Simple mathematical models of gene regulatory dynamics

DOI10.1007/978-3-319-45318-7zbMath1360.92002OpenAlexW2550116789MaRDI QIDQ2374254

Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron

Publication date: 14 December 2016

Published in: Lecture Notes on Mathematical Modelling in the Life Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-45318-7

zbMATH Keywords

chemical Langevin equationdeterministic modellactose operontryptophan operonbistable switchescell growth effectsdynamics with burstinginducible regulationlysis-lysogeny switchmaster equation modellingprokaryotic gene regulationrepressible regulationsteady state density function

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biochemistry, molecular biology (92C40) Research exposition (monographs, survey articles) pertaining to biology (92-02) Systems biology, networks (92C42)

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The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks ⋮ Stochastic models of regulation of transcription in biological cells ⋮ A spatial measure-valued model for chemical reaction networks in heterogeneous systems ⋮ Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm ⋮ Self-sustaining positive feedback loops in discrete and continuous systems ⋮ Limit theorems for generalized density-dependent Markov chains and bursty stochastic gene regulatory networks ⋮ Operon dynamics with state dependent transcription and/or translation delays ⋮ Travelling fronts in time-delayed reaction–diffusion systems ⋮ Mathematical models of gene expression

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