# Inferring repeat protein energetics from evolutionary information

## TL;DR

This paper introduces a method to infer the energetic variations in repeat proteins from evolutionary sequence data, enabling prediction of folding energies and generation of natural-like synthetic sequences.

## Contribution

It presents a novel energetic force field model for repeat proteins that accounts for amino acid interactions and relates sequence variations to stability and folding energy.

## Key findings

- The model accurately predicts folding free energy changes for mutants.
- It can generate synthetic sequences statistically similar to natural proteins.
- The approach links sequence covariation to energetic and structural properties.

## Abstract

Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing covariations in extant sequences. Still, many natural proteins that fold into the same structural topology show different stabilization energies, and these are often related to their physiological behavior. We propose a description for the energetic variation given by sequence modifications in repeat proteins, systems for which the overall problem is simplified by their inherent symmetry. We explicitly account for single amino acid and pair-wise interactions and treat higher order correlations with a single term. We show that the resulting force field can be interpreted with structural detail. We trace the variations in the energetic scores of natural proteins and relate them to their experimental characterization. The resulting energetic force field allows the prediction of the folding free energy change for several mutants, and can be used to generate synthetic sequences that are statistically indistinguishable from the natural counterparts.