A simple model of backbone flexibility improves modeling of side-chain conformational variability

The considerable flexibility of side-chains in folded proteins is important for protein stability and function, and may have a role in mediating allosteric interactions. While sampling side-chain degrees of freedom has been an integral part of several successful computational protein design methods, the predictions of these approaches have not been directly compared to experimental measurements of side-chain motional amplitudes. In addition, protein design methods frequently keep the backbone fixed, an approximation that may substantially limit the ability to accurately model side-chain flexibility. Here, we describe a Monte Carlo approach to modeling side-chain conformational variability and validate our method against a large dataset of methyl relaxation order parameters derived from nuclear magnetic resonance (NMR) experiments (17 proteins and a total of 530 data points). We also evaluate a model of backbone flexibility based on Backrub motions, a type of conformational change frequently observed in ultra-high-resolution X-ray structures that accounts for correlated side-chain backbone movements. The fixed-backbone model performs reasonably well with an overall rmsd between computed and predicted side-chain order parameters of 0.26. Notably, including backbone flexibility leads to significant improvements in modeling side-chain order parameters for ten of the 17 proteins in the set. Greater accuracy of the flexible backbone model results from both increases and decreases in side-chain flexibility relative to the fixed-backbone model. This simple flexible-backbone model should be useful for a variety of protein design applications, including improved modeling of protein-protein interactions, design of proteins with desired flexibility or rigidity, and prediction of correlated motions within proteins.