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

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Abstract
A mathematical model, based on 2nd-order reaction kinetics, was previously used to describe the covalent assembly of immunoglobulin G (IgG) in vitro from its H and L chains. In the present paper, the same model was 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 Ig 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 2 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 2 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 tumors and cell lines previously studied. The 3 major IgG subclasses have distinctive values of PHH/PHL (mean value 53 for IgG1, 12 for IgG2a and 2.8 for IgG2b); for IgGs of the same subclass, the values of PHH/PHL are similar; the mean in vivo values of PHH/PHL are very close to those determined from in vitro assembly experiments. The individual values of PHH/PHL were used to simulate pulse-chase experiments in the various tumor and cell lines. Considering the source and magnitude of experimental error, the theoretical pathways of assembly agree with those determined qualitatively from the pulse-chase experiments.

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