Efficient generative modeling of protein sequences using simple autoregressive models

TL;DR

This paper introduces simple autoregressive models for protein sequence generation that are highly accurate and computationally efficient, enabling better exploration of protein sequence space compared to more complex models.

Contribution

The authors propose and validate simple autoregressive models that match the performance of complex models at a fraction of the computational cost, with added mathematical advantages.

Findings

Models perform similarly to complex approaches but are 100-1000 times faster.

Able to estimate sequence probabilities and functional sequence space size.

Discovered approximately 10^68 possible sequences for response regulators.

Abstract

Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between $10^2$ and $10^3$). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. $10^{68}$ possible sequences, which nevertheless constitute only the astronomically small fraction $10^{-80}$ of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models.