  The methodology named LIFE (Linear-in-Flux-Expressions) was developed with
the purpose of simulating and analyzing large metabolic systems. With LIFE, the
number of model parameters is reduced by accounting for correlations among the
parameters of the system. Perturbation analysis on LIFE systems results in less
overall variability of the system, leading to results that more closely
resemble empirical data. These systems can be associated to graphs, and
characteristics of the graph give insight into the dynamics of the system. This
work addresses two main problems: 1. for fixed metabolite levels, find all
fluxes for which the metabolite levels are an equilibrium, and 2. for fixed
fluxes, find all metabolite levels which are equilibria for the system. We
characterize the set of solutions for both problems, and show general results
relating stability of systems to the structure of the associated graph. We show
that there is a structure of the graph necessary for stable dynamics. Along
with these general results, we show how stability analysis from the fields of
network flows, compartmental systems, control theory and Markov chains apply to
LIFE systems.
