Kinetic analysis of biphasic protein modification reactions

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).