  In this paper I show that, for a class of reaction networks, the discrete
stochastic nature of the reacting species and reactions results in qualitative
and quantitative differences between the mean of exact stochastic simulations
and the prediction of the corresponding deterministic system. The differences
are independent of the number of molecules of each species in the system under
consideration. These reaction networks are open systems of chemical reactions
with no zero-order reaction rates systems. They are characterized by at least
two stationary points, one of which is a nonzero stable point, and one unstable
trivial solution (stability based on a linear stability analysis of the
deterministic system). Starting from a nonzero initial condition, the
deterministic system never reaches the zero stationary point due to its
unstable nature. In contrast, the result presented here proves that this
zero-state is the only stable stationary state for the discrete stochastic
system. This result generalizes previous theoretical studies and simulations of
specific systems and provides a theoretical basis for analyzing a class of
systems that exhibit such inconsistent behavior. This result has implications
in the simulation of infection, apoptosis, and population kinetics, as it can
be shown that for certain models the stochastic simulations will always yield
different predictions for the mean behavior than the deterministic simulations.
