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 homologs 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 de-correlated escape profiles slow viral adaptation by forcing longer, higher-cost escape paths. SIGNIFICANCEViruses evolve to evade our immune defenses, but with constraints. Like navigating a minefield, each step toward immune escape comes at the potential cost of structural stability and functionality. We show that despite the vast mutational space, immune escape is funneled into a small set of predictable pathways. Using a statistical-physics model grounded in antibody experiments and SARS-CoV-2 epidemiology data, we identify these escape funnels--enabling therapies designed to block them before they are ever used.