Kinetic implications of the occurrence of several relaxations in the conformational transition of mnemonical enzymes.

If the conformational transition involved in enzyme memory occurs in several elementary steps, the time constant of the overall 'slow' relaxation is mostly determined by the individual values of the rate constants pertaining to the overall transconformation. The extent of kinetic co-operativity of the enzyme reaction, however, is mostly controlled by the degree of reversibility of the elementary steps of the conformational transition. There is then no simple relation between the time scale of the 'slow' transition and the extent of kinetic co-operativity of the enzyme reaction. A slow transition of about 10(-3) s-1 is therefore perfectly compatible with a strong positive or negative co-operativity and in particular with the negative co-operativity observed with wheat germ hexokinase LI. The relationship that has been established recently [Pettersson, G. (1986) Eur. J. Biochem. 154, 167-170] between the 'slow' enzyme relaxation and the extent of kinetic co-operativity holds only in the specific case where the transconformation occurs in one step. Owing to the possible occurrence of a multistep conformation change, the lack of this relationship means nothing as to the validity, or the invalidity, of the concept of mnemonical transition. More informative than the time scale of the 'slow' transition is its dependence with respect to glucose and glucose 6-phosphate, which both react with the enzyme. The effect of reaction products on the modulation of kinetic co-operativity is also of cardinal importance in the diagnosis of enzyme memory. Since an alternative model has been recently proposed by Pettersson (cited above) to explain the mechanistic origin of kinetic co-operativity of monomeric enzymes, the effect of products on the kinetic co-operativity predicted by this alternative model has been studied theoretically, in order to determine whether it is consistent with the experimental results obtained with wheat germ hexokinase LI. This analysis shows that the predictions of this model are in total disagreement with both the predictions of the mnemonical model and the experimental results obtained with wheat germ hexokinase LI, as well as with other enzymes. This alternative model cannot therefore be considered as a sensible explanation of the mechanistic origin of co-operativity of monomeric enzymes. It is therefore concluded that the mnemonical model which rests on numerous experimental results, obtained by different research groups, on different enzymes is the simplest and most likely explanation of the kinetic subtleties displayed by some monomeric enzymes, and in particular wheat germ hexokinase LI.