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

Epistasis complicates our understanding of protein sequence-function relationships and impedes our ability to build accurate predictive models for novel genotypes. Although pairwise epistasis has been extensively studied in proteins, the significance of higher-order epistasis for protein sequence-function relationships remains contentious, largely due to challenges in fitting higher-order epistatatic interactions for full-length proteins. Here, we introduce a novel transformer-based approach. The key feature of our method is that we can adjust the order of interactions fit by the model by changing the number of attention layers while also accounting for any global nonlinearity induced by the experimental conditions. This allows us to test if inclusion of higher-order interactions leads to enhanced model performance. Applying our method to 10 large protein sequence-function datasets, we found that the importance of higher-order epistasis differs substantially between proteins, accounting for up to 60% of the total variance attributed to epistasis. We also found that including 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 derived from combining mutagenesis data from 4 orthologous green fluorescencent proteins. Our findings suggest that higher-order epistasis often does play an important role in protein sequence-function relationships, and thus should be properly incorporated during protein engineering and evolutionary data analysis.