Protein NMR Structure Refinement Based on Bayesian Inference for Dynamical Ordering of Biomacromolecules

<p>Nuclear Magnetic Resonance (NMR) spectroscopy is the only tool to investigate the three-dimensional (3D) structures and dynamics of biomacromolecules at atomic resolution, in solution or in more natural environments such as living cells. On the other hand, since NMR data are principally only peak signals from atomic nuclei and often with imperfections and uncertainty, structural information must be properly extracted from the signals to build 3D conformations by NMR structure calculation. In NMR spectra of unstable or inhomogeneous samples, data become more sparse due to their low signal-to-noise ratio, making it difficult to determine accurate 3D structures. In order to more efficiently analyze the data, Rieping et al. proposed a new structure calculation method based on Bayes' theorem. We modified this approach in the CYANA program, allowing us to deduce the posterior probability of molecular ensembles with prior distributions, based on the Amber physical force field as well as on empirical knowledge, and to automate unambiguous and ambiguous NOE cross peak assignments. The sampling scheme for obtaining posterior probability is performed by a hybrid Monte Carlo algorithm, combined with Markov chain Monte Carlo (MCMC) by the Gibbs sampler, and a molecular dynamics simulation (MD) for collecting a canonical ensemble of conformations. Since it is not trivial to search the entire function space particularly for exploring the conformational prior due to the extraordinarily large conformation space of proteins, we perform the replica exchange method, in which several MCMC calculations with different temperatures are run in parallel as replicas. Simulated data and randomly deleted experimental peaks show that this new structure calculation method can provide accurate structures even with fewer peaks than the conventional method. We expect that solution NMR with our method will be a useful technique for the study of the”dynamical ordering” of biomacromolecules.</p>