A methodology for calculating the rarity of diverse proteins based on functional specificity and thermodynamic stability

A key question in protein studies is the proportion of amino acid sequences that correspond to functional proteins, often called protein rarity. This issue underlies the relationship between mutations and disease, theories on the origin of proteins, and strategies for engineering new proteins. Recent literature has detailed how to employ estimates of protein rarity to evaluate the required biasing of functional sequences in sequence space to allow for evolutionary paths to connect distinct proteins. One challenge in addressing rarity has been an imprecise definition of function and a lack of consistency in methodology. This study introduces a new methodology, referred to as PRISM, to evaluate protein rarity based on the impact of mutations on stability. PRISM offers a suite of methods that are simpler than traditional approaches while providing accurate upper-bound rarity estimates. The specific method applied is determined by the protein’s function and available empirical data on how accumulating mutations affect its stability and performance. PRISM is applied to several proteins, and the accuracy of the methods is demonstrated by comparing the results to rarity estimates from previous studies. The calculated rarities align with previous research that concludes functional sequences are often exceedingly rare. The application of PRISM is outlined for research in protein engineering, protein evolution, and pathology.