Free energy estimates of all-atom protein structures using generalized belief propagation

We present a technique for approximating the free energy of protein structures using generalized belief propagation (GBP). The accuracy and utility of these estimates are then demonstrated in two different application domains. First, we show that the entropy component of our free energy estimates can useful in distinguishing native protein structures from decoys-structures with similar internal energy to that of the native structure, but otherwise incorrect. Our method is able to correctly identify the native fold from among a set of decoys with 87.5% accuracy over a total of 48 different immunoglobulin folds. The remaining 12.5% of native structures are ranked among the top four of all structures. Second, we show that our estimates of Delta Delta G upon mutation upon mutation for three different data sets have linear correlations of 0.63-0.70 with experimental measurements and statistically significant p-values. Together, these results suggest that GBP is an effective means for computing free energy in all-atom models of protein structures. GBP is also efficient, taking a few minutes to run on a typical sized protein, further suggesting that GBP may be an attractive alternative to more costly molecular dynamic simulations for some tasks.