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Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
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Author to whom correspondence should be addressed.
Current address: General Probiotics Inc., St. Paul, MN 55114, USA
Entropy 2018, 20(9), 700; https://doi.org/10.3390/e20090700
Received: 3 August 2018 / Revised: 5 September 2018 / Accepted: 6 September 2018 / Published: 12 September 2018
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. View Full-Text
Keywords: stochastic chemical reactions; probability distributions; maximum entropy; lagrange multipliers stochastic chemical reactions; probability distributions; maximum entropy; lagrange multipliers
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Vlysidis, M.; Kaznessis, Y.N. Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers. Entropy 2018, 20, 700.

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