An essential feature of the adaptive immune system is the proliferation of
antigen-specific lymphocytes during an immune reaction to form a large pool of
effector cells. This proliferation must be regulated to ensure an effective
response to infection while avoiding immunopathology. Recent experiments in
mice have demonstrated that the expansion of a specific clone of T cells in
response to cognate antigen obeys a striking inverse power law with respect to
the initial number of T cells. Here, we show that such a relationship arises
naturally from a model in which T cell expansion is limited by decaying levels
of presented antigen. The same model also accounts for the observed dependence
of T cell expansion on affinity for antigen and on the kinetics of antigen
administration. Extending the model to address expansion of multiple T cell
clones competing for antigen, we find that higher affinity clones can suppress
the proliferation of lower affinity clones, thereby promoting the specificity
of the response. Employing the model to derive optimal vaccination protocols,
we find that exponentially increasing antigen doses can achieve a nearly
optimized response. We thus conclude that the dynamics of presented antigen is
a key regulator of both the size and specificity of the adaptive immune
response
