scholarly journals Stochastic chemical kinetics and the total quasi-steady-state assumption: Application to the stochastic simulation algorithm and chemical master equation

2008 ◽  
Vol 129 (9) ◽  
pp. 095105 ◽  
Author(s):  
Shev MacNamara ◽  
Alberto M. Bersani ◽  
Kevin Burrage ◽  
Roger B. Sidje
Keyword(s):  
Steady State ◽  
Master Equation ◽  
Stochastic Simulation ◽  
Chemical Kinetics ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Quasi Steady State ◽  
Simulation Algorithm ◽  
Stochastic Chemical Kinetics ◽  
State Assumption

scholarly journals APPROXIMATE EXPONENTIAL ALGORITHMS TO SOLVE THE CHEMICAL MASTER EQUATION

2015 ◽  
Vol 20 (3) ◽  
pp. 382-395
Author(s):  
Azam Mooasvi ◽  
Adrian Sandu
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Stochastic Simulation Algorithm ◽  
Approximate Solutions ◽  
Chemical Master Equation ◽  
Matrix Exponential ◽  
Stochastic Chemical Kinetics ◽  
Stochastic Simulation Algorithms ◽  
The Matrix ◽  
Simulation Algorithms

This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the matrix exponential to evolve probability densities in time. A sampling of the approximate solutions of the chemical master equation is used to derive accelerated stochastic simulation algorithms. Numerical experiments compare the new methods with the established stochastic simulation algorithm and the tau-leaping method.

scholarly journals Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

2021 ◽  
Author(s):  
Farida Ansari
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Growth Factor Receptor ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Biochemical Networks ◽  
Random Time Change ◽  
Simulation Strategy ◽  
Epidermal Growth ◽  
Exact Stochastic Simulation

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

scholarly journals Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

2021 ◽  
Author(s):  
Farida Ansari
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Growth Factor Receptor ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Biochemical Networks ◽  
Random Time Change ◽  
Simulation Strategy ◽  
Epidermal Growth ◽  
Exact Stochastic Simulation

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

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