Phase diagrams for biophysical fitness landscape design

Populations evolve toward the top of fitness landscapes in the way that physical particles experience forces toward the bottom of a potential energy landscape. We recently introduced fitness landscape design (FLD) as a means of customizing the shape of a protein's biophysical fitness landscape by using antibody sequences and concentrations as tunable control parameters. Until now, previous evidence for the feasibility of FLD has been numerical and simulated. Here, we derive an explicit analytical theory for the FLD phase diagram, providing tight bounds on the designability frontiers describing the extent to which fitnesses of different protein sequences can be tuned independently of each other. We then leverage a recently published experimental dataset of binding affinities between over 62,000 antibody variants and each of three glycoprotein antigens to construct experimental FLD phase diagrams, which show close agreement with theory. These results support the feasibility of engineering quantitatively programmable fitness landscapes for laboratory protein evolution experiments.