6533b827fe1ef96bd1285a87

RESEARCH PRODUCT

Dynamical Features of the MAP Kinase Cascade

Juliette HellAlan D. Rendall

subject

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

description

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 applications of these techniques could be extended in the future.

yearjournalcountryeditionlanguage
2017-01-01
https://doi.org/10.1007/978-3-319-45833-5_6