Further theoretical refinement on the internal thermodynamics of perfect enzymes

By solving simultaneously the equation for 'uniform binding' [Albery & 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.