scholarly journals The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation

2010 ◽  
Vol 132 (7) ◽  
pp. 074101 ◽  
Author(s):  
Brian Drawert ◽  
Michael J. Lawson ◽  
Linda Petzold ◽  
Mustafa Khammash
Keyword(s):  
Master Equation ◽  
Reaction Diffusion ◽  
Projection Algorithm ◽  
Efficient Simulation ◽  
Finite State ◽  
Stochastic Reaction

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

scholarly journals STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies

2012 ◽  
Vol 6 (1) ◽  
pp. 36 ◽  
Author(s):  
Iain Hepburn ◽  
Weiliang Chen ◽  
Stefan Wils ◽  
Erik De Schutter
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Models ◽  
Efficient Simulation ◽  
Stochastic Reaction

scholarly journals A Parallel Implementation of the Finite State Projection Algorithm for the Solution of the Chemical Master Equation

2020 ◽  
Author(s):  
Huy Vo ◽  
Brian Munsky
Keyword(s):  
Master Equation ◽  
High Performance ◽  
Parallel Implementation ◽  
Chemical Species ◽  
Chemical Master Equation ◽  
Kolmogorov Equation ◽  
Projection Algorithm ◽  
Reaction Networks ◽  
Modeling Framework ◽  
Finite State

AbstractStochastic reaction networks are a popular modeling framework for biochemical processes that treat the molecular copy numbers within a single cell as a continuous time Markov chain, whose forward Chapman-Kolmogorov equation is known in biochemistry literature as the chemical master equation (CME). The solution of the CME contains extremely useful information that can be compared to experimental data in order to improve the quantitative understanding of biochemical reaction networks within the cell. However, this solution is costly to compute as it requires integrating an enormous system of differential equations that grows exponentially with the number of chemical species. To address this issue, we introduce a novel multiple-sinks Finite State Projection algorithm that approximates the CME with an adaptive sequence of reduced-order models with an effecient parallelization based on MPI. The implementation is tested on models of sizable state spaces using a high-performance computing node on Amazon Web Services, showing favorable scalability.

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