ArticlePloS one2013
The Goodwin model: behind the Hill function.
Article in PloS one, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 51 papers.
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51 citing papers in PubMed.
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- Time after time - circadian clocks through the lens of oscillator theory.FEBS letters · 2026Review
- On the mechanisms of epidermal stemness and differentiation.NPJ systems biology and applications · 2025Article
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- Simplifications and approximations in a single-gene circuit modeling.Scientific reports · 2024Article
- The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms.Journal of the Royal Society, Interface · 2023Article
- Systematic analysis of negative and positive feedback loops for robustness and temperature compensation in circadian rhythms.NPJ systems biology and applications · 2023Article
- Article
- Cdk1-mediated threonine phosphorylation of Sam68 modulates its RNA binding, alternative splicing activity and cellular functions.Nucleic acids research · 2022Article
- Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations.Interface focus · 2022Article
- Evolution of the repression mechanisms in circadian clocks.Genome biology · 2022Article
- Exploiting Information and Control Theory for Directing Gene Expression in Cell Populations.Frontiers in microbiology · 2022Review
- Cannabinoid signaling and risk in Huntington's disease.Frontiers in computational neuroscience · 2022Article
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2 authors.
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Abstract
The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.
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