Two-dimensional Fourier transform of arbitrarily sampled NMR data sets.

Area of Science:

• Chemistry
• Spectroscopy
• Data Science

Background:

• Nuclear Magnetic Resonance (NMR) spectroscopy is crucial for molecular structure determination.
• Processing multi-dimensional NMR data, especially with arbitrary sampling, presents significant computational challenges.
• Conventional methods often involve sequential one-dimensional transforms, limiting efficiency for high-dimensional datasets.

Purpose of the Study:

• To introduce a new simultaneous multi-variable Fourier transform procedure for NMR data processing.
• To enable efficient analysis of high-dimensional NMR spectra acquired with non-standard sampling schemes.
• To demonstrate the method's applicability to complex biological molecules.

Main Methods:

• Developed a simultaneous multi-variable Fourier transform algorithm for NMR data.
• Applied the transform to two-dimensional (2D) and three-dimensional (3D) spectral data.
• Validated the method on a 3D HNCO spectrum of a protein sample using radial and spiral sampling.

Main Results:

• The new procedure calculates spectra for pairs of frequencies in 2D transforms, bypassing sequential 1D transforms.
• It allows Fourier transformation of arbitrarily sampled time-domain data, accommodating non-uniform sampling.
• Successfully processed a 3D HNCO spectrum, demonstrating feasibility for complex biological samples.

Conclusions:

• The proposed simultaneous multi-variable Fourier transform offers an efficient alternative for processing high-dimensional NMR data.
• This method supports analysis of spectra acquired with arbitrary sampling, provided the Nyquist theorem is met across all time domains.
• It significantly enhances the speed and scope of NMR data analysis, particularly for complex systems like proteins.