Importance of higher-order epistasis in large protein sequence-function relationships

Protein sequence-function relationships are inherently complex, as amino acids at different positions can interact in highly unpredictable ways. A key question for protein evolution and engineering is how often epistasis extends beyond pairwise interactions to involve three or more positions. Although experimental data has accumulated rapidly in recent years, addressing this question remains challenging, as the number of possible interactions is typically enormous even for proteins of moderate size. Here, we introduce an interpretable machine learning framework for studying higher-order epistasis scalable to full-length proteins. Our model builds on the transformer architecture, with key modifications allowing us to assess the importance of higher-order interactions by fitting a series of models with increasing complexity. Applying our method to 10 large protein sequence-function datasets, we found that while additive effects explain the majority of the variance, within the epistatic component, the contribution of higher-order epistasis ranges from negligible to up to 60%. We also found higher-order epistasis is particularly important for generalizing locally sampled fitness data to distant regions of sequence space and for modeling an additional multi-peak fitness landscape. Our findings suggest that higher-order epistasis can play important roles in protein sequence-function relationships, and thus should be properly considered in protein engineering and evolutionary data analysis.