An equation-system from the Michaelis-Menten kinetics for glycolysis
following Dan Fraenkel at Harvard Medical School is analyzed. It turns
out that it is very difficult or resilient to numeric computation. However
using non-linear equation solvers of the kind Groebner basis in computer
algebra system the exact parametric solution is found.
This puts lights on the resilience and the explanation for the difficulties is indeed quite remarkable. The reason is the proximity of the datasets to a singularity in the "solution-space". This gives rise to a considerable numerical instability. The remedy seems to be to move further away from equilibrium or simply away from steady state, as Sune Danø has pointed out, in order that the problem should not be that ill-conditioned.
Possibly the Michaelis-Menten kinetics should also be improved or replaced by something better!
A lot of other interesting methodological issues is actualised as well.