  It is difficult to predict how antibodies will behave when mixed together,
even after each has been independently characterized. Here, we present a
statistical mechanical model for the activity of antibody mixtures that
accounts for whether pairs of antibodies bind to distinct or overlapping
epitopes. This model requires measuring $n$ individual antibodies and their
$n(n-1)/2$ pairwise interactions to predict the $2^n$ potential combinations.
We apply this model to epidermal growth factor receptor (EGFR) antibodies and
find that the activity of antibody mixtures can be predicted without positing
synergy at the molecular level. In addition, we demonstrate how the model can
be used in reverse, where straightforward experiments measuring the activity of
antibody mixtures can be used to infer the molecular interactions between
antibodies. Lastly, we generalize this model to analyze engineered multidomain
antibodies, where components of different antibodies are tethered together to
form novel amalgams, and characterize how well it predicts recently designed
influenza antibodies.
