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RESEARCH PRODUCT
Sustained oscillations in the MAP kinase cascade.
Juliette HellAlan D. Rendallsubject
0301 basic medicineStatistics and ProbabilitySingular perturbationDynamical systems theoryMolecular Networks (q-bio.MN)Dynamical Systems (math.DS)MAP kinase cascadeGeneral Biochemistry Genetics and Molecular BiologyQuantitative Biology::Subcellular Processes03 medical and health sciencessymbols.namesakeSimple (abstract algebra)Classical Analysis and ODEs (math.CA)FOS: MathematicsQuantitative Biology - Molecular NetworksSustained oscillationsMathematics - Dynamical SystemsHopf bifurcationPhysics030102 biochemistry & molecular biologyGeneral Immunology and MicrobiologyFutile cycleApplied MathematicsQuantitative Biology::Molecular NetworksGeneral Medicine030104 developmental biologyClassical mechanicsMathematics - Classical Analysis and ODEsModeling and SimulationFOS: Biological sciencessymbolsPeriodic orbitsGeneral Agricultural and Biological Sciencesdescription
Abstract The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focuses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-12-01 | Mathematical biosciences |