Epistasis in Allosteric Proteins: Can Biophysical Models Provide a Better Framework for Prediction and Understanding?

The prediction of epistasis, or the interaction between mutations, is a complex challenge impacting protein science, healthcare, and biotechnology. For allosteric proteins, the prediction of epistatic effects is further complicated by the intricate networks of conformational states and binding interactions inherent to their function. Here, we explore these issues by systematically comparing biophysical and phenomenological models to analyze mutational effects and epistasis for the lac repressor protein, LacI. Using an extensive dataset consisting of dose-response measurements for 164 LacI variants, we find that while the phenomenological Hill model provides slightly better predictive accuracy, the biophysical model fits the data more parsimoniously, with significantly less epistasis in its parameters. Our results highlight the importance of the multi-state, multi-dimensional nature of allosteric function and the potential benefits of using biophysical models for the analysis of mutational effects and epistasis.