Ultrahigh-Resolution 1H−13C HSQC Spectra of Metabolite Mixtures Using Nonlinear Sampling and Forward Maximum Entropy Reconstruction

To obtain a comprehensive assessment of metabolite levels from extracts of leukocytes, we have recorded ultrahigh-resolution 1H−13C HSQC NMR spectra of cell extracts, which exhibit spectral signatures of numerous small molecules. However, conventional acquisition of such spectra is time-consuming and hampers measurements on multiple samples, which would be needed for statistical analysis of metabolite concentrations. Here we show that the measurement time can be dramatically reduced without loss of spectral quality when using nonlinear sampling (NLS) and a new high-fidelity forward maximum-entropy (FM) reconstruction algorithm. This FM reconstruction conserves all measured time-domain data points and guesses the missing data points by an iterative process. This consists of discrete Fourier transformation of the sparse time-domain data set, computation of the spectral entropy, determination of a multidimensional entropy gradient, and calculation of new values for the missing time-domain data points with a conjugate gradient approach. Since this procedure does not alter measured data points, it reproduces signal intensities with high fidelity and does not suffer from a dynamic range problem. As an example we measured a natural abundance 1H−13C HSQC spectrum of metabolites from granulocyte cell extracts. We show that a high-resolution 1H−13C HSQC spectrum with 4k complex increments recorded linearly within 3.7 days can be reconstructed from one-seventh of the increments with nearly identical spectral appearance, indistinguishable signal intensities, and comparable or even lower root-mean-square (rms) and peak noise patterns measured in signal-free areas. Thus, this approach allows recording of ultrahigh resolution 1H−13C HSQC spectra in a fraction of the time needed for recording linearly sampled spectra.