The Goodwin model: behind the Hill function.
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2013-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC3731313?pdf=render |
| _version_ | 1818944262552682496 |
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| author | Didier Gonze Wassim Abou-Jaoudé |
| author_facet | Didier Gonze Wassim Abou-Jaoudé |
| author_sort | Didier Gonze |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T07:40:26Z |
| format | Article |
| id | doaj.art-20aa3a6bdd364555913921ac32ec41ef |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-20T07:40:26Z |
| publishDate | 2013-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-20aa3a6bdd364555913921ac32ec41ef2022-12-21T19:48:07ZengPublic Library of Science (PLoS)PLoS ONE1932-62032013-01-0188e6957310.1371/journal.pone.0069573The Goodwin model: behind the Hill function.Didier GonzeWassim Abou-JaoudéThe 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.http://europepmc.org/articles/PMC3731313?pdf=render |
| spellingShingle | Didier Gonze Wassim Abou-Jaoudé The Goodwin model: behind the Hill function. PLoS ONE |
| title | The Goodwin model: behind the Hill function. |
| title_full | The Goodwin model: behind the Hill function. |
| title_fullStr | The Goodwin model: behind the Hill function. |
| title_full_unstemmed | The Goodwin model: behind the Hill function. |
| title_short | The Goodwin model: behind the Hill function. |
| title_sort | goodwin model behind the hill function |
| url | http://europepmc.org/articles/PMC3731313?pdf=render |
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