Kinetics of irreversible enzyme inhibition: The tsou plot in irreversible binding co-operativity

Kinetics of protein modification reactions

“…Such plots have been used to obtain, by a process of extrapolation, the maximum extent of protein modification, i.e., the total number of reactive groups per protein molecule. It is common practice to construct and interpret such plots of fractional enzyme activity versus extent of protein modification on an intuitive basis, despite the firm theoretical treatment of this topic by Tsou (1962), and the elaborations on this by Horiike & McCormick (1979), Stevens & Colman (1980), and Rakitzis (1978aRakitzis ( , 1980b. Tsou (1962) has employed a statistical method of studying the relationship between fractional enzyme activity and extent of protein modification.…”

“…] combine statistical and time-dependence considerations when studying the modification of a catalytically active protein. Rakitzis (1978a) has pointed out that, in the case of enzyme protein modification reactions which are described by summations of exponential functions of reaction time, the conclusions of Tsou (1962) can also be arrived at by a juxtaposition of the equation describing protein modification and the equation describing enzyme inactivation. It is accordingly seen that it is wrong to extrapolate the initial portion of the plot of fractional enzyme activity versus number of groups modified per molecule of protein, and interpret the intercept of this on the axis representing the number of groups modified to mean the number of groups of the 'fast' reacting set; an exception to this is strong irreversible binding co-operativity (Rakitzis, 1980b).…”

Kinetics of protein-modification reactions. Determination of the fractional concentration of enzyme protein groups, or group reactivities, essential for catalytic function

“…(a) modification of one particular protein group abolishes catalytic function for the active site associated with that group, or (b) modification of one particular protein group abolishes catalytic function for both enzyme active sites of -the protein molecule. (Rakitzis, 1978). In case (a), the value for the fractional concentrationof group reactivities essential for catalytic function is 0.5, while in case (b), this value is equal to unity.…”

“…The number of enzyme protein reactive groups, i, per enzyme active site, essential for catalytic function, may be determined by plotting the (1 /i)th power of fractional enzyme activity versus the extent of protein groups modification (Tsou, 1962;Stevens & Colman, 1980;Horiike et al, 1984;Rakitzis, 1984a,b). However, this procedure is not applicable in cases where there is interaction between sites during the modification process (Tsou, 1962;Rakitzis, 1978). Also, in cases where protein modification is described by a summation ofexponential functions ofreaction time, this procedure is only applicable to the fraction of groups exhibiting the slowest exponential function of reaction time (Tsou, 1962).…”

“…However, this method is accurate only in cases where the fractional concentration of group reactivities essential for catalytic function is close to unity. The number of protein reactive groups, per enzyme active site, essential for catalytic function may also be determined by a comparison of protein-modification, and of enzyme-inactivation, rate constants (Ray & Koshland, 1961;Rakitzis, 1977Rakitzis, , 1978. However, in cases where the kinetic description of these processes consists of a summation of exponential functions ofreaction time, a comparison of rate constants is not feasible without a thorough analysis of the enzyme protein modification, and inactivation, event into the microscopic reaction components constituting the overall process.…”