  We introduce a new model for the dynamics of centroblasts and centrocytes in
a germinal center. The model reduces the germinal center reaction to the
elements considered as essential and embeds proliferation of centroblasts,
point mutations of the corresponding antibody types represented in a shape
space, differentiation to centrocytes, selection with respect to initial
antigens, differentiation of positively selected centrocytes to plasma or
memory cells and recycling of centrocytes to centroblasts. We use exclusively
parameters with a direct biological interpretation such that, once determined
by experimental data, the model gains predictive power. Based on the experiment
of Han et al. (1995b) we predict that a high rate of recycling of centrocytes
to centroblasts is necessary for the germinal center reaction to work reliably.
Furthermore, we find a delayed start of the production of plasma and memory
cells with respect to the start of point mutations, which turns out to be
necessary for the optimization process during the germinal center reaction. The
dependence of the germinal center reaction on the recycling probability is
analyzed.
