Phylogenetic Corrections and Higher-Order Sequence Statistics in Protein Families: The Potts Model vs MSA Transformer

Abstract: Recent generative learning models applied to protein multiple sequence alignment (MSA) datasets include simple and interpretable physics-based Potts covariation models and other machine learning models such as MSA-Transformer (MSA-T). The best models accurately reproduce MSA statistics induced by the biophysical constraints within proteins, raising the question of which functional forms best model the underlying physics. The Potts model is usually specified by an effective potential including pairwise residue-residue interaction terms, but it has been suggested that MSA-T can capture the effects induced by effective potentials which include more than pairwise interactions and implicitly account for phylogenetic structure in the MSA. Here we compare the ability of the Potts model and MSA-T to reconstruct higher-order sequence statistics reflecting complex biological sequence constraints. We find that the model performance depends greatly on the treatment of phylogenetic relationships between the sequences, which can induce non-biophysical mutational covariation in MSAs. When using explicit corrections for phylogenetic dependencies, we find the Potts model outperforms MSA-T in detecting epistatic interactions of biophysical origin.