Analysis of nonlinear properties of immune network reactions

On the basis of biochemical reaction dynamics, the temporal behavior of the immune network system was analyzed theoretically to promote the analysis of quantitative changes in the reactions of immune disorders and organ substitution. The idiotype immune network reaction system was expressed by 64 nonlinear differential equations that comprised four kinds of antibodies and B-cell subpopulations. All four kinds of antibodies decreased rapidly. With the progress of the reactions, they have increased gradually. The single and double bound antibodies increased rapidly from the onset of the reaction. The single-bound antibodies did not show a definite increase after the rapid increasing phase. The antibody-antibody complex increased parallel with the double bound antibodies. The effects of rate constant expand to all the immune complexes in the network system. The double bound antibodies and antibody-antibody complexes were oscillatory functions of a given antibody. Therefore, the idiotypic immune network system must be a chaotic one. The present theoretical method is available to evaluate the total ability of immune reaction system that operates as a network system.