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Circular dichroism (CD) spectroscopy is a widely used technique for the evaluation of protein secondary structures that has a significant impact for the understanding of molecular biology. However, the quantitative analysis of protein secondary structures based on CD spectra is still a hard work due to the serious overlap of the spectra corresponding to different structural motifs. Here, Tchebichef image moment (TM) approach is introduced for the first time, which can effectively extract the chemical features in CD spectra for the quantitative analysis of protein secondary structures. The proposed approach was applied to analyze reference set and the obtained results were evaluated by the strict statistical parameters such as correlation coefficient, cross-validation correlation coefficient and root mean squared error. Compared with several specialized prediction methods, TM approach provided satisfactory results, especially for turns and unordered structures. Our study indicates that TM approach can be regarded as a feasible tool for the analysis of the secondary structures of proteins based on CD spectra. An available TMs package is provided and can be used directly for secondary structures prediction.

For the more complex samples, chemical higher-order data can be collected from various information sources, which become the necessary foundation of accurate analysis. In this article, the Tchebichef cubic moment (TCM) was developed for the analysis of chemical third-order data for the first time. Then, the proposed TCM approach was applied to the fluorescence excitation–emission time data for the analysis of adrenaline and noradrenaline in urinary samples (Data I) and the data fusion of the excitation–emission matrix (EEM), NMR, and liquid chromatography-mass spectrometry (LC-MS) spectra for the determination of the five target components (Data II). For Data I, all of the cross-validation correlation coefficients (R cv 2) of the obtained linear models on the calibration set were more than 0.9937 and the prediction root-mean-square errors (RMSEp) of the external independent test samples were less than 0.0250 μM. For Data II, all of the R cv 2 were higher than 0.9846 and RMSEp were less than 0.2267 μM. Compared with several conventional methods, the proposed method was more convenient and accurate. This study provides another effective approach to the analysis of complex samples based on their chemical third-order data.