  We investigate the stability properties of two different classes of metabolic
cycles using a combination of analytical and computational methods. Using
principles from structural kinetic modeling (SKM), we show that the stability
of metabolic networks with certain structural regularities can be studied using
a combination of analytical and computational techniques. We then apply these
techniques to a class of single input, single output metabolic cycles, and find
that the cycles are stable under all conditions tested. Next, we extend our
analysis to a small autocatalytic cycle, and determine parameter regimes within
which the cycle is very likely to be stable. We demonstrate that analytical
methods can be used to understand the relationship between kinetic parameters
and stability, and that results from these analytical methods can be confirmed
with computational experiments. In addition, our results suggest that elevated
metabolite concentrations and certain crucial saturation parameters can
strongly affect the stability of the entire metabolic cycle. We discuss our
results in light of the possibility that evolutionary forces may select for
metabolic network topologies with a high intrinsic probability of being stable.
Furthermore, our conclusions support the hypothesis that certain types of
metabolic cycles may have played a role in the development of primitive
metabolism despite the absence of regulatory mechanisms.
