Stochastic models of regulation of transcription in biological cells.
Averaging principle
Gene expression
Regulation
Stochastic model
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
29 09 2023
29 09 2023
Historique:
received:
23
01
2023
accepted:
14
09
2023
revised:
06
06
2023
medline:
2
10
2023
pubmed:
30
9
2023
entrez:
29
9
2023
Statut:
epublish
Résumé
In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for "fast" variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.
Identifiants
pubmed: 37775568
doi: 10.1007/s00285-023-01998-2
pii: 10.1007/s00285-023-01998-2
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
65Informations de copyright
© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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