  Affinity maturation produces antibodies that bind antigens with high
specificity by accumulating mutations in the antibody sequence. Mapping out the
antibody-antigen affinity landscape can give us insight into the accessible
paths during this rapid evolutionary process. By developing a carefully
controlled null model for noninteracting mutations, we characterized epistasis
in affinity measurements of a large library of antibody variants obtained by
Tite-Seq, a recently introduced Deep Mutational Scan method yielding physical
values of the binding constant. We show that representing affinity as the
binding free energy minimizes epistasis. Yet, we find that epistatically
interacting sites contribute substantially to binding. In addition to negative
epistasis, we report a large amount of beneficial epistasis, enlarging the
space of high-affinity antibodies as well as their mutational accessibility.
These properties suggest that the degeneracy of antibody sequences that can
bind a given antigen is enhanced by epistasis - an important property for
vaccine design.
