Abstract

The total number of amino acid sequences that can fold to a target protein structure, known as "designability", is a fundamental property of proteins that contributes to their structure and function robustness. The highly designable structures always have higher thermodynamic stability, mutational stability, fast folding, regular secondary structures, and tertiary symmetries. Although it has been studied on lattice models for very short chains by exhaustive enumeration, it remains a challenge to estimate the designable quantitatively for real proteins. In this study, we designed a new deep neural network model that samples protein sequences given a backbone structure using sequential Monte Carlo method. The sampled sequences with proper weights were used to estimate the designability of several real proteins. The designed sequences were also tested using the latest AlphaFold2 and RoseTTAFold to confirm their foldabilities. We report this as the first study to estimate the designability of real proteins.