34 citations · 59 across the 14 of their papers we have counts for
8 papers · 1 filter
Lumping of reaction networks: Generic and critical parameters
Justin Eilertsen, Valery G. Romanovski, Santiago Schnell +1
We investigate linear lumping for parameter-dependent mass action reaction networks, distinguishing between generic and critical parameter regimes. For generic parameters -- those…
The Michaelis--Menten reaction at low substrate concentrations: Pseudo-first-order kinetics and conditions for timescale separation
Justin Eilertsen, Santiago Schnell, Sebastian Walcher
We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-…
Rigorous estimates for the quasi-steady state approximation of the Michaelis-Menten reaction mechanism at low enzyme concentrations
Justin Eilertsen, Santiago Schnell, Sebastian Walcher
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 rea…
Natural parameter conditions for singular perturbations of chemical and biochemical reaction networks
Justin Eilertsen, Santiago Schnell, Sebastian Walcher
We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for smal…
Hunting : The origin and validity of quasi-steady-state reductions in enzyme kinetics
Justin Eilertsen, Malgorzata Anna Tyczynska, Santiago Schnell
The estimation of the kinetic parameters requires the careful design of experiments under a constrained set of conditions. Many estimates reported in the literature incorporate pro…
On the validity of the stochastic quasi-steady-state approximation in open enzyme catalyzed reactions: Timescale separation or singular perturbation?
Justin Eilertsen, Santiago Schnell
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-stead…
On the quasi-steady-state approximation in an open Michaelis--Menten reaction mechanism
Justin Eilertsen, Marc R. Roussel, Santiago Schnell +1
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 les…
The Quasi-Steady-State Approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetic
Justin Eilertsen, Santiago Schnell
In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the len…