| Contents |
| This talk is concerned with mathematical models for the MAP kinase cascade, a
pattern of chemical reactions of central importance in molecular biology. It
is based on work done in collaboration with Juliette Hell. Existing numerical
and heuristic work indicates that the ODE models for this biological system
exhibit a variety of dynamical behaviour including more than one stable
stationary solution for given parameter values, periodic solutions and chaos.
It will be shown how a rigorous mathematical treatment of some of these
features of the model can be given using bifurcation theory and geometric
singular perturbation theory. A central aspect of this is the phenomenon of
sequestration which leads to the appearance of networks with feedback as a
limit of networks without manifest feedback. |
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