Monostability and bistability of biological switches
| Autor: | Camille Pouchol, Jules Guilberteau, Nastassia Pouradier Duteil |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| Rok vydání: | 2021 |
| Předmět: |
0303 health sciences
Conjecture Dynamical systems theory Bistability Quantitative Biology::Molecular Networks Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Ode [SDV.BC.BC]Life Sciences [q-bio]/Cellular Biology/Subcellular Processes [q-bio.SC] Fixed point Systems modeling Agricultural and Biological Sciences (miscellaneous) 03 medical and health sciences 0302 clinical medicine 030220 oncology & carcinogenesis Modeling and Simulation Ordinary differential equation Statistical physics Multistability 030304 developmental biology Mathematics |
| Zdroj: | Journal of Mathematical Biology Journal of Mathematical Biology, 2021 |
| ISSN: | 1432-1416 0303-6812 |
| DOI: | 10.1007/s00285-021-01687-y |
| Popis: | International audience; Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological trait'). In this paper, we focus on simple ODE systems modeling two molecules which each negatively (or positively) regulate the other. It is well-known that such models may lead to monostability or multistability, depending on the selected parameters. However, extensive numerical simulations have led systems biologists to conjecture that in the vast majority of cases, there cannot be more than two stable points. Our main result is a proof of this conjecture. More specifically, we provide a criterion ensuring at most bistability, which is indeed satisfied by most commonly used functions. This includes Hill functions, but also a wide family of convex and sigmoid functions. We also determine which parameters lead to monostability, and which lead to bistability, by developing a more general framework encompassing all our results. |
| Databáze: | OpenAIRE |
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