  We present a sequence-based probabilistic formalism that directly addresses
co-operative effects in networks of interacting positions in proteins,
providing significantly improved contact prediction, as well as accurate
quantitative prediction of free energy changes due to non-additive effects of
multiple mutations. In addition to these practical considerations, the
agreement of our sequence-based calculations with experimental data for both
structure and stability demonstrates a strong relation between the statistical
distribution of protein sequences produced by natural evolutionary processes,
and the thermodynamic stability of the structures to which these sequences
fold.
