Generative power of a protein language model trained on multiple sequence alignments

Computational models starting from large ensembles of evolutionarily related protein sequences capture a representation of protein families and learn constraints associated to protein structure and function. They thus open the possibility for generating novel sequences belonging to protein families. Protein language models trained on multiple sequence alignments, such as MSA Transformer, are highly attractive candidates to this end. We propose and test an iterative method that directly uses the masked language modeling objective to generate sequences using MSA Transformer. We demonstrate that the resulting sequences generally score better than those generated by Potts models, and even than natural sequences, for homology, coevolution and structure-based measures. Moreover, MSA Transformer better reproduces the higher-order statistics and the distribution of sequences in sequence space of natural data than Potts models, although Potts models better reproduce first- and second-order statistics. MSA Transformer is thus a strong candidate for protein sequence generation and protein design.