A statistical mechanical method to optimize energy functions for protein folding

We present a method for deriving energy functions for protein folding by ma ximizing the thermodynamic average of the overlap with the native state. Th e method has been tested by using the pairwise contact approximation of the energy function and generating alternative structures by threading sequenc es over a database of 1,169 structures. With the derived energy function, m ost native structures: (i) have minimal energy and (ii) are thermodynamical ly rather stable, and (iii) the corresponding energy landscapes are smooth. Precisely, 92% of the 1,013 x-ray structures are stabilized. Most failures can be attributed to the neglect of interactions between chains forming po lychain proteins and of interactions with cofactors, When these are conside red, only nine cases remain unexplained. In contrast, 38% of NMR structures are not assigned properly.