  We introduce a novel, multi-scale model for affinity maturation, which aims
to capture the intra-clonal, inter-clonal and epitope-specific organization of
the B cell population in a germinal center. We describe the evolution of the B
cell population via a quasispecies dynamics, with species corresponding to
unique B cell receptors (BCRs), where the desired multi-scale structure is
reflected on the mutational connectivity of the accessible BCR space, and on
the statistical properties of its fitness landscape. Within this mathematical
framework, we study the competition among classes of BCRs targeting different
antigen epitopes, and construct an effective \emph{immunogenic space} where
epitope immunodominance relations can be universally characterized. We finally
study how varying the relative composition of a mixture of antigens with
variable and conserved domains allows for a parametric exploration of this
space, and identify general principles for the rational design of two-antigen
cocktails.
