Kinetic manifestations of allosteric interactions in models of regulatory enzymes with “indirect” co-operativity

The shape of the plots of initial reaction rate (ν) versus initial substrate concentration ([S] 0) and versus initial concentration of allosteric effector ([F] 0) for the model of allosteric enzyme of Monod, Wyman & Changeux (1965) and for the model of dissociating regulatory enzyme has been analysed by means of the inconstant exponent ( q) for substrate or effector concentration, respectively. It has been shown that allosteric interactions in above-mentioned models with “indirect” co-operativity may be manifested not only by the sigmoidal shape of the plot of ν versus [S] 0 or ν versus [F] 0 (with one point of inflexion) but also by the increase in the magnitude of exponent q in progress of saturation process of the enzyme by the substrate or by the effector in the absence of the sigmoidal shape of these plots. It has been shown also that the plot of ν versus [S] 0 has two inflexion points when the parameters have certain definite values. One of these inflexion points (or even both at definite values of the parameters) is hardly discernible. At certain definite values of the parameters two inflexion points may be kinetically manifested by such phenomenon as “negative” co-operativity ( q < 1). This is possible if one of the interconvertable enzyme forms exceeds another not only in the affinity to the substrate but also in the value of the rate constant for catalytic breakdown of the enzyme-substrate complex.