ArticleChemical engineering science2012
Efficient Moment Matrix Generation for Arbitrary Chemical Networks.
Article in Chemical engineering science, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Time-dependent product-form Poisson distributions for reaction networks with higher order complexes.Journal of mathematical biology · 2020Article
- Algebraic expressions of conditional expectations in gene regulatory networks.Journal of mathematical biology · 2019Article
- Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation.Entropy (Basel, Switzerland) · 2019Review
- Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers.Entropy (Basel, Switzerland) · 2018Article
- On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure.Entropy (Basel, Switzerland) · 2018Article
- Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.Chemical engineering science · 2017Article
- On a theory of stability for nonlinear stochastic chemical reaction networks.The Journal of chemical physics · 2015Article
- Chemical master equation closure for computer-aided synthetic biology.Methods in molecular biology (Clifton, N.J.) · 2015Article
- Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks.Current opinion in chemical engineering · 2014Article
- A closure scheme for chemical master equations.Proceedings of the National Academy of Sciences of the United States of America · 2013Article
Corrections and comments
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Authors and funding
2 authors.
Funding
Abstract
As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analogue to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite the drawbacks of the method, in particular non-linearity in even the simplest of cases, the use of moment equations combined with moment-closure techniques has been used effectively in many fields. The techniques currently available to generate moment equations rely upon analytical expressions that are not efficient upon scaling. Additionally, the resulting moment-dependent matrix is lower diagonal and demands massive memory allocation in extreme cases. Here it is demonstrated that by utilizing factorial moments and the probability generating function (the Z-transform of the probability distribution) a recursive algorithm is produced. The resulting method is scalable and particularly efficient when high-order moments are required. The matrix produced is banded and often demands substantially less memory resources.
Identifiers
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.