3]. On the other hand, for open MM-type reactions, the qualifier that establishes the accuracy of the stochastic QSSA is far more restrictive than the criterion that certifies the effectiveness of the corresponding deterministic QSSA [16,19]. This big question that follows is: why?…”

Section: Introductionmentioning

confidence: 99%

On the validity of the stochastic quasi-steady-state approximation in open enzyme catalyzed reactions: Timescale separation or singular perturbation?

Eilertsen¹,

Schnell²

2021

Preprint

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The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steadystate approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction of the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis-Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasisteady-state approximation. In this paper, we explain this discrepancy through the rigorous application of geometric singular perturbation theory. In so doing, we illustrate a common misconception in the application of the quasi-steady-state approximation: a problem which involves timescale separation is not always a singular perturbation problem.

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mentioning

confidence: 99%

“…While the QSS reductions of the closed Michaelis-Menten reaction are wellstudied, analyses pertaining to the validity of the QSSA in open reaction environments are somewhat sparse [1,18,44,45]. The question we address is therefore: when is further reduction of (7) possible?…”

mentioning

confidence: 99%

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

Eilertsen¹,

Roussel²,

Schnell³

et al. 2021

Preprint

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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-steadystate scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant slow 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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The Status of the QSSA Approximation in Stochastic Simulations of Reaction Networks

Cited by 5 publications

References 20 publications

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

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

On the validity of the stochastic quasi-steady-state approximation in open enzyme catalyzed reactions: Timescale separation or singular perturbation?

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

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