Model-based assignment and inference of protein backbone Nuclear Magnetic Resonances

Nuclear Magnetic Resonance (NMR) spectroscopy is a key experimental technique used to study protein structure, dynamics, and interactions. NMR methods face the bottleneck of spectral analysis, in particular determining the resonance assignments, which help define the mapping between atoms in the protein and peaks in the spectra. A substantial amount of noise in spectral data, along with ambiguities in interpretation, make this analysis a daunting task, and there exists no generally accepted measure of uncertainty associated with the resulting solutions. This paper develops a model-based inference approach that addresses the problem of characterizing uncertainty in backbone resonance assignment. We argue that NMR spectra are subject to random variation, and ignoring this stochasticity can lead to false optimism and erroneous conclusions. We propose a Bayesian statistical model that accounts for various sources of uncertainty and provides an automatable framework for inference. While assignment has previously been viewed as a deterministic optimization problem, we demonstrate the importance of considering all solutions consistent with the data, and develop an algorithm to search this space within our statistical framework. Our approach is able to characterize the uncertainty associated with backbone resonance assignment in several ways: 1) it quantifies of uncertainty in the individually assigned resonances in terms of their posterior standard deviations; 2) it assesses the information content in the data with a posterior distribution of plausible assignments; and 3) it provides a measure of the overall plausibility of assignments. We demonstrate the value of our approach in a study of experimental data from two proteins, Human Ubiquitin and Cold-shock protein A from E. coli. In addition, we provide simulations showing the impact of experimental conditions on uncertainty in the assignments.