scholarly journals Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

scholarly journals Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

scholarly journals Stochastic simulation algorithms for Interacting Particle Systems

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247046
Author(s):  
Timothy C. Stutz ◽  
Alfonso Landeros ◽  
Jason Xu ◽  
Janet S. Sinsheimer ◽  
Mary Sehl ◽  
...  
Keyword(s):  
Stochastic Simulation ◽  
Stochastic Systems ◽  
Interacting Particle Systems ◽  
Computational Cost ◽  
Stochastic Simulation Algorithm ◽  
Particle Systems ◽  
Stochastic Simulation Algorithms ◽  
Interacting Particle ◽  
Wide Range ◽  
Spatio Temporal

Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.

scholarly journals Accelerated Simulations of Chemical Reaction Systems using the Stochastic Simulation Algorithm on GPUs

2020 ◽  
Author(s):  
James C. Pino ◽  
Martina Prugger ◽  
Alexander L. R. Lubbock ◽  
Leonard A. Harris ◽  
Carlos F. Lopez
Keyword(s):  
Stochastic Simulation ◽  
Graphics Processing Units ◽  
Large Scale ◽  
Computational Cost ◽  
Stochastic Simulation Algorithm ◽  
Gillespie Algorithm ◽  
Simulation Algorithm ◽  
Modeling Framework ◽  
Cellular Processes ◽  
Didactic Material

1AbstractStochasticity due to fluctuations in chemical reactions can play important roles in cellular network-driven processes. Although the Stochastic Simulation Algorithm (SSA, aka Gillespie Algorithm) has long been accepted as a suitable method to solve the time-dependent chemical master equation, its computational cost is prohibitive for large scale complex networks such as those found in cellular processes. Here we present GPU-SSA, an implementation of the SSA formalism utilizing Graphics Processing Units for use in Python using the PySB modeling framework. We show that the GPU implementation of SSA can achieve significant speedup compared to parallel CPU or single-core CPU implementations. We further include supplementary didactic material to demonstrate how to incorporate GPU-SSA workflows for interested readers.

Stochastic Simulation of the Cell Cycle Model for Budding Yeast

2011 ◽  
Vol 9 (2) ◽  
pp. 390-405
Author(s):  
Di Liu
Keyword(s):  
Cell Cycle ◽  
Stochastic Simulation ◽  
Budding Yeast ◽  
Computational Cost ◽  
Stochastic Simulation Algorithm ◽  
Simulation Algorithm ◽  
Cycle Model ◽  
Dynamical Features

AbstractWe use the recently proposed Nested Stochastic Simulation Algorithm (Nested SSA) to simulate the cell cycle model for budding yeast. The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

scholarly journals Effective Time-Stepping For The Tau-Leaping Method for Stochastic Simulation Of Well-Stirred Biochemical Networks

2021 ◽  
Author(s):  
Mahmuda Binte Mostofa Ruma
Keyword(s):  
Mathematical Models ◽  
Stochastic Simulation ◽  
Practical Interest ◽  
Cellular Level ◽  
Biochemical Networks ◽  
Biological Processes ◽  
Time Stepping ◽  
Effective Time ◽  
Numerical Tests ◽  
Biochemical Systems

Biological processes at the cellular level are noisy. The noise arises due to random molecular collisions, and may be substantial in systems with low molecular counts in some species. This thesis introduces a variable tau-leaping method for the simulation of stochastic discrete mathematical models of well-stirred biochemical systems which is theoretically justified. Numerical tests on several models of biochemical systems of practical interest illustrate the advantages of the adaptive tau-leap method over the existing schemes.

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