We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. We assume that the rate of maturation of B cells in the bone marrow decreases with increasing idiotypic stimulation. Terminal differentiation of peripheral B cells into antibody forming cells, on the other hand, has a log-bell shaped dependence upon the stimulus. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by anti-antibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production (which is determined by the rates of B cell formation and antibody secretion), an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state is the only attractor of the system; the virgin state has become unstable. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the maturation of bone marrow B cells of the other clone. If a clone of the idiotypically interacting pair is autoreactive the B cells always differentiate into antibody forming cells and some antibody is secreted due to the stimulus provided by the self antigen. Consequently, there is no virgin state for auto-reactive clones in this system. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states at an antibody production slightly larger than in the non-autoreactive case. If only one clone is autoreactive, the asymmetry of the activated states at large antibody production implies that the system acts quite differently on the self antigen when we compare pairs resting in one state or the other. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypiccontrol of autoantibodies is rather large, when the anti-idiotype affects only the differentiation of B cells.
You can ftp the manuscript (postscript file) described by the above abstract by clicking here.