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Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers
The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving t...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513230/ https://www.ncbi.nlm.nih.gov/pubmed/33265789 http://dx.doi.org/10.3390/e20090700 |
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author | Vlysidis, Michail Kaznessis, Yiannis N. |
author_facet | Vlysidis, Michail Kaznessis, Yiannis N. |
author_sort | Vlysidis, Michail |
collection | PubMed |
description | The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie’s original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently. |
format | Online Article Text |
id | pubmed-7513230 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75132302020-11-09 Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers Vlysidis, Michail Kaznessis, Yiannis N. Entropy (Basel) Article The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present a new alternative method for numerically solving the time evolution of stochastic reaction networks. Based on the assumption that the entropy of the reaction network is maximum, Lagrange multipliers are introduced. The proposed method derives equations that model the time derivatives of these Lagrange multipliers. We present detailed steps to transform moment equations to Lagrange multiplier equations. In order to demonstrate the method, we present examples of non-linear stochastic reaction networks of varying degrees of complexity, including multistable and oscillatory systems. We find that the new approach is as accurate and significantly more efficient than Gillespie’s original exact algorithm for systems with small number of interacting species. This work is a step towards solving stochastic reaction networks accurately and efficiently. MDPI 2018-09-12 /pmc/articles/PMC7513230/ /pubmed/33265789 http://dx.doi.org/10.3390/e20090700 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Vlysidis, Michail Kaznessis, Yiannis N. Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title | Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title_full | Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title_fullStr | Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title_full_unstemmed | Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title_short | Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers |
title_sort | solving stochastic reaction networks with maximum entropy lagrange multipliers |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513230/ https://www.ncbi.nlm.nih.gov/pubmed/33265789 http://dx.doi.org/10.3390/e20090700 |
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