Acquisition of the covalent quaternary structure of an immunoglobulin G molecule. Theoretical reoxidation models

A theoretical format suitable for analyzing diverse complex kinetic systems where reaction pathways may exhibit cooperativity, is developed to account for the in vitro kinetics of air reoxidation of a human IgGlkappa immunoglobulin, in which the four interchain disulfide bonds have been reduced (Sears, D.W., et al. (1977), Biochemistry 16 (preceding paper in this issue)). The equations relate experimentally determined concentrations of the reactants, product, and macroscopic intermediates to the probability of occurrence of any of 12 distinct microscopic states. The concentrations of the macroscopic species--light chains (L), heavy chains (H), covalently associated intermediates HL, H2, H2L, and product H2L2--are also explicitly related to an observable function of those concentrations, the sulfhydryl titer, r. Since values of r can be calculated for any microscopic state of the system, the theory is in principle capable of a complete description of the experimental reaction course. In practice, limited experimental information precludes a unique solution of the equations at present, and it was not judged worthwhile to attempt curve fitting or approximation of probability terms with adjustable parameters of unknown physical significance. Certain special cases of the theory are, however, readily and exactly solved. These include models in which reoxidation is a random process and others in which the probabilities for inter-HL and inter-HH bond formation are different but independent of one another. The experimental results in the case of the IgGlkappa studied here clearly depart form the predicted behavior in either of these models. The initial probability for formation of a bond between a heavy and light chain is 1.5 to 2 times greater than for a bond between heavy chains. From the fact that this ratio changes as the reaction proceeds, and from the pattern of variation in concentration of intermediates during the reaction, it is concluded that the reoxidation process is not random, and that the bonds do not form independently, exhibiting instead kinetic cooperativity. The results are discussed in terms of assembly pathways in this and related systems. A novel feature of the theory is that it eliminates time as an explicit variable in the treatment of the kinetic process. This makes it especially useful for discerning whether the formation of one bond influences the reaction probability of another in a system where several similar or intrinsically identical reactions occur, and where kinetic order is difficult to establish. While the theory here is formulated in terms of the reoxidation reactions, it is, for example, equally applicable to the reduction process described (Sears, D.W., et al. (1977b), Biochemistry 16 (following paper in this issue)).