Benchmarking inverse statistical approaches for protein structure and design with exactly solvable models

TL;DR

This study benchmarks inverse statistical methods for protein structure prediction using lattice protein models, showing they effectively capture structural and energetic features, including design of new sequences, despite underlying complexities.

Contribution

It demonstrates that inverse statistical approaches can reliably infer protein energetics and structure from sequence data using lattice models, revealing their capabilities and limitations.

Findings

Inferred Potts Hamiltonians reflect native and competing fold energetics.

Potts models enable design of new sequences with desired folds.

Effective couplings depend on both positive and negative design factors.

Abstract

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.