Signal Deconvolution and Generative Topographic Mapping Regression for Solid-State NMR of Multi-Component Materials

Abstract

Solid-state nuclear magnetic resonance (ssNMR) spectroscopy provides information on native structures and the dynamics for predicting and designing the physical properties of multi-component solid materials. However, such an analysis is difficult because of the broad and overlapping spectra of these materials. Therefore, signal deconvolution and prediction are great challenges for their ssNMR analysis. We examined signal deconvolution methods using a short-time Fourier transform (STFT) and a non-negative tensor/matrix factorization (NTF, NMF), and methods for predicting NMR signals and physical properties using generative topographic mapping regression (GTMR). We demonstrated the applications for macromolecular samples involved in cellulose degradation, plastics, and microalgae such as Euglena gracilis. During cellulose degradation, ¹³C cross-polarization (CP)-magic angle spinning spectra were separated into signals of cellulose, proteins, and lipids by STFT and NTF. GTMR accurately predicted cellulose degradation for catabolic products such as acetate and CO₂. Using these methods, the ¹H anisotropic spectrum of poly-ε-caprolactone was separated into the signals of crystalline and amorphous solids. Forward prediction and inverse prediction of GTMR were used to compute STFT-processed NMR signals from the physical properties of polylactic acid. These signal deconvolution and prediction methods for ssNMR spectra of macromolecules can resolve the problem of overlapping spectra and support macromolecular characterization and material design.

Keywords: Euglena gracilis; T2 relaxation; anisotropy; cellulose degradation; macromolecules; plastics; prediction; short-time Fourier transform; signal deconvolution; solid-state NMR.

Figure 1

Concept diagram of a material development cycle based on signal deconvolution and prediction for the solid-state nuclear magnetic resonance (ssNMR) of multi-component materials. (a) Free induction decay (FID) is transformed into a dataset with time and frequency axes by short-time Fourier transform (STFT). (b) In the case of a three-dimensional dataset such as one with multiple samples and conditions, the FID is separated into each component based on the factors of time, frequency, and samples (or condition) by tensor factorization. (c) In the case of two-dimensional datasets such as a matrix with time and frequency axes, the FID is separated into each component based on factors of time and frequency by matrix factorization. (d) The generative topographic mapping regression (GTMR) accurately predicted the cellulose degradation process shown by catabolic products such as acetate and CO₂. (e) Forward prediction and inverse prediction of GTMR were used to compute the STFT-processed NMR (STFT–NMR) signals from the physical properties of the plastics. This approach is an iterative procedure to achieve convergence between experimental and predicted spectra.

Figure 2

Application of non-negative Tucker decomposition (NTD) to ¹³C cross-polarization–magic-angle spinning (CP-MAS) in the cellulose degradation process. (a) Original spectra of ¹³C CP-MAS in cellulose degradation process. (b) Tensor factorization of STFT–NMR signals. (c–f) Spectral patterns (cellulose, lipids, proteins, and noise) when signals were separated into four components. (g) Time change of separated components. (h) Composition of separated components.

Figure 3

Application of non-negative matrix factorization (NMF) to static ¹H solid-state NMR of poly-ε-caprolactone (PCL). (a) Experimental anisotropic spectrum (gray) and spectra of rigid (green) and mobile (orange) components separated by NMF. (b) Experimental spectra of double-quantum (DQ) filtered ssNMR (green) and magic-and-polarization echo (MAPE) filtered ssNMR (orange).

Figure 4

Application of GTMR to NMR data in the cellulose degradation process. (a) Visualization and prediction of the concentration of acetate. (b) Visualization and prediction of the concentration of CO₂.

Figure 5

Application of GTMR for predicting NMR data from thermal properties in PLA. (a–c) T_g, T_m, and T_d in data map. (d) Coordinates corresponding to the target thermal properties in data map. (e) Predicted ¹³C CP-MAS spectrum using GTMR.