High affinity memory cell production in the germinal centers. How far can selection reach?

The stage at which somatic hypermutation occurs in the dynamics of the germinal center reaction, the mechanism underlying it, the difference in selective advantage that various affinities of antibody receptors confer, are all open questions in B cell immunology. We develop a one pass selection model, as suggested by the GC architecture, that is, B cells once selected are placed into a long-lived (memory) pool. We use this model to explore the upper bound on the efficiency of affinity maturation, measured in terms of the fraction and absolute number of high affinity cells in the selected population. We contrast the replication- and transcription-related mutation mechanisms in terms of this parameters. We show that the amplification that selection gives to a clone is bounded by a logarithmic function of the ratio between the binding rate, which confers it selective advantage, and the death rate for that clone. We conclude that one pass selection scenario cannot give rise to a large high affinity population {\em within} the germinal center itself, although there still is the pending question of why would such a population be generated when immune memory seems to require significantly less.