Toward ultimate NMR resolution with deep learning

Resolution in NMR is defined as the ability to distinguish and accurately determine signal positions while mitigating overlap. In the pursuit of ultimate resolution, we introduce peak probability presentations (P³), a statistical spectral representation that assigns a probability to each spectral point, indicating the likelihood that a peak maximum occurs at that location. The mapping between the traditional spectrum and P³ is achieved using MR-Ai, a physics-inspired and computationally efficient deep-learning neural network. P³ is validated on 60 database proteins and showcased on the challenging Tau and MATL1 proteins. Using synthetic spectra, we show that the achieved peak-localization precision closely approaches the theoretical limits set by the Cramér-Rao lower bound and Bayesian Monte Carlo estimates. Furthermore, MR-Ai enables the coprocessing of multiple spectra, facilitating direct information exchange between datasets to enhance spectral quality, particularly in cases of highly sparse sampling.