"Viral" expansion of enzyme flux and use of quasi-chemical approximation for two-state enzymes with enzyme-enzyme interactions

Two examples of enzyme systems with interactions, at steady state, are treated here. In both cases, the enzyme cycle has two states and quasi-equilibrium in spatial distributions obtains at steady state (because f alpha + f beta = 1). The first example is a dilute solution of enzyme molecules in a solvent. The flux (turnover) per molecule is expanded in powers of the enzyme concentration (a "viral" expansion). Aggregation of the enzyme molecules in solution is considered as a special case. In the second example, we treat an arbitrary lattice of enzyme molecules, with nearest-neighbor interactions, using the well-known quasi-chemical approximation. The flux per molecule is obtained. Critical behavior and hysteresis are illustrated.