Generative Capacity of Probabilistic Protein Sequence Models

Variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict the effect of mutations. Despite encouraging results, a quantitative characterization of the VAE-generated probability distribution is still lacking. In particular, it is currently unclear whether or not VAEs can faithfully reproduce the complex multi-residue mutation patterns observed in natural sequences arising due to epistasis. In other words, are frequently observed subsequences assigned a correspondingly large probability by the VAE? Using a set of sequence statistics we comparatively assess the accuracy, or "generative capacity", of three GPSMs: a pairwise Potts Hamiltonian, a vanilla VAE, and a site-independent model, using natural and synthetic datasets. We show that the vanilla VAE's generative capacity lies between the pairwise Potts and site-independent models. Importantly, our work measures GPSM generative capacity in terms of higher-order sequence covariation and provides a new framework for evaluating and interpreting GPSM accuracy that emphasizes the role of epistasis.