Unsupervised Analysis of Small Molecule Mixtures by Wavelet-Based Super-Resolved NMR
Abstract
:1. Introduction
2. Results and Discussion
3. Materials and Methods
3.1. NMR to WPT Spectral Conversion
3.2. Spectral Library and Augmented Dataset Creation
3.3. Automated Spectral Analysis Algorithm
- Calculate WPT and WPT shift spectrum from an NMR spectrum;
- Match the WPT shift spectrum with the WPT shift spectral library:
- (a)
- p = count the number of matches for each molecule in the library;
- (b)
- The probability for a molecule to be in the mixture = p/the number of peaks in the WPT shift spectrum of the molecule;
- (c)
- Continue for all the molecules in the library, and short-list the ones with non-zero probabilities into the list, L I.
- Optimize the short-listed molecules by a gradient descent method:
- (a)
- Define the WPT shift NMR spectrum of a molecular mixture as the target variable, ;
- (b)
- Create a design matrix, , from the intersection of the chemical shift values from and the intensities of the spectra for the molecules in L I;
- (c)
- Minimize , where is the dimension of and is the probabilities associated with the molecules in L I, using a gradient descent method with a learning rate, = 0.1;
- (d)
- An optimized list of molecules, L II, associated with non-zero probabilities is obtained.
- The top 15 entries from L II are used as the input to another optimization step:
- (a)
- Define the WPT NMR spectrum of a molecular mixture as the target variable, ;
- (b)
- Create a design matrix, , from the intersection of the chemical shift values from and the intensities of the spectra for the molecules in L II;
- (c)
- Minimize using a gradient descent method with the learning rate chosen randomly from a uniform distribution between 0.01 and 0.1;
- (d)
- An optimized list of molecules associated with probabilities greater than 0.1 is obtained.
3.4. An Example of How the Scheme Works
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
WPT | Wavelet packet transform |
DWT | Discrete wavelet transform |
NMR | Nuclear magnetic resonance |
Appendix A. Overview of Wavelet Transform
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Mixture No. | Number of Molecules | Molecules (Proportions %) | True Positive Rate | False Positive Rate |
---|---|---|---|---|
5 | 3 | Caffeine (39), ribitol (33), cis-jasmone (28) | 1.0 | 0.04 |
23 | 4 | Nerolidol (35), 1,8-cineole (22), leaf alcohol (22), furfuryl alcohol (21) | 1.0 | 0.04 |
35 | 5 | Sorbitol (28), eugenol (26), ribitol (18), ascorbic acid (15), salicylic acid (13) | 1.0 | 0.03 |
20 | 6 | Ribitol (20), eugenol (19), cis-jasmone (18), 5-methylfurfural (17), ascorbic acid (15), 1,8-cineole (12) | 1.0 | 0.04 |
Parameters | True Positive Rate | False Positive Rate |
---|---|---|
Mean | 0.97 | 0.05 |
Median | 1.0 | 0.04 |
Standard Deviation | 0.09 | 0.03 |
Chemical Shift | Target, Y | Design Matrix, X | |||
---|---|---|---|---|---|
… | |||||
… | |||||
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Sinha Roy, A.; Srivastava, M. Unsupervised Analysis of Small Molecule Mixtures by Wavelet-Based Super-Resolved NMR. Molecules 2023, 28, 792. https://doi.org/10.3390/molecules28020792
Sinha Roy A, Srivastava M. Unsupervised Analysis of Small Molecule Mixtures by Wavelet-Based Super-Resolved NMR. Molecules. 2023; 28(2):792. https://doi.org/10.3390/molecules28020792
Chicago/Turabian StyleSinha Roy, Aritro, and Madhur Srivastava. 2023. "Unsupervised Analysis of Small Molecule Mixtures by Wavelet-Based Super-Resolved NMR" Molecules 28, no. 2: 792. https://doi.org/10.3390/molecules28020792