Stability results for a model of repression with external control

Mahaffy, Joseph M.; Jorgensen, David A.; Vanderheyden, Robert L.

doi:10.1090/qam/1178425

Authors: Joseph M. Mahaffy, David A. Jorgensen and Robert L. Vanderheyden
Journal: Quart. Appl. Math. 50 (1992), 415-435
MSC: Primary 92D25; Secondary 92C30
DOI: https://doi.org/10.1090/qam/1178425
MathSciNet review: MR1178425
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Abstract: A stability analysis is performed for a mathematical model with negative feedback, diffusion, and time delays. The model of a cell includes three biochemical species that interact to control the transport of an extracellular nutrient. This study examines the effects of diffusion, cell size, and extracellular nutrient concentration on the model. With certain assumptions the symmetry, a linearized version of the model is studied in detail. The characteristic equation is shown to have no solutions with positive real part when extracellular nutrient concentration or the diffusivities are sufficiently small or the radius of the cell is sufficiently large. These results are compared to an earlier study that showed that biochemical oscillations could occur for certain parameter values. A discussion is provided for how the bifurcations from regions of stability to regions of instability could affect the biological response of the cell.

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