2019
DOI: 10.1007/s00285-019-01426-4
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Path integral approach to generating functions for multistep post-transcription and post-translation processes and arbitrary initial conditions

Abstract: Stochastic fluctuations in the copy number of gene products have perceivable effects on the functioning of gene regulatory networks (GRN). The Master equation (ME) provides a theoretical basis for studying such effects. However, solving the ME can be a task that ranges from simple to difficult to impossible using conventional methods. Therefore, discovering new techniques for solving the ME is an important part of research on stochastic GRN. In this paper, we present a novel approach to obtaining the generatin… Show more

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Cited by 10 publications
(12 citation statements)
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“…Interestingly, the T‐DNA insertion sites in A1‐11, A1‐16, and A1‐3 were related to transcription factor Hsf1, whereas different phenotypes were observed in these three mutants. It was hypothesized that R. toruloides may have other single‐nucleotide mutations that were related to gene deficiency [27], transcription [33], or post‐transcription [34] which need more studies in the future.…”
Section: Resultsmentioning
confidence: 99%
“…Interestingly, the T‐DNA insertion sites in A1‐11, A1‐16, and A1‐3 were related to transcription factor Hsf1, whereas different phenotypes were observed in these three mutants. It was hypothesized that R. toruloides may have other single‐nucleotide mutations that were related to gene deficiency [27], transcription [33], or post‐transcription [34] which need more studies in the future.…”
Section: Resultsmentioning
confidence: 99%
“…In practice the ME is useful only when solvable analytically or when it can be numerically integrated. New analytic and numerical techniques for solving the ME are constantly being developed, either by means of improving stochastic simulation algorithms (Gibson and Bruck 2000;Gillespie 2001;Cao et al 2004Cao et al , 2005a, or by solving the ME exactly/approximately (Jahnke and Huisinga 2007;Albert and Rooman 2016;Albert 2019;Shahrezaei and Swain 2008;Pendar et al 2013;Bokes et al 2012a, b;Popović et al 2016;Veerman et al 2018), or by a mix of the former two (Burrage et al 2004;Jahnke and Altıntan 2010;Albert 2016b, a;Duso and Zechner 2018;Alfonsi et al 2005;Kurasov et al 2018). In this paper, we enlarge this list by one.…”
Section: Introductionmentioning
confidence: 99%
“…Mathematical modelling has been proved useful in understanding the mechanisms of stochastic gene expression. The underlying probability distributions are typically defined as solutions to a specific master equation (Paulsson 2005;Veerman et al 2018;Albert 2019). Explicit solutions to the master equation, especially at steady state, can be found for models with few components (Bokes et al 2012;Zhou and Liu 2015) and/or with special structural properties (Kumar et al 2015;Anderson and Cotter 2016).…”
Section: Introductionmentioning
confidence: 99%
“…The underlying probability distributions are typically defined as solutions to a specific master equation (Paulsson 2005 ; Veerman et al. 2018 ; Albert 2019 ). Explicit solutions to the master equation, especially at steady state, can be found for models with few components (Bokes et al.…”
Section: Introductionmentioning
confidence: 99%