2013
DOI: 10.1073/pnas.1306481110
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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 d… Show more

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Cited by 102 publications
(108 citation statements)
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References 25 publications
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“…In both cases, the derived moment closure functions are consistent with the species being (jointly) lognormally distributed. Hausken and Moxnes 23 set higher mixed moments to zero and assumed a Dirac distribution, while Smadbeck and Kaznessis 24 applied an information theoretic point of view to close the equations based on the assumption that a finite set of moments holds all information about the system.…”
Section: Introductionmentioning
confidence: 99%
“…In both cases, the derived moment closure functions are consistent with the species being (jointly) lognormally distributed. Hausken and Moxnes 23 set higher mixed moments to zero and assumed a Dirac distribution, while Smadbeck and Kaznessis 24 applied an information theoretic point of view to close the equations based on the assumption that a finite set of moments holds all information about the system.…”
Section: Introductionmentioning
confidence: 99%
“…The section starts with an outline of ZI-closure and then provides the algorithm for determining the maximum entropy distribution. It concludes with a Schlögl model example to clarify the calculation of several important equations [39, 40]. This section expands upon a previously described ODE solving scheme and steady-state determination method [39].…”
Section: Methods For Multiscale Models Of Biomolecular Systemsmentioning
confidence: 99%
“…Although the approach has been validated for small networks of nonlinear chemical reactions with simple dynamics (Constantino et al, 2016; Smadbeck and Kaznessis, 2013), we present in this paper the first results for oscillatory systems.…”
Section: Theoretical Backgroundmentioning
confidence: 98%
“…Recently, our group proposed a closure scheme for the moment equations called Zero-Information, or ZI-closure (Smadbeck and Kaznessis, 2013). The method is based on the maximization of the entropy of the unknown probability distribution constrained to its lower order moments, so that higher order ones may be calculated.…”
Section: Theoretical Backgroundmentioning
confidence: 99%