The catalytic performance of an enzyme, whether it is monomeric or oligomeric, depends on extra costs of energy in passing from the initial ground state to the various transition states, along the reaction co-ordinate. The improvement, during evolution, of the catalytic performance of individual subunits implies that three structural requirements are met in the course of an enzyme reaction: the unstrained enzyme subunits exist in the ground states under two conformations, one corresponding to the non-liganded state and the other to the liganded state; the inter-subunit strain is relieved in the various transition states; the subunits bound to the various transition states S not equal to, X not equal to and P not equal to have the same conformation. These structural requirements are precisely those which have been used to derive structural rate equations for polymeric enzymes. When subunits are loosely coupled, their arrangement controls the various rate constants, but not the extra costs of energy required to reach the various transition states. Moreover, one cannot expect the rate curve to display any sigmoidicity under these conditions. If subunits are tightly coupled and if the strained non-liganded and half-liganded states are destabilized with respect to the corresponding unstrained states, that is if they contain more conformational energy, the oligomeric enzyme is more catalytically efficient than the ideally isolated subunits. Moreover, if the available conformational energy of the half-liganded state is more than twice that of the non-liganded state, kinetic co-operativity is positive and the rate curve is sigmoidal. It is therefore the extent of inter-subunit strain in the half-liganded state which controls the appearance of sigmoidal kinetic behaviour. If subunits are tightly coupled but if inter-subunit strain is relieved in both the non-liganded and fully-liganded states, the half-liganded state controls both the catalytic efficiency of the enzyme and the sigmoidicity of the rate curve. Sigmoidicity and high catalytic efficiency are to be observed when this half-liganded state is destabilized relative to the corresponding unstrained state.(ABSTRACT TRUNCATED AT 400 WORDS)