Inverse statistical approaches, modeling pairwise correlations between
amino acids in the sequences of similar proteins across many different
organisms, can successfully extract protein structure (contact)
information. I will present a recent work, in collaboration with S. Cocco
and E. Shakhnovich, where we benchmark those statistical approaches on
exactly solvable models of proteins, folding on a 3D lattice, to assess
the reasons underlying their success and their limitations. We show that
the inferred parameters (effective pairwise interactions) of the
statistical models have clear and quantitative interpretations in terms of
positive (favoring the native fold) and negative (disfavoring competing
folds) protein sequence design. New sequences randomly drawn from the
statistical models are likely to fold into the native structures when
effective pairwise interactions are accurately inferred, a performance
which cannot be achieved with independent-site models.