Bayesian estimation of NMR restraint potential and weight: a validation on a representative set of protein structures

The classical procedure for nuclear magnetic resonance structure calculation allocates empirical distance ranges and uses historical values for weighting factors. However, Bayesian analysis suggests that there are more optimal choices for potential shape (bounds-free log-harmonic shape) and restraints weights. We compare the classical protocol with the Bayesian approach for more than 300 protein structures. We analyze the conformation similarity to the corresponding X-ray crystal structure, the distribution of the conformations around their average, and independent validation criteria. On average, the log-harmonic potential reduces the difference to the X-ray crystal structure. If the log-harmonic potential is used, the constant weighting tightens the distribution around the average conformation, with respect to the distributions obtained with Bayesian weighting. Conversely, the structure quality is improved by the Bayesian weighting over the classical procedure, whereas constant weighting worsens some criteria. The quality improvement obtained with the log-harmonic potential coupled to Bayesian weighting validates this approach on a representative set of protein structures.