Efficient generative modeling of protein sequences using simple autoregressive models

Jeanne Trinquier, Guido Uguzzoni, Andrea Pagnani, Francesco Zamponi and Martin Weigt ()
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Jeanne Trinquier: Institut de Biologie Paris Seine
Guido Uguzzoni: Politecnico di Torino
Andrea Pagnani: Politecnico di Torino
Francesco Zamponi: Université PSL, CNRS, Sorbonne Université, Université de Paris
Martin Weigt: Institut de Biologie Paris Seine

Nature Communications, 2021, vol. 12, issue 1, 1-11

Abstract: 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 102 and 103). 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. 1068 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.

Date: 2021
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DOI: 10.1038/s41467-021-25756-4

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