Maximum entropy reconstruction of spectra containing antiphase peaks

Abstract

Two-dimensional nuclear magnetic resonance methods have in recent years been used to great effect to study the three-dimensional structure and conformation of small proteins, DNA fragments, and other biological macromolecules. To maximize resolution and sensitivity (and consequently information content), spectra have been recorded in the phase-sensitive mode giving particularly impressive results (I, 2). Nevertheless, currently available NMR methods are limited in their applicability to larger macromolecules by problems caused by (1) increased linewidths and spectral crowding and (2) decreased sensitivity. In an attempt to alleviate these problems in two-dimensional spectra we are investigating the use of the maximum entropy method (MEM) for reconstruction of NMR spectra from free induction decay data. In previous papers we have demonstrated the potential of MEM reconstructions for simultaneous noise suppression and resolution enhancement in both ‘H and i3C one-dimensional NMR spectra (3, 4). This feature coupled with the ability of MEM to suppress truncation and other artifacts suggested that the method could be particularly useful for processing 2D NMR spectra. However, an apparent difficulty arises because signals in many phase-sensitive two-dimensional spectra are antiphase. Maximum entropy necessarily reconstructs positive oscillator number densities. Fortunately, the solution is straightforward. We merely allow two types of oscillators, one giving positive signals and the other negative, and seek the maximum entropy distribution over both frequency and type. Here, we report our first reconstructions of spectra containing antiphase peaks. For simplicity, we used one-dimensional data containing both positive and negative spectral lines. The entropy is simply