Implications for affinity maturation in the germinal centers

From this one-pass selection model of the germinal center reaction, with the many variants I analyzed, it is clear that the observed numbers of high affinity cells can only be generated if mutant cells are selected and amplified very often during the germinal center reaction. If, as would be expected from random mutation, there is only a very small proportion of high affinity cells among the cells that enter the light zone, for instance on the order of 10^-4, consistent with the estimates of Radmacher et al. (1998), then only a handful of high affinity mutants would be generated over the entire GC reaction. Note that this estimate concerns a simple model antigen, in which one point mutation increases the affinity of the B cell receptor by a factor of 10. If more than one point mutation were required to produce the high affinity mutant, it becomes quite unlikely that a high affinity cell carrying all these mutations would ever be produced. Thus, almost trivially, a low frequency of generation of high affinity mutants restricts the output of high affinity from a germinal center to very low numbers. One might argue that even these small numbers could be expanded to a larger population of high affinity cells. I could envision this happening in two ways. One would be that the selected cells do not exit the germinal center, but can undergo further division in the germinal centers. If centrocytes do not divide, then this scenario reduces to recycling. The second way is that there is an expansion stage between the germinal center and the memory compartment. While this may well be possible, it would only affect the amplification factor that I calculated above if this expansion were associated with affinity selection. Otherwise, the ratio between various affinity classes would not be affected. This case was not considered in the above model, as it would involve a treatment of the dynamics of the memory compartment as well. There is yet another experimental finding that makes the one-pass scenario unlikely. This is the ratio of high affinity cells in germinal centers. While the high affinity mutation is not always discovered within a germinal center, GCs where the high affinity mutation is found have a high proportion of high affinity cells (1998). If the rare high affinity mutants are to dominate the germinal centers, assuming that they do not readily leave the germinal centers, it is necessary that almost all germline cells die. This in turn implies that the total cellular output from a single germinal center dominated by high affinity cells is very low.

When all of the GCs in an animal are considered, one-pass selection can give rise to an appreciable population of memory cells if the stringency of affinity-based selection is low. From stathmokinetic data (1995), I can estimate that the input into the light zone in a fully developed GC is about 1000 cells/day. If this input is sustained for about 2 weeks of the typical 3 week GC reaction, then the 300-500 GCs reported in the splenic response to NP-CGG (1991) would have a total light zone input of $4 - 7 \times 10^6$ cells. If 10% of these cells were selected (as we would obtain with the default parameter values from the above model), then the total output from the GCR would surpass 10⁵ cells. Even with some cell loss in the periphery, a reasonable size memory population would be achieved. However, this population would consist mostly of low affinity cells. To generate high affinity cells the stringency of selection would most likely need to be higher. If the frequency at which high affinity cells are generated is 1 per day, and only these cells were selected, then 300-500 germinal centers would produce of the order on 10³ to 10⁴ cells. The frequency at which B cells in an unselected repertoire respond to antigen is 10^-5 to 10^-4. Thus, the total number of initially responding B cells in a mouse with a total of 10⁸ B cells is 10³ to 10⁴. With the higher stringency of selection needed to generate a high affinity memory population, there would be no amplification in the number of responding cells, contrary to the observation of both significantly higher levels of antibody production and higher affinity in secondary responses. Again, this number would be considerably lower if the generation of a high affinity mutant required multiple point mutations.

I would like to point out that systems in which selection is due to an agent that decays over time are more generally encountered in the fields of immunology and infectious disease. Thus, the intuitions built from studying the above model might prove helpful in other situations. These may include, for example, clonal selection of B cells by a non-replicating antigen whose concentration decreases in time, outside of the germinal center reaction. Further examples may include adding fresh media to a culture of growing bacteria and the spread of an epidemic. The selective agent in these cases is the nutrient, in the first case, and individuals that are susceptible to infection, in the latter.