Constrained Evolutionary Funnels Shape Viral Immune Escape

Understanding how viral proteins adapt under immune pressure while preserving structural viability is crucial for anticipating the emergence of antibody-resistant variants. Here, we present a probabilistic framework that predicts the evolutionary trajectories of viral escape, revealing immune evasion is funneled through a remarkably small number of viable paths compared to total mutational space. These escape funnels arise from the combined constraints of protein viability and escape from antibodies, which we model using a generative model trained on structural 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 the SARS-CoV-2 receptor binding domain, our framework reveals convergent evolution patterns, accurately predicts mutation sites in emerged variants of concern, and explains the differential effectiveness of antibody cocktails. In particular, we show that combinations of antibodies with de-correlated escape profiles slow viral adaptation by increasing the mutational effort and viability cost required for escape.