34 citations · 59 across the 14 of their papers we have counts for
14 papers
Timescale disparity and the reduction of the chemical master equation: A geometric approach via the linear noise approximation
Justin Eilertsen, Wylie Stroberg
The chemical master equation dictates the stochastic behavior of chemical reaction networks in small volumes that are well-mixed and homogeneous. Although the Gillespie algorithm i…
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…
Accuracy versus Predominance: Reassessing the validity of the quasi-steady-state approximation
Kashvi Srivastava, Justin Eilertsen, Victoria Booth +1
The application of the standard quasi-steady-state approximation to the Michaelis--Menten reaction mechanism is a textbook example of biochemical model reduction, derived using sin…
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-…
On the reduction of stochastic chemical reaction networks
Justin Eilertsen, Wylie Stroberg
The linear noise approximation (LNA) describes the random fluctuations from the mean-field concentrations of a chemical reaction network due to intrinsic noise. It is also used as…
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…
On the anti-quasi-steady-state conditions of enzyme kinetics
Justin Eilertsen, Santiago Schnell, Sebastian Walcher
Quasi-steady state reductions for the irreversible Michaelis--Menten reaction mechanism are of interest both from a theoretical and an experimental design perspective. A number of…
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…
Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel
Justin Eilertsen, Kashvi Srivastava, Santiago Schnell
The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuat…
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…
Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theor…