Phase diagrams for biophysical fitness landscape design

Viral populations often evolve toward the top of fitness landscapes by mutating their surface proteins to escape host antibodies and/or to bind more tightly to host cell receptors. As they climb fitness landscapes, newly mutated strains can spread across host populations, causing new waves of infection and death. As a pandemic preparedness strategy, we recently introduced computational protocols collectively called fitness landscape design (FLD) [Mohanty and Shakhnovich, Proc. Natl. Acad. Sci. (2026)], which consist of using antibody sequences and concentrations as tunable control parameters to proactively restructure the shape of a viral surface protein's biophysical fitness landscape for optimal suppression of dangerous escape mutants. 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 in the case of viral surface protein evolution in the presence of a neutralizing antibody, 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 influenza surface glycoproteins 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.