Distribution profiles and their dynamic transition in stochastic gene transcription
type: Item
instance of: scholarly article
title: Distribution profiles and their dynamic transition in stochastic gene transcription
zbMATH Open document ID: 1273.34066
author: Feng Jiao
author: Moxun Tang
author: Jianshe Yu
published in: Journal of Differential Equations
publication date: 2013-04-17T00:00:00Z
review text: The authors express the mass function \(P_m(t)\) of the gene transcription in single cells, as a simple mathematical functions of the rate constants defined in the two-state model. The basic idea is to transform the master equations of \(P_m(t)\) into several special types of second-order ordinary differential equations using the method of characteristics (see for example the book of [\textit{L. C. Evans}, Partial differential equations. 2nd ed. Providence, RI: American Mathematical Society (2010; Zbl 1194.35001)]). In the second section, they derive the exact form of the probability generating function (Theorem 3 and Theorem 4) and express the probability mass function in elementary forms (Theorem 5 from the third section). The main results are given in Theorem 1 and Theorem 2 and their proofs are given in the last section. Also, some numerical examples are given. These results generalize some similar results due to \textit{J. Peccoud} and \textit{B. Ycart} [Theor. Popul. Biol. 48, No. 2, 222--234 (1995; Zbl 0865.92006)], D. T. Gillespie (2007), Tang M. (2008), S. Iyer-Biswas F. Hayot and C. Ayaprakash (2009) or B. Munsky, G. Neuert and A. van Oudenaarden (2012).
reviewed by: Romeo Negrea
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 92D20
zbMATH DE Number: 6154861
zbMATH Keywords: gene transcription
zbMATH Keywords: master equation
zbMATH Keywords: probability mass functions
zbMATH Keywords: generating functions
zbMATH Keywords: bimodal distribution
zbMATH Keywords: distribution profiles
zbMATH Keywords: spectral solutions
zbMATH Keywords: method of characteristics
MaRDI profile type: Publication
full work available at URL: j.jde.2013.01.019
OpenAlex ID: W1999776089
DOI: 10.1016/J.JDE.2013.01.019
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description: scientific article; zbMATH DE number 6154861