Constrained evolutionary funnels shape viral immune escape.

Understanding how viral proteins adapt under immune pressure while preserving viability is crucial for anticipating antibody-resistant variants. We present a probabilistic framework that predicts viral escape trajectories and shows that immune evasion is channeled into a small set of viable "escape funnels" within the vast mutational space. These escape funnels arise from the combined constraints of protein viability and antibody escape, modeled using a generative model trained on homologous sequences and deep mutational scanning data. We derive a mean-field approximation of evolutionary path ensembles, enabling us to quantify both the fitness and entropy of escape routes. Applied to SARS-CoV-2 receptor binding domain, our framework reveals convergent evolution patterns, predicts mutation sites in variants of concern, and explains differences in antibody-cocktail effectiveness. In particular, cocktails with decorrelated escape profiles slow viral adaptation by forcing longer, higher-cost escape paths.