Genetic control models with diffusion and delays

DOI10.1016/0025-5564(88)90081-8zbMath0684.92012OpenAlexW2034684613MaRDI QIDQ1825789

Joseph M. Mahaffy

Publication date: 1988

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(88)90081-8

zbMATH Keywords

time delaystranslationcell divisioncytoplasmtranscriptionspatial diffusionmitosiscell sizecompartmental model of genetic control by repression

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Physiological, cellular and medical topics (92Cxx)

Related Items (20)

Gene expression time delays and Turing pattern formation systems ⋮ Sensitivity analysis for dynamic systems with time-lags ⋮ Effect of time delay on pattern formation: Competition between homogenisation and patterning ⋮ Computational modelling of cancer development and growth: modelling at multiple scales and multiscale modelling ⋮ Spatio-temporal models of synthetic genetic oscillators ⋮ Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways ⋮ Small binding-site clearance delays are not negligible in gene expression modeling ⋮ The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression ⋮ Stability and Hopf bifurcation analysis of a gene expression model with diffusion and time delay ⋮ Spatial-stochastic modelling of synthetic gene regulatory networks ⋮ A minimal spatio-temporal model of the NF-\(\kappa \)B signalling pathway exhibits a range of behaviours ⋮ Hopf bifurcation in a DDE model of gene expression ⋮ Mean field analysis of a spatial stochastic model of a gene regulatory network ⋮ Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53-Mdm2 pathways: insights from spatio-temporal modelling ⋮ Oscillations in non-mass action kinetics models of biochemical reaction networks arising from pairs of subnetworks ⋮ Bifurcation analysis for a model of gene expression with delays ⋮ An efficient numerical method for coupled systems of singularly perturbed parabolic delay problems ⋮ Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations ⋮ Mathematical modeling of the intracellular protein dynamics: the importance of active transport along microtubules ⋮ Qualitative theory of compartmental systems with lags.

Cites Work

• Unnamed Item
• Global asymptotic stability of the size distribution in probabilistic models of the cell cycle
• Models of genetic control by repression with time delays and spatial effects
• Interaction of spatial diffusion and delays in models of genetic control by repression
• A stochastic model of cell division (with application to fission yeast)
• The qualitative dynamics of a class of biochemical control circuits
• The Effects of Dimension and Size for a Compartmental Model of Repression
• A test for stability of linear differential delay equations
• Time lag in systems described by difference or differential equations
• Global asymptotic stability of certain models for protein synthesis and repression

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