Direct or \(\Delta\)? Understanding Two Routes to Mutant Binding Affinity Prediction

Predicting how protein mutations alter ligand binding is crucial for understanding drug response and identifying compounds effective across variants. In modern biomolecular modeling, increasingly capable models coexist with comparatively limited mutation-specific affinity data, making the formulation of the prediction target itself an important modeling choice. Mutant affinity can be predicted either directly or through its change relative to the wild type (WT), yet it remains unclear when one route should be preferred over the other. We develop a statistical framework for comparing the two routes, Direct and Delta ($\Delta$), under the same input. The analysis shows when WT–mutant pairing can simplify affinity-change prediction by canceling shared variation, how this advantage depends on training size, and how interacting prediction errors affect the reconstructed mutant affinity. A linear-Gaussian analysis further characterizes conditions under which the preferred route can change with sample size. Controlled simulations reproduce the predicted finite-sample behavior, while experiments on PLATINUM and DAVIS-Complete reveal distinct real-data regimes: the $\Delta$-route advantage narrows as Direct prediction improves on PLATINUM, whereas sample-specific affinity-change prediction becomes increasingly informative with additional data on DAVIS-Complete. These results highlight the framework as a tool both explanatory and practical for modeling. Our code will be publicly available.