scholarly journals Stochastic quasi-steady state approximations for asymptotic solutions of the chemical master equation

2014 ◽  
Vol 140 (18) ◽  
pp. 184109 ◽  
Author(s):  
Tomás Alarcón
Keyword(s):  
Steady State ◽  
Master Equation ◽  
Chemical Master Equation ◽  
Asymptotic Solutions ◽  
Quasi Steady State

Theory of the reactant-stationary kinetics for a coupled enzyme assay

2017 ◽  
Author(s):  
Justin Eilertsen ◽  
Wylie Stroberg ◽  
Santiago Schnell
Keyword(s):  
Steady State ◽  
Reaction Mechanism ◽  
Enzyme Assay ◽  
Asymptotic Solutions ◽  
Heuristic Methods ◽  
Nonlinear Ordinary Differential Equations ◽  
Quasi Steady State ◽  
Reaction Conditions ◽  
Asymptotic Expressions ◽  
Single Enzyme

<div>A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both reactions are governed by the single substrate, single enzyme Michaelis-Menten reaction mechanism. It is demonstrated that the kinetics are in influenced by the intersection of invariant slow manifolds. Based on this intersection of manifolds, we derive asymptotic solutions using both perturbation and heuristic methods using the quasi-steady state and reactant-stationary assumptions. Furthermore, we derive a particular asymptotic solution, analogous to the Schnell-Mendoza equation for Michaelis-Menten type reactions, that approximates the evolution of the observable reaction in the event that the non-observable reaction is completed much faster than the observable reaction. Conditions for the validity of the asymptotic solutions are also rigorously derived showing that these asymptotic expressions are applicable under the reactant-stationary kinetics.</div>

Network reconstruction based on steady-state data

2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
Reverse Engineering ◽  
Theoretical Method ◽  
Network Reconstruction ◽  
Quasi Steady State ◽  
State Data

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.

Sign in / Sign up

Export Citation Format

Share Document