This thesis conducts a study on the stability of steady states in the
glycolysis of in silico models of Saccharomyces cerevisiae. Such un-
controlled models could reach unstable steady states that are unlikely
to occur in vivo. Little work has previously been done to examine
stability of such models.
The glycolysis is modeled as a system of nonlinear dierential equa-
tions. This is done by using rate equations describing the rate of change
in concentration of each metabolite involved in glycolysis. By lineariz-
ing this system around dierent equilibria and calculating the eigen-
values of the associated jacobian matrices the stability of the steady
states can be determined. Additionally perturbation analysis adds fur-
ther insight into the stability of the steady state.
Given the large range of possible initial conditions which result in
dierent steady states, a physiologically feasible one, as well as the
environment around it, is chosen to be the subject of this study. A
steady state is stable if all the eigenvalues of the Jacobian matrix are
negative. The model created by Teusink et al, and expanded upon by
Pritchard et, for the glycolysis in S.cerevisiae is used as the primary
model of the study.
The steady state does not have strictly negative eigenvalues: Two
of them are very close to zero, with one positive, within error tolerance
of our numerical methods. This means that linear analysis cannot
determine whether the steady state is stable. The whole nonlinear
system has to be considered. After performing perturbation analysis
we conclude that the steady state is most likely stable in the Lyapunov
2012. , 62 p.