  We show that the thermodynamic limit of a bistable
phosphorylation-dephosphorylation cycle has a selection rule for the "more
stable" macroscopic steady state. The analysis is akin to the Maxwell
construction. Based on the chemical master equation approach, it is shown that,
except at a critical point, bistability disappears in the stochastic model when
fluctuation is sufficiently low but unneglectable. Onsager's Gaussian
fluctuation theory applies to the unique macroscopic steady state. With initial
state in the basin of attraction of the "less stable" steady state, the
deterministic dynamics obtained by the Law of Mass Action is a metastable
phenomenon. Stability and robustness in cell biology are stochastic concepts.
