Inverse statistical physics of protein sequences: a key issues review

This review explores the application of inverse statistical physics to protein sequence analysis. As evolutionary processes conserve protein structure and function despite significant sequence divergence, the statistical patterns within large families of homologous protein sequences contain implicit information about these constraints. By treating these sequences as samples from a Boltzmann distribution, researchers can use inverse methods to reconstruct the underlying energy landscape, providing insights into protein folding, interaction networks, and mutational effects.

The core methodology involves constructing a generalized Potts model, which uses local fields to represent site-specific amino acid conservation and pairwise couplings to capture coevolutionary constraints between residues. Because the exact inference of these parameters is computationally intractable for large proteins, the authors discuss several approximation schemes. These include mean-field approximations, pseudolikelihood maximization (PLM), and adaptive cluster expansion (ACE). While simpler methods like PLM are highly efficient for predicting the topology of coevolutionary networks, more precise methods like ACE are necessary when the goal is to generate synthetic sequences or accurately estimate model energies.

The ability to extract structural information from sequence data alone has transformed bioinformatics. The strongest coevolutionary couplings identified by these models consistently correspond to physical residue-residue contacts, which can be used to predict tertiary structures. Furthermore, the Potts model framework allows for the quantitative scoring of mutations, aiding in the identification of disease-causing variants or escape mutations in viral pathogens like HIV. The review highlights that even relatively simple pairwise models can generate functional artificial sequences, suggesting that pairwise correlations capture the essential physics of protein folding.