Assembly of three major subclasses of mouse immunoglobulin G: a theoretical model for covalent assembly in vivo

A mathematical model, based on second-order reaction kinetics, has been used to describe the covalent assembly of immunoglobulin G(IgG) in vitro from its heavy (H) and light (L) chains (Percy, M.E., Baumal, R., Dorrington, K.J. & Percy, J. (1976) Can. J. Biochem. 54, 675-687). In the present paper, the same model has now been applied to the steady-state assembly of IgG in vivo. This mathematical approach permits a quantitative comparison of the pathways of covalent assembly used by given immunoglobulins in vivo and in vitro. The assumptions in the model are: the species L, H, HL, HH, HHL and LHHL belong to a common pool; incompleted IgG intermediates may freely assemble to form HL, HH, HHL and LHHL; the reaction rate for covalent linkage between any two reacting species is proportional to the products of the number densities of the reactants and to a parameter P which takes the value PHH if the reaction joins two H chains, and PHL if it joins an H and L chain. In vivo values of PHH/PHL were determined for the 18 mouse myeloma tumours and cell lines studied by Baumal et al. (Baumal, R., Potter, M. & Scharff, M. (1971) J. Exp. Med. 134, 1316-1334). From these analyses, we have arrived at the following conclusions: (1) the three major IgG subclasses have distinctive values of PHH/PHL (mean value 53 for IgG1, 12 for IgG2a and 2.8 for IgG2b); (2) for IgGs of the same subclass, the values of PHH/PHL are similar; (3) the mean in vivo values of PHH/PHL are very close to those determined from in vitro assembly experiments. Finally, the individual values of PHH/PHL have been used to simulate pulse-chase experiments in the various tumours and cell lines. Considering the sources and magnitude of experimental error, the theoretical pathways of assembly agree with those determined qualitatively from the pulse-chase experiments.