Interacting enzyme systems at steady state: location of the phase transition in approximations of the mean field type.

We consider a phase transition "loop," obtained from a mean field type of approximate treatment of a closed steady-state Ising system. Where is the cut (stable path) across the loop located? The general procedure, in answering this question, is to pass to an open version of the same system and use the cut that appears automatically in this case (no loop is possible in an open system). This is equivalent to finding the point at which the two phases have equal total probability in the open system. It is shown here that this procedure, when applied to a system of two-state enzyme molecules, is formally equivalent to well-known thermodynamic methods (Maxwell's theorem, etc.). These can be applied directly to the closed system without considering the open system explicitly. However, for enzyme molecules with more than two states, the "thermodynamic" method generally fails and one must fall back on the open system procedure mentioned above. Practical implementation of this procedure is not easy.