Journal
JOURNAL OF THE ROYAL SOCIETY INTERFACE
Volume 20, Issue 203, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsif.2023.0123
Keywords
biological oscillators; time delay; cell cycle; Goodwin oscillator; negative feedback loops; nonlinear dynamics
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This study compares the effects of feedback on the periodic rise and fall of protein concentrations or activities through mathematical models. It finds that different mechanisms impose different constraints on the production and degradation rates of proteins, leading to biochemical oscillations.
Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.
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