Kinetic analysis of biphasic protein modification reactions

Abstract

A mathematical analysis of biphasic protein modification reactions is presented, and it is shown that, in addition to the protein species modification reactions, one more time-dependent step must be postulated to exist in the reaction process. This step involves the interconversion of the different protein species, such as binding of ligand with protein, or the change in the isomerization state of the protein. The kinetic description of the reaction process is effected through a second order homogeneous linear differential equation, with time as the independent variable, and unmodified protein concentration as the dependent variable. A simple procedure of graphical analysis of the experimental data is described, and it is shown that, by a process of elimination, the nature of the protein species interconversion time-dependent step may be recognized, and also the dependence of the protein species inactivation rate constants on various parameters in the preparation may be evaluated. The method is illustrated by the detailed analysis of one example from the literature, the inactivation of phosphorylase b by 5,5-dithiobis (2-nitrobenzoic acid).

Kinetic Analysis of Parallel Reactions, the Initial Reactant of which Presents with two Interconvertible Isomeric Forms (hydrolysis and hydroxylaminolysis of 6-phosphogluconolactone)

“…The isomerization rate constants (k ? and k @ ) may be determined from the relationships (Rakitzis, 1980(Rakitzis, , 1984:…”

Kinetics of protein modification reactions

“…When one of the species transformation reactions of eqn. (1) is not a process of rapid equilibrium, this equation reduces to (Rakitzis, 1980a):…”

“…An analysis of the data of Sanner & Tron (1975), on the modification of the two fast-reacting sulphhydryl groups of phosphorylase b by 5,5'-dithiobis-(2-nitrobenzoic acid), by the procedure outlined above, has been presented (Rakitzis, 1980a). Some aspects of the relationship described by eqn.…”

“…Quite often protein modification data, which when plotted according to the method of Ray & Koshland (1961) give different values for the 'fast' and 'slow' reacting sets of residues, for different modifying agent concentrations, have been interpreted to mean the existence of two or more independently reacting sets, i.e., have been interpreted along the lines of eqns. (6)-(8) (see Rakitzis, 1980a).…”

Kinetics of protein modification reactions. Plot of fractional enzyme activity versus extent of protein modification in cases where all modifiable groups are essential for enzyme activity

“…It has been shown (Rakitzis, 1980a) that aversus-p plots that are concave upwards may be produced if enzyme activity loss is described by a summation of two or more exponential functions of reaction time. However, if enzyme activity loss is described by a single exponential function of reaction time, then the a-versus-p plot may only be of the following kinds: (a) rectilinear, if the rate constant for enzyme inactivation is equal to the rate constant for protein modification; (b) concave downwards, if enzyme protein modification is described by a summation of two or more exponential functions of reaction time the coefficients of which are positive; (c) concave upwards, if i> 1, or if enzyme protein modification is described by a summation of exponential functions of reaction time, at least one of the coefficients of which is negative [protein modification co-operativity, differential ligand and protein conformation effects on modification (Rakitzis, 1977(Rakitzis, , 1980b].…”