scholarly journals Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

2018 ◽  
Vol 148 (9) ◽  
pp. 094108 ◽  
Author(s):  
Narmada Herath ◽  
Domitilla Del Vecchio
Keyword(s):  
Time Scale ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Biochemical Reaction Networks ◽  
Scale Separation ◽  
Time Scale Separation ◽  
Linear Noise Approximation

scholarly journals Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks

2014 ◽  
Vol 11 (97) ◽  
pp. 20140054 ◽  
Author(s):  
Bence Mélykúti ◽  
João P. Hespanha ◽  
Mustafa Khammash
Keyword(s):  
Gene Regulation ◽  
Time Scale ◽  
Standard Technique ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Regulation Mechanism ◽  
Enzymatic Reactions ◽  
Biochemical Reaction Networks ◽  
Time Scale Separation ◽  
Equilibrium Distributions

Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus–response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules.

Singular Perturbation Modeling of Nonlinear Processes with Non Explicit Time-Scale Separation

1996 ◽  
Vol 29 (1) ◽  
pp. 5799-5804 ◽  
Author(s):  
Aditya Kumar ◽  
Panagiotis D. Christofides ◽  
Prodromos Daoutidis
Keyword(s):  
Singular Perturbation ◽  
Time Scale ◽  
Nonlinear Processes ◽  
Scale Separation ◽  
Time Scale Separation
Sign in / Sign up

Export Citation Format

Share Document