ZI-Closure Scheme: A Method to Solve and Study Stochastic Reaction Networks

Vlysidis, Michail; Constantino, Pedro H.; Kaznessis, Yiannis N.

doi:10.1007/978-3-319-62627-7_8

Cited by 2 publications

(6 citation statements)

References 16 publications

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“…The difference in the accuracy can be associated with the order of closure that is used to generate the LMEs (in this case 4 or

, Figure 3 ). The accuracy of the Lagrange multipliers approach depends on the number of lower-order moments, M [ 29 ]. The higher the value of M , the more accurate results the method can produce.…”

Section: Resultsmentioning

confidence: 99%

“…After, a certain value of M , the improvement in accuracy is insignificant. For more information on how the lower-order moments affects probability distributions the reader is directed to the literature [ 29 ]. It has been reported that the Brusselator requires more than fourth-order moments for accurate results [ 46 ].…”

Section: Resultsmentioning

confidence: 99%

“…The solid lines are solutions calculated based on LMEs with tenth-order closure (

). The closure order is chosen based on the findings of [ 29 ]. The dots represent results from 500,000 SSA trajectories.…”

Section: Figurementioning

confidence: 99%

“…To circumvent the challenges of solving moment equations in time, we propose the use of Lagrange multipliers [ 22 , 28 , 29 ]. The connection between moments and Lagrange multipliers relies on the maximum entropy principle, which states the system attains a probability distribution that maximizes its entropy [ 20 , 22 , 28 , 30 , 31 ].…”

Section: Introductionmentioning

confidence: 99%

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Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers

Vlysidis

Kaznessis

2018

Entropy

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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.

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“…The difference in the accuracy can be associated with the order of closure that is used to generate the LMEs (in this case 4 or

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…The solid lines are solutions calculated based on LMEs with tenth-order closure (

). The closure order is chosen based on the findings of [ 29 ]. The dots represent results from 500,000 SSA trajectories.…”

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers

Vlysidis

Kaznessis

2018

Entropy

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“…The Jacobian matrix is given by: J i,j = ∂µ i ∂λ i = −µ i,j + µ i • µ j , where [8]. The algorithm of the application can be found in [9].…”

Section: Approachmentioning

confidence: 99%

ZICS: an application for calculating the stationary probability distribution of stochastic reaction networks

Vlysidis¹,

C.²,

Kaznessis³

2018

Preprint

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Stochastic formalisms are necessary to describe the behavior of many biological systems. However, there remains a lack of numerical methods available to calculate the stationary probability distributions of stochastic reaction networks. We have previously development a numerical approach to calculate stationary probability distributions of stochastic networks, named ZI closure scheme. In this work, we present ZICS (Zero-Information Closure Scheme), a free applications based on ZI-closure scheme.

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ZI-Closure Scheme: A Method to Solve and Study Stochastic Reaction Networks

Cited by 2 publications

References 16 publications

Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers

Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers

ZICS: an application for calculating the stationary probability distribution of stochastic reaction networks

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