Sequence Space Localization in the Immune System Response to Vaccination and Disease

We introduce a model of protein evolution to explain limitations in the immune system response to vaccination and disease. The phenomenon of original antigenic sin, wherein vaccination creates memory sequences that can increase susceptibility to future exposures to the same disease, is explained as stemming from localization of the immune system response in antibody sequence space. This localization is a result of the roughness in sequence space of the evolved antibody affinity constant for antigen and is observed for diseases with high year-to-year mutation rates, such as influenza.

Figure 1

The evolved affinity constant to a second antigen after exposure to an original antigen that differs by probability $p$ (solid line). The dotted line represents the affinity constant without previous exposure. The affinity constant is generated by exponentiating, as in Eq. (4), the average of the best binding energy, using 5000 instances of the model. In the inset is shown the affinity of the memory sequences for the mutated antigen.

Figure 2

The affinity distribution of antibodies from naive $B$ cells (hatched) or memory cells (open) for the antigen of second exposure. In the inset is shown the binding constant that evolves in the primary response when an initial selection step retains only the top fraction of the naive cells.