  The MEK/ERK signalling pathway is involved in cell division, cell
specialisation, survival and cell death. Here we study a polynomial dynamical
system describing the dynamics of MEK/ERK proposed by Yeung et al. with their
experimental setup, data and known biological information. The experimental
dataset is a time-course of ERK measurements in different phosphorylation
states following activation of either wild-type MEK or MEK mutations associated
with cancer or developmental defects. We demonstrate how methods from
computational algebraic geometry, differential algebra, Bayesian statistics and
computational algebraic topology can inform the model reduction, identification
and parameter inference of MEK variants, respectively. Throughout, we show how
this algebraic viewpoint offers a rigorous and systematic analysis of such
models.
