ArticleProceedings of the National Academy of Sciences of the United States of America2013
A closure scheme for chemical master equations.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 22 papers.
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22 citing papers in PubMed.
- A stochastic vs deterministic perspective on the timing of cellular events.Nature communications · 2024Article
- Advanced methods for gene network identification and noise decomposition from single-cell data.Nature communications · 2024Article
- Metastable dynamics of neural circuits and networks.Applied physics reviews · 2022Review
- Stochastic dynamics of predator-prey interactions.PloS one · 2021Article
- Identifiability analysis for stochastic differential equation models in systems biology.Journal of the Royal Society, Interface · 2020Article
- Discrete and continuous models of probability flux of switching dynamics: Uncovering stochastic oscillations in a toggle-switch system.The Journal of chemical physics · 2019Article
- Algebraic expressions of conditional expectations in gene regulatory networks.Journal of mathematical biology · 2019Article
- Learning moment closure in reaction-diffusion systems with spatial dynamic Boltzmann distributions.Physical review. E · 2019Article
- 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
- Linear mapping approximation of gene regulatory networks with stochastic dynamics.Nature communications · 2018Article
- Learning dynamic Boltzmann distributions as reduced models of spatial chemical kinetics.The Journal of chemical physics · 2018Article
- Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks.Journal of the Royal Society, Interface · 2018Article
- Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.Chemical engineering science · 2017Article
- An efficient moments-based inference method for within-host bacterial infection dynamics.PLoS computational biology · 2017Article
- A moment-convergence method for stochastic analysis of biochemical reaction networks.The Journal of chemical physics · 2016Article
- Delay chemical master equation: direct and closed-form solutions.Proceedings. Mathematical, physical, and engineering sciences · 2015Article
- 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
- Accurate reconstruction of viral quasispecies spectra through improved estimation of strain richness.BMC bioinformatics · 2015Article
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2 authors.
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Abstract
Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.
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