Subunit Interactions in Enzyme Catalysis

Abstract

The activation free energy of any chemical process, carried out by a polymeric enzyme, can be split up into various energetic components. The mathematical formulation of this splitting allows the writing of every phenomenological rate constant in terms of the corresponding intrinsic constant and interaction coefficients. Those interaction coefficients are dimensionless parameters simply linked to thermodynamic functions expressing the contributions of the various types of subunit interactions to the free energy of activation. With the usual formulation of Koshland only saturation functions can be written, whereas with the new thermodynamic formulation the expression (in terms of molecular parameters) of both the substrate‐binding isotherms and the steady‐state rate equations are made easy. The rate equations obtained are obviously dependent upon the “geometry” of the enzyme molecule and are, in fact, structural rate equations; that is, their formulation is changed on assuming different protomer conformations and interactions. These equations have been written for various models of subunit interactions (simple sequential, partially‐concerted, fully‐concerted, and exclusive allosteric) pertaining to dimeric and tetrameric enzymes. The saturation functions and the steady‐state rate equations, both expressed with the same structural formulation, have been compared for the above models. It appears, as a general rule, that it is impossible to reduce the structural rate equations to the corresponding saturation functions, even for systems occurring in a pseudo‐equilibrium state. The only exception to this general rule is the allosteric model with exclusive binding. It is thus impossible, with the exception of the above case, to describe velocity data with the concept of saturation function. This result is at variance with an assumption commonly made. The possible shapes of the plots relating the reciprocal of the rate to the reciprocal of substrate concentration, have been analytically established and simulated by computer, for the above models of subunit interactions in dimeric enzymes. It appears that with regard to the steady‐state velocity, subunit interaction can generate not only “positive” or “negative cooperativity”, but also “substrate inhibition”.