ArticleJournal of mathematical biology2016
Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle.
Article in Journal of mathematical biology, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- Curating models from BioModels: Developing a workflow for creating OMEX files.bioRxiv : the preprint server for biology · 2024Article
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- A geometric analysis of the SIRS epidemiological model on a homogeneous network.Journal of mathematical biology · 2021Article
- Geometric singular perturbation analysis of a dynamical target mediated drug disposition model.Journal of mathematical biology · 2019Article
- Article
- Parameter-robustness analysis for a biochemical oscillator model describing the social-behaviour transition phase of myxobacteria.Proceedings. Mathematical, physical, and engineering sciences · 2018Article
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2 authors.
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Abstract
A minimal model describing the embryonic cell division cycle at the molecular level in eukaryotes is analyzed mathematically. It is known from numerical simulations that the corresponding three-dimensional system of ODEs has periodic solutions in certain parameter regimes. We prove the existence of a stable limit cycle and provide a detailed description on how the limit cycle is generated. The limit cycle corresponds to a relaxation oscillation of an auxiliary system, which is singularly perturbed and has the same orbits as the original model. The singular perturbation character of the auxiliary problem is caused by the occurrence of small Michaelis constants in the model. Essential pieces of the limit cycle of the auxiliary problem consist of segments of slow motion close to several branches of a two dimensional critical manifold which are connected by fast jumps. In addition, a new phenomenon of exchange of stability occurs at lines, where the branches of the two-dimensional critical manifold intersect. This novel type of relaxation oscillations is studied by combining standard results from geometric singular perturbation with several suitable blow-up transformations.
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