Reversibility of One-Substrate Reactions

Because of the principle of microscopic reversibility each molecular process (in contrast to a macroscopic process) may occur in both forward and backward directions. As a consequence the end product P of an enzymatic conversion can act as a competitive inhibitor of the enzyme or, depending on the thermodynamic equilibrium, be transformed to the substrate S. If the interconversion of the ES to the EP complex is the rate-determining step the rapid equilibrium assumption is valid and the rate equation can be derived easily. 

Reaction rate for the formation of the product P Maximum reaction rate of the forward reaction Maximum reaction rate of the backward reaction 

Again the denominator represents the dissociation equilibria of the ES complex and the EP complexes. Both partial reactions, the forward and the backward reactions, are catalyzed simultaneously both substrates S and P are competing for the same enzyme. If the Us.max value in Eq. (37) equals zero, the equation reflects competitive inhibition of the enzyme by the product P (see Eq.(27)). 

(37) is a result of the rate equation of the forward reaction reduced by the rate equation of the backward reaction, both having the same denominator. The numerator represents the first-order kinetics of the forward and the backward reactions. If the equilibrium of the reaction is reached, the numerator becomes zero. From the equilibrium condition (Eq. (38)), 

This relation, representing the ratio of the rate constants of the first order kinetics is known as the Haldane equation . Haldane equations can be formulated for every kinetic model describing an equilibrium reaction, just by setting the numerator to zero. 

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