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Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units
For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3323590/ https://www.ncbi.nlm.nih.gov/pubmed/22506001 http://dx.doi.org/10.1371/journal.pone.0033384 |
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author | Vigelius, Matthias Meyer, Bernd |
author_facet | Vigelius, Matthias Meyer, Bernd |
author_sort | Vigelius, Matthias |
collection | PubMed |
description | For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. |
format | Online Article Text |
id | pubmed-3323590 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-33235902012-04-13 Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units Vigelius, Matthias Meyer, Bernd PLoS One Research Article For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway. Public Library of Science 2012-04-10 /pmc/articles/PMC3323590/ /pubmed/22506001 http://dx.doi.org/10.1371/journal.pone.0033384 Text en Vigelius, Meyer. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Vigelius, Matthias Meyer, Bernd Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title | Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title_full | Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title_fullStr | Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title_full_unstemmed | Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title_short | Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units |
title_sort | multi-dimensional, mesoscopic monte carlo simulations of inhomogeneous reaction-drift-diffusion systems on graphics-processing units |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3323590/ https://www.ncbi.nlm.nih.gov/pubmed/22506001 http://dx.doi.org/10.1371/journal.pone.0033384 |
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