0000000000563975

AUTHOR

Juliette Hell

showing 3 related works from this author

Sustained oscillations in the MAP kinase cascade.

2016

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.

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 SciencesMathematical biosciences
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Dynamical Features of the MAP Kinase Cascade

2017

The MAP kinase cascade is an important signal transduction system in molecular biology for which a lot of mathematical modelling has been done. This paper surveys what has been proved mathematically about the qualitative properties of solutions of the ordinary differential equations arising as models for this biological system. It focuses, in particular, on the issues of multistability and the existence of sustained oscillations. It also gives a concise introduction to the mathematical techniques used in this context, bifurcation theory and geometric singular perturbation theory, as they relate to these specific examples. In addition further directions are presented in which the application…

0301 basic medicineHopf bifurcationSingular perturbationComputer scienceContext (language use)MAP kinase cascade01 natural sciences010305 fluids & plasmas03 medical and health sciencessymbols.namesake030104 developmental biologyBifurcation theoryOrdinary differential equation0103 physical sciencessymbolsSustained oscillationsStatistical physicsMultistability
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A proof of bistability for the dual futile cycle

2014

Abstract The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is…

Singular perturbationBistabilityFutile cycleMolecular Networks (q-bio.MN)Quantitative Biology::Molecular NetworksApplied MathematicsGeneral EngineeringOdeDynamical Systems (math.DS)General MedicineDual (category theory)Computational MathematicsBifurcation theoryMathematics - Classical Analysis and ODEsFOS: Biological sciencesOrdinary differential equationClassical Analysis and ODEs (math.CA)FOS: MathematicsApplied mathematicsQuantitative Biology - Molecular NetworksMathematics - Dynamical SystemsSpecial caseGeneral Economics Econometrics and FinanceAnalysisMathematicsNonlinear Analysis: Real World Applications
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