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By solving simultaneously the equation for 'uniform binding' [Albery &amp; Knowles (1976) Biochemistry 15, 5631-5640] and the equation for 'differential binding' [Chin (1983) J. Am. Chem. Soc. 105, 6502-6503], I derived the following simple equation for perfect enzymes (with single substrate and single product) under irreversible conditions: K2 = beta(1 + Rs)/1-beta(1 + Rs) where K2 is the internal equilibrium constant and beta is the Brönsted coefficient of the elementary catalytic step, and Rs is defined as [S]0/Ks, with [S]0 being the physiological substrate concentration and Ks being the substrate dissociation constant. The equation suggests that the perfect enzyme can have different internal thermodynamic properties depending on physiological conditions.

Further theoretical refinement on the internal thermodynamics of perfect enzymes