Multiway Modeling of 2D NMR Spectra for Enhanced Chemical Characterization of Complex Mixtures

One-dimensional (1D) proton nuclear magnetic resonance (NMR) spectroscopy is widely used for complex mixture analysis because of its high reproducibility, minimal sample preparation, and inherent quantitative capabilities. However, 1D NMR remains constrained by three interrelated limitations: signal overlap among compounds, chemical-shift variability of the same compounds across samples, and masking of low signal-to-noise features by neighboring high-intensity resonances. Two-dimensional (2D) NMR spectroscopy can reduce these limitations by dispersing spectral information over a second dimension and providing additional structural information. Yet its broader implementation in large-scale studies remains limited by a major data-processing bottleneck: the analysis of multisample, high-dimensional 2D NMR data sets. When acquired across multiple samples, 2D NMR spectra form three-way tensors that contain richer chemical information than conventional 1D data sets but are not readily handled by standard NMR data analysis workflows. In this paper, we discuss how localized 2D spectral alignment combined with tensor decomposition and shift-tolerant multilinear modeling, including PARAFAC, PARAFAC2, and shift-invariant approaches, can recover overlapped, shifted, and low-intensity signals from complex 2D NMR spectra. These workflows hold considerable promise for advancing NMR-based complex mixture analysis by expanding metabolite coverage, improving deconvolution of elusive signals, and enabling more reliable quantification of low-abundance biomarkers in large-scale studies.