pH-induced co-operative effects in hysteretic enzymes. 1. A theoretical model of a new type of co-operative behaviour controlled by pH.

A new model which provides an explanation for pH-induced co-operativity of hysteretic enzymes is proposed. The essence of the model is that a region, or a domain, of the enzyme undergoes a spontaneous 'slow' conformational change which does not affect the geometry of the active site. The region which undergoes this spontaneous conformational transition bears an ionizable group. Kinetic co-operativity occurs if the pK of this ionizable group changes upon this conformational transition. Thus co-operativity does not arise from a distortion of the active site. An interesting prediction of the model is that at 'extreme' pH values co-operativity must be suppressed. Although the kinetic equation pertaining to the model is of the 2:2 type, co-operativity is not maximum or minimum at half-saturation of the enzyme by the substrate, as occurs with 2:2 binding isotherms. A new index of maximum or minimum kinetic co-operativity, whether this extreme occurs at half-saturation or not, has been proposed which allows the change of kinetic co-operativity to be followed as a function of pH. It is believed that this model will be useful in explaining the behaviour of enzymes attached to biological polyelectrolytes, such as membranes or cell envelopes.