Application of Singular Spectrum Analysis (SSA), Independent Component Analysis (ICA) and Empirical Mode Decomposition (EMD) for automated solvent suppression and automated baseline and phase correction from multi-dimensional NMR spectra

A common problem on protein structure determination by NMR spectroscopy is due to the solvent artifact. Typically, a deuterated solvent is used instead of normal water. However, several experimental methods have been developed to suppress the solvent signal in the case that one has to use a protonated solvent or if the signals of the remaining protons even in a highly deuterated sample are still too strong. For a protein dissolved in 90% H2O / 10% D2O, the concentration of solvent protons is about five orders of magnitude greater than the concentration of the protons of interest in the solute. Therefore, the evaluation of multi-dimensional NMR spectra may be incomplete since certain resonances of interest (e.g. Hα proton resonances) are hidden by the solvent signal and since signal parts of the solvent may be misinterpreted as cross peaks originating from the protein. The experimental solvent suppression procedures typically are not able to recover these significant protein signals. Many post-processing methods have been designed in order to overcome this problem. In this work, several algorithms for the suppression of the water signal have been developed and compared. In particular, it has been shown that the Singular Spectrum Analysis (SSA) can be applied advantageously to remove the solvent artifact from NMR spectra of any dimensionality both digitally and analogically acquired. In particular, the investigated time domain signals (FIDs) are decomposed into water and protein related components by means of an initial embedding of the data in the space of time-delayed coordinates. Eigenvalue decomposition is applied on these data and the component with the highest variance (typically represented by the dominant solvent signal) is neglected before reverting the embedding. Pre-processing (group delay management and signal normalization) and post-processing (inverse normalization, Fourier transformation and phase and baseline corrections) of the NMR data is mandatory in order to obtain a better performance of the suppression. The optimal embedding dimension has been empirically determined in accordance to a specific qualitative and quantitative analysis of the extracted components applied on a back-calculated two-dimensional spectrum of HPr protein from Staphylococcus aureus. Moreover, the investigation of experimental data (three-dimensional 1H13C HCCH-TOCSY spectrum of Trx protein from Plasmodium falciparum and two-dimensional NOESY and TOCSY spectra of HPr protein from Staphylococcus aureus) has revealed the ability of the algorithm to recover resonances hidden underneath the water signal. Pathological diseases and the effects of drugs and lifestyle can be detected from NMR spectroscopy applied on samples containing biofluids (e.g. urine, blood, saliva). The detection of signals of interest in such spectra can be hampered by the solvent as well. The SSA has also been successfully applied to one-dimensional urine, blood and cell spectra. The algorithm for automated solvent suppression has been introduced in the AUREMOL software package (AUREMOL_SSA). It is optionally followed by an automated baseline correction in the frequency domain (AUREMOL_ALS) that can be also used out the former algorithm. The automated recognition of baseline points is differently performed in dependence on the dimensionality of the data. In order to investigate the limitations of the SSA, it has been applied to spectra whose dominant signal is not the solvent (as in case of watergate solvent suppression and in case of back-calculated data not including any experimental water signal) determining the optimal solvent-to-solute ratio. The Independent Component Analysis (ICA) represents a valid alternative for water suppression when the solvent signal is not the dominant one in the spectra (when it is smaller than the half of the strongest solute resonance). In particular, two components are obtained: the solvent and the solute. The ICA needs as input at least as many different spectra (mixtures) as the number of components (source signals), thus the definition of a suitable protocol for generating a dataset of one-dimensional ICA-tailored inputs is straightforward. The ICA has revealed to overcome the SSA limitations and to be able to recover resonances of interest that cannot be detected applying the SSA. The ICA avoids all the pre- and post-processing steps, since it is directly applied in the frequency domain. On the other hand, the selection of the component to be removed is automatically detected in the SSA case (having the highest variance). In the ICA, a visual inspection of the extracted components is still required considering that the output is permutable and scale and sign ambiguities may occur. The Empirical Mode Decomposition (EMD) has revealed to be more suitable for automated phase correction than for solvent suppression purposes. It decomposes the FID into several intrinsic mode functions (IMFs) whose frequency of oscillation decreases from the first to the last ones (that identifies the solvent signal). The automatically identified non-baseline regions in the Fourier transform of the sum of the first IMFs are separately evaluated and genetic algorithms are applied in order to determine the zero- and first-order terms suitable for an optimal phase correction. The SSA and the ALS algorithms have been applied before assigning the two-dimensional NOESY spectrum (with the program KNOWNOE) of the PSCD4-domain of the pleuralin protein in order to increase the number of already existing distance restraints. A new routine to derive 3JHNHα couplings from torsion angles (Karplus relation) and vice versa, has been introduced in the AUREMOL software. Using the newly developed tools a refined three-dimensional structure of the PSCD4-domain could be obtained

Removing Water Artefacts from 2D Protein NMR Spectra using GEVD with Congruent Matrix Pencils

Multidimensional H nmr spectra of biomolecules dissolved in light water are contaminated by an intense water artefact. We discuss the application of the generalized eigenvalue decomposition (GEVD) method using a matrix pencil to explore the time structure of the signals in order to separate out the water artefacts. Simulated as well as experimental 2D NOESY spectra of proteins are studied. Results are compared to those obtained with the FastICA algorithm