Local interactions in protein folding determined through an inverse folding model

We adopt a model of inverse folding in which folding stability results from the combination of the hydrophobic effect with local interactions responsible for secondary structure preferences. Site-specific amino acid distributions can be calculated analytically for this model. We determine optimal parameters for the local interactions by fitting the complete inverse folding model to the site-specific amino acid distributions found in the Protein Data Bank. This procedure reduces drastically the influence on the derived parameters of the preference of different secondary structures for buriedness, which affects local interaction parameters determined through the standard approach based on amino acid propensities. The quality of the fit is evaluated through the likelihood of the observed amino acid distributions given the model and the Bayesian Information Criterion, which indicate that the model with optimal local interaction parameters is strongly preferable to the model where local interaction parameters are determined through propensities. The optimal model yields a mean correlation coefficient r = 0.96 between observed and predicted amino acid distributions. The local interaction parameters are then tested in threading experiments, in combination with contact interactions, for their capacity to recognize the native structure and structures similar to the native against unrelated ones. In a challenging test, proteins structurally aligned with the Mammoth algorithm are scored with the effective free energy function. The native structure gets the highest stability score in 100% of the cases, a high recognition rate comparable to that achieved against easier decoys generated by gapless threading. We then examine proteins for which at least one highly similar template exists. In 61% of the cases, the structure with the highest stability score excluding the native belongs to the native fold, compared to 60% if we use local interaction parameters derived from the usual amino acid propensities and 52% if we use only contact interactions. A highly similar structure is present within the five best stability scores in 82%, 81916, and 76% of the cases, for local interactions determined through inverse folding, through propensity, and set to zero, respectively. These results indicate that local interactions improve substantially the performances of contact free energy functions in fold recognition, and that similar structures tend to get high stability scores, although they are often not high enough to discriminate them from unrelated structures. This work highlights the importance to apply more challenging tests, as the recognition of homologous structures, for testing stability scores for protein folding.