Approximating the solution of the chemical master equation by combining finite state projection and stochastic simulation

2013 ◽  
Author(s):  
Aron Hjartarson ◽  
Jakob Ruess ◽  
John Lygeros
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Chemical Master Equation ◽  
Finite State

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.

Modeling Stochastic Gene Regulatory Networks Using Direct Solutions of Chemical Master Equation and Rare Event Sampling

2016 ◽  
pp. 80-122
Author(s):  
Youfang Cao ◽  
Anna Terebus ◽  
Jie Liang
Keyword(s):  
Master Equation ◽  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Rare Event ◽  
Planck Equation ◽  
Chemical Master Equation ◽  
Copy Numbers ◽  
Finite State ◽  
Gene Regulatory

Stochasticity plays important roles in many biological networks. A fundamental framework for studying the full stochasticity is the Discrete Chemical Master Equation (dCME). Under this framework, the combination of copy numbers of molecular species defines the microstate of the molecular interactions in the network. The probability distribution over these microstates provide a full description of the properties of a stochastic molecular network. However, it is challenging to solve a dCME. In this chapter, we will first discuss how to derive approximation methods including Fokker-Planck equation and the chemical Langevin equation from the dCME. We also discuss the widely used stochastic simulation method. After that, we focus on the direct solutions to the dCME. We first discuss the Finite State Projection (FSP) method, and then introduce the recently developed finite buffer method (fb-dCME) for directly solving both steady state and time-evolving probability landscape of dCME. We show the advantages of the fb-dCME method using two realistic gene regulatory networks.

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